From fb702dadb71c924ff1a31c34cb786bce6e418b72 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Thu, 22 Oct 2026 12:48:00 -0500 Subject: [PATCH 1/4] Prove source-bound information and snapshot cut limits --- .../actual-query-information-bounds/NOTICE.md | 39 + .../PACKAGE-MANIFEST.json | 552 + .../actual-query-information-bounds/PROOF.md | 210 + .../actual-query-information-bounds/README.md | 117 + .../SOURCE-MANIFEST.json | 591 + .../SOURCE-PINS.md | 61 + .../VALIDATION.md | 43 + .../snapshot-audit/review_snapshot_rows.py | 217 + .../cover-algebra/review_query_moments.py | 91 + .../review/independent_residual.py | 162 + .../residual-syndrome/verify_residual.py | 225 + .../frozen/source-domain/review_cover.py | 185 + .../temporal-reuse/QUERY-FIFTH-MOMENT.json | 118 + .../check_query_fifth_moment.py | 169 + .../check_query_fourth_moment.py | 292 + .../notices/LICENSE | 201 + .../research/gauge44-slots-t16/NOTICE.md | 24 + .../gauge44-slots-t16/UPSTREAM-NOTICE.md | 34 + .../gauge44-slots-t16/construction/NOTICE.md | 9 + .../research/gauge44-slots-t16/t16/NOTICE.md | 39 + .../CENTRE-FREE-PROGRAMS.json.gz | Bin 0 -> 211301 bytes .../lanes/circuit-interface/INTERFACE.json | 1441 + .../snapshot-audit/SNAPSHOT-ROWS-REVIEW.json | 445 + .../snapshot-audit/SNAPSHOT-ROWS-REVIEW.md | 98 + .../snapshot-audit/review_snapshot_rows.py | 216 + .../payload/lanes/cover-algebra/ALGEBRA.json | 105 + .../MOVABLE-RANK8-CUTS-REVIEW.json | 275 + .../MOVABLE-RANK8-CUTS-REVIEW.md | 93 + .../cover-algebra/MOVABLE-SNAPSHOT-CUTS.md | 160 + .../payload/lanes/cover-algebra/PROOF.md | 239 + .../cover-algebra/QUERY-MOMENTS-REVIEW.json | 24 + .../cover-algebra/QUERY-MOMENTS-REVIEW.md | 49 + .../QUERY-SUPPORT-DISTANCE-REVIEW.json | 53 + .../RANK5-UNION-CUTS-REVIEW.json | 235 + .../cover-algebra/RANK5-UNION-CUTS-REVIEW.md | 68 + .../cover-algebra/SNAPSHOT-FLAG-CUT.json | 174 + .../lanes/cover-algebra/SNAPSHOT-FLAG-CUT.md | 112 + .../SNAPSHOT-SUPPORT-REVIEW.json | 26836 +++ .../cover-algebra/check_snapshot_flag_cut.py | 118 + .../review_movable_rank8_cuts.py | 179 + .../cover-algebra/review_query_moments.py | 91 + .../review_query_support_distance.py | 87 + .../cover-algebra/review_rank5_union_cuts.py | 177 + .../cover-algebra/review_snapshot_support.py | 165 + .../lanes/cover-algebra/verify_algebra.py | 248 + .../encoded-controller/CONTROLLER-CHECKS.json | 63 + .../lanes/encoded-controller/CONTROLLER.md | 202 + .../BACKWARD-SNAPSHOT-INTERVALS.json.gz | Bin 0 -> 414717 bytes .../history-encoding/LOW-BIRTH-UNION-CUTS.md | 162 + .../MOVABLE-CUT-THEOREM-REVIEW.json | 14 + .../MOVABLE-CUT-THEOREM-REVIEW.md | 38 + .../MOVABLE-FULL-RANK-CUTS.json | 4904 + .../history-encoding/MOVABLE-RANK8-CUTS.md | 95 + .../QUERY-SUPPORT-DISTANCE.json | 478 + .../QUERY-SUPPORT-DISTANCE.md | 129 + .../history-encoding/RANK5-UNION-CUTS.json | 165393 +++++++++++++++ .../SNAPSHOT-CONE-OBSTRUCTION.json | 21549 ++ .../SNAPSHOT-CONE-OBSTRUCTION.md | 129 + .../SNAPSHOT-FLAG-CUT-REVIEW.json | 65 + .../SNAPSHOT-FLAG-CUT-REVIEW.md | 65 + .../check_query_support_distance.py | 114 + .../check_snapshot_cone_obstruction.py | 160 + .../review_snapshot_flag_cut.py | 161 + .../interface-proof/NATIVE-LIFT-REVIEW.json | 68 + .../payload/lanes/interface-proof/PROOF.md | 244 + .../payload/lanes/residual-syndrome/PROOF.md | 336 + .../lanes/residual-syndrome/RESIDUAL.json | 134 + .../review/ACCEPTED-AMENDMENTS.json | 19 + .../review/INDEPENDENT-RECEIPT.json | 307 + .../review/REVIEW-EDITS.json | 14 + .../review/REVIEW-STATUS.json | 27 + .../lanes/residual-syndrome/review/REVIEW.md | 115 + .../review/independent_residual.py | 154 + .../residual-syndrome/verify_residual.py | 218 + .../lanes/source-domain/COVER-REVIEW.json | 39 + .../lanes/source-domain/COVER-REVIEW.md | 97 + .../lanes/source-domain/review_cover.py | 182 + .../lanes/source-domain/verify_domain.py | 193 + .../temporal-reuse/QUERY-FIFTH-MOMENT.json | 118 + .../temporal-reuse/QUERY-FOURTH-MOMENT.json | 517 + .../lanes/temporal-reuse/QUERY-MOMENTS.md | 303 + .../temporal-reuse/SPECTRAL-BOUND-REVIEW.json | 315 + .../temporal-reuse/SPECTRAL-BOUND-REVIEW.md | 163 + .../check_query_fifth_moment.py | 169 + .../check_query_fourth_moment.py | 285 + .../temporal-reuse/check_source_matrix.py | 106 + .../temporal-reuse/review_spectral_bound.py | 281 + .../payload/upstream/CANONICAL-WORD.json.gz | Bin 0 -> 84805 bytes .../payload/upstream/DATA-PHASES.json | 1 + .../payload/upstream/GLOBAL-TEMPLATE.json.gz | Bin 0 -> 607002 bytes .../payload/upstream/LOCAL-PROGRAMS.json.gz | Bin 0 -> 209318 bytes .../actual-query-information-bounds/replay.py | 164 + .../validation/REPLAY.json | 185 + .../REVIEW.json | 240 + .../actual-query-information-bounds/REVIEW.md | 147 + .../REVIEWED-PACKAGE-HASHES.json | 112 + .../SOURCE-AND-REPLAY-CHECKS.json | 42 + .../cold-replay/REPLAY.json | 185 + 98 files changed, 234268 insertions(+) create mode 100644 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research/actual-query-information-bounds/frozen/source-domain/review_cover.py create mode 100644 research/actual-query-information-bounds/frozen/temporal-reuse/QUERY-FIFTH-MOMENT.json create mode 100644 research/actual-query-information-bounds/frozen/temporal-reuse/check_query_fifth_moment.py create mode 100644 research/actual-query-information-bounds/frozen/temporal-reuse/check_query_fourth_moment.py create mode 100644 research/actual-query-information-bounds/notices/LICENSE create mode 100644 research/actual-query-information-bounds/notices/research/gauge44-slots-t16/NOTICE.md create mode 100644 research/actual-query-information-bounds/notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md create mode 100644 research/actual-query-information-bounds/notices/research/gauge44-slots-t16/construction/NOTICE.md create mode 100644 research/actual-query-information-bounds/notices/research/gauge44-slots-t16/t16/NOTICE.md create mode 100644 research/actual-query-information-bounds/payload/lanes/circuit-interface/CENTRE-FREE-PROGRAMS.json.gz create mode 100644 research/actual-query-information-bounds/payload/lanes/circuit-interface/INTERFACE.json create mode 100644 research/actual-query-information-bounds/payload/lanes/circuit-interface/snapshot-audit/SNAPSHOT-ROWS-REVIEW.json create mode 100644 research/actual-query-information-bounds/payload/lanes/circuit-interface/snapshot-audit/SNAPSHOT-ROWS-REVIEW.md create mode 100644 research/actual-query-information-bounds/payload/lanes/circuit-interface/snapshot-audit/review_snapshot_rows.py create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/ALGEBRA.json create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.json create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.md create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-SNAPSHOT-CUTS.md create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/PROOF.md create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-MOMENTS-REVIEW.json create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-MOMENTS-REVIEW.md create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-SUPPORT-DISTANCE-REVIEW.json create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/RANK5-UNION-CUTS-REVIEW.json create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/RANK5-UNION-CUTS-REVIEW.md create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/SNAPSHOT-FLAG-CUT.json create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/SNAPSHOT-FLAG-CUT.md create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/check_snapshot_flag_cut.py create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/review_movable_rank8_cuts.py create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/review_query_moments.py create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/review_query_support_distance.py create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/review_rank5_union_cuts.py create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/review_snapshot_support.py create mode 100644 research/actual-query-information-bounds/payload/lanes/cover-algebra/verify_algebra.py create mode 100644 research/actual-query-information-bounds/payload/lanes/encoded-controller/CONTROLLER-CHECKS.json create mode 100644 research/actual-query-information-bounds/payload/lanes/encoded-controller/CONTROLLER.md create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/LOW-BIRTH-UNION-CUTS.md create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-CUT-THEOREM-REVIEW.json create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-CUT-THEOREM-REVIEW.md create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-FULL-RANK-CUTS.json create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-RANK8-CUTS.md create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/QUERY-SUPPORT-DISTANCE.json create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/QUERY-SUPPORT-DISTANCE.md create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/RANK5-UNION-CUTS.json create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.json create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.json create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.md create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/check_query_support_distance.py create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/check_snapshot_cone_obstruction.py create mode 100644 research/actual-query-information-bounds/payload/lanes/history-encoding/review_snapshot_flag_cut.py create mode 100644 research/actual-query-information-bounds/payload/lanes/interface-proof/NATIVE-LIFT-REVIEW.json create mode 100644 research/actual-query-information-bounds/payload/lanes/interface-proof/PROOF.md create mode 100644 research/actual-query-information-bounds/payload/lanes/residual-syndrome/PROOF.md create mode 100644 research/actual-query-information-bounds/payload/lanes/residual-syndrome/RESIDUAL.json create mode 100644 research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/ACCEPTED-AMENDMENTS.json create mode 100644 research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/INDEPENDENT-RECEIPT.json create mode 100644 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research/actual-query-information-bounds/payload/lanes/temporal-reuse/review_spectral_bound.py create mode 100644 research/actual-query-information-bounds/payload/upstream/CANONICAL-WORD.json.gz create mode 100644 research/actual-query-information-bounds/payload/upstream/DATA-PHASES.json create mode 100644 research/actual-query-information-bounds/payload/upstream/GLOBAL-TEMPLATE.json.gz create mode 100644 research/actual-query-information-bounds/payload/upstream/LOCAL-PROGRAMS.json.gz create mode 100644 research/actual-query-information-bounds/replay.py create mode 100644 research/actual-query-information-bounds/validation/REPLAY.json create mode 100644 research/publication-reviews/actual-query-information-bounds/REVIEW.json create mode 100644 research/publication-reviews/actual-query-information-bounds/REVIEW.md create mode 100644 research/publication-reviews/actual-query-information-bounds/REVIEWED-PACKAGE-HASHES.json create mode 100644 research/publication-reviews/actual-query-information-bounds/SOURCE-AND-REPLAY-CHECKS.json create mode 100644 research/publication-reviews/actual-query-information-bounds/cold-replay/REPLAY.json diff --git a/research/actual-query-information-bounds/NOTICE.md b/research/actual-query-information-bounds/NOTICE.md new file mode 100644 index 0000000000..0a368da469 --- /dev/null +++ b/research/actual-query-information-bounds/NOTICE.md @@ -0,0 +1,39 @@ +# Attribution and license + +This package preserves results from Ali Romman's centre-encoding campaign. +OpenAI Codex assisted with the research, proofs, code, and package review. +The recorded independent reviews are reviews by separate agents. No +independent human review is claimed. New material uses Apache-2.0; the +[license](notices/LICENSE) is included. + +The historical native word and phase data come from commit +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. The original notices remain +unchanged: + +- [Gauge44 notice](notices/research/gauge44-slots-t16/NOTICE.md). +- [Construction notice](notices/research/gauge44-slots-t16/construction/NOTICE.md). +- [T16 integration notice](notices/research/gauge44-slots-t16/t16/NOTICE.md). +- [Upstream notice](notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md). + +These sources retain the Jeremy Kothe, Chafik Boukhalfa, Hao Yan, icekylinx, +Rohan Arun, and other supplier, compiler, owner, and controller credit. +The complete notices define that ancestry. This package does not claim the +source word, route recipes, or earlier supplier results as new work. + +The campaign root supplied the fourth-moment target and the pair-union cut +idea. The encoded-controller lane supplied the actual query interface. +The temporal-reuse lane proved and checked the five-moment result and the +source matrix binding. The history-encoding lane supplied the support +distance, cone obstruction, and exact cut certificates. The cover-algebra +lane supplied the general cut theorem, global flag bound, routed-projection +bound, and independent moment, support, and cut reviews. The source-domain +lane independently checked the cover traces. The circuit-interface lane +supplied the scalar words and full snapshot source review. The +interface-proof lane supplied the local native lift. The residual-syndrome +lane supplied the residual theorem and its separate exact algebra review. + +[SOURCE-MANIFEST.json](SOURCE-MANIFEST.json) records the exact campaign +paths and hashes. Original proofs and unchanged receipts retain their +author and AI disclosures. Portable checker changes concern input paths +and their explicit source pins. The original changed files remain under +[frozen](frozen). diff --git a/research/actual-query-information-bounds/PACKAGE-MANIFEST.json b/research/actual-query-information-bounds/PACKAGE-MANIFEST.json new file mode 100644 index 0000000000..79c0cb3408 --- /dev/null +++ b/research/actual-query-information-bounds/PACKAGE-MANIFEST.json @@ -0,0 +1,552 @@ +{ + "files": [ + { + "bytes": 2203, + "path": "NOTICE.md", + "sha256": "40e1cf742e31b0146f7dfb506871651fbce1545ed1e9b6d73926bc1cce8eca79" + }, + { + "bytes": 10470, + "path": "PROOF.md", + "sha256": "898388f738b6857e176831629d03a18734beca2d3732a15c1e80081e6c366ad0" + }, + { + "bytes": 7760, + "path": "README.md", + "sha256": "a98ded794a2cdbe18a02e31498623ed95f69ae7e9efb5931e866c4d61797f3f4" + }, + { + "bytes": 30455, + "path": "SOURCE-MANIFEST.json", + "sha256": "7b01de4de8e46f22f641be44afaed8e10af8a0a141341a0436b05fa3ff662c87" + }, + { + "bytes": 3547, + "path": "SOURCE-PINS.md", + "sha256": 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a/research/actual-query-information-bounds/PROOF.md b/research/actual-query-information-bounds/PROOF.md new file mode 100644 index 0000000000..97d4e5a488 --- /dev/null +++ b/research/actual-query-information-bounds/PROOF.md @@ -0,0 +1,210 @@ +# Exact statements and proof map + +This file states only the results included in this package. The linked +source notes contain the full proofs and retain their historical context. +Different sections have different hypotheses. + +## 1. One fixed source in nine charts + +Let `G` be the finite cover group containing the actual chart routes. Let +one complete field have dimension `N=|G| dim(W)` on the full module +`C[G] tensor W`. Use the right regular cover action. The selected ordinary +ports are the complement of the two fixed eight-port minors A and T. +Their source matrix obeys `R_U R_U*=48I`. + +For the nine actual routes `D_s`, set + +```text +B_s = R_U D_s, +P_s = B_s* B_s / 48, +S = P_0 + ... + P_8. +``` + +Each `P_s` is a projection of rank `8N`. The exact normalized moments of +S are `72,120,244,1649/3,47467/36`. A positive stage that occurs once in +a cyclic projection word can be removed at trace factor `1/12`. This uses +its fresh coordinate block and the actual port bases. It is not a freeness +assumption. The alternating fourth-order contraction is `23/216`. The only +new fifth-order type has contraction `23/2592`; the finite route check uses +194,400 supported triples and finds exactly 4,320 matching terms. + +Use weighted Cauchy with `9-S` and `f(S)=19S-6S^2`. Since `0<=S<=9I`, +the first five moments give + +```text +tr((9-S) f(S))/N = 5016, +tr((9-S) f(S)^2)/N = 57057, +9 rank(S)/N - 72 >= 5016^2/57057 = 40128/91. +``` + +Hence `rank(S)/N >= 15560/273`. A cache through which all nine queries +of this one source factor has at least this dimension in complete-field +units. It needs at least 57 whole fields. Whole eight-field cohorts require +at least eight cohorts, or 64 fields. + +The bound is sharp for the continuous positive-measure problem with these +five moments and spectrum in `[0,9]`. The witness has nodes +`0,(19-2 sqrt(22))/12,(19+2 sqrt(22))/12,9`, nonzero mass `15560/273`, +and mass `8/7833` at nine. This is not a claim about integer multiplicities +or the spectrum of the actual finite operator. + +Full proof: [QUERY-MOMENTS.md](payload/lanes/temporal-reuse/QUERY-MOMENTS.md). +Review: [QUERY-MOMENTS-REVIEW.md](payload/lanes/cover-algebra/QUERY-MOMENTS-REVIEW.md). +The replay checks the source matrix, exact physical-to-logical chart +alignment, route order, all stated contractions, and both moment bounds. +It does not construct a cache or replace changing controller sources with +one fixed source. + +## 2. Support distance and a common snapshot span + +Let R be the actual `8 by 112` query matrix. Every nonzero complex scalar +row `aR` has at least 53 nonzero ports. The 112 old-root coefficient +directions all attain 53. + +The columns consist of 14 signed quartets. If t coefficients on a quartet +are nonzero, the respective lower bounds for its eight evaluations are +`0,8,4,6,5` for `t=0,1,2,3,4`. A generic real projection preserves each +complex zero sum and does not kill any nonzero coefficient. Equal-sum +subsets of positive real coefficients form an antichain. The permutation +chain count, together with opposite sign pairs, gives the quartet bounds. +The exact check adds those bounds over all 255 nonempty coefficient supports. +The minimum is 53. + +Restrict to the valid input family `X=JY`, with all helper and private inputs +zero. The actual snapshot support theorem states that a row in frame U +uses only ports whose labels are perpendicular to U. Every actual frame +of rank at least two permits at most 20 ports. Thus two such birth fields +cannot form a nonzero query: they use at most 40 ports. + +If m independent birth fields span k query dimensions, their coefficient +code has minimum nonzero weight at least three. Deletion of two coordinates +is injective, so `k<=m-2`. For full fields, use a linear section of the +reconstruction map and delete two field blocks. The same proof gives +`kd<=(m-2)d`. This requires each birth field to have source-port support at +most 20, with no extra uncounted source reads. + +Full proof: [QUERY-SUPPORT-DISTANCE.md](payload/lanes/history-encoding/QUERY-SUPPORT-DISTANCE.md). +Review: [QUERY-SUPPORT-DISTANCE-REVIEW.json](payload/lanes/cover-algebra/QUERY-SUPPORT-DISTANCE-REVIEW.json). +This is a field-count bound for one common span. It does not price a general +shared network. + +## 3. One snapshot cone + +The pinned snapshot source contains 12,271 exact scalar rows, 16,687 +availability intervals, and 1,004 actual frames. The independent source +replay checks all 712 formal inputs, all interval endpoints and interiors, +and the final map `(x,y,h,c)->(x-Jy,y,h,0)`. + +For each positive proper actual frame U, put +`E_U={p:q_p is not perpendicular to U}`. The exact minor certificate gives +`rank(R_E_U)=8` for all 1,002 choices of U. On `X=JY`, helper/private zero, +and Y supported on `E_U`, every snapshot at a containing frame vanishes. +Every completed X and helper baseline also vanishes. The required queries +can take all eight independent values. Therefore no nonzero completed query +can be formed from that cone, even when all times and all these baselines +are granted. + +Full proof: [SNAPSHOT-CONE-OBSTRUCTION.md](payload/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md). +Source review: [SNAPSHOT-ROWS-REVIEW.md](payload/lanes/circuit-interface/snapshot-audit/SNAPSHOT-ROWS-REVIEW.md). +The theorem does not include captures from incomparable cones, a changed +core, or new observations inside a native child. + +## 4. Shared linear networks and exact cuts + +A node v has a fixed free observation matrix `A_v`. A finite causal linear +circuit may share, add, and cancel values at a node. All unlisted input +channels are absent. For a set of nodes Omega containing the output nodes, +let `A_Omega` stack all inside observations and granted baselines. Then + +```text +d_Omega = rank(Q restricted to kernel(A_Omega)) + = rank([A_Omega; Q]) - rank(A_Omega) + <= sum of entering field capacities. +``` + +Restrict the input to the kernel. An induction in circuit order shows that +every inside value depends only on values that entered the cut. Re-entry is +charged again. This proof does not require an upward-closed cut. + +If nonnegative rational cut weights charge every allowed edge by at most +its cost, the weighted demand is a lower bound for the whole network cost. +For N-dimensional fields, each demand and capacity scales by N. In the +application, a frame edge `U -> V` preserves logical content, requires +`U subset V`, and costs `dim(V)-dim(U)` per carried field. The original +core and source-port meaning remain fixed. + +The global flag certificate uses binary basis +`[243,249,311,132,131,489,442,405,178]`. The nine source-shell ranks are +`[0,1,1,2,8,6,8,8,8]`, with sum 42. Pivot inclusion charges each increasing +edge by its dimension increase. The proof applies to shared values and +cancellation. It does not add separate output-tree bounds. + +The rank-five certificate covers frames +`630,631,632,633,635,637,734,735,736,737,739,741`. Each displayed overlap +has dimension five. Five unit cuts are injective on it, so every requested +k-dimensional subspace costs at least `5k` before the common merge. +No new observations enter afterward; completion costs at least `4k`. +The resulting bound is `9k`. The independent review checks the complete +712-column overlap and every actual inclusion edge in each stated model. + +For each rank-eight cone V in `{983,991}`, seven unit cuts have exact +source restriction rank eight and valid edge charges. Append FULL to +those cuts and add the singleton FULL cut. Every direct edge `U -> FULL` +is charged by at most `9-dim(U)`. Each cut is injective on any requested +k-query subspace. Thus the bound is `8k`, even if branches bypass V and +merge only at FULL. Proper frames must remain actual subframes of one +chosen V. The two cone certificates cannot be combined without checking +the new cross-cone edges and observations. + +The [general cut proof](payload/lanes/cover-algebra/MOVABLE-SNAPSHOT-CUTS.md) +and its [proof review](payload/lanes/history-encoding/MOVABLE-CUT-THEOREM-REVIEW.md) +state the linear model. The numerical results have separate +[global](payload/lanes/history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.md), +[rank-five](payload/lanes/cover-algebra/RANK5-UNION-CUTS-REVIEW.md), and +[rank-eight](payload/lanes/cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.md) reviews. +The global result here is 42. No global bound of 64 is claimed. + +## 5. A complete residual channel + +This section uses the pinned nine-stage bank recipe and the separate +abstract routed interface `R_s R_s*=56I`. Let `C_0` be the old controller +before its final signed swap. Let C omit all nine centre blocks. Define +`d=dim(intersection_s im(R_s*))` on the full regular cover. + +The nine old-prefix bank rows have rank eight and unique relation +`c=(1,-1,-1,1,1,-1,-1,1,1)`. Every proper subset is independent. Write +`V_s=R_s(v_s tensor I)` and stack them in V. The kernel of `V*` has +dimension d, so `rank(V)=72|G|-d`. + +For the bank symplectic form Omega and strict lower block matrix +`L_ij=V_i Omega V_j*` for `i>j`, the chronological recurrence gives + +```text +C_0^-1 C - I = Omega V* (4I-L)^-1 V. +``` + +The relation coefficient has bank area four. On `ker(V*)`, the form +`4I-L` equals `-47/14` times the common-image inner product under its +specified identification. It is nonsingular. Thus the decoder loses no +additional rank, and `rank(C-C_0)=72|G|-d`. Every proper omitted-stage set +S gives exact rank `8|S||G|`. + +The separate two-projection cover theorem gives `d<=8|G|/183`. It uses +the full regular action, actual route products, and exact traces `4/7` +and `27/343`. Therefore the residual rank is greater than `71|G|` per +replica and greater than `1151|G|` across all 16 independent replicas. +A complete linear residual channel needs 72 or 1,152 whole cover arrays, +respectively. A joint encoder across replicas does not change the latter +ceiling. + +Full proof: [residual-syndrome/PROOF.md](payload/lanes/residual-syndrome/PROOF.md). +Reviews: [residual algebra](payload/lanes/residual-syndrome/review/REVIEW.md) +and [cover traces](payload/lanes/source-domain/COVER-REVIEW.md). +Application to the native controller inherits the +[local lift](payload/lanes/interface-proof/PROOF.md) and +[endpoint normal form](payload/lanes/encoded-controller/CONTROLLER.md). +Their native replay is not repeated in this package. + +This bound concerns one declared residual channel. It does not count peak +workspace, native child rank, or a procedure with later data reads. No +complete kappa calculation changes. diff --git a/research/actual-query-information-bounds/README.md b/research/actual-query-information-bounds/README.md new file mode 100644 index 0000000000..3eb7a4334c --- /dev/null +++ b/research/actual-query-information-bounds/README.md @@ -0,0 +1,117 @@ +# Information bounds for the actual routed queries + +This package gives scoped information bounds for the historical complex +nine-stage word. It combines exact proofs, finite certificates, and their +independent agent reviews. It does not change the complete kappa calculation. +It does not give a universal circuit lower bound. + +The [proof](PROOF.md) states the separate models. The +[source manifest](SOURCE-MANIFEST.json) records every input and each portable +edit. The [source pins](SOURCE-PINS.md) identify the historical supplier. +[NOTICE.md](NOTICE.md) preserves contributor credit and the AI disclosure. + +| Model | Result | Exact source and review | +| --- | --- | --- | +| Nine queries of one fixed arbitrary source on the full regular cover | First five moments `72,120,244,1649/3,47467/36`; dimension at least `15560/273` complete fields; at least 57 whole fields or 64 fields in whole eight-field cohorts | [Moment proof](payload/lanes/temporal-reuse/QUERY-MOMENTS.md), [independent review](payload/lanes/cover-algebra/QUERY-MOMENTS-REVIEW.md) | +| Actual query row space and actual snapshots of rank at least two | Exact source-port support distance 53; a k-query common span needs at least `k+2` birth fields | [Support proof](payload/lanes/history-encoding/QUERY-SUPPORT-DISTANCE.md), [independent review](payload/lanes/cover-algebra/QUERY-SUPPORT-DISTANCE-REVIEW.json) | +| One positive proper actual snapshot cone | No nonzero completed query in any of the 1,002 cones, with all snapshot times granted | [Cone proof](payload/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md), [full source review](payload/lanes/circuit-interface/snapshot-audit/SNAPSHOT-ROWS-REVIEW.md) | +| Same-content monotone snapshot networks, with the original core fixed | General cut lemma; global bound 42; bound `9k` for twelve specified rank-five query spaces; bound `8k` for cones 983 and 991, including direct FULL bypass edges | [Cut theorem](payload/lanes/cover-algebra/MOVABLE-SNAPSHOT-CUTS.md), [global review](payload/lanes/history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.md), [rank-five review](payload/lanes/cover-algebra/RANK5-UNION-CUTS-REVIEW.md), [rank-eight review](payload/lanes/cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.md) | +| One complete linear residual channel for the specified nine-stage controller | Exact residual rank `72|G|-d`; with the separate cover bound, 72 complete arrays per replica or 1,152 across 16 replicas | [Residual proof](payload/lanes/residual-syndrome/PROOF.md), [algebra review](payload/lanes/residual-syndrome/review/REVIEW.md), [cover review](payload/lanes/source-domain/COVER-REVIEW.md) | + +The numbers in different rows cannot be added. The fixed-source hypothesis +does not apply automatically when a controller reads changing sources. +The snapshot field count does not price a shared network. The rank-eight +cone bounds do not give a global bound of 64. The residual channel count +does not bound peak workspace or a procedure that reads the source again. + +## Reproduction + +Use Python 3.11 or later with SymPy 1.14.0. All other dependencies are in +the standard library. Run from this package directory with a new output +directory outside the package: + +```sh +python3 -I -O -B replay.py --output /absolute/path/to/new-query-bounds-replay +``` + +Expected final line: + +```text +PASS_ACTUAL_QUERY_INFORMATION_BOUNDS_PACKAGE +``` + +The command runs 17 exact checks in sequence. It requires at least 3 GiB +of free disk space. It writes logs, all regenerated receipts, and `REPLAY.json` +under the output path. It does not need Git, network access, a workspace +checkout, or a search solver. It uses one Python process at a time. + +The replay rebuilds the actual source matrix by reverse propagation. It +enumerates all 194,400 supported fifth-order triples. It rebuilds every +scalar snapshot row on all 712 formal inputs and checks all 16,687 +availability intervals. It then checks the support distance, cone minors, +cut weights, exact source restrictions, and every allowed cut edge in the +specified certificates. The independent rank-five review checks the full +712-column query overlap. The independent cover review uses all 73 binary +axes. The independent residual review uses separate exact SymPy examples. + +Each complete generated JSON receipt must equal its expected receipt, +including JSON types. The portable source-hash changes are explicit in +`REPLAY.json` and `SOURCE-MANIFEST.json`. The optional sixth-moment cover +extension is omitted; the replay checks the complete baseline receipt after +the five named optional extension fields are removed. No other mathematical +field is omitted from receipt comparison. + +The source proofs retain their historical commands and dependency paths. +Use the package command above for the portable replay. The original versions +of changed files remain under [frozen](frozen). The mathematical checks are +unchanged. The changes replace local Git and workspace reads with the same +hash-pinned archive members and update the resulting checker hashes. + +## Validation boundary + +The checked supplier source is commit +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. This is a historical source. +At publication base `b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`, the +[selected record](https://github.com/CrocSwap/integer-mult-bounds/blob/b58ad9ef4d4e861b0eaa5dba41742bdc072dca51/certificates/selected-result.json) +uses [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470) +and kappa `60403/20000000 = 0.00302015`. This package does not prove that +the historical bounds apply to that changed construction. + +The full snapshot replay checks scalar content and canonical frames. +It does not check a new capture word, chronological schedule, native phases, +owner assignment, precision, tape cost, or complete recursive price. The +local native lift and the controller endpoint normal form remain separate +inherited application dependencies for the residual theorem. Their source +proofs and receipts are included; their native checks were not rerun here. +No proof assistant or independent human review is claimed. + +No LP or failed search is used as impossibility evidence. The package uses +only the accepted finite cuts. It omits the low-rank screens, movable-cut +searches, and the unreviewed sixth-moment extension. + +## Related models + +[PR #4700](https://github.com/CrocSwap/integer-mult-bounds/pull/4700) fixes +the later PR4610 scalar graph and proves a 64-rank floor for its eight +retained centre calls under binary monotone chart changes. It permits a +different class of edits and does not supply the global snapshot-network +bound that is open here. +[PR #4200](https://github.com/CrocSwap/integer-mult-bounds/pull/4200) treats +closed private walks for copies of one unchanged BIT total. +[PR #4267](https://github.com/CrocSwap/integer-mult-bounds/pull/4267) treats +a formal orbit query grammar, and +[PR #4269](https://github.com/CrocSwap/integer-mult-bounds/pull/4269) treats +constant-direction scalar callers over a cubic algebra. These are distinct +models. The overlap check does not claim novelty against all literature. + +## Open next questions + +1. Determine the global unchanged-core snapshot-network cost above the + proved floor of 42. A first step is one exact certificate on the complete + allowed graph. Shared edges prevent the addition of separate cone bounds. +2. Determine the actual fixed-source query rank beyond the first five + moments. Those moments alone attain the stated continuous relaxation + bound, so a stronger result needs additional information. +3. Test the hypotheses on a later supplier before using these bounds there. + The source matrices, observation graph, routes, and endpoint contracts + must be bound to that supplier. 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"b447b1358e3376089639446f3d264565d75a75e1e471d29a0f8e5aa097f7f0c9" + }, + { + "bytes": 4617, + "extraction": "source_matrix and its constants; local member loader; a receipt entry point", + "origin": "work/centre-encoding-campaign-20261014/lanes/temporal-reuse/review_spectral_bound.py", + "path": "payload/lanes/temporal-reuse/check_source_matrix.py", + "sha256": "8e15afb0cb54c52867e61bc727eeb42b6020285bf69093a78431702d07503ddb", + "source_sha256": "83de0b4694a8ef1ee501130bca9ddedf6e265f6be44b855e61e327646a7529d9" + } + ], + "historical_source_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "portable_adaptations": [ + { + "original_sha256": "c22539e007c763b2d92d2932c4d84080ccda8549774d6be8b7705575a03a253f", + "path": "payload/lanes/temporal-reuse/check_query_fourth_moment.py", + "portable_sha256": "e7ff30dfdc23dd929599c05aa037a082060906021d5e9a40e9f586e680d0449e", + "reason": "Read the same pinned archive members from the package. All mathematical operations stay unchanged." + }, + { + "original_sha256": "bea72f2bafab8cc38142557d6d3a1bee5f4db1f9a2a75668fce146ca6ebba4f0", + "path": "payload/lanes/temporal-reuse/check_query_fifth_moment.py", + "portable_sha256": "2eee310e2db3593d4844e9806be695c869d0c101e881d677b5429232beb0e0a4", + "reason": "Pin the portable fourth-moment checker. No mathematical operation changes." + }, + { + "original_sha256": "d346e38c1dc323d3304c94e7faf14384ac7970bb7b7775c49749a90a509fa0e9", + "path": "payload/lanes/temporal-reuse/QUERY-FIFTH-MOMENT.json", + "portable_sha256": "562d05a6f830f88d36efc148f81a01f3dfa95afbcab8195a9b5add02a5fdb742", + "reason": "Change only the fourth-checker source hash for the portable replay." + }, + { + "original_sha256": "9f3cff9ff7459800afff681c18276ebc0d6a140a66b58af76b3140015889518c", + "path": "payload/lanes/cover-algebra/review_query_moments.py", + "portable_sha256": "877c902c658fef004511fbd55e4265ac6a6f044d8f8e2e294db29ef33aeca2c8", + "reason": "Pin the portable checkers and fifth receipt. No mathematical operation changes." + }, + { + "original_sha256": "ef74bba4dd9afe205242a8b5471741f13304bff8e2f714ccbc673a73ec928109", + "path": "payload/lanes/circuit-interface/snapshot-audit/review_snapshot_rows.py", + "portable_sha256": "c8a72435ce0dc8c8f2c387f2ce24bc3e900f9559d3fdc824e4fc4ee4055921fc", + "reason": "Read the identical pinned canonical word from the package." + }, + { + "original_sha256": "847a21d79fcaa1e19793f43348478e6966344d3067b22795f3b2becd68074a97", + "path": "payload/lanes/residual-syndrome/verify_residual.py", + "portable_sha256": "a8b1c54f36ee7daa4ca68b7f48689389078541ee4e7212f3ea5a36dca32ccdbb", + "reason": "Replace Git access with a pinned local controller member and name the CLI input source-dir." + }, + { + "original_sha256": "8071d3a27df0eb08d8694e75c30c0aa557fed51e5dfe5e0b5e31c122c38699cc", + "path": "payload/lanes/residual-syndrome/review/independent_residual.py", + "portable_sha256": "4da89227ea82871e28b615d8442273ccacee2adddb8cf0aef999a9fff2c2d38a", + "reason": "Read the identical pinned controller member from the package. The independent SymPy calculations stay unchanged." + }, + { + "original_sha256": "b447b1358e3376089639446f3d264565d75a75e1e471d29a0f8e5aa097f7f0c9", + "path": "payload/lanes/source-domain/review_cover.py", + "portable_sha256": "79b8638f4d00f9bda89e193cdde5574e5139784b11bcc53fb6227e3ccd3abc09", + "reason": "Read the three same pinned members from the package. Keep independent forward source reconstruction and 73-axis route checks." + } + ], + "publication_base_commit": "b58ad9ef4d4e861b0eaa5dba41742bdc072dca51", + "schema": 1 +} diff --git a/research/actual-query-information-bounds/SOURCE-PINS.md b/research/actual-query-information-bounds/SOURCE-PINS.md new file mode 100644 index 0000000000..1d1e478b26 --- /dev/null +++ b/research/actual-query-information-bounds/SOURCE-PINS.md @@ -0,0 +1,61 @@ +# Source pins and portable dependency closure + +The supplier source is the historical commit +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. Its +[selected replay archive](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/community-frontier1042-audit/selected-replay.tar.gz) +has SHA256 +`22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754`. +The packaging step checked all 19,299,540 archive bytes, required one +regular member at each selected path, and copied only the four consumed +members. The portable replay checks the member hashes. It does not need +or re-download the full archive. + +| Original archive member | SHA256 of stored bytes | +| --- | --- | +| `slots/local/CANONICAL-WORD.json.gz` | `16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219` | +| `slots/local/LOCAL-PROGRAMS.json.gz` | `241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a` | +| `t16/global/base/work/complex-nine-native/DATA-PHASES.json` | `c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa` | +| `t16/global/base/split-centres/GLOBAL-TEMPLATE.json.gz` | `a179dad87651aba340a5a8ddbcd86a8e757cad87b8a1f8bad48106fbecd38518` | + +The actual query interface has SHA256 +`5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3`. +The snapshot source has decompressed SHA256 +`3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c`. +The clean scalar programs have decompressed SHA256 +`fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877`. +These payload hashes define mathematical equality independently of gzip +container metadata. + +The campaign results were local source files. Their original paths and +SHA256 values are recorded in [SOURCE-MANIFEST.json](SOURCE-MANIFEST.json). +Do not treat their local paths as prior public commit links. Their first +public commit must preserve that provenance. The manifest also records each +portable edit, its old hash, its new hash, and its reason. + +The portable checkers use the same exact calculations. The fourth-moment, +snapshot-source, residual, and independent cover loaders read bundled +members. The dependent moment checker pins use the new checker hashes. +The narrow source-matrix checker extracts the reviewed reverse-propagation +routine from `temporal-reuse/review_spectral_bound.py`. It does not rerun +or claim the separate spectral subset theorem. + +The copy of `source-domain/verify_domain.py` supplies only its source +constants, member hash check, and exact forward centre reconstruction to +the cover reviewer. The remaining functions are retained source context +and are not executed by this package. The historical spectral checker is +also retained as provenance for the extracted routine; its old `main` +entry point is not part of the portable replay. + +The native application dependencies are the local lift and the global +endpoint normal form. Their proofs and receipts are included under +`payload/lanes/interface-proof` and `payload/lanes/encoded-controller`. +They are inherited application evidence. The package reruns the exact +scalar and algebraic claims listed in the README, not a native supplier +admission or its complete price. + +Publication base: +`b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`. +The selected frontier at that pin is the conditional joint-helper result +from [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470). +It has kappa `60403/20000000`. The historical source pins above are not +changed to match that newer construction. Applicability to it is unproved. diff --git a/research/actual-query-information-bounds/VALIDATION.md b/research/actual-query-information-bounds/VALIDATION.md new file mode 100644 index 0000000000..6ff763d16e --- /dev/null +++ b/research/actual-query-information-bounds/VALIDATION.md @@ -0,0 +1,43 @@ +# Validation record + +The portable package replay passed on 22 October 2026. It used Python +3.14.7 and SymPy 1.14.0, with isolation and optimization enabled. All +17 exact checks ran in sequence. The run took 63.873 seconds on this host; +that time is not a performance claim. + +```text +PASS_ACTUAL_QUERY_INFORMATION_BOUNDS_PACKAGE +``` + +[validation/REPLAY.json](validation/REPLAY.json) records each status, +duration, output hash, and the exact source-manifest and replay-script +hashes. The [logs](validation/logs) retain the literal command outputs. +The replay checks the full typed JSON receipts, with the declared portable +source-hash updates. The optional cover sixth-moment fields are omitted +because that extension is outside this package's claims. + +The run checked the reverse source reconstruction, fourth and fifth +moments, independent moment arithmetic, all 712 snapshot input columns, +all 16,687 availability intervals, the cone support law and exact minors, +support distance 53, the global cut bound 42, the twelve rank-five cut +certificates, the two rank-eight certificates with their FULL extensions, +the cover traces, and the residual factorization. Separate implementations +checked the moment arithmetic, support, global cut, rank-five and rank-eight +cuts, cover traces, and residual algebra. + +The inherited controls ran as part of these checks. They include wrong +route order, changed snapshot coefficient/frame/interval, invalid quartet +data, an overstated quartet bound, wrong flag order, an understated edge +charge, a missing controller bridge, a wrong triangular sign, and the +constant-cover representation that does not satisfy the full-cover trace +premise. Exact receipts state the coverage of each control. No new search +was run. + +The package proof review corrected one summary sentence: the kernel with +dimension d is `ker(V*)`, not `ker(V)`. The full historical residual proof +already used the correct adjoint. No numerical result changed. + +The local native-lift receipt and global endpoint normal-form proof are +retained application dependencies. Their native checks were not rerun. +No new physical word, full supplier replay, recursive price, Lean proof, +or application to the selected PR4470 construction was checked. diff --git a/research/actual-query-information-bounds/frozen/circuit-interface/snapshot-audit/review_snapshot_rows.py b/research/actual-query-information-bounds/frozen/circuit-interface/snapshot-audit/review_snapshot_rows.py new file mode 100644 index 0000000000..9a66733e8a --- /dev/null +++ b/research/actual-query-information-bounds/frozen/circuit-interface/snapshot-audit/review_snapshot_rows.py @@ -0,0 +1,217 @@ +"""Rebuild all backward snapshot rows from the pinned scalar event word.""" + +from bisect import bisect_right +from collections import Counter, defaultdict +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +ROOT = LANES.parents[2] +PINS = { + 'core': 'fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877', + 'word': '16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219', + 'interface': '5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3', + 'snapshots': '3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c', + 'proof': 'be9575e1cac8706c42fddff243f435935e098d197edaf7f8689352c93b7e3961', + 'receipt': '35698700474f2309a4eea2f192a5afbd2f42f580a7e0e510a0bb5687a87fdc2d', +} + + +def require(condition, reason): + if not condition: + raise ValueError(reason) + + +def read(path, key, compressed=False, pin_compressed=False, parse=True): + data = path.read_bytes() + raw = gzip.decompress(data) if compressed else data + require(sha256(data if pin_compressed else raw).hexdigest() == PINS[key], 'Source pin: '+key) + return json.loads(raw) if parse else raw + + +def combine(target, source, coefficient): + for col, value in source.items(): + new = target.get(col, Q(0))+coefficient*value + if new: + target[col] = new + else: + target.pop(col, None) + + +def index(token): + require(isinstance(token, list) and len(token) == 2, 'A literal field token') + namespace, position = token + require((namespace == 'L' and 0 <= position < 704) or + (namespace == 'C' and 0 <= position < 8), 'An original field index') + return position+(704 if namespace == 'C' else 0) + + +def intervals_partition(intervals, first, last): + by_wire = defaultdict(list) + for lo, hi, wire, frame, row in intervals: + require(first <= lo <= hi <= last and 0 <= wire < 704, 'A declared interval range') + by_wire[wire].append((lo, hi)) + require(set(by_wire) == set(range(704)), 'Every persistent wire has an interval') + for spans in by_wire.values(): + spans.sort() + require(spans[0][0] == first and spans[-1][1] == last, 'The complete boundary range') + require(all(a[1]+1 == b[0] for a, b in zip(spans, spans[1:])), 'No interval gap or overlap') + + +def reject(function, reason): + try: + function() + except ValueError: + return + raise ValueError('The control was not rejected: '+reason) + + +def main(): + events = read(LANES/'circuit-interface/CENTRE-FREE-PROGRAMS.json.gz', 'core', True)['backward'] + word = read(ROOT/'work/five-pr-sprint-20261013/lanes/centre-sharing/CANONICAL-WORD.json.gz', 'word', True, True) + interface = read(LANES/'circuit-interface/INTERFACE.json', 'interface') + snapshots = read(LANES/'history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz', 'snapshots', True) + source_receipt = read(LANES/'history-encoding/SNAPSHOT-CONE-OBSTRUCTION.json', 'receipt') + read(LANES/'history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md', 'proof', parse=False) + require(snapshots['pins'] == {'word': PINS['word'], 'core': PINS['core'], 'R': PINS['interface']}, 'All snapshot source pins') + require(snapshots['R'] == interface['R'] and snapshots['frames'] == word['frames'], 'Actual query and frame source equality') + query = [{int(j): Q(v) for j, v in row.items()} for row in interface['R']] + ports = interface['ports'] + j_rows = [{p: Q(1)} for p in range(112)] + for p, row in enumerate(j_rows): + for query_row in query: + combine(row, query_row, -query_row.get(p, Q(0))/4) + + first, last = snapshots['first_canonical_boundary'], snapshots['last_canonical_boundary'] + require((first, last) == (8106, 24913), 'The complete pinned canonical range') + intervals = snapshots['intervals'] + intervals_partition(intervals, first, last) + updates = defaultdict(list) + for t, event in enumerate(events): + if event[0] == 'climb': + updates[event[2]].append(t) + elif event[0] == 'scalar': + updates[index(event[1][1])].append(t) + supplied_rows = [{int(j): Q(v) for j, v in row.items()} for row in snapshots['rows']] + checks_at = defaultdict(list) + for item in intervals: + lo, hi, wire, frame, row = item + require(0 <= frame < len(word['frames']) and 0 <= row < len(supplied_rows), 'An interval row and frame index') + next_update = bisect_right(updates[wire], lo) + require(next_update == len(updates[wire]) or updates[wire][next_update] > hi, 'No scalar or canonical-frame change inside a constant interval') + checks_at[lo].append((wire, frame, row)) + if hi != lo: + checks_at[hi].append((wire, frame, row)) + + def support(row): + reduced = {p-112: value for p, value in row.items() if 112 <= p < 224} + for p, value in row.items(): + if p < 112: + combine(reduced, j_rows[p], value) + return reduced + + rows = [{i: Q(1)} for i in range(712)] + frames = word['start'][:]+[0]*8 + profile, macros = Counter(), Counter() + private_uses, checked_pairs, reduced_rows = [], set(), {} + endpoint_checks = support_coefficients = 0 + last_scalar = -1 + check_example = None + for t, event in enumerate(events): + kind = event[0] + if kind == 'climb': + _, _, target, before, after, rank = event + require(0 <= target < 704 and frames[target] == before, 'The original native source frame') + require(len(word['frames'][after])-len(word['frames'][before]) == rank, 'The exact native rank increment') + frames[target] = after + profile[rank] += 1 + elif kind == 'scalar': + op, frame = event[1:] + target = index(op[1]) + require(frames[target] == frame, 'Every scalar target has the declared canonical frame') + if target >= 704: + private_uses.append((t, target, 'write')) + macros[op[0]] += 1 + last_scalar = t + if op[0] == 'clear': + rows[target] = {} + elif op[0] == 'scale': + coefficient = Q(op[2], op[3]) + rows[target] = {p: coefficient*v for p, v in rows[target].items() if coefficient*v} + else: + require(op[0] in ('copy', 'add'), 'An allowed scalar operation') + other = index(op[2]) + require(other != target and frames[other] == frame, 'A distinct source in the same canonical frame') + if other >= 704: + private_uses.append((t, other, 'read')) + if op[0] == 'copy': + rows[target] = rows[other].copy() + else: + combine(rows[target], rows[other], Q(op[3], op[4])) + else: + require(kind in ('phase', 'adapter', 'residual_adapter'), 'A known inherited operator event') + for wire, frame, row_index in checks_at.get(t, ()): + require(frames[wire] == frame and rows[wire] == supplied_rows[row_index], 'A fresh full712 prefix row and frame match the interval endpoint') + endpoint_checks += 1 + if check_example is None: + check_example = (rows[wire].copy(), supplied_rows[row_index].copy(), frames[wire], frame) + pair = frame, row_index + if pair not in checked_pairs: + checked_pairs.add(pair) + if row_index not in reduced_rows: + reduced_rows[row_index] = support(rows[wire]) + for port, coefficient in reduced_rows[row_index].items(): + require(all((ports[port] & u).bit_count() % 2 == 0 for u in word['frames'][frame]), 'The exact fresh-row support law') + support_coefficients += 1 + if t == 8702: + require(all(not row for row in rows[704:]), 'All original private fields are zero after their last use') + + expected = [{i: Q(1)} for i in range(712)] + for p in range(112): + combine(expected[p], {112+q: v for q, v in j_rows[p].items()}, Q(-1)) + expected[704:] = [{} for _ in range(8)] + require(rows == expected, 'All712 final columns of the clean backward map') + require(rows == [{int(j): Q(v) for j, v in row.items()} for row in snapshots['final_rows']], 'The supplied full final rows') + require(frames == word['final']+[0]*8, 'The complete inherited canonical endpoints') + require(last_scalar == last and events[8703] == ['phase', 'A'], 'The exact final scalar cut and post-private phase') + require(max(t for t, _, _ in private_uses) == 8702, 'No original private read or write after8702') + require(all(not support(rows[p]) for p in list(range(112))+list(range(224, 712))), 'The completed X and all helper/private baselines vanish on the test family') + require(len(checked_pairs) == source_receipt['distinct_frame_row_pairs'] == 16023 and + support_coefficients == source_receipt['exact_nonzero_support_coefficients'] == 98056, 'The complete claimed support coverage') + require(profile == {1:2412, 2:418, 3:432, 4:142, 5:82}, 'The native profile of the unchanged core') + full_helpers = [p for p in range(224, 704) if frames[p] == 1] + require(len(full_helpers) == 402, 'The exact number of FULL helper baseline fields') + + actual, supplied, actual_frame, supplied_frame = check_example + wrong = supplied.copy() + wrong[711] = wrong.get(711, Q(0))+1 + reject(lambda: require(actual == wrong, 'Changed arbitrary private coefficient'), 'A changed snapshot row') + reject(lambda: intervals_partition(intervals[1:], first, last), 'A missing interval') + reject(lambda: require(actual_frame == (supplied_frame+1) % len(word['frames']), 'Changed frame index'), 'A changed native frame') + + receipt = { + 'status': 'PASS_INDEPENDENT_BACKWARD_SNAPSHOT_ROWS', 'source_pins': PINS, + 'producer_or_checker_imports': [], 'all_formal_input_columns': 712, + 'constant_intervals': len(intervals), 'interval_endpoint_checks': endpoint_checks, + 'interval_interior_update_checks': len(intervals), + 'complete_interval_wire_count': 704, 'distinct_frame_row_support_checks': len(checked_pairs), + 'exact_nonzero_support_coefficients': support_coefficients, + 'native_profile': dict(sorted(profile.items())), 'scalar_macros': dict(sorted(macros.items())), + 'last_original_private_event': 8702, 'all_eight_private_fields_zero_after_last_use': True, + 'last_scalar_event': last_scalar, 'FULL_helper_baseline_fields': full_helpers, + 'controls': {'changed_private_coefficient': 'rejected', 'missing_interval': 'rejected', 'changed_frame': 'rejected'}, + 'scope': 'Independent full712 scalar-row reconstruction, interval coverage, native canonical frame accesses and support law. The source minor/cone proof review is separate. Exact native phases for a new capture word, merged-flow synthesis, costs and hosting are not supplied.', + 'reviewer_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + } + (HERE/'SNAPSHOT-ROWS-REVIEW.json').write_text(json.dumps(receipt, sort_keys=True, indent=2)+'\n') + print(receipt['status']) + print(json.dumps({k:receipt[k] for k in ('constant_intervals', 'interval_endpoint_checks', 'distinct_frame_row_support_checks', 'exact_nonzero_support_coefficients', 'last_original_private_event', 'reviewer_sha256')}, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/actual-query-information-bounds/frozen/cover-algebra/review_query_moments.py b/research/actual-query-information-bounds/frozen/cover-algebra/review_query_moments.py new file mode 100644 index 0000000000..75859602b5 --- /dev/null +++ b/research/actual-query-information-bounds/frozen/cover-algebra/review_query_moments.py @@ -0,0 +1,91 @@ +"""Check the exact moment arithmetic and the finite source contractions.""" + +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import json + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent +PINS = { + "QUERY-MOMENTS.md": "91121028d7f084d3c1d53a16ca8a3634ce4ede59fcab31c9a74c4a221c7d75e5", + "check_query_fourth_moment.py": "c22539e007c763b2d92d2932c4d84080ccda8549774d6be8b7705575a03a253f", + "QUERY-FOURTH-MOMENT.json": "df32110bbd285e3036bdb2082e3307b24edc7515953cab7a1b3b6b684adc1e66", + "check_query_fifth_moment.py": "bea72f2bafab8cc38142557d6d3a1bee5f4db1f9a2a75668fce146ca6ebba4f0", + "QUERY-FIFTH-MOMENT.json": "d346e38c1dc323d3304c94e7faf14384ac7970bb7b7775c49749a90a509fa0e9", +} + + +def need(value, message): + if not value: + raise ValueError(message) + + +def main(): + for name, expected in PINS.items(): + need(sha256((LANES / "temporal-reuse" / name).read_bytes()).hexdigest() == expected, "A source pin differs: " + name) + source_path = LANES / "circuit-interface/INTERFACE.json" + source = json.loads(source_path.read_text()) + a = [0, 7, 20, 27, 36, 46, 57, 111] + t = [21, 37, 47, 76, 81, 87, 92, 110] + ordinary = [p for p in range(112) if p not in a + t] + roots = [[Q(row.get(str(p), 0)) for row in source["R"]] for p in ordinary] + dot = lambda x, y: sum((v * w for v, w in zip(x, y)), Q()) + need(all(dot(v, v) == 4 for v in roots), "A column norm differs") + need(all(sum((v[i] * v[j] for v in roots), Q()) == 48 * int(i == j) for i in range(8) for j in range(8)), "The ordinary Gram differs") + products = [[dot(x, y) for y in roots] for x in roots] + need(all(sum(bool(v) for v in row) == 45 for row in products), "The supported degree differs") + off = [products[p][q] for p in range(96) for q in range(96) if p != q and products[p][q]] + need(len(off) == 4224 and set(map(abs, off)) == {Q(2)}, "The off-diagonal root products differ") + fourth_numerator = 8 * 192**2 + sum(16 * x * x for x in off) + need(Q(fourth_numerator, 48**4) == Q(23, 216), "The alternating contraction differs") + # The reviewed finite route check says that all fifth-order matches have s=t. + # Contract those terms directly, without its coefficient-table implementation. + fifth_numerator = sum((192 * products[r][r]**3 for r in range(96)), Q()) + fifth_numerator += sum((64 * x * x for x in off), Q()) + need(fifth_numerator == 2260992 and Q(fifth_numerator, 48**5) == Q(23, 2592), "The fifth contraction differs") + fifth = json.loads((LANES / "temporal-reuse/QUERY-FIFTH-MOMENT.json").read_text()) + need(fifth["supported_triples"] == 194400 and fifth["matched_group_terms"] == 4320 and fifth["identity_matches"] == 96, "The finite match receipt differs") + patterns = fifth["match_equality_patterns"] + need(patterns == {"(False, True, False)": 4224, "(True, True, True)": 96}, "The match classification differs") + m = [Q(96), Q(72), Q(120), Q(244), Q(1649, 3), Q(47467, 36)] + # The fourth-moment word count follows cyclic idempotence and singleton deletion. + k = 9 + m4 = 8*k + 4*k*(k-1) + Q(23, 216)*k*(k-1) + m4 += Q(k*(k-1)*(k-2), 3) + Q(k*(k-1)*(k-2)*(k-3), 216) + need(m4 == m[4], "The fourth word count differs") + v1, v2 = m[1], m[2] + h11, h12, h22 = m[2:5] + determinant = h11*h22 - h12*h12 + bound4 = (v1*v1*h22 - 2*v1*v2*h12 + v2*v2*h11) / determinant + need(bound4 == Q(4104, 73), "The optimal quadratic Cauchy bound differs") + need((h22*v1-h12*v2) / (-h12*v1+h11*v2) == -Q(13, 4), "The fourth optimizing polynomial differs") + weighted = [9*m[i] - m[i+1] for i in range(1, 5)] + v1, v2, h22 = weighted[0], weighted[1], weighted[3] + h11, h12 = weighted[1:3] + determinant = h11*h22 - h12*h12 + bound5 = (m[1] + (v1*v1*h22 - 2*v1*v2*h12 + v2*v2*h11) / determinant) / 9 + need(bound5 == Q(15560, 273), "The weighted quadratic bound differs") + need((h22*v1-h12*v2) / (-h12*v1+h11*v2) == -Q(19, 6), "The fifth optimizing polynomial differs") + moment = [bound5] + m[1:] + need(all(moment[i+3] - Q(73, 6)*moment[i+2] + Q(1459, 48)*moment[i+1] - Q(273, 16)*moment[i] == 0 for i in range(3)), "The extremal measure recurrence differs") + mass9 = (moment[2] - Q(19, 6)*moment[1] + Q(91, 48)*moment[0]) / Q(2611, 48) + mean = (moment[1] - 9*mass9) / (bound5-mass9) + need(mass9 == Q(8, 7833) and 1 < mean < 2 and 0 < bound5 < 96, "The extremal masses are not positive") + # The two remaining nodes are (19 +/- 2 sqrt(22))/12. + need(7**2 < 88 < 19**2 and 5**2 < 88 < 17**2, "The node intervals differ") + result = { + "status": "PASS_INDEPENDENT_QUERY_MOMENT_PROOF_AND_ARITHMETIC_REVIEW", + "source_pins": PINS, + "matrix_source_sha256": sha256(source_path.read_bytes()).hexdigest(), + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "checks": {"ordinary_columns": 96, "off_diagonal_support": len(off), "fourth_contraction": str(Q(fourth_numerator, 48**4)), "fifth_contraction": str(Q(fifth_numerator, 48**5)), "rank4": str(bound4), "rank5": str(bound5), "whole_fields": 57, "eight_field_cohorts": 8, "positive_measure_attains_first_five_moments": True}, + "scope": "Independent proof review and exact arithmetic. The frozen finite route-support enumerations are inspected dependencies; this review does not rerun or replace them. The capacity statement uses the full fixed-source regular-cover payload module. No changing-source, native-child, cache construction, or supplier claim." + } + (HERE / "QUERY-MOMENTS-REVIEW.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/frozen/residual-syndrome/review/independent_residual.py b/research/actual-query-information-bounds/frozen/residual-syndrome/review/independent_residual.py new file mode 100644 index 0000000000..b8dc4ba508 --- /dev/null +++ b/research/actual-query-information-bounds/frozen/residual-syndrome/review/independent_residual.py @@ -0,0 +1,162 @@ +"""Audit the residual formula with source matrices and separate exact examples.""" + +from hashlib import sha256 +from pathlib import Path +import gzip +import io +import json +import subprocess +import tarfile + +import sympy as s + + +ROOT = Path(__file__).resolve().parents[5] +REPO = ROOT / "worktrees/k5-centre-sharing" +BASE = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f" +ARCHIVE = "research/community-frontier1042-audit/selected-replay.tar.gz" +MEMBER = "t16/global/base/split-centres/GLOBAL-TEMPLATE.json.gz" +HERE = Path(__file__).resolve().parent + + +def require(value, label): + if not value: + raise RuntimeError(label) + + +def elementary(event, coupling=None): + a = s.eye(8) + if event["kind"] == "local": + i = 2 * event["pair"] + if event["reverse"]: + a[i, i + 1] = -1 + else: + a[i + 1, i] = 1 + if coupling is not None: + return s.eye(8 * coupling.rows) + s.kronecker_product(a - s.eye(8), coupling) + elif event["kind"] == "bridge": + i, j, q = event["dst"], event["src"], event["coefficient"] + a[2 * i, 2 * j] = q + a[2 * j + 1, 2 * i + 1] = -q + elif event["kind"] == "terminal": + a = s.diag(*[s.Matrix([[0, 1], [-1, 0]]) for _ in range(event["pairs"])]) + return a + + +def exact_case(recipe, bank_rows, centre_rows, removed): + dim = centre_rows[0].cols + width = centre_rows[0].rows + require(all(r * r.T == 56 * s.eye(width) for r in centre_rows), "Row Gram") + actual = s.eye(8 * dim) + ideal = s.eye(8 * dim) + for event in recipe: + if event["kind"] == "terminal": + continue + if event["kind"] == "local": + stage = event["stage"] + r = centre_rows[stage] + k = s.eye(dim) - r.T * r / 4 if stage in removed else s.eye(dim) + native = elementary(event, k) + else: + native = s.kronecker_product(elementary(event), s.eye(dim)) + actual = native * actual + ideal = s.kronecker_product(elementary(event), s.eye(dim)) * ideal + residual = ideal.inv() * actual - s.eye(8 * dim) + if not removed: + require(residual.is_zero_matrix, "Empty subset") + return {"stages": [], "rank": 0} + v = s.Matrix.vstack(*[s.kronecker_product(bank_rows[i, :], centre_rows[i]) for i in sorted(removed)]) + omega = s.kronecker_product(s.diag(*[s.Matrix([[0, 1], [-1, 0]])] * 4), s.eye(dim)) + gram = v * omega * v.T + blocks = len(removed) + lower = s.zeros(blocks * width) + for i in range(blocks): + for j in range(i): + lower[i * width:(i + 1) * width, j * width:(j + 1) * width] = gram[i * width:(i + 1) * width, j * width:(j + 1) * width] + middle = 4 * s.eye(v.rows) - lower + require(residual == omega * v.T * middle.inv() * v, "Interaction factorization") + require(residual.rank() == v.rank(), "No decoder cancellation") + require(residual != omega * v.T * (4 * s.eye(v.rows) + lower).inv() * v, + "Wrong triangular sign was not detected") + null = v.T.nullspace() + if null: + basis = s.Matrix.hstack(*null) + compressed = basis.T * middle * basis + require(compressed.det() != 0, "Kernel compression") + return {"stages": sorted(removed), "rank": residual.rank(), "syndrome_nullity": len(null)} + + +def main(): + raw = subprocess.check_output(["git", "show", BASE + ":" + ARCHIVE], cwd=REPO) + require(sha256(raw).hexdigest() == "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754", "Archive pin") + with tarfile.open(fileobj=io.BytesIO(raw), mode="r:gz") as archive: + member = archive.extractfile(MEMBER).read() + require(sha256(member).hexdigest() == "a179dad87651aba340a5a8ddbcd86a8e757cad87b8a1f8bad48106fbecd38518", "Controller pin") + template = json.loads(gzip.decompress(member)) + recipe = template["recipe"] + omega = s.diag(*[s.Matrix([[0, 1], [-1, 0]])] * 4) + prefix = s.eye(8) + rows = [] + for event in recipe: + if event["kind"] == "local": + source = 2 * event["pair"] + int(event["reverse"]) + rows.append(s.eye(8)[source, :] * prefix) + step = elementary(event) + require(step * omega * step.T == omega, "Source step is not symplectic") + prefix = step * prefix + require(prefix == s.eye(8), "Old endpoint") + v = s.Matrix.vstack(*rows) + relation = v.T.nullspace() + require(len(relation) == 1, "Bank relation dimension") + c = relation[0] / relation[0][0] + require(list(c) == [1, -1, -1, 1, 1, -1, -1, 1, 1], "Bank relation") + minors = [v[[i for i in range(9) if i != j], :].det() for j in range(9)] + require(all(value != 0 for value in minors), "A maximal proper subset is dependent") + gram = v * omega * v.T + area = sum(c[i] * c[j] * gram[i, j] for i in range(9) for j in range(i)) + compression = s.Rational(4, 56) * (c.T * c)[0] - area + require(area == 4 and compression == -s.Rational(47, 14), "Kernel form") + data_sets = [] + for replica in range(16): + calls = [call for call in template["calls"] if call["replica"] == replica] + require([call["stage"] for call in calls] == list(range(9)), "Replica stages") + families = {owner[0] for call in calls for owner in call["owners"] if owner[0] < 14336} + require(families == set(range(896 * replica, 896 * (replica + 1))), "Replica data namespace") + data_sets.append(families) + require(len(set.union(*data_sets)) == sum(map(len, data_sets)), "Replica data overlap") + r = s.Matrix([[6, 4, 2, 0, 0, 0], [0, 0, 0, 6, 4, 2]]) + one = s.Matrix([[6, 4, 2, 0, 0, 0], [0, 0, 0, 2, 6, 4]]) + zero = s.Matrix([[2, 6, 4, 0, 0, 0], [0, 0, 0, 2, 6, 4]]) + examples = {} + for name, alternate, shared in (("two_shared", r, 2), ("one_shared", one, 1), ("none_shared", zero, 0)): + centres = [r, alternate, r, alternate, r, r, alternate, r, alternate] + result = exact_case(recipe, v, centres, set(range(9))) + require(result["syndrome_nullity"] == shared and result["rank"] == 18 - shared, "Common-image rank") + examples[name] = result + centres = [r, zero, r, one, zero, r, one, zero, r] + proper = [exact_case(recipe, v, centres, set(range(9)) - {missing}) for missing in range(9)] + require(all(item["rank"] == 16 for item in proper), "Maximal proper residual rank") + per_replica = 72 - s.Rational(8, 183) + require(s.ceiling(per_replica) == 72 and s.ceiling(16 * per_replica) == 1152, "Whole-array count") + report = { + "status": "PASS_INDEPENDENT_RESIDUAL_ALGEBRA_REVIEW", + "source_base": BASE, + "controller_member_sha256": sha256(member).hexdigest(), + "bank_rows": [list(map(int, row)) for row in v.tolist()], + "bank_relation": list(map(int, c)), + "maximal_proper_minors": list(map(int, minors)), + "area": str(area), "compression": str(compression), + "independent_data_replicas": len(data_sets), + "data_families_per_replica": 896, + "exact_examples": examples, + "maximal_proper_residual_examples": proper, + "conditional_whole_array_bounds": {"per_replica": 72, "all_replicas": 1152}, + "dependencies_not_reproved": ["Native global normal form", "Routed-projection dimension bound"], + "scope": "Exact algebra review. No claim about concurrent workspace, native rank cost, or supplier admission.", + } + (HERE / "INDEPENDENT-RECEIPT.json").write_text(json.dumps(report, indent=2, sort_keys=True) + "\n") + print(report["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/frozen/residual-syndrome/verify_residual.py b/research/actual-query-information-bounds/frozen/residual-syndrome/verify_residual.py new file mode 100644 index 0000000000..4bef3cb14f --- /dev/null +++ b/research/actual-query-information-bounds/frozen/residual-syndrome/verify_residual.py @@ -0,0 +1,225 @@ +"""Check the controller source and the residual factorization.""" + +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import io +import json +import subprocess +import tarfile + + +BASE = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f" +ARCHIVE = "research/community-frontier1042-audit/selected-replay.tar.gz" +ARCHIVE_HASH = "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754" +MEMBER = "t16/global/base/split-centres/GLOBAL-TEMPLATE.json.gz" +MEMBER_HASH = "a179dad87651aba340a5a8ddbcd86a8e757cad87b8a1f8bad48106fbecd38518" +INTERFACE_HASH = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def eye(n): + return [[Q(i == j) for j in range(n)] for i in range(n)] + + +def transpose(a): + return list(map(list, zip(*a))) + + +def multiply(a, b): + bt = transpose(b) + return [[sum(x*y for x, y in zip(row, col)) for col in bt] for row in a] + + +def subtract(a, b): + return [[x-y for x, y in zip(row, col)] for row, col in zip(a, b)] + + +def rank(a): + b = [list(map(Q, row)) for row in a] + r = 0 + for j in range(len(b[0])): + k = next((i for i in range(r, len(b)) if b[i][j]), None) + if k is None: + continue + b[r], b[k] = b[k], b[r] + d = b[r][j] + b[r] = [x/d for x in b[r]] + for i in range(r+1, len(b)): + d = b[i][j] + if d: + b[i] = [x-d*y for x, y in zip(b[i], b[r])] + r += 1 + if r == len(b): + break + return r + + +def inverse(a): + n = len(a) + b = [list(map(Q, row))+e for row, e in zip(a, eye(n))] + for j in range(n): + k = next(i for i in range(j, n) if b[i][j]) + b[j], b[k] = b[k], b[j] + d = b[j][j] + b[j] = [x/d for x in b[j]] + for i in range(n): + if i != j: + d = b[i][j] + if d: + b[i] = [x-d*y for x, y in zip(b[i], b[j])] + return [row[n:] for row in b] + + +def omega(n): + out = [[Q(0) for _ in range(8*n)] for _ in range(8*n)] + for pair in range(4): + for j in range(n): + x, y = (2*pair)*n+j, (2*pair+1)*n+j + out[x][y], out[y][x] = Q(1), Q(-1) + return out + + +def controller(recipe, kernels, include_terminal=False): + n = len(kernels[0]) + c = eye(8*n) + for event in recipe: + kind = event['kind'] + if kind == 'local': + pair, stage = event['pair'], event['stage'] + source = 2*pair+int(event['reverse']) + target = 2*pair+int(not event['reverse']) + sign = -1 if event['reverse'] else 1 + old = [row.copy() for row in c[source*n:(source+1)*n]] + delta = multiply(kernels[stage], old) + for j, row in enumerate(delta): + t = target*n+j + c[t] = [a+sign*b for a, b in zip(c[t], row)] + elif kind == 'bridge': + i, j, q = event['dst'], event['src'], event['coefficient'] + for bank_t, bank_s, factor in ((2*i, 2*j, q), (2*j+1, 2*i+1, -q)): + for p in range(n): + t, s = bank_t*n+p, bank_s*n+p + c[t] = [a+factor*b for a, b in zip(c[t], c[s])] + elif kind == 'terminal' and include_terminal: + for pair in range(event['pairs']): + for p in range(n): + x, y = 2*pair*n+p, (2*pair+1)*n+p + c[x], c[y] = c[y], [-q for q in c[x]] + return c + + +def bank_sources(recipe): + c = eye(8) + rows = [] + for event in recipe: + if event['kind'] == 'local': + i = event['pair'] + source = 2*i+int(event['reverse']) + target = 2*i+int(not event['reverse']) + sign = -1 if event['reverse'] else 1 + rows.append(c[source].copy()) + c[target] = [a+sign*b for a, b in zip(c[target], c[source])] + elif event['kind'] == 'bridge': + i, j, q = event['dst'], event['src'], event['coefficient'] + c[2*i] = [a+q*b for a, b in zip(c[2*i], c[2*j])] + c[2*j+1] = [a-q*b for a, b in zip(c[2*j+1], c[2*i+1])] + return rows, c + + +def toy_check(recipe, sources, distinct): + # These exact rows have norm squared 56. They are not cover data. + rows = [[Q(6), Q(4), Q(2)] for _ in range(9)] + if distinct: + rows[1] = [Q(2), Q(6), Q(4)] + require(all(sum(x*x for x in row) == 56 for row in rows), 'Toy row norm') + kernels = [subtract(eye(3), [[x*y/4 for y in row] for x in row]) for row in rows] + actual = controller(recipe, kernels) + ideal = controller(recipe, [eye(3)]*9) + residual = subtract(multiply(inverse(ideal), actual), eye(24)) + v = [[b*x for b in source for x in row] for source, row in zip(sources, rows)] + om = omega(3) + g = multiply(multiply(v, om), transpose(v)) + b = [[4*Q(i == j)-(g[i][j] if i > j else 0) for j in range(9)] for i in range(9)] + predicted = multiply(multiply(multiply(om, transpose(v)), inverse(b)), v) + require(residual == predicted, 'The residual factorization failed') + expected = 9 if distinct else 8 + require(rank(v) == rank(residual) == expected, 'The residual rank is wrong') + wrong = [[4*Q(i == j)+(g[i][j] if i > j else 0) for j in range(9)] for i in range(9)] + rejected = residual != multiply(multiply(multiply(om, transpose(v)), inverse(wrong)), v) + require(rejected, 'The wrong-sign control did not fail') + return {'syndrome_rank': rank(v), 'residual_rank': rank(residual), + 'wrong_triangular_sign_rejected': rejected} + + +def run(repo, interface): + raw = subprocess.run(['git', 'show', BASE+':'+ARCHIVE], cwd=repo, + check=True, capture_output=True).stdout + require(sha256(raw).hexdigest() == ARCHIVE_HASH, 'The archive pin changed') + with tarfile.open(fileobj=io.BytesIO(raw), mode='r:gz') as archive: + member = archive.extractfile(MEMBER).read() + require(sha256(member).hexdigest() == MEMBER_HASH, 'The controller pin changed') + recipe = json.loads(gzip.decompress(member))['recipe'] + source = interface.read_bytes() + require(sha256(source).hexdigest() == INTERFACE_HASH, 'The interface pin changed') + data = json.loads(source) + r = [[Q(row.get(str(p), '0')) for p in range(112)] for row in data['R']] + require(multiply(r, transpose(r)) == [[56*Q(i == j) for j in range(8)] for i in range(8)], + 'The centre matrix Gram identity failed') + require([event['stage'] for event in recipe if event['kind'] == 'local'] == list(range(9)), + 'The selected stages changed') + sources, ideal = bank_sources(recipe) + require(controller(recipe, [eye(1)]*9, True) == eye(8), 'The ideal controller is not identity') + require(ideal == [[-x for x in row] for row in omega(1)], 'The ideal preterminal map changed') + relation = [Q(x) for x in (1, -1, -1, 1, 1, -1, -1, 1, 1)] + require(all(sum(relation[i]*sources[i][j] for i in range(9)) == 0 for j in range(8)), + 'The stated bank relation failed') + require(all(rank(sources[:i]+sources[i+1:]) == 8 for i in range(9)), + 'A proper subset of the bank rows is dependent') + bank_g = multiply(multiply(sources, omega(1)), transpose(sources)) + area = sum(relation[i]*relation[j]*bank_g[i][j] for i in range(9) for j in range(i)) + require(area == 4, 'The bank relation area changed') + compression = sum(x*x for x in relation)*Q(4, 56)-area + require(compression == Q(-47, 14), 'The relation compression changed') + first_bridge = next(i for i, event in enumerate(recipe) if event['kind'] == 'bridge') + omitted = recipe[:first_bridge]+recipe[first_bridge+1:] + require(controller(omitted, [eye(1)]*9, True) != eye(8), 'The missing-bridge control did not fail') + return { + 'status': 'PASS_SELECTED_CONTROLLER_RESIDUAL_FACTORIZATION', + 'base': BASE, 'archive': ARCHIVE, 'archive_sha256': ARCHIVE_HASH, + 'controller_member': MEMBER, 'controller_member_sha256': MEMBER_HASH, + 'interface_sha256': INTERFACE_HASH, + 'bank_sources': [[int(x) for x in row] for row in sources], + 'bank_relation': [int(x) for x in relation], + 'bank_source_rank': 8, 'independent_eight_row_subsets': 9, + 'bank_relation_area': str(area), 'relation_compression': str(compression), + 'same_centre_space_toy': toy_check(recipe, sources, False), + 'distinct_centre_space_toy': toy_check(recipe, sources, True), + 'missing_bridge_rejected': True, + 'proved_in_note': { + 'full_residual_rank': '72 |G| - dim(intersection_s im(R_s^*))', + 'proper_subset_residual_rank': '8 |S| |G| for every proper set S of omitted stages', + 'conditional_two_stage_bound': 'rank / |G| >= 13168/183 > 71', + 'relation_compression': '-47/14 times the ambient common-image inner product', + }, + 'scope': 'Exact controller algebra and finite rational checks. The group rank bound uses the separate routed-projection theorem. No native correction, child-cost lower bound, supplier admission, or kappa claim.', + } + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--repo', type=Path, required=True) + parser.add_argument('--interface', type=Path, required=True) + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + result = run(args.repo, args.interface) + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(result['status']) + print('proper_subsets=independent residual_rank=72|G|-common_image_dimension') + print('native_supplier_or_kappa_claim=false') diff --git a/research/actual-query-information-bounds/frozen/source-domain/review_cover.py b/research/actual-query-information-bounds/frozen/source-domain/review_cover.py new file mode 100644 index 0000000000..62aad2e9ab --- /dev/null +++ b/research/actual-query-information-bounds/frozen/source-domain/review_cover.py @@ -0,0 +1,185 @@ +"""Independently check the cover trace and its fixed-stock application.""" + +from collections import defaultdict +from fractions import Fraction as Q +from hashlib import sha256 +from importlib.util import module_from_spec, spec_from_file_location +from pathlib import Path +import argparse +import gzip +import io +import json +import tarfile + + +PHASES = "t16/global/base/work/complex-nine-native/DATA-PHASES.json" +PHASES_SHA = "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" +INTERFACE_SHA = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def parity(a, b): + return (a & b).bit_count() % 2 + + +def apply(columns, x): + answer = 0 + for i, col in enumerate(columns): + if (x >> i) & 1: + answer ^= col + return answer + + +def product(left, right): + return tuple(apply(left, col) for col in right) + + +def swap_route(q, basis, stage): + first = 9 + 8 * (stage - 1) + columns = [1 << i for i in range(73)] + for i in range(9): + columns[i] = q if (q >> i) & 1 else 0 + for j, b in enumerate(basis): + if (b >> i) & 1: + columns[i] ^= 1 << (first + j) + columns[first:first + 8] = basis + return tuple(columns) + + +def run(repo, campaign): + own_source = Path(__file__).with_name("verify_domain.py") + spec = spec_from_file_location("domain_source", own_source) + source = module_from_spec(spec) + spec.loader.exec_module(source) + interface_file = campaign / "lanes/circuit-interface/INTERFACE.json" + interface_raw = interface_file.read_bytes() + require(sha256(interface_raw).hexdigest() == INTERFACE_SHA, "The interface changed") + interface = json.loads(interface_raw) + with tarfile.open(fileobj=io.BytesIO(source.source(repo, source.ARCHIVE)), mode="r:gz") as stream: + phase_raw = stream.extractfile(PHASES).read() + require(sha256(phase_raw).hexdigest() == PHASES_SHA, "The data phases changed") + phases = json.loads(phase_raw) + word = json.loads(gzip.decompress(source.pin(source.WORD, stream.extractfile(source.WORD).read()))) + programs = json.loads(gzip.decompress(source.pin(source.PROGRAMS, stream.extractfile(source.PROGRAMS).read()))) + r = source.clean_centre_map(word, programs["forward"]) + require(r == [[Q(interface["R"][i].get(str(j), "0")) for j in range(112)] + for i in range(8)], "The interface matrix differs from the frozen word") + ports = word["ports"] + require([x["q"] for x in phases["recipes"]] == ports, "The phase port order changed") + a = [[sum(r[k][i] * r[k][j] for k in range(8)) for j in range(112)] for i in range(112)] + identity = tuple(1 << i for i in range(73)) + routes = [] + full_dimension_checks = 0 + for q, recipe in zip(ports, phases["recipes"]): + basis = recipe["idle_children"][0]["orthogonal_axes"][:8] + require(len(basis) == 8 and all(x < 512 and not parity(q, x) for x in basis), + "The pinned local complement is invalid") + require(all(parity(x, y) == (i == j) for i, x in enumerate(basis) + for j, y in enumerate(basis)), "The pinned complement is not orthonormal") + route1 = swap_route(q, basis, 1) + routes.append(route1) + for stage in range(1, 9): + route = swap_route(q, basis, stage) + require(product(route, route) == identity, "A full route is not an involution") + require(all(parity(x, y) == (i == j) for i, x in enumerate(route) + for j, y in enumerate(route)), "A full route is not orthogonal") + transport = list(identity) + for j in range(8): + left, right = 9 + j, 9 + 8 * (stage - 1) + j + transport[left], transport[right] = transport[right], transport[left] + require(product(product(tuple(transport), route1), tuple(transport)) == route, + "The 73-dimensional stage embedding changed") + full_dimension_checks += 1 + + buckets = defaultdict(list) + for b in range(112): + for c in range(112): + if a[b][c]: + buckets[product(routes[b], routes[c])].append((b, c)) + require(len(buckets) == 5825, "The full group labels have different collisions") + require(buckets[identity] == [(i, i) for i in range(112)], "The identity bucket changed") + require(all(len(items) == 1 for g, items in buckets.items() if g != identity), + "Different ordered edges have the same group element") + + # Sum the trace coefficients from the actual group product equality. + # This does not use the two-case closed formula in the reviewed verifier. + fourth_integer = Q(0) + for items in buckets.values(): + for b, c in items: + for aa, d in items: + fourth_integer += a[aa][b] * a[b][c] * a[c][d] * a[d][aa] + first = sum(a[i][i] ** 2 for i in range(112)) / 56 ** 2 + second = fourth_integer / 56 ** 4 + require((first, second) == (Q(4, 7), Q(27, 343)), "The independent trace differs") + tau_m2 = 16 - 2 * first + tau_m4 = 16 - 4 * first + 2 * second + rank_bound = tau_m2 ** 2 / tau_m4 + shift = Q(13, 196) + common_bound = (second - 2 * shift * first + 8 * shift ** 2) / (1 - shift) ** 2 + require((rank_bound, common_bound) == (Q(2912, 183), Q(8, 183)), "The rank bound changed") + + g01, g10 = product(routes[0], routes[1]), product(routes[1], routes[0]) + require(g01 != g10, "The ordering control does not distinguish multiplication") + require(all(apply(g01, 1 << i) == apply(routes[0], apply(routes[1], 1 << i)) + for i in range(73)), "The matrix product order is wrong") + require(all(g01[i] == 1 << i for i in range(17, 73)), "The 17D support is not fixed") + require(all(g[i] == 1 << i for g in buckets for i in range(17, 73)), + "A group product escapes the 17D block") + + seen = {0} + todo = [0] + while todo: + i = todo.pop() + for j in range(112): + if i != j and a[i][j] and j not in seen: + seen.add(j) + todo.append(j) + require(len(seen) == 112, "The nullspace code graph is not connected") + + margin = Q(896, 73) + repeated_moment = Q(72 * 896) / (73 * (896 - rank_bound)) + single_global_moment = Q(72 * 14336) / (73 * (14336 - rank_bound)) + require(rank_bound > margin and repeated_moment > 1, "The repeated code was not rejected") + require(single_global_moment < 1, "The multiplicity control is not effective") + # On constant cover functions every group element acts as identity. + # In that representation Q=P, so their difference has rank zero. + trivial_trace_pq = sum(a[i][j] ** 2 for i in range(112) for j in range(112)) / 56 ** 2 + require(trivial_trace_pq == 8 != first, "The quotient control does not change the trace") + + reviewed = {name: sha256((campaign / "lanes/cover-algebra" / name).read_bytes()).hexdigest() + for name in ("PROOF.md", "verify_algebra.py")} + return { + "status": "PASS_INDEPENDENT_73D_COVER_TRACE_REVIEW", + "reviewed_files_sha256": reviewed, "interface_sha256": INTERFACE_SHA, + "source_base": source.BASE, "phase_source_sha256": PHASES_SHA, + "source_matrix_rederived": True, "full_73d_routes_checked": full_dimension_checks, + "nonidentity_group_product_buckets": len(buckets) - 1, + "trace_PQ": str(first), "trace_PQPQ": str(second), + "difference_trace_square": str(tau_m2), "difference_trace_fourth": str(tau_m4), + "rank_lower_bound_per_cover_element": str(rank_bound), + "common_range_upper_bound_per_cover_element": str(common_bound), + "allowed_codimension_per_replica": str(margin), + "rank_bound_excess": str(rank_bound - margin), + "fixed_stock_moment_if_one_coded_bank_per_replica": str(repeated_moment), + "single_coded_bank_in_all_16_replicas_is_not_excluded_at_zero": str(single_global_moment), + "trivial_representation_control": {"trace_PQ": str(trivial_trace_pq), "rank_difference": 0}, + "code_projector_graph_component_sizes": [len(seen)], + "review_findings": ["Corrected a contradictory index condition in the proof case split; the moment value was unchanged."], + "not_reviewed": ["optional sixth moment", "native phase implementation", "new supplier", "new kappa"], + } + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--repo", required=True, type=Path) + parser.add_argument("--campaign", required=True, type=Path) + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + result = run(args.repo, args.campaign) + args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(result["status"]) + print("routes73=896 trace_PQ=4/7 trace_PQPQ=27/343 rank>=2912/183>896/73") diff --git a/research/actual-query-information-bounds/frozen/temporal-reuse/QUERY-FIFTH-MOMENT.json b/research/actual-query-information-bounds/frozen/temporal-reuse/QUERY-FIFTH-MOMENT.json new file mode 100644 index 0000000000..0b423239df --- /dev/null +++ b/research/actual-query-information-bounds/frozen/temporal-reuse/QUERY-FIFTH-MOMENT.json @@ -0,0 +1,118 @@ +{ + "status": "PASS_ACTUAL_QUERY_FIFTH_MOMENT", + "fourth_checker_sha256": "c22539e007c763b2d92d2932c4d84080ccda8549774d6be8b7705575a03a253f", + "fourth_receipt_sha256": "df32110bbd285e3036bdb2082e3307b24edc7515953cab7a1b3b6b684adc1e66", + "new_word": [ + 1, + 2, + 1, + 2, + 0 + ], + "supported_triples": 194400, + "matched_group_terms": 4320, + "identity_matches": 96, + "match_equality_patterns": { + "(False, True, False)": 4224, + "(True, True, True)": 96 + }, + "integer_trace_numerator": 2260992, + "trace_denominator": 254803968, + "new_word_trace_per_cover": "23/2592", + "fixed_source_bounds": [ + { + "charts": 1, + "fifth_moment_per_cover": "8", + "weighted_quadratic_rank_per_cover": "8", + "whole_fields": 8, + "eight_field_cohorts": 1 + }, + { + "charts": 2, + "fifth_moment_per_cover": "3283/108", + "weighted_quadratic_rank_per_cover": "2120/133", + "whole_fields": 16, + "eight_field_cohorts": 2 + }, + { + "charts": 3, + "fifth_moment_per_cover": "32023/432", + "weighted_quadratic_rank_per_cover": "3464/147", + "whole_fields": 24, + "eight_field_cohorts": 3 + }, + { + "charts": 4, + "fifth_moment_per_cover": "15901/108", + "weighted_quadratic_rank_per_cover": "5000/163", + "whole_fields": 31, + "eight_field_cohorts": 4 + }, + { + "charts": 5, + "fifth_moment_per_cover": "55925/216", + "weighted_quadratic_rank_per_cover": "6728/181", + "whole_fields": 38, + "eight_field_cohorts": 5 + }, + { + "charts": 6, + "fifth_moment_per_cover": "22657/54", + "weighted_quadratic_rank_per_cover": "8648/201", + "whole_fields": 44, + "eight_field_cohorts": 6 + }, + { + "charts": 7, + "fifth_moment_per_cover": "276857/432", + "weighted_quadratic_rank_per_cover": "10760/223", + "whole_fields": 49, + "eight_field_cohorts": 7 + }, + { + "charts": 8, + "fifth_moment_per_cover": "50531/54", + "weighted_quadratic_rank_per_cover": "13064/247", + "whole_fields": 53, + "eight_field_cohorts": 7 + }, + { + "charts": 9, + "fifth_moment_per_cover": "47467/36", + "weighted_quadratic_rank_per_cover": "15560/273", + "whole_fields": 57, + "eight_field_cohorts": 8 + } + ], + "finite_free_moment_comparison": [ + "72", + "120", + "244", + "1649/3", + "47467/36" + ], + "nine_chart_optimizing_weight": "9-lambda", + "nine_chart_optimizing_polynomial": "19 lambda - 6 lambda^2", + "moment_relaxation_attainment": { + "nodes": [ + "0", + "(19-2 sqrt(22))/12", + "(19+2 sqrt(22))/12", + "9" + ], + "nonzero_mass": "15560/273", + "mass_at_9": "8/7833", + "interior_mass": "1934592/33943", + "interior_mean": "1157/916", + "recurrence": "x^3-(73/6)x^2+(1459/48)x-273/16", + "ambient_total_mass": 96 + }, + "scope": "The full fixed-source logical regular-cover module. No freeness assumption.", + "not_claimed": [ + "Equality of higher moments", + "A cache construction", + "A native-child bound", + "A result for changing source histories", + "A supplier or kappa improvement" + ] +} diff --git a/research/actual-query-information-bounds/frozen/temporal-reuse/check_query_fifth_moment.py b/research/actual-query-information-bounds/frozen/temporal-reuse/check_query_fifth_moment.py new file mode 100644 index 0000000000..f866bfdad6 --- /dev/null +++ b/research/actual-query-information-bounds/frozen/temporal-reuse/check_query_fifth_moment.py @@ -0,0 +1,169 @@ +"""Check the remaining fifth-order route word and its exact rank bound.""" + +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from itertools import product +from pathlib import Path +import importlib.util +import json + + +HERE = Path(__file__).resolve().parent +FOURTH_CHECKER_PIN = "c22539e007c763b2d92d2932c4d84080ccda8549774d6be8b7705575a03a253f" +FOURTH_RECEIPT_PIN = "df32110bbd285e3036bdb2082e3307b24edc7515953cab7a1b3b6b684adc1e66" + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def trace_word(word): + w = list(word) + while len(w) > 1: + remove = next((i for i in range(len(w)) if w[i] == w[(i+1) % len(w)]), None) + if remove is None: + break + w.pop(remove) + if len(w) == 1: + return Q(8) + if len(w) == 2: + return Q(2, 3) + counts = Counter(w) + if len(w) == 4 and len(counts) == 2: + return Q(23, 216) + unique = next((i for i, s in enumerate(w) if s and counts[s] == 1), None) + if unique is not None: + w.pop(unique) + return trace_word(w)/12 + need(len(w) == 5 and counts[0] == 1 and sorted(counts.values()) == [1, 2, 2], + "An unsupported fifth-order word remains") + return Q(23, 2592) + + +def composition_sum(moments, total, factors): + if factors == 0: + return Q(total == 0) + return sum((moments[i]*composition_sum(moments, total-i, factors-1) + for i in range(total+1)), Q(0)) + + +def free_moment_comparison(): + """Check only the finite noncrossing moment recurrence.""" + alpha = Q(1, 12) + bernoulli = [Q(1)]+[alpha]*5 + cumulants = [Q(0)] + for n in range(1, 6): + cumulants.append(alpha-sum((cumulants[k]*composition_sum(bernoulli, n-k, k) + for k in range(1, n)), Q(0))) + moments = [Q(1)] + for n in range(1, 6): + moments.append(sum((9*cumulants[k]*composition_sum(moments, n-k, k) + for k in range(1, n+1)), Q(0))) + expected = [Q(72), Q(120), Q(244), Q(1649, 3), Q(47467, 36)] + need([96*x for x in moments[1:]] == expected, "The finite free-moment comparison differs") + return list(map(str, expected)) + + +def main(): + path = HERE/"check_query_fourth_moment.py" + need(sha256(path.read_bytes()).hexdigest() == FOURTH_CHECKER_PIN, "Fourth checker changed") + raw = (HERE/"QUERY-FOURTH-MOMENT.json").read_bytes() + need(sha256(raw).hexdigest() == FOURTH_RECEIPT_PIN, "Fourth receipt changed") + spec = importlib.util.spec_from_file_location("independent_fourth", path) + fourth = importlib.util.module_from_spec(spec) + spec.loader.exec_module(fourth) + roots, bases, dots, _ = fourth.source() + terms, _ = fourth.covariance(1, 2, roots, bases, dots) + r1 = [fourth.route(b, 1) for b in bases] + r2 = [fourth.route(b, 2) for b in bases] + relative = [fourth.compose(a, b) for a, b in zip(r1, r2)] + neighbors = [[j for j in range(96) if dots[i][j]] for i in range(96)] + need(all(len(x) == 45 for x in neighbors), "The supported degree differs") + total = triples = matches = identity_matches = 0 + match_patterns = Counter() + for r in range(96): + for s in neighbors[r]: + left = fourth.compose(relative[r], r2[s]) + for t in neighbors[s]: + triples += 1 + key = fourth.compose(left, r1[t]) + if key not in terms: + continue + matches += 1 + match_patterns[str((r == s, s == t, r == t))] += 1 + coefficient = terms[key] + if coefficient is None: + identity_matches += 1 + value = 192*dots[r][t] + else: + p, q, scalar = coefficient + value = scalar*dots[r][p]*dots[q][t] + total += dots[r][s]*dots[s][t]*value + need((triples, matches, identity_matches, total) == (194400, 4320, 96, 2260992), + "The fifth-order coefficient aggregation differs") + fifth = Q(total, 48**5) + need(fifth == Q(23, 2592), "The new cyclic trace differs") + rows = [] + for k in range(1, 10): + moments = [Q(x) for x in json.loads(raw)["fixed_source_bounds"][k-1]["moments_per_cover"]] + moments.append(sum((trace_word(w) for w in product(range(k), repeat=5)), Q(0))) + m1, m2, m3, m4, m5 = moments + v1, v2 = k*m1-m2, k*m2-m3 + h11, h12, h22 = k*m2-m3, k*m3-m4, k*m4-m5 + determinant = h11*h22-h12*h12 + if determinant: + rank = (m1+(v1*v1*h22-2*v1*v2*h12+v2*v2*h11)/determinant)/k + else: + rank = Q(8) + fields = (rank.numerator+rank.denominator-1)//rank.denominator + rows.append({"charts": k, "fifth_moment_per_cover": str(m5), + "weighted_quadratic_rank_per_cover": str(rank), + "whole_fields": fields, "eight_field_cohorts": (fields+7)//8}) + need(rows[-1]["fifth_moment_per_cover"] == "47467/36", "The nine-chart fifth moment differs") + rank = Q(rows[-1]["weighted_quadratic_rank_per_cover"]) + need(rank == Q(15560, 273) == 57-Q(1, 273), "The fifth-moment rank bound differs") + + # A positive four-atom measure attains the moment relaxation. + moment = [rank, Q(72), Q(120), Q(244), Q(1649, 3), Q(47467, 36)] + for i in range(3): + need(moment[i+3]-Q(73, 6)*moment[i+2]+Q(1459, 48)*moment[i+1] + -Q(273, 16)*moment[i] == 0, "The extremal cubic recurrence fails") + mass9 = (moment[2]-Q(19, 6)*moment[1]+Q(91, 48)*moment[0])/Q(2611, 48) + need(mass9 == Q(8, 7833), "The top atom mass differs") + interior_mass = rank-mass9 + interior_mean = (moment[1]-9*mass9)/interior_mass + need(1 < interior_mean < 2 and 0 < mass9 < rank < 96, + "The extremal measure is not positive") + # Its interior nodes are (19 +/- 2 sqrt(22))/12, one in (0,1), one in (2,3). + need(7*7 < 4*22 < 19*19 and 5*5 < 4*22 < 17*17, + "The interior node intervals differ") + result = {"status": "PASS_ACTUAL_QUERY_FIFTH_MOMENT", + "fourth_checker_sha256": FOURTH_CHECKER_PIN, + "fourth_receipt_sha256": FOURTH_RECEIPT_PIN, + "new_word": [1, 2, 1, 2, 0], "supported_triples": triples, + "matched_group_terms": matches, "identity_matches": identity_matches, + "match_equality_patterns": dict(sorted(match_patterns.items())), + "integer_trace_numerator": total, "trace_denominator": 48**5, + "new_word_trace_per_cover": str(fifth), "fixed_source_bounds": rows, + "finite_free_moment_comparison": free_moment_comparison(), + "nine_chart_optimizing_weight": "9-lambda", + "nine_chart_optimizing_polynomial": "19 lambda - 6 lambda^2", + "moment_relaxation_attainment": { + "nodes": ["0", "(19-2 sqrt(22))/12", "(19+2 sqrt(22))/12", "9"], + "nonzero_mass": str(rank), "mass_at_9": str(mass9), + "interior_mass": str(interior_mass), "interior_mean": str(interior_mean), + "recurrence": "x^3-(73/6)x^2+(1459/48)x-273/16", + "ambient_total_mass": 96}, + "scope": "The full fixed-source logical regular-cover module. No freeness assumption.", + "not_claimed": ["Equality of higher moments", "A cache construction", "A native-child bound", + "A result for changing source histories", "A supplier or kappa improvement"]} + (HERE/"QUERY-FIFTH-MOMENT.json").write_text(json.dumps(result, indent=2)+"\n") + print(json.dumps({"status": result["status"], "m5": "47467/36", + "rank_per_cover": "15560/273", "whole_fields": 57, + "moment_relaxation_is_sharp": True})) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/frozen/temporal-reuse/check_query_fourth_moment.py b/research/actual-query-information-bounds/frozen/temporal-reuse/check_query_fourth_moment.py new file mode 100644 index 0000000000..9fce6f08ae --- /dev/null +++ b/research/actual-query-information-bounds/frozen/temporal-reuse/check_query_fourth_moment.py @@ -0,0 +1,292 @@ +"""Check exact routed query moments from the actual port bases.""" + +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from io import BytesIO +from itertools import product +from pathlib import Path +import gzip +import json +import subprocess +import tarfile + + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[3] +LANES = HERE.parent +BASE = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f" +ARCHIVE = "research/community-frontier1042-audit/selected-replay.tar.gz" +ARCHIVE_PIN = "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754" +PHASE_MEMBER = "t16/global/base/work/complex-nine-native/DATA-PHASES.json" +PHASE_PIN = "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" +WORD_MEMBER = "slots/local/CANONICAL-WORD.json.gz" +WORD_PIN = "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219" +INTERFACE_PIN = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" +R_REVIEW_PIN = "9639db0bdbc82255ef85273ac15a0aff68d5c659190557bf331d260eb714964f" +A = [0, 7, 20, 27, 36, 46, 57, 111] +T = [21, 37, 47, 76, 81, 87, 92, 110] +DIM = 33 + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def checked(raw, pin): + need(sha256(raw).hexdigest() == pin, "Source pin differs") + return raw + + +def apply(columns, vector): + result = 0 + while vector: + bit = vector & -vector + result ^= columns[bit.bit_length()-1] + vector ^= bit + return result + + +def compose(left, right): + """Return the product left*right. Vectors meet right first.""" + return tuple(apply(left, x) for x in right) + + +def transpose(columns): + return tuple(sum(((x >> i) & 1) << j for j, x in enumerate(columns)) + for i in range(len(columns))) + + +def route(basis, stage, dimension=DIM): + columns = [1 << i for i in range(dimension)] + if not stage: + return tuple(columns) + start = 9+8*(stage-1) + q = basis[0] + for i in range(9): + columns[i] = q*((q >> i) & 1) + for j, b in enumerate(basis[1:]): + columns[i] ^= ((b >> i) & 1) << (start+j) + for j, b in enumerate(basis[1:]): + columns[start+j] = b + return tuple(columns) + + +def phase_form(axes): + linear, quadratic = [0]*73, [0]*73 + for axis in axes: + for i in range(73): + if (axis >> i) & 1: + linear[i] = (linear[i]+1) % 4 + quadratic[i] ^= axis & ~((1 << (i+1))-1) + return linear, quadratic + + +def alignment_translation(left_axes, right_axes): + left, lq = phase_form(left_axes) + right, rq = phase_form(right_axes) + need(lq == rq and all((x-y) % 2 == 0 for x, y in zip(left, right)), + "The frame alignment has a nontranslation phase defect") + return sum(1 << i for i, (x, y) in enumerate(zip(left, right)) if (x-y) % 4 == 2) + + +def source(): + checked((HERE/"SPECTRAL-BOUND-REVIEW.json").read_bytes(), R_REVIEW_PIN) + interface = json.loads(checked((LANES/"circuit-interface/INTERFACE.json").read_bytes(), INTERFACE_PIN)) + raw = subprocess.check_output(["git", "show", BASE+":"+ARCHIVE], + cwd=ROOT/"worktrees/k5-centre-sharing") + checked(raw, ARCHIVE_PIN) + with tarfile.open(fileobj=BytesIO(raw), mode="r:gz") as archive: + phases = json.loads(checked(archive.extractfile(PHASE_MEMBER).read(), PHASE_PIN)) + word = json.loads(gzip.decompress(checked(archive.extractfile(WORD_MEMBER).read(), WORD_PIN))) + need(interface["ports"] == word["ports"] == [x["q"] for x in phases["recipes"]], + "Port orders differ") + U = sorted(set(range(112))-set(A)-set(T)) + roots = [tuple(int(row.get(str(p), 0)) for row in interface["R"]) for p in U] + bases = [] + for p in U: + entry = phases["recipes"][p] + axes = entry["idle_children"][0]["orthogonal_axes"] + need(axes[8:] == [1 << i for i in range(9, 17)], "The source complement axes differ") + basis = (entry["q"], *axes[:8]) + need(all((x & y).bit_count() % 2 == (i == j) + for i, x in enumerate(basis) for j, y in enumerate(basis)), + "A source basis is not orthogonal") + bases.append(basis) + dots = [[sum(x*y for x, y in zip(a, b)) for b in roots] for a in roots] + need([dots[p][p] for p in range(96)] == [4]*96, "A root norm differs") + need(all(sum(r[i]*r[j] for r in roots) == 48*(i == j) + for i in range(8) for j in range(8)), "The ordinary Gram differs") + full = [[route(basis, s, 73) for basis in bases] for s in range(9)] + identity = tuple(1 << i for i in range(73)) + for s in range(9): + for p in range(96): + need(transpose(full[s][p]) == full[s][p] and + compose(full[s][p], full[s][p]) == identity, "A route is not an orthogonal involution") + alignment_checks = 0 + for p, actual_port in enumerate(U): + q = bases[p][0] + for s in range(9): + image = full[s][p] + exterior = [1 << i for i in range(9, 9+8*s)] + before = [q] if s == 0 else image[:9+8*(s-1)] + after = image[:9+8*s] + pre = apply(image, alignment_translation(before, [q]+exterior)) + post = apply(image, alignment_translation(after, [1 << i for i in range(9)]+exterior)) + need(phases["recipes"][actual_port]["stage_alignment"][s] == + {"entry_X": pre, "entry_Y": pre, "exit_X": post, "exit_Y": post}, + "A full-payload native alignment differs") + alignment_checks += 1 + pairs = [] + for s in range(9): + for t in range(s+1, 9): + relative = [compose(full[s][p], full[t][p]) for p in range(96)] + need(len(set(relative)) == 96, "Relative port routes collide") + pairs.append([s, t, len(set(relative))]) + # All positive-stage permutations are common coordinate permutations. + conjugacy_checks = 0 + for t in range(2, 9): + swap = list(identity) + for j in range(8): + swap[9+j], swap[9+8*(t-1)+j] = swap[9+8*(t-1)+j], swap[9+j] + for p in range(96): + need(compose(swap, compose(full[1][p], swap)) == full[t][p], + "Positive-stage conjugacy fails") + conjugacy_checks += 1 + fresh_checks = 0 + for p in range(96): + for q in range(96): + fixes = all(apply(full[1][p], bases[q][j+1]) == 1 << (9+j) for j in range(8)) + need(fixes == (p == q), "Fresh-block port test fails") + fresh_checks += 1 + ordered = apply(compose(full[1][0], full[2][0]), 1 << 9) + reversed_order = apply(compose(full[2][0], full[1][0]), 1 << 9) + need(ordered == bases[0][1] and reversed_order == 1 << 17 and ordered != reversed_order, + "The route-order control does not distinguish the two products") + return roots, bases, dots, {"regular_cover": "The actual orthogonal cover group", + "ordinary_ports": U, "archive_sha256": ARCHIVE_PIN, + "phase_member_sha256": PHASE_PIN, "canonical_word_sha256": WORD_PIN, + "interface_sha256": INTERFACE_PIN, "source_matrix_review_sha256": R_REVIEW_PIN, + "full_payload_alignment_checks": alignment_checks, + "route_order_control": {"port": U[0], "input_axis": 512, + "rho1_rho2_image": ordered, + "rho2_rho1_image": reversed_order}, + "relative_pairs": pairs, "positive_stage_conjugacy_checks": conjugacy_checks, + "fresh_block_port_checks": fresh_checks} + + +def covariance(s, t, roots, bases, dots): + """Store coefficients of (B_s B_t*)(B_t B_s*) without scale factors.""" + identity = tuple(1 << i for i in range(DIM)) + relative = [compose(route(b, s), route(b, t)) for b in bases] + terms = {identity: None} + support = 0 + for p in range(96): + for q in range(96): + if p == q or not dots[p][q]: + continue + key = compose(relative[p], transpose(relative[q])) + need(key not in terms, "A supported ordered pair has a group collision") + terms[key] = (p, q, dots[p][q]) + support += 1 + identity_matrix = [[sum(4*r[i]*r[j] for r in roots) for j in range(8)] for i in range(8)] + need(identity_matrix == [[192*(i == j) for j in range(8)] for i in range(8)], + "Identity coefficient differs") + square = sum(x*x for row in identity_matrix for x in row) + square += sum(dots[p][q]**2*dots[p][p]*dots[q][q] + for entry in terms.values() if entry is not None for p, q, _ in [entry]) + need(support == 4224 and square == 565248, "Fourth pair count differs") + return terms, {"stages": [s, t], "nonidentity_terms": support, + "collision_multiplicities": {"1": support}, + "integer_frobenius_square": square, + "alternating_trace_per_cover": str(Q(square, 48**4))} + + +def inner_coeff(left, right, dots): + total = 0 + common = left.keys() & right.keys() + for key in common: + a, b = left[key], right[key] + if a is None or b is None: + need(a is None and b is None, "Only one coefficient is the identity term") + total += 8*192**2 + else: + p, q, x = a + r, s, y = b + total += x*y*dots[p][r]*dots[q][s] + return len(common), total + + +def trace_word(word): + """Reduce fourth-order words by idempotence and the singleton lemma.""" + w = list(word) + while len(w) > 1: + remove = next((i for i in range(len(w)) if w[i] == w[(i+1) % len(w)]), None) + if remove is None: + break + w.pop(remove) + if len(w) == 1: + return Q(8) + if len(w) == 2: + return Q(2, 3) + counts = Counter(w) + if len(w) == 4 and len(counts) == 2: + need(w[0] == w[2] and w[1] == w[3], "An unreduced pair word is not alternating") + return Q(23, 216) + unique = next((i for i, s in enumerate(w) if s and counts[s] == 1), None) + need(unique is not None, "An unsupported trace type remains") + w.pop(unique) + return trace_word(w)/12 + + +def moments(): + rows = [] + for k in range(1, 10): + mm = [sum((trace_word(w) for w in product(range(k), repeat=j)), Q(0)) + for j in range(1, 5)] + m1, m2, m3, m4 = mm + det = m2*m4-m3*m3 + if det: + rank = (m1*m1*m4-2*m1*m2*m3+m2**3)/det + else: + rank = m1*m1/m2 + fields = (rank.numerator+rank.denominator-1)//rank.denominator + rows.append({"charts": k, "moments_per_cover": list(map(str, mm)), + "quadratic_rank_per_cover": str(rank), + "whole_fields": fields, "eight_field_cohorts": (fields+7)//8}) + need(rows[-1]["moments_per_cover"] == ["72", "120", "244", "1649/3"], "Nine-chart moments differ") + need(rows[-1]["quadratic_rank_per_cover"] == "4104/73", "The quadratic bound differs") + return rows + + +def main(): + roots, bases, dots, binding = source() + cache, pairs = {}, [] + for s, t in ((0, 1), (0, 2), (1, 0), (1, 2), (1, 3)): + cache[s, t], row = covariance(s, t, roots, bases, dots) + pairs.append(row) + mixed = [] + for s, t, u in ((0, 1, 2), (1, 0, 2), (1, 2, 3)): + count, total = inner_coeff(cache[s, t], cache[s, u], dots) + need(count == 1 and total == 294912, "Mixed-three support or trace differs") + mixed.append({"word": [s, t, s, u], "common_group_support": count, + "integer_coefficient_inner_product": total, + "trace_per_cover": str(Q(total, 48**4))}) + result = {"status": "PASS_ACTUAL_QUERY_FOURTH_MOMENT", "source_binding": binding, + "route_product": "B_s B_t* uses rho_s(p) rho_t(p); vectors meet t first.", + "pair_cases": pairs, "mixed_three_cases": mixed, + "distinct_stage_trace": "96/12^k for 1 <= k <= 9", + "singleton_rule": "A positive stage occurring once can be deleted at trace factor 1/12.", + "fixed_source_bounds": moments(), + "nine_chart_optimizing_polynomial": "13 lambda - 4 lambda^2", + "scope": "Simultaneous linear queries of one arbitrary fixed source in the full logical regular-cover module, with any payload multiplicity.", + "not_claimed": ["A native-child lower bound", "A bound on changing controller sources", + "A supplier or kappa improvement"]} + (HERE/"QUERY-FOURTH-MOMENT.json").write_text(json.dumps(result, indent=2)+"\n") + print(json.dumps({"status": result["status"], "nine_chart_moments": ["72", "120", "244", "1649/3"], + "rank_per_cover": "4104/73", "whole_fields": 57, "eight_field_cohorts": 8})) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/notices/LICENSE b/research/actual-query-information-bounds/notices/LICENSE new file mode 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You may reproduce and distribute copies of the + Work or Derivative Works thereof in any medium, with or without + modifications, and in Source or Object form, provided that You + meet the following conditions: + + (a) You must give any other recipients of the Work or + Derivative Works a copy of this License; and + + (b) You must cause any modified files to carry prominent notices + stating that You changed the files; and + + (c) You must retain, in the Source form of any Derivative Works + that You distribute, all copyright, patent, trademark, and + attribution notices from the Source form of the Work, + excluding those notices that do not pertain to any part of + the Derivative Works; and + + (d) If the Work includes a "NOTICE" text file as part of its + distribution, then any Derivative Works that You distribute must + include a readable copy of the attribution notices contained + within such NOTICE file, excluding those notices that do not + pertain to any part of the Derivative Works, in at least one + of the following places: within a NOTICE text file distributed + as part of the Derivative Works; within the Source form or + documentation, if provided along with the Derivative Works; or, + within a display generated by the Derivative Works, if and + wherever such third-party notices normally appear. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/NOTICE.md b/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/NOTICE.md new file mode 100644 index 0000000000..30d0c8cd3c --- /dev/null +++ b/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/NOTICE.md @@ -0,0 +1,24 @@ +# Gauge44 attribution and scope + +New contributions by icekylinx, with OpenAI GPT-6 Astra assistance. +Local review and packaging used OpenAI Codex. Apache-2.0 applies; +the license is included. The full original PR635 notice is preserved as +UPSTREAM-NOTICE.md and construction/UPSTREAM-NOTICE.md. + +The new contribution is the changed source-branch gauge and retired-row +completion, source-carried coordinate totals, exact 44-cold-end realization, +and explicit all72 whole-family assignment using concave capacity matching +with integer majorization certificates. The center-carrier generalization +retains the exact ordered common frames and complete native local contract. +Independent local, price, interface and owner fixed-point checks are included. + +The construction retains the credited PR635 K-triangle and porting machinery, +earlier joint-prefix/HPE/frame ancestry and icekylinx's prior factory work. +#645 used the same cited PR543 bit supplier as PR635. This package (research/gauge44-leaver8) cites the merged PR589 bit supplier instead, with a derived rank-mass deficit (PROOF-NOTE-BIT.md); #645's retained PR543-based evidence is historical. It builds #645's word without K-triangles (PartialK) and stacks earlier community jp8 layers on it (G44Stack), adds the p6n ends (NoTriReopen), entrance promotions (BlockInvert) a read-set exchange (BRoute), chafreaky's #741 frames, JointXF's joint exchange, NewBArch's triangle-hybrid B rewrite and LeaverSAT's eight k8 leaver cells (with LeaverSAT2's frame re-optimisation); see README. All-size, realization, +hosting, precision/tape, analytic-transfer and bit H1-H5 assumptions remain +conditional. No upstream license, credit, source pin or AI disclosure is +replaced by this notice. + +PR641 and PR642 were checked as concurrent reported frontier comparisons. +Their endpoints and owner maps are not included here. See CONSTRUCTION.md, +hosting/PROOF.md, independent/ and README.md for the exact contribution scope. diff --git a/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md b/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md new file mode 100644 index 0000000000..ebc24a0168 --- /dev/null +++ b/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md @@ -0,0 +1,34 @@ +# Attribution and scope + +Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map. + +Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses): +- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`). +- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`). +- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`). +- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`). +- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`). + +Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR. + +In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency. + +DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional. + +**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following: +- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`); +- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order; +- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency); +- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run. + +The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk. + +**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged. + +**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes: +- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom. +- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky). +- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md). +- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents). + +Build on this at your own risk. diff --git a/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/construction/NOTICE.md b/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/construction/NOTICE.md new file mode 100644 index 0000000000..16b0507070 --- /dev/null +++ b/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/construction/NOTICE.md @@ -0,0 +1,9 @@ +# Construction delta notice + +Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0. + +`construct_gauge_xcentre.py` modifies PR635's credited `construct_k_triangle.py`, which in turn extends icekylinx's PR531/PR514/PR425 factory lineage. Its original source comments are retained. The K-triangle schedule and the upstream porting, JP8 frame, kernel and HPE procedures are reused from the pinned source checkouts and are not new contributions of this delta. + +The new source-copy exchanges, complementary factory basis, carrier assignment, exact cold44 constructor and compact reproduction driver are described in `../CONSTRUCTION.md`. + +`UPSTREAM-NOTICE.md` is the complete unmodified notice from the pinned PR635 package. `LICENSE` is that package's Apache-2.0 license. All further notices and source credits of the referenced upstream packages remain applicable and are retained in the source checkouts rather than vendored again here. diff --git a/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/t16/NOTICE.md b/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/t16/NOTICE.md new file mode 100644 index 0000000000..403f4afffb --- /dev/null +++ b/research/actual-query-information-bounds/notices/research/gauge44-slots-t16/t16/NOTICE.md @@ -0,0 +1,39 @@ +# Attribution and license + +Apache-2.0. New construction and integration: Hao Yan (@FanPUYen), 2026. +Prepared with substantial OpenAI Codex assistance, including separately tasked +AI agents for owner construction, independent mathematical/code checking and +native verification. These are not claims of independent human peer review. + +The exact local supplier is Jeremy Kothe's accepted PR799 X4 word, layered on +Chafik Boukhalfa's PR741 frame changes and PR685 owner construction. Chafik's +PR795 fixed-inventory optimality result motivated changing the replica count. +The original owner bytes, scalar program, local frame and width inventory, +native phase and wrapper implementations retain their existing authorship. + +Credit icekylinx for the source gauge and supplier/admission pipeline; +DreamingOfClouds for the PR589 bit transport and inherited cold-end work; +eumemic for the PR555 bit supplier and earlier supplier work; Rohan Arun for +the native exact-complex recurrence correction; Jeremy Diviney, jaymosley07, +and the other retained owner/allocation contributors; and the complete +PR514/PR484/PR507/PR558 controller, physical hosting and verification lineage. +This list is cumulative credit, not approval of every claim in those PRs. + +All original notices and licenses remain in the referenced source packages: + +- `research/gauge44-frames-x/{NOTICE,UPSTREAM-NOTICE}.md` +- `research/complex-sw4-frame8/PROVENANCE.md` +- `research/e8-bit-p111-tuned/tune/README.md` +- the repository `CONTRIBUTORS.md` and source-package licenses. + +The verifier copies pinned global source files into an external replay +directory and applies an explicit checked edit list. Original attribution +comments are preserved in those generated derivatives. No original source +file or historical certificate is rewritten. + +The optional ancestry-reuse coverage guard addresses the omission issue +identified by Lucas (@ljste) in PR838 and the related PR847 integration by +Chinmay (@chinmayarvind23). Its fixed inventories were read from the accepted +PR741 source; no pending implementation is imported. Charles Bethin's +concurrent PR850 strengthens the fixed-inventory owner-profile theorem and +was checked for overlap before publication; that inventory is changed here. diff --git a/research/actual-query-information-bounds/payload/lanes/circuit-interface/CENTRE-FREE-PROGRAMS.json.gz b/research/actual-query-information-bounds/payload/lanes/circuit-interface/CENTRE-FREE-PROGRAMS.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..2e4dcc40a9a59c741dc2d02965b098a6d24b7ac6 GIT binary patch literal 211301 zcmaHS2Uru!*EfWOUJ`mQNeo4#iBxGJ2|+2Ms8}dM)F?=k-YyVILJ5Q@QUwAEDoRxW z0RfSsD8xdOCZI;?y;;6R@4fH;EzidjcJ`c^Ju_!_&g|^@ouiP<&9?go`jywTKs{ei z{j{O6X2>@v{ENK0e^Wr3lI%b3+0!yL-!aF@`N(w)b}G9{N_lVZsi#{f;%j2-@z$cM zNyER!eSUQ+{M!EON3Yq>t&Q=YkN?`bG5&Mv>5rv?Uz>9;eSR$f{Dr@E%zkZk{`!&j z^hc-JuceA#KYjlCweV|g{MV21sGaRku2DO^fBl&H>-$pgc=N9Tv$0=OfBl+!dHToN z%b&|T+uNVEQ?{oT{`wWu{nM!LX@%yFR9Ix;_%H9sty8PYAQaSTXU6;~+)aOUACwqw z?dJM3u+SA2(mC?iMozR_%-sr(9~mu)kg;F$dt#bgMGO?gL#&>{E6q4(xy1)>@Q4q( 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The source minor/cone proof review is separate. Exact native phases for a new capture word, merged-flow synthesis, costs and hosting are not supplied.", + "source_pins": { + "core": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877", + "interface": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "proof": "be9575e1cac8706c42fddff243f435935e098d197edaf7f8689352c93b7e3961", + "receipt": "35698700474f2309a4eea2f192a5afbd2f42f580a7e0e510a0bb5687a87fdc2d", + "snapshots": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", + "word": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219" + }, + "status": "PASS_INDEPENDENT_BACKWARD_SNAPSHOT_ROWS" +} diff --git a/research/actual-query-information-bounds/payload/lanes/circuit-interface/snapshot-audit/SNAPSHOT-ROWS-REVIEW.md b/research/actual-query-information-bounds/payload/lanes/circuit-interface/snapshot-audit/SNAPSHOT-ROWS-REVIEW.md new file mode 100644 index 0000000000..76878112f9 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/circuit-interface/snapshot-audit/SNAPSHOT-ROWS-REVIEW.md @@ -0,0 +1,98 @@ +# Independent check of the backward snapshot rows + +The exact row and interval check passes. No source or producer module is +imported. The checker reads the pinned clean backward event word, the +original canonical frame list, the actual R matrix, and the frozen +snapshot payload. It rebuilds every scalar row on all 712 formal input +columns. + +The source snapshot payload has decompressed SHA256 +`3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c`. +The full pins are in `SNAPSHOT-ROWS-REVIEW.json`. + +## Coverage + +The 16,687 intervals cover all 704 persistent wires at every boundary +from event 8106 through event 24913. They have no gap or overlap. The +checker verifies that no scalar target update or canonical native-frame +change occurs inside an interval. It compares 24,199 interval endpoints +with fresh full-input rows and frames. + +The complete final map is `(x,y,h,c) -> (x-Jy,y,h,0)`. All 480 arbitrary +helper rows are identity in their canonical coordinates, with the +inherited native endpoints. The private fields are cleared. The check +does not replace those canonical helper identities by a physical +identity claim across different helper frames. + +The fresh rows also satisfy the claimed support law after the test +substitution `x=Jy`, `h=0`, `c=0`: at frame U, a remaining Y coefficient +can use only a port whose binary label is perpendicular to U. This +checks 16,023 distinct frame/row pairs and 98,056 nonzero coefficients. +The final X and all helper/private rows vanish on this test family. +The exact query minors and the full cone theorem have a separate review +in the cover-algebra lane. This receipt is an independent source-row +check, not a second full minor review. + +After event 17606, a non-FULL canonical view may need the specified +inverse exit monomial. The negative support argument can grant that +view, since a zero source row remains zero under an invertible map. +This does not make such a view free in a new capture construction. + +Three controls reject an added arbitrary private coefficient, an omitted +interval, and an incorrect frame label. The native profile is unchanged: +`{1:2412,2:418,3:432,4:142,5:82}`. + +## Exact private lifetime and repair cut + +Event 8702 is the last original private read or write. It clears C7; +all eight private fields are zero at this cut. Phase A starts at event +8703. No later original event reads, writes, or advances any C field. +The final scalar event is 24913. At that cut, all 112 X fields and 402 +helper fields have the canonical FULL frame. + +Thus a new protocol that starts after event 8702 can use C0 as a serial +snapshot temporary and C1 through C7 as seven query accumulators. One +additional owned field would supply an eighth accumulator. A cleared +zero field can receive a new frame label without a physical operation, +because its exact physical value is zero. A positive construction must +check that zero state before each such label change and must emit every +nonzero completion with its complete native phase. + +Suppose a supplied snapshot protocol gives eight FULL rows + +```text +q = RY + L X_out + H h_full, +``` + +where `X_out=X-JY` is the unchanged completed core output and `h_full` +contains only the 402 available FULL helper fields. Subtract both +baseline terms from all eight q fields before changing any X field. +Then the 448 signed-quarter entries of K give + +```text +X_out -= Kq = X-JY-KRY = X-Y. +``` + +These final additions cost 5376 real primitives, followed by the query +clears. This is a conditional exact suffix. No snapshot synthesis or +favourable native-rank total is supplied here. In particular, it does +not bypass the single-cone obstruction. A merged protocol must provide +its actual capture times, views, coefficients, completion recipes, +storage lifetimes, recursive-child hosting, and full invoice. + +## Reproduction + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/circuit-interface/snapshot-audit/review_snapshot_rows.py +``` + +Expected status: + +```text +PASS_INDEPENDENT_BACKWARD_SNAPSHOT_ROWS +``` + +No source file is changed. No new native phase sweep, recursive replay, +global owner admission, or supplier improvement is claimed. Before any +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/actual-query-information-bounds/payload/lanes/circuit-interface/snapshot-audit/review_snapshot_rows.py b/research/actual-query-information-bounds/payload/lanes/circuit-interface/snapshot-audit/review_snapshot_rows.py new file mode 100644 index 0000000000..a50b5d574d --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/circuit-interface/snapshot-audit/review_snapshot_rows.py @@ -0,0 +1,216 @@ +"""Rebuild all backward snapshot rows from the pinned scalar event word.""" + +from bisect import bisect_right +from collections import Counter, defaultdict +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +PINS = { + 'core': 'fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877', + 'word': '16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219', + 'interface': '5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3', + 'snapshots': '3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c', + 'proof': 'be9575e1cac8706c42fddff243f435935e098d197edaf7f8689352c93b7e3961', + 'receipt': '35698700474f2309a4eea2f192a5afbd2f42f580a7e0e510a0bb5687a87fdc2d', +} + + +def require(condition, reason): + if not condition: + raise ValueError(reason) + + +def read(path, key, compressed=False, pin_compressed=False, parse=True): + data = path.read_bytes() + raw = gzip.decompress(data) if compressed else data + require(sha256(data if pin_compressed else raw).hexdigest() == PINS[key], 'Source pin: '+key) + return json.loads(raw) if parse else raw + + +def combine(target, source, coefficient): + for col, value in source.items(): + new = target.get(col, Q(0))+coefficient*value + if new: + target[col] = new + else: + target.pop(col, None) + + +def index(token): + require(isinstance(token, list) and len(token) == 2, 'A literal field token') + namespace, position = token + require((namespace == 'L' and 0 <= position < 704) or + (namespace == 'C' and 0 <= position < 8), 'An original field index') + return position+(704 if namespace == 'C' else 0) + + +def intervals_partition(intervals, first, last): + by_wire = defaultdict(list) + for lo, hi, wire, frame, row in intervals: + require(first <= lo <= hi <= last and 0 <= wire < 704, 'A declared interval range') + by_wire[wire].append((lo, hi)) + require(set(by_wire) == set(range(704)), 'Every persistent wire has an interval') + for spans in by_wire.values(): + spans.sort() + require(spans[0][0] == first and spans[-1][1] == last, 'The complete boundary range') + require(all(a[1]+1 == b[0] for a, b in zip(spans, spans[1:])), 'No interval gap or overlap') + + +def reject(function, reason): + try: + function() + except ValueError: + return + raise ValueError('The control was not rejected: '+reason) + + +def main(): + events = read(LANES/'circuit-interface/CENTRE-FREE-PROGRAMS.json.gz', 'core', True)['backward'] + word = read(LANES.parent/'upstream/CANONICAL-WORD.json.gz', 'word', True, True) + interface = read(LANES/'circuit-interface/INTERFACE.json', 'interface') + snapshots = read(LANES/'history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz', 'snapshots', True) + source_receipt = read(LANES/'history-encoding/SNAPSHOT-CONE-OBSTRUCTION.json', 'receipt') + read(LANES/'history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md', 'proof', parse=False) + require(snapshots['pins'] == {'word': PINS['word'], 'core': PINS['core'], 'R': PINS['interface']}, 'All snapshot source pins') + require(snapshots['R'] == interface['R'] and snapshots['frames'] == word['frames'], 'Actual query and frame source equality') + query = [{int(j): Q(v) for j, v in row.items()} for row in interface['R']] + ports = interface['ports'] + j_rows = [{p: Q(1)} for p in range(112)] + for p, row in enumerate(j_rows): + for query_row in query: + combine(row, query_row, -query_row.get(p, Q(0))/4) + + first, last = snapshots['first_canonical_boundary'], snapshots['last_canonical_boundary'] + require((first, last) == (8106, 24913), 'The complete pinned canonical range') + intervals = snapshots['intervals'] + intervals_partition(intervals, first, last) + updates = defaultdict(list) + for t, event in enumerate(events): + if event[0] == 'climb': + updates[event[2]].append(t) + elif event[0] == 'scalar': + updates[index(event[1][1])].append(t) + supplied_rows = [{int(j): Q(v) for j, v in row.items()} for row in snapshots['rows']] + checks_at = defaultdict(list) + for item in intervals: + lo, hi, wire, frame, row = item + require(0 <= frame < len(word['frames']) and 0 <= row < len(supplied_rows), 'An interval row and frame index') + next_update = bisect_right(updates[wire], lo) + require(next_update == len(updates[wire]) or updates[wire][next_update] > hi, 'No scalar or canonical-frame change inside a constant interval') + checks_at[lo].append((wire, frame, row)) + if hi != lo: + checks_at[hi].append((wire, frame, row)) + + def support(row): + reduced = {p-112: value for p, value in row.items() if 112 <= p < 224} + for p, value in row.items(): + if p < 112: + combine(reduced, j_rows[p], value) + return reduced + + rows = [{i: Q(1)} for i in range(712)] + frames = word['start'][:]+[0]*8 + profile, macros = Counter(), Counter() + private_uses, checked_pairs, reduced_rows = [], set(), {} + endpoint_checks = support_coefficients = 0 + last_scalar = -1 + check_example = None + for t, event in enumerate(events): + kind = event[0] + if kind == 'climb': + _, _, target, before, after, rank = event + require(0 <= target < 704 and frames[target] == before, 'The original native source frame') + require(len(word['frames'][after])-len(word['frames'][before]) == rank, 'The exact native rank increment') + frames[target] = after + profile[rank] += 1 + elif kind == 'scalar': + op, frame = event[1:] + target = index(op[1]) + require(frames[target] == frame, 'Every scalar target has the declared canonical frame') + if target >= 704: + private_uses.append((t, target, 'write')) + macros[op[0]] += 1 + last_scalar = t + if op[0] == 'clear': + rows[target] = {} + elif op[0] == 'scale': + coefficient = Q(op[2], op[3]) + rows[target] = {p: coefficient*v for p, v in rows[target].items() if coefficient*v} + else: + require(op[0] in ('copy', 'add'), 'An allowed scalar operation') + other = index(op[2]) + require(other != target and frames[other] == frame, 'A distinct source in the same canonical frame') + if other >= 704: + private_uses.append((t, other, 'read')) + if op[0] == 'copy': + rows[target] = rows[other].copy() + else: + combine(rows[target], rows[other], Q(op[3], op[4])) + else: + require(kind in ('phase', 'adapter', 'residual_adapter'), 'A known inherited operator event') + for wire, frame, row_index in checks_at.get(t, ()): + require(frames[wire] == frame and rows[wire] == supplied_rows[row_index], 'A fresh full712 prefix row and frame match the interval endpoint') + endpoint_checks += 1 + if check_example is None: + check_example = (rows[wire].copy(), supplied_rows[row_index].copy(), frames[wire], frame) + pair = frame, row_index + if pair not in checked_pairs: + checked_pairs.add(pair) + if row_index not in reduced_rows: + reduced_rows[row_index] = support(rows[wire]) + for port, coefficient in reduced_rows[row_index].items(): + require(all((ports[port] & u).bit_count() % 2 == 0 for u in word['frames'][frame]), 'The exact fresh-row support law') + support_coefficients += 1 + if t == 8702: + require(all(not row for row in rows[704:]), 'All original private fields are zero after their last use') + + expected = [{i: Q(1)} for i in range(712)] + for p in range(112): + combine(expected[p], {112+q: v for q, v in j_rows[p].items()}, Q(-1)) + expected[704:] = [{} for _ in range(8)] + require(rows == expected, 'All712 final columns of the clean backward map') + require(rows == [{int(j): Q(v) for j, v in row.items()} for row in snapshots['final_rows']], 'The supplied full final rows') + require(frames == word['final']+[0]*8, 'The complete inherited canonical endpoints') + require(last_scalar == last and events[8703] == ['phase', 'A'], 'The exact final scalar cut and post-private phase') + require(max(t for t, _, _ in private_uses) == 8702, 'No original private read or write after8702') + require(all(not support(rows[p]) for p in list(range(112))+list(range(224, 712))), 'The completed X and all helper/private baselines vanish on the test family') + require(len(checked_pairs) == source_receipt['distinct_frame_row_pairs'] == 16023 and + support_coefficients == source_receipt['exact_nonzero_support_coefficients'] == 98056, 'The complete claimed support coverage') + require(profile == {1:2412, 2:418, 3:432, 4:142, 5:82}, 'The native profile of the unchanged core') + full_helpers = [p for p in range(224, 704) if frames[p] == 1] + require(len(full_helpers) == 402, 'The exact number of FULL helper baseline fields') + + actual, supplied, actual_frame, supplied_frame = check_example + wrong = supplied.copy() + wrong[711] = wrong.get(711, Q(0))+1 + reject(lambda: require(actual == wrong, 'Changed arbitrary private coefficient'), 'A changed snapshot row') + reject(lambda: intervals_partition(intervals[1:], first, last), 'A missing interval') + reject(lambda: require(actual_frame == (supplied_frame+1) % len(word['frames']), 'Changed frame index'), 'A changed native frame') + + receipt = { + 'status': 'PASS_INDEPENDENT_BACKWARD_SNAPSHOT_ROWS', 'source_pins': PINS, + 'producer_or_checker_imports': [], 'all_formal_input_columns': 712, + 'constant_intervals': len(intervals), 'interval_endpoint_checks': endpoint_checks, + 'interval_interior_update_checks': len(intervals), + 'complete_interval_wire_count': 704, 'distinct_frame_row_support_checks': len(checked_pairs), + 'exact_nonzero_support_coefficients': support_coefficients, + 'native_profile': dict(sorted(profile.items())), 'scalar_macros': dict(sorted(macros.items())), + 'last_original_private_event': 8702, 'all_eight_private_fields_zero_after_last_use': True, + 'last_scalar_event': last_scalar, 'FULL_helper_baseline_fields': full_helpers, + 'controls': {'changed_private_coefficient': 'rejected', 'missing_interval': 'rejected', 'changed_frame': 'rejected'}, + 'scope': 'Independent full712 scalar-row reconstruction, interval coverage, native canonical frame accesses and support law. The source minor/cone proof review is separate. Exact native phases for a new capture word, merged-flow synthesis, costs and hosting are not supplied.', + 'reviewer_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + } + (HERE/'SNAPSHOT-ROWS-REVIEW.json').write_text(json.dumps(receipt, sort_keys=True, indent=2)+'\n') + print(receipt['status']) + print(json.dumps({k:receipt[k] for k in ('constant_intervals', 'interval_endpoint_checks', 'distinct_frame_row_support_checks', 'exact_nonzero_support_coefficients', 'last_original_private_event', 'reviewer_sha256')}, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/ALGEBRA.json b/research/actual-query-information-bounds/payload/lanes/cover-algebra/ALGEBRA.json new file mode 100644 index 0000000000..32773421be --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/ALGEBRA.json @@ -0,0 +1,105 @@ +{ + "arithmetic": "Integer group coefficients and Fraction", + "common_range_dimension_upper_bound_from_third_moment": "1211492/360389295", + "common_range_dimension_upper_bound_per_cover_element": "8/183", + "corner_port": 11, + "distinct_nonidentity_edge_products": 5824, + "equal_J_subspace_codimension_lower_bound_from_third_moment": "5763805736/360389295", + "equal_J_subspace_codimension_lower_bound_per_cover_element": "2912/183", + "gram_entry_distribution": { + "-2": 1904, + "0": 6608, + "2": 3920, + "4": 112 + }, + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "isoclinic_braid_third_moment_required": "3095/67228", + "nonbraid_witness": { + "coefficient_in_K0_K1_K0_minus_K1_K0_K1_corner_0_0": "-1/8", + "coefficient_in_P0_P1_P0_minus_P1_P0_P1_corner_0_0": "1/21952", + "group_columns": [ + 2, + 524, + 521, + 517, + 16, + 32, + 64, + 128, + 256, + 13, + 1024, + 2048, + 4096, + 8192, + 16384, + 32768, + 65536 + ] + }, + "noncommutation_witness": { + "coefficient_in_commutator_P0_P1_corner_0_0": "-1/784", + "group_columns": [ + 5661, + 5662, + 19, + 7, + 5635, + 32, + 64, + 128, + 256, + 5131, + 4619, + 1547, + 2048, + 8192, + 16384, + 32768, + 65536 + ] + }, + "nonisoclinic_witness": { + "coefficient_in_P0_P1_P0_corner_0_0": "1/10976", + "coefficient_in_any_scalar_multiple_of_P0": "0", + "group_columns": [ + 5661, + 5662, + 19, + 7, + 5635, + 32, + 64, + 128, + 256, + 5131, + 4619, + 1547, + 2048, + 8192, + 16384, + 32768, + 65536 + ] + }, + "normalized_trace_P0": "8", + "normalized_trace_P0_P1": "4/7", + "normalized_trace_P0_P1_cubed": "1609241/120472576", + "normalized_trace_P0_P1_squared": "27/343", + "normalized_trace_P0_minus_P1_fourth_power": "4758/343", + "normalized_trace_P0_minus_P1_squared": "104/7", + "representation": "Full binary orthogonal matrices; no phase specialization", + "scope": "Exact group-algebra relations and a full-cover dimension bound. No changed supplier, paid router, or kappa claim.", + "sixth_moment_calculation": { + "collision_distribution": { + "1": 302748, + "2": 50, + "105": 112 + }, + "group_elements": 302910, + "walks": 314608 + }, + "source_base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "star_transposition_checks": 3136, + "status": "PASS_EXACT_ROUTED_PROJECTION_ALGEBRA" +} diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.json b/research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.json new file mode 100644 index 0000000000..c36afc915f --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.json @@ -0,0 +1,275 @@ +{ + "cases": [ + { + "all_internal_edges": 810, + "bound_for_all_eight_queries": 64, + "bound_per_query_dimension": 8, + "contained_frames": 122, + "extended_charge_histogram": { + "0": 77, + "1": 173, + "2": 140, + "3": 139, + "4": 100, + "5": 98, + "6": 73, + "7": 84, + "8": 48 + }, + "extended_cuts": 8, + "extended_edges": 932, + "hasse_edges": 238, + "internal_cuts": 7, + "merge_frame": 983, + "source_test_minors": [ + { + "determinant": "-64", + "ports": [ + 3, + 4, + 8, + 12, + 19, + 26, + 40, + 55 + ] + }, + { + "determinant": "-64", + "ports": [ + 1, + 6, + 23, + 24, + 28, + 34, + 35, + 50 + ] + }, + { + "determinant": "64", + "ports": [ + 23, + 24, + 28, + 32, + 35, + 45, + 73, + 84 + ] + }, + { + "determinant": "128", + "ports": [ + 4, + 5, + 8, + 18, + 26, + 39, + 56, + 100 + ] + }, + { + "determinant": "64", + "ports": [ + 22, + 23, + 29, + 33, + 35, + 45, + 75, + 82 + ] + }, + { + "determinant": "128", + "ports": [ + 3, + 4, + 8, + 17, + 26, + 38, + 54, + 102 + ] + }, + { + "determinant": "-128", + "ports": [ + 5, + 8, + 12, + 17, + 18, + 26, + 38, + 69 + ] + }, + { + "determinant": "-128", + "ports": [ + 1, + 6, + 22, + 28, + 29, + 32, + 48, + 109 + ] + } + ] + }, + { + "all_internal_edges": 820, + "bound_for_all_eight_queries": 64, + "bound_per_query_dimension": 8, + "contained_frames": 124, + "extended_charge_histogram": { + "0": 79, + "1": 180, + "2": 152, + "3": 120, + "4": 102, + "5": 101, + "6": 75, + "7": 85, + "8": 50 + }, + "extended_cuts": 8, + "extended_edges": 944, + "hasse_edges": 246, + "internal_cuts": 7, + "merge_frame": 991, + "source_test_minors": [ + { + "determinant": "128", + "ports": [ + 4, + 5, + 8, + 18, + 26, + 39, + 56, + 100 + ] + }, + { + "determinant": "-64", + "ports": [ + 1, + 6, + 23, + 24, + 28, + 34, + 35, + 50 + ] + }, + { + "determinant": "-128", + "ports": [ + 3, + 5, + 8, + 17, + 26, + 38, + 55, + 101 + ] + }, + { + "determinant": "64", + "ports": [ + 23, + 24, + 28, + 32, + 35, + 45, + 73, + 84 + ] + }, + { + "determinant": "-64", + "ports": [ + 1, + 6, + 22, + 23, + 24, + 28, + 32, + 48 + ] + }, + { + "determinant": "-128", + "ports": [ + 1, + 6, + 22, + 28, + 29, + 32, + 48, + 109 + ] + }, + { + "determinant": "64", + "ports": [ + 4, + 7, + 8, + 26, + 64, + 66, + 68, + 76 + ] + }, + { + "determinant": "-32", + "ports": [ + 2, + 9, + 10, + 11, + 13, + 16, + 25, + 41 + ] + } + ] + } + ], + "checker_sha256": "0d08ff149f29f522d337495bd76779a207457c77801dceb9360b71820989ba39", + "exact_snapshot_rows_reduced": 9882, + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "not_checked": [ + "Cross-cone networks", + "Synthetic intermediate frames", + "A global all-frame bound", + "Chronological native recipes", + "Complete supplier pricing" + ], + "reviewed_certificate_sha256": "62c3b26274ef80a75bbc90b680ceeed9ed24fb158fd7db32594995859c875951", + "reviewed_proof_sha256": "9e8ebc108a758883e9811798900bbaa7c42ffa90ac960953a7596d3427f50708", + "scope": "At least8k native rank for any k-dimensional centre-query output at FULL when every proper frame is an actual subframe of one chosen V in{983,991}. Branches may bypass V. All snapshot times, frame zero, and arbitrary scalar sharing are granted.", + "snapshot_decompressed_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", + "status": "PASS_INDEPENDENT_MOVABLE_RANK8_CUTS" +} diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.md b/research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.md new file mode 100644 index 0000000000..1996f2fbb4 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.md @@ -0,0 +1,93 @@ +# Independent review of the two movable rank-eight certificates + +Both certificates pass. For either actual frame V equal to 983 or 991, +every k-dimensional centre-query subspace costs at least `8k` native +rank in the stated contained-frame model. All eight queries therefore +cost at least 64. The review also proves the FULL extension below. + +The reviewed proof `history-encoding/MOVABLE-RANK8-CUTS.md` has SHA256 +`9e8ebc108a758883e9811798900bbaa7c42ffa90ac960953a7596d3427f50708`. +The reviewed certificate `MOVABLE-FULL-RANK-CUTS.json` has SHA256 +`62c3b26274ef80a75bbc90b680ceeed9ed24fb158fd7db32594995859c875951`. +No material finding remains. + +## Independent exact checks + +The review imports no producer or flow code. It reads the pinned +snapshot payload and actual interface. It rebuilds all binary subspaces, +all actual frames contained in each V, all strict inclusion edges, and +the Hasse graph. It checks exact nonzero 8-by-8 source minors for all +source tests. These minors prove that every used restriction is injective +on the full eight-dimensional query space, and hence on each of its +subspaces. + +The review substitutes `X=JY` in the actual snapshot rows and sets all +480 helper inputs and private inputs to zero. It checks the resulting +source supports. Every free observation in each accepted cut vanishes +on its source test. All FULL snapshots also vanish on this family. + +Each case has seven upward-closed unit cuts. Every stated entering edge +is checked. Every direct inclusion edge is charged at most its dimension +increase, including edges outside the Hasse graph. The exact counts are + +| V | Contained frames | Hasse edges | All strict inclusion edges | +|---|---:|---:|---:| +| 983 | 122 | 238 | 810 | +| 991 | 124 | 246 | 820 | + +Frame zero is included. All snapshot times are granted. Thus the result +does not rely on a chronological schedule that might omit an observation. + +## FULL extension + +The producer proof requires the query fields to reach V before their +last completion. That requirement can be removed within the same cone. +Append FULL to each of its seven cuts. Add an eighth unit cut containing +only FULL, with any one of the verified full-rank source tests. + +For an old contained edge, the charge is unchanged. For a direct edge +from U to FULL, the charge is + + charge(U -> V) + 1 <= 8 - dim(U) + 1. + +This is at most the cost `9-dim(U)`. For U equal to V, the charge is +one. The independent checker tests every one of these added edges +directly, as well as the old edges. + +All eight tests are injective on every requested k-dimensional query +subspace. Their demands therefore sum to `8k`. This proves the bound +for any network in which every proper frame is an actual subframe of +one chosen V. Branches can complete directly to FULL and merge there; +they need not materialize a common intermediate value at V. + +## Scope and units + +The native ranks are in the original nine-coordinate units. Repeating +each axis lambda times multiplies every stated native rank by lambda. +For an arbitrary payload dimension N, the source restrictions and the +capacity of each field both acquire the factor N. The bound in field +units remains `8k`. + +The model retains the logical content of each frame transition. It +allows arbitrary scalar sharing and cancellation. It permits all actual +contained observations at all times, but it does not add observations +from another cone or a changed core. Synthetic intermediate frames and +unpriced changes to logical address meaning are outside this certificate. + +The two certificates cannot be added or combined into a global bound +without checking the new edges and observations. No all-frame bound of +64, improved native word, or complete supplier invoice is claimed. + +## Reproduction + +Run from the repository root: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/cover-algebra/review_movable_rank8_cuts.py +``` + +The fresh run passes with assertions disabled. Its receipt is +`MOVABLE-RANK8-CUTS-REVIEW.json`. The receipt contains exact source +minors, all source pins, edge counts, and the review checker hash. +The search or optimality of its integer-flow routine is not part of +this review. diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-SNAPSHOT-CUTS.md b/research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-SNAPSHOT-CUTS.md new file mode 100644 index 0000000000..72f953b0f3 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/MOVABLE-SNAPSHOT-CUTS.md @@ -0,0 +1,160 @@ +# Movable cuts for passive snapshot networks + +A cut need not contain every frame at which its source test gives zero +observations. It can use a smaller node set. The rank of the required +output on that test is still a valid cut demand. Upward closure is useful +for a search, but is not required for the cut proof. + +This note gives a theorem for the declared snapshot model. It gives no +new numerical bound for the actual nine-coordinate network. + +## Linear observation model + +Work over Q or C. Let x be the full logical input vector. A node v has +a fixed free observation matrix A_v. A circuit can read these values at +the node and perform arbitrary scalar linear operations there. It can +split or reuse a computed value. Each paid edge e carries n_e fields +and has cost c_e per field. Each output field is a prescribed row of +Qx, at an output node. + +All carried fields start at zero unless their initial values are included +as free observations. The computation is a finite causal linear circuit. +There is no unlisted input to a node. This includes passive snapshots +of a fixed core. It does not include an edit to that core which changes +the observation matrices. + +For the application, nodes are canonical frames. An allowed edge U to W +has U contained in W and cost `dim W - dim U`. Its field keeps the same +logical content when its native frame changes. The declared edge set +must include every transition allowed in the proposed network. Granting +extra edges or observation times only makes a lower bound harder. + +## Cut theorem + +Let Omega be any node set that contains all output nodes. Stack all free +observation rows inside Omega into A_Omega. This stack must include any +terminal baseline that the model grants at an inside node. Put + + H_Omega = kernel(A_Omega), + d_Omega = rank(Q restricted to H_Omega). + +Then + + sum_(e entering Omega) n_e >= d_Omega. (1) + +To prove (1), restrict the input to H_Omega. All free observations inside +the cut are zero. At each operation inside the cut, its output is a +linear combination of values that entered through cut edges. This follows +by induction over the finite circuit. It also holds when a value leaves +the cut and later returns. Each entering field contributes at most one +dimension. The final output has rank d_Omega, which proves (1). + +No upward closure assumption occurs in this proof. If all edges follow +frame inclusion, upward cuts avoid re-entry and are a useful restricted +family for an exact search. + +The demand can be computed without a kernel basis: + + d_Omega = rank([A_Omega; Q]) - rank(A_Omega). (2) + +Here the semicolon means vertical row stacking. Equation (2) follows +by quotienting the row space by row(A_Omega). It is the strongest demand +obtainable from an input subspace on which every inside observation +vanishes: every such subspace is contained in H_Omega. + +If a field has payload dimension N, use the actual block observation +matrices. Each entering field has rank at most N. In the scalar tensor +model, A_Omega and Q are tensored with I_N, so both sides of (1) scale +by N. The bound in field units is unchanged. This statement requires +the stated nodes, observations, and edge costs; it does not permit an +unpriced change to a frame or to its logical address meaning. + +## Weighted certificates + +Choose finitely many cuts Omega_j and nonnegative rational weights w_j. +If every allowed edge satisfies + + sum_(j: e enters Omega_j) w_j <= c_e, + +then every admitted network has total paid rank at least + + sum_j w_j d_(Omega_j). (3) + +Multiply (1) by each weight and sum. The edge inequality bounds the +charge to every carried field by its paid cost. This proves (3), with +arbitrary sharing, cancellation, and unequal edge multiplicities. + +An exact certificate needs only the cuts, their test spaces or exact +demands, nonnegative rational weights, and all edge-charge inequalities. +The method that proposes the weights does not enter the proof. + +## Source-port tests for the actual snapshots + +For the pinned clean backward word, use the valid input family +`X=JY` with all 480 helper inputs and private inputs zero. All completed +X and restored helper baselines are then zero. The accepted support +certificate states that an observation at U uses only ports p with +`q_p` perpendicular to U. + +For a source-port set E, define + + Omega_E = {U: for every p in E, q_p is not perpendicular to U}. + +On inputs Y supported on E, every observation in Omega_E is zero. This +set is upward closed. For any cut Omega contained in Omega_E and with +all output nodes inside, the demand is at least + + rank(R_E), + +or `rank((SR)_E)` for a requested query subspace with coefficient matrix +S. The smaller cut has the same test demand. Only its entering edges +change. + +For a fixed node cut Omega, the largest coordinate source test allowed +by this support law is + + E_Omega = {p: q_p is not perpendicular to U for every U in Omega}. + +Replacing E by E_Omega does not change any edge charge and cannot lower +the demand. In contrast, replacing Omega by the larger Omega_E can move +the charge to different edges. That replacement is not free in a family +of weighted cuts. + +If restriction to E is injective on a query space of dimension r, then +the same cut has demand k for every k-dimensional subspace of that +space. Thus a certificate whose positive cuts are all injective gives +a bound proportional to k. No sum of bounds from different common-merge +models follows unless their cuts form one feasible certificate on the +complete allowed graph. + +## Why movable placement can strengthen a certificate + +Consider the chain of frames `0 < span(e1) < FULL2`, together with its +direct `0 -> FULL2` edge. Costs are the dimension increases. There is +one source coordinate with label e1 and one required query equal to +that coordinate. Grant its free observation only at frame zero. + +The maximal zero-observation cut is `{span(e1), FULL2}`. Its single-cut +bound is one. The smaller cut `{FULL2}` also has demand one. Give both +cuts weight one. A rank-one edge enters one cut; the direct rank-two +edge enters both. The joint bound is two. Thus a certificate restricted +to maximal zero-observation sets can miss the full path cost. + +This is an example for the cut theorem. It is not a claim about a new +actual snapshot path. + +## Exact scope for the next certificate + +The actual source payload is +`history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz`, with decompressed +SHA256 `3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c`. +The independently checked support law is recorded in +`cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json`. + +A global certificate must state whether it permits all actual frames, +only one contained-frame graph, or synthetic intermediate frames. It +must charge every allowed edge. It must also state where new observations +stop. A certificate for one common merge cannot be added to another +one without checking shared edges and fields. Chronological phase +recipes, changed native cores, and operator changes to logical address +meaning remain separate obligations. diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/PROOF.md b/research/actual-query-information-bounds/payload/lanes/cover-algebra/PROOF.md new file mode 100644 index 0000000000..b35c89ac6c --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/PROOF.md @@ -0,0 +1,239 @@ +# Routed centre projections + +This note studies the centre-free scalar interface in the campaign's +`circuit-interface/INTERFACE.json`. The source commit is +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. The source file hash is +`5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3`. +The route construction is in `temporal-reuse/verify_routes.py`. +These files are campaign evidence. This note does not replace their independent +native-map reviews. + +## Result and scope + +Let `J_0` be the 112-port scalar interface. Let `J_s` be the same interface +in any positive-stage swap chart. On an arbitrary full regular cover, + +\[ +\frac{\operatorname{rank}(J_s-J_0)}{|G|}\geq\frac{2912}{183}. +\] + +Here `G` is any finite cover group that contains the route matrices, and the +group acts by right translation on its full regular representation. The bound +also holds on a disjoint union of regular orbits, with the same normalization. +The chart can use any orthonormal basis of each port's orthogonal complement. +Thus the bound does not depend on the particular chart basis in the selected +supplier. + +Any linear subspace on which `J_s` and `J_0` agree has at least this +codimension. This excludes a lossless common-`J` restriction. The bound alone +does not exclude an encoding with new state, a new child invoice, or a new +controller. + +The exact selected charts also fail scalar Temperley--Lieb, commutation, and +the braid relation for `J_0,J_s`. The first two failures hold for every chart +basis in the stated swap-chart class. The braid witness below is specific to +the selected chart. + +## Source facts + +Write `R` for the 8 by 112 centre matrix, `A=R^T R`, and + +\[ +P=A/56,\qquad J=I-14P. +\] + +The supplied exact scalar map proves `R R^T=56I`. Thus `P` is an orthogonal +projection of rank 8. The independent calculation in `verify_algebra.py` +also checks these facts about all entries of `A`: + +* Each diagonal entry is 4. +* There are 5,824 nonzero off-diagonal entries. Each is 2 or -2. +* If `A_qp` is nonzero and `q` is not `p`, the binary port vectors obey + `q^T p=0`. + +It follows that `tr(A^2)=56 tr(A)=25088` and `tr(A)=448`. + +## Route matrices and distinct edge products + +Work on `L` direct sum `E_s`, where `L` has binary dimension 9 and `E_s` +has binary dimension 8. Both use the dot product. A port has `q^T q=1`. +Let the columns of `B_q` be an orthonormal basis of `q`-perp. The swap chart +has matrix + +\[ +\rho_q=\begin{pmatrix}q q^T&B_q\\B_q^T&0\end{pmatrix},\qquad +B_q^TB_q=I_8,\quad B_qB_q^T=I_9+q q^T. +\] + +It is an orthogonal involution. Different ports have different routes, +because the local block is `q q^T`. + +For a nonzero off-diagonal entry `A_qp`, the local block of the product is + +\[ +(\rho_q\rho_p)_{LL}=B_q B_p^T. +\] + +Its kernel is the line spanned by `p`; its image is `q`-perp. Over the +binary field a nonzero line has one nonzero vector. The matrix therefore +determines both `q` and `p`. Consequently all 5,824 ordered edge products +are distinct. None is the identity. The products at `q=p` are all the identity. +This proof uses no choice of the bases `B_q`. + +The checker verifies the rank, kernel, and image of every selected edge +product as a binary 17 by 17 matrix. It also verifies all 3,136 +star-transposition identities over all 112 ports and all pairs of positive +stages. Those identities give the stated `S_9` stage action. They do not +give relations between the projections below. + +## Two exact trace moments + +Use the involution on the real group algebra that sends each group element +to its inverse. Set + +\[ +D=\operatorname{diag}(\rho_q),\qquad Q=DPD. +\] + +Both `P` and `Q` are self-adjoint projections. For a group-algebra matrix, +let `tau` be the sum of the identity coefficients on its diagonal. On a +full regular cover this is the ordinary trace divided by `|G|`. + +Because the routes are distinct, only equal port indices contribute to the +identity coefficient in `P Q`. Hence + +\[ +\tau(P)=\tau(Q)=8,\qquad +\tau(PQ)=\frac{112\cdot4^2}{56^2}=\frac47. +\] + +An identity term in `(P Q)^2` must satisfy +`rho_b rho_c = rho_a rho_d`, with `A_bc A_da` nonzero. The edge-product +lemma gives exactly two cases: + +* Both products are the identity: `b=c` and `a=d`. +* Both products are nonidentity: `b=a`, `c=d`, and `b` is not `c`. + +The resulting coefficient sum is + +\[ +\begin{split} +\tau((PQ)^2) +&=\frac{16}{56^4} + \left(\sum_{a,b}A_{ab}^2+\sum_{a\ne b}A_{ab}^2\right)\\ +&=\frac{16(25088+23296)}{56^4}=\frac{27}{343}. +\end{split} +\] + +This argument works in the full group algebra. It does not evaluate the +cover at a phase value or identify two different group elements. + +## Rank bound and the equality subspace + +Set `M=P-Q`. Cyclicity of `tau` and the projection identities give + +\[ +\tau(M^2)=16-2\tau(PQ)=\frac{104}{7}, +\] + +\[ +\tau(M^4)=16-4\tau(PQ)+2\tau((PQ)^2)=\frac{4758}{343}. +\] + +Let the nonzero real eigenvalues of `M` on the full regular cover be +`lambda_1,...,lambda_r`. Cauchy--Schwarz gives + +\[ +(\operatorname{tr}M^2)^2\le r\operatorname{tr}M^4. +\] + +After division by the cover size, + +\[ +\frac{\operatorname{rank}M}{|G|} +\geq\frac{(104/7)^2}{4758/343}=\frac{2912}{183}. +\] + +Since `J_s-J_0=-14(Q-P)`, the same rank bound holds for the routed +interfaces. It is additive on independent copies. A code on which these +two interfaces agree must lie in the kernel of their difference, so its +codimension is at least this rank. + +One can also express the result as a bound on common centre information. +The normalized dimension of `im(P)` intersect `im(Q)` is at most `8/183`. +To see this, apply the nonnegative polynomial +`(t-13/196)^2/(1-13/196)^2` to `PQP` on `im(P)`. Each eigenvalue 1 +contributes 1. The two trace moments give an upper bound `8/183`. + +## Exact failures of smaller algebras + +Use port index 0, whose binary label is 11, and port index 1, whose label +is 19. Let `g=rho_0 rho_1`. The edge-product lemma gives + +\[ +[g](PQP)_{00}=\frac{16}{56^3}=\frac1{10976}. +\] + +Every scalar multiple of `P` has zero coefficient at this nonidentity +element. Therefore `P Q P=lambda P` fails for every scalar `lambda`. +This is a formal group-algebra counterexample. + +At the same group element, + +\[ +[g](PQ-QP)_{00}=-\frac4{56^2}=-\frac1{784}. +\] + +This failure also holds for every allowed chart basis. Indeed the first +term uses products `rho_i rho_0` and the second uses `rho_0 rho_i`. +On the nonzero off-diagonal support these ordered products are distinct. + +For the selected chart, the checker gives a further group element with +coefficient `1/21952` in `(PQP-QPQ)_{00}`. Both `P` and `Q` have the same +diagonal entry, so the braid difference + +\[ +J_0J_1J_0-J_1J_0J_1 +=14\cdot13(P-Q)-14^3(PQP-QPQ) +\] + +has coefficient `-1/8` at this entry. Its full binary matrix is in +`ALGEBRA.json`. + +The optional sixth-moment calculation retains every group coefficient of +`(R D R^T)^3`. It gives + +\[ +\tau((PQ)^3)=\frac{1609241}{120472576}. +\] + +There are 314,608 contributing walks and 302,910 distinct group elements. +The exact coefficient sums give the stronger selected-chart codimension +bound `5763805736/360389295`. This stronger bound is not needed for the +basis-independent result. It has not yet received an independent replay. + +## Reproduction and open next questions + +From the workspace root, run: + +```sh +python3 -I -B work/centre-encoding-campaign-20261014/lanes/cover-algebra/verify_algebra.py --interface work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json --out work/centre-encoding-campaign-20261014/lanes/cover-algebra/ALGEBRA.json --sixth-moment +``` + +The printed result is `PASS_EXACT_ROUTED_PROJECTION_ALGEBRA`. +The calculation uses one CPU and exact integer or rational arithmetic. + +The next controller question is whether a word that revisits a physical +stage can use these larger algebras at a favourable full cost. A word that +uses each fresh external stage only once has a separate support obstruction: +an off-diagonal edge in stage `s` cannot fix `E_s` pointwise. Other stages +do fix `E_s` pointwise. The `encoded_controller` worker is checking the +bridge alphabet and the native-frame obligations for that argument. + +The rank theorem also leaves encodings that add state or change recursive +children open. The `source_domain` worker is applying the bound to the +unchanged-child invoice. That application requires its own dimension count. + +This work used AI assistance. It builds on the selected supplier and on the +campaign's centre-free interface and route calculations. It makes no supplier +admission or multiplication-exponent claim. diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-MOMENTS-REVIEW.json b/research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-MOMENTS-REVIEW.json new file mode 100644 index 0000000000..fa66a03898 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-MOMENTS-REVIEW.json @@ -0,0 +1,24 @@ +{ + "checker_sha256": "9f3cff9ff7459800afff681c18276ebc0d6a140a66b58af76b3140015889518c", + "checks": { + "eight_field_cohorts": 8, + "fifth_contraction": "23/2592", + "fourth_contraction": "23/216", + "off_diagonal_support": 4224, + "ordinary_columns": 96, + "positive_measure_attains_first_five_moments": true, + "rank4": "4104/73", + "rank5": "15560/273", + "whole_fields": 57 + }, + "matrix_source_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "scope": "Independent proof review and exact arithmetic. The frozen finite route-support enumerations are inspected dependencies; this review does not rerun or replace them. The capacity statement uses the full fixed-source regular-cover payload module. No changing-source, native-child, cache construction, or supplier claim.", + "source_pins": { + "QUERY-FIFTH-MOMENT.json": "d346e38c1dc323d3304c94e7faf14384ac7970bb7b7775c49749a90a509fa0e9", + "QUERY-FOURTH-MOMENT.json": "df32110bbd285e3036bdb2082e3307b24edc7515953cab7a1b3b6b684adc1e66", + "QUERY-MOMENTS.md": "91121028d7f084d3c1d53a16ca8a3634ce4ede59fcab31c9a74c4a221c7d75e5", + "check_query_fifth_moment.py": "bea72f2bafab8cc38142557d6d3a1bee5f4db1f9a2a75668fce146ca6ebba4f0", + "check_query_fourth_moment.py": "c22539e007c763b2d92d2932c4d84080ccda8549774d6be8b7705575a03a253f" + }, + "status": "PASS_INDEPENDENT_QUERY_MOMENT_PROOF_AND_ARITHMETIC_REVIEW" +} diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-MOMENTS-REVIEW.md b/research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-MOMENTS-REVIEW.md new file mode 100644 index 0000000000..6e2497a531 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-MOMENTS-REVIEW.md @@ -0,0 +1,49 @@ +# Review of the fourth and fifth query moments + +The pinned proof passes this bounded review. The independent arithmetic +checker imports no producer. It rebuilds the actual 96-column Gram and +root products, checks both coefficient contractions, checks the two +optimized moment bounds, and checks the positive measure that attains +the first five moments. The exact pins are in the review receipt. + +The order in the singleton argument is valid. Every factor other than +the unique positive-stage factor fixes its fresh block pointwise. If +their whole product is I, that factor belongs to the same pointwise +stabilizer. Applied to each fresh axis, the factor then requires the +two actual port complement bases to agree. Their missing lines agree, +so the ports are equal. Deletion gives the factor 4/48=1/12. Cyclic +trace and projection idempotence can then be used in either order. + +The fifth-order coefficient contraction has the correct transpose. +The covariance table is self-adjoint. If the last three factors have +group word g, their matrix coefficient contracts with the coefficient +at g inverse. Thus the two scalar products are (r_r dot r_p) and +(r_q dot r_t). The inspected finite route check finds only s=t. +There are 96 diagonal matches and 4,224 off-diagonal matches. They give +96*12288+4224*256=2,260,992. This proves the stated 23/2592 contraction +once that finite support check is supplied. This review does not repeat +the 194,400-word route enumeration. + +The payload statement uses the complete regular-cover module. A +nonidentity cover route has no diagonal cover block. Tensoring with an +honest unitary payload representation preserves the regular trace; +the fieldwise change of basis V_d removes that representation. This +argument would not justify a full-field storage bound from only a +constant-payload subspace. The proof makes that distinction explicit. +The exact physical-to-logical chart binding remains its pinned native +dependency. + +The optimized fourth bound is 4104/73 fields. The fifth bound is +15560/273=57-1/273 fields. Both require 57 whole fields, or eight +whole eight-field cohorts. The fifth bound is sharp for the stated +continuous moment relaxation. Its positive measure has nodes zero, +(19-2 sqrt(22))/12, (19+2 sqrt(22))/12, and nine. The cubic recurrence +and the mass 8/7833 at nine give all five moments. The two interior +nodes lie on opposite sides of their required weighted mean, so their +masses are positive. No assertion about the actual finite spectrum +or higher moments is needed. + +The result concerns nine queries of one fixed arbitrary source. It +does not impose that simultaneous-query requirement on a controller +whose source changes. It gives no native-child lower bound or cache +construction. No sixth-moment work was done for this review. diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-SUPPORT-DISTANCE-REVIEW.json b/research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-SUPPORT-DISTANCE-REVIEW.json new file mode 100644 index 0000000000..f40da77ceb --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/QUERY-SUPPORT-DISTANCE-REVIEW.json @@ -0,0 +1,53 @@ +{ + "actual_frame_support_maxima": { + "0": 112, + "1": 56, + "2": 20, + "3": 10, + "4": 8, + "5": 8, + "6": 4, + "7": 2, + "8": 1, + "9": 0 + }, + "attaining_directions": 112, + "checker_sha256": "8e7ac1aaadbc6af5c2d30b805704dc7012f5ba4e1d1776ab32ee6455b2bbbf84", + "findings": [], + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "nonzero_table": [ + 0, + 8, + 4, + 6, + 5 + ], + "not_rerun": [ + "The full scalar core", + "The snapshot producer", + "A native cache program" + ], + "proof_review": [ + "A generic real projection keeps each nonzero coefficient nonzero and preserves every complex zero sum.", + "Positive equal-sum subsets form an antichain. Opposite zero sign patterns give the even count bound.", + "A scalar coefficient code with distance at least three remains injective after any two coordinate deletions.", + "For block fields, choose a linear section of the surjective reconstruction map. Its kd-dimensional image has block distance at least three." + ], + "proof_sha256": "132a94c9f7e5ea3f5901455cded5685e6c3b1968ea4553b3c019f55a559ecb66", + "quartet_count": 14, + "scope": "A k-dimensional query span needs at least k+2 birth fields when each has source support at most20. This does not price a multilevel shared network.", + "snapshot_decompressed_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", + "source_checker_sha256": "d9bff383c911653f17087849203f3a64dc4d511f27f6a243bbfa7f3d175d9a09", + "source_receipt_sha256": "6c22878f6259772183263ae192422f8089113a11629662aee31fd82cea4824ce", + "status": "PASS_INDEPENDENT_QUERY_SUPPORT_DISTANCE_53_REVIEW", + "support_size_minima": { + "1": 56, + "2": 76, + "3": 78, + "4": 53, + "5": 73, + "6": 75, + "7": 77, + "8": 70 + } +} diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/RANK5-UNION-CUTS-REVIEW.json b/research/actual-query-information-bounds/payload/lanes/cover-algebra/RANK5-UNION-CUTS-REVIEW.json new file mode 100644 index 0000000000..293a965d30 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/RANK5-UNION-CUTS-REVIEW.json @@ -0,0 +1,235 @@ +{ + "cases": [ + { + "actual_edges": 71, + "actual_nodes": 21, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 19, + "3": 21, + "4": 10 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 630, + "positive_cuts": 5, + "support_tests": 623, + "total_bound_per_query": 9 + }, + { + "actual_edges": 71, + "actual_nodes": 21, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 19, + "3": 21, + "4": 10 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 631, + "positive_cuts": 5, + "support_tests": 607, + "total_bound_per_query": 9 + }, + { + "actual_edges": 71, + "actual_nodes": 21, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 19, + "3": 21, + "4": 10 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 632, + "positive_cuts": 5, + "support_tests": 623, + "total_bound_per_query": 9 + }, + { + "actual_edges": 71, + "actual_nodes": 21, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 19, + "3": 21, + "4": 10 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 633, + "positive_cuts": 5, + "support_tests": 607, + "total_bound_per_query": 9 + }, + { + "actual_edges": 71, + "actual_nodes": 21, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 19, + "3": 21, + "4": 10 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 635, + "positive_cuts": 5, + "support_tests": 607, + "total_bound_per_query": 9 + }, + { + "actual_edges": 71, + "actual_nodes": 21, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 19, + "3": 21, + "4": 10 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 637, + "positive_cuts": 5, + "support_tests": 607, + "total_bound_per_query": 9 + }, + { + "actual_edges": 75, + "actual_nodes": 22, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 20, + "3": 23, + "4": 11 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 734, + "positive_cuts": 5, + "support_tests": 657, + "total_bound_per_query": 9 + }, + { + "actual_edges": 75, + "actual_nodes": 22, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 20, + "3": 23, + "4": 11 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 735, + "positive_cuts": 5, + "support_tests": 656, + "total_bound_per_query": 9 + }, + { + "actual_edges": 75, + "actual_nodes": 22, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 20, + "3": 23, + "4": 11 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 736, + "positive_cuts": 5, + "support_tests": 656, + "total_bound_per_query": 9 + }, + { + "actual_edges": 75, + "actual_nodes": 22, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 20, + "3": 23, + "4": 11 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 737, + "positive_cuts": 5, + "support_tests": 656, + "total_bound_per_query": 9 + }, + { + "actual_edges": 75, + "actual_nodes": 22, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 20, + "3": 23, + "4": 11 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 739, + "positive_cuts": 5, + "support_tests": 656, + "total_bound_per_query": 9 + }, + { + "actual_edges": 75, + "actual_nodes": 22, + "completion_bound_per_query": 4, + "edge_charge_histogram": { + "1": 21, + "2": 20, + "3": 23, + "4": 11 + }, + "every_positive_cut_rank": 5, + "exact_query_overlap": 5, + "internal_bound_per_query": 5, + "merge_frame": 741, + "positive_cuts": 5, + "support_tests": 656, + "total_bound_per_query": 9 + } + ], + "checker_sha256": "fb4d62ce46609842cb18f0b92b7071a4179530c31923071cc644037cfe7d252c", + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "not_checked": [ + "Other merge frames and the other displayed-space certificates in the proof", + "Synthetic intermediate frames", + "Cross-merge sharing", + "Chronological native recipes", + "A global64 bound", + "Supplier pricing" + ], + "reviewed_certificate_sha256": "caf4ea536cc79ec7cd585b9f3d4714efc86874785cf463dc215d0158caff5607", + "reviewed_proof_sha256": "d85d71839a600f7d8d0cb511530ca2d1169f0efa543f8c342d2b2cbfe9396629", + "scope": "Every subspace of the exact maximal five-query space at each of the twelve listed rank-five frames costs at least nine rank units per query in the actual positive-frame common-merge network. Same-content monotone transport and no new observations after the merge are required. All source times are granted.", + "snapshot_decompressed_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", + "status": "PASS_INDEPENDENT_RANK5_UNION_CUT_REVIEW" +} diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/RANK5-UNION-CUTS-REVIEW.md b/research/actual-query-information-bounds/payload/lanes/cover-algebra/RANK5-UNION-CUTS-REVIEW.md new file mode 100644 index 0000000000..e9d38bb07a --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/RANK5-UNION-CUTS-REVIEW.md @@ -0,0 +1,68 @@ +# Independent review of the rank-five union cuts + +The rank-five claim in `history-encoding/LOW-BIRTH-UNION-CUTS.md` passes +independent review. The reviewed proof has SHA256 +`d85d71839a600f7d8d0cb511530ca2d1169f0efa543f8c342d2b2cbfe9396629`. +The reviewed certificate has SHA256 +`caf4ea536cc79ec7cd585b9f3d4714efc86874785cf463dc215d0158caff5607`. + +For each of the twelve listed rank-five merge frames, every subspace of +dimension `k` in its exact five-query overlap needs at least `9k` native +rank in the stated model. This result permits shared paths and scalar +cancellation. It does not give a bound for a network that shares work +between different merge spaces. + +## Proof check + +Fix a source-port test set `E`. A cut contains only nodes at which every +free observation is zero when Y is supported on E, X equals JY, and all +helper inputs are zero. The output query restricted to E must therefore +pass through the edges that enter the cut. Each carried field has at +most one field of rank. Thus the restriction rank is a lower bound for +the number of fields that enter the cut. This remains true when fields +split, merge, or cancel. + +The five accepted cuts each have unit weight. Every actual inclusion +edge is charged at most its dimension increase. Each test restriction +is injective on the full five-query space. It is therefore injective +on every subspace of that space. The internal bound is `5k`. With no +new observations after the common rank-five merge, completion to FULL9 +costs at least `4k`. These two bounds give `9k`. + +For a payload of dimension N, each restriction rank and each carried +field capacity is multiplied by N. The same bound holds in field units. +The model retains the logical meaning of each frame. It does not permit +free changes to that meaning through address operators. + +## Independent exact checks + +Run from the repository root: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/cover-algebra/review_rank5_union_cuts.py +``` + +The checker imports no producer. It reads the pinned snapshot and +interface data and rebuilds the following facts with rational arithmetic: + +- All twelve merge frames have dimension five. +- The complete 712-column observation quotient has query overlap of + exactly five at each frame. The 78 helpers with non-FULL final frames + remain in this quotient. +- The displayed five-query basis belongs to that overlap. +- All actual positive contained frames and all their inclusion edges + agree with the certificate. +- Every used source-port test has zero observation at each inside node. +- Each of the five positive cuts is upward closed, has weight one, and + has restriction rank five. +- Every edge charge is at most its native rank cost. + +The exact check passes with assertions disabled. Its receipt is +`RANK5-UNION-CUTS-REVIEW.json`. The checker and source hashes are in that +receipt. + +This review does not rerun a floating-point search. It does not check +the other displayed-space certificates in the source proof, chronological +native recipes, synthetic intermediate frames, cross-merge sharing, a +global bound of 64, or a complete supplier invoice. No material finding +remains in the reviewed rank-five claim. diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/SNAPSHOT-FLAG-CUT.json b/research/actual-query-information-bounds/payload/lanes/cover-algebra/SNAPSHOT-FLAG-CUT.json new file mode 100644 index 0000000000..c298fc71f6 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/SNAPSHOT-FLAG-CUT.json @@ -0,0 +1,174 @@ +{ + "checker_sha256": "b49857d0005b19880309c2790378fe1b956a5ada092b94a4814d2bc016ab1b28", + "exact_shell_ranks": [ + 0, + 1, + 1, + 2, + 8, + 6, + 8, + 8, + 8 + ], + "flag_basis": [ + 243, + 249, + 311, + 132, + 131, + 489, + 442, + 405, + 178 + ], + "frame_shell_support_tests": 23279, + "not_checked": [ + "A constructive merged cache network", + "Internal native-child cuts", + "A changed core", + "Logical address re-gauging", + "A complete supplier invoice" + ], + "rank_sum": 42, + "retained_edge_count": 2880, + "scope": "Same-content monotone frame networks, arbitrary scalar sharing and all snapshot times. This bound does not prove64 or optimality.", + "shells": [ + [], + [ + 87 + ], + [ + 82 + ], + [ + 47, + 108 + ], + [ + 4, + 9, + 16, + 26, + 38, + 52, + 70, + 102 + ], + [ + 1, + 15, + 20, + 29, + 90, + 95, + 103 + ], + [ + 6, + 23, + 37, + 43, + 55, + 59, + 69, + 75, + 79, + 92, + 111 + ], + [ + 2, + 11, + 13, + 18, + 27, + 31, + 33, + 40, + 41, + 49, + 57, + 62, + 65, + 67, + 72, + 73, + 78, + 84, + 88, + 97, + 100, + 105 + ], + [ + 0, + 3, + 5, + 7, + 8, + 10, + 12, + 14, + 17, + 19, + 21, + 22, + 24, + 25, + 28, + 30, + 32, + 34, + 35, + 36, + 39, + 42, + 44, + 45, + 46, + 48, + 50, + 51, + 53, + 54, + 56, + 58, + 60, + 61, + 63, + 64, + 66, + 68, + 71, + 74, + 76, + 77, + 80, + 81, + 83, + 85, + 86, + 89, + 91, + 93, + 94, + 96, + 98, + 99, + 101, + 104, + 106, + 107, + 109, + 110 + ] + ], + "sources": { + "core_decompressed_sha256": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877", + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "snapshot_decompressed_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", + "support_review_sha256": "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7" + }, + "status": "PASS_SHARED_MONOTONE_CACHE_DAG_LOWER_BOUND_42" +} diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/SNAPSHOT-FLAG-CUT.md b/research/actual-query-information-bounds/payload/lanes/cover-algebra/SNAPSHOT-FLAG-CUT.md new file mode 100644 index 0000000000..90b1a52c1f --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/SNAPSHOT-FLAG-CUT.md @@ -0,0 +1,112 @@ +# A shared cache-network cut bound + +The retained snapshot model needs at least 42 units of native rank to +produce all eight FULL centre queries. This bound permits scalar sharing +between outputs. It does not prove the desired bound of 64, and it does +not give a construction below 64. + +The model is the same-content monotone frame network in +`CHRONOLOGICAL-CACHE-PATHS.md`. It grants every recorded snapshot time, +scalar COPY and ADD operations, arbitrary owned cache storage, and final +X and helper cleanup. The core is unchanged. A transition from frame +`U` to a containing frame `V` costs at least `dim(V)-dim(U)` per field. +The proof does not cover logical address re-gauging between frames. + +## The flag cuts + +Choose an ordered binary basis `v_0,...,v_8` of the nine-dimensional +address space. Express each frame in this basis, and use row echelon +form with the lowest nonzero coordinate as leading coordinate. Let +`P(U)` be the set of leading positions of `U`. + +Every nonzero vector in `U` has a leading position in `P(U)`, and every +position in `P(U)` occurs. Therefore + +\[ +U\subseteq V\quad\Longrightarrow\quad P(U)\subseteq P(V), +\qquad |P(U)|=\dim U. \tag{1} +\] + +For each position `i`, form the cut `Omega_i` of all network nodes whose +frame has `i` in its pivot set. A transition `U -> V` enters exactly +`dim(V)-dim(U)` such cuts. An ADD or COPY at one frame enters no cut. + +Give each port `q_p` its dual coordinates + +\[ +b_j(p)=q_p\cdot v_j. +\] + +Let `E_i` contain the ports whose largest nonzero dual-coordinate index +is `i`. These nine sets partition all 112 ports. + +If `i` is a pivot of `U`, choose a vector of `U` whose leading coordinate +is `i`. For `p` in `E_i`, its dot product with that vector is one. The +exact snapshot support law therefore makes every observation in +`Omega_i` zero on the valid input family + +\[ +x=Jy,\qquad h=c=0,\qquad \operatorname{supp}y\subseteq E_i. \tag{2} +\] + +The completed X and restored helper rows are also zero. The eight +required FULL queries on (2) have rank + +\[ +r_i=\operatorname{rank}R_{E_i}. \tag{3} +\] + +Every dependence on (2) that reaches a FULL output must enter +`Omega_i` across a native cache edge. A field on such an edge can carry +at most one full field dimension of linear information. Thus the sum +of incoming field capacities is at least `r_i`. This is the cut +inequality from the general row-flow model. It is valid with arbitrary +fanout, scalar combinations, cancellations, and reuse inside the cut. + +Sum the nine inequalities. By (1), every edge is charged at most its +native-rank cost. Hence + +\[ +\boxed{\text{native rank}\ \geq\sum_{i=0}^8\operatorname{rank}R_{E_i}.} \tag{4} +\] + +The argument holds for full native payload arrays. If one field has +dimension `d`, the demand in (3) is `r_i d` and an entering field has +capacity at most `d`. The factor cancels. No constant-array restriction +or independent-output-tree assumption is used. + +## The exact witness + +The basis used in the certificate is + +```text +[243, 249, 311, 132, 131, 489, 442, 405, 178] +``` + +The exact rational shell ranks are + +```text +[0, 1, 1, 2, 8, 6, 8, 8, 8] +``` + +Their sum is 42. `check_snapshot_flag_cut.py` checks the binary basis, +all nine rational ranks, all 23,279 frame/shell separation cases, and +the cut charge on all 2,880 distinct retained native edges. It pins the +independent exact snapshot support review. It imports no source +producer. + +Run: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/cover-algebra/check_snapshot_flag_cut.py +``` + +The result is `PASS_SHARED_MONOTONE_CACHE_DAG_LOWER_BOUND_42`, saved in +`SNAPSHOT-FLAG-CUT.json`. A bounded search of 20,000 binary bases found +this witness. The search is not an optimality proof. The exact checker +does not rely on the search result beyond the displayed basis. + +The single-tree bound of eight still does not add across shared output +trees. Equation (4) is a separate valid shared-network bound. 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"-48": 2, + "-64": 45, + "32": 790, + "64": 38 + }, + "nonzero_port_incidence_checks": 104088, + "normal_lines_absent": [ + 42, + 7, + 25, + 52, + 82, + 127, + 97, + 76 + ], + "not_checked": [ + "The full snapshot producer replay", + "A new native cache word", + "Chronological branching synthesis", + "A complete supplier invoice" + ], + "phase_scope": "Scalar rows are read in the canonical view. Non-FULL views after event 17605 require the supplied endpoint monomial adapter.", + "proper_frame_minor_count": 1002, + "rows": 12271, + "scope": "One nonzero birth frame and all later containing frames. This does not exclude a merged network with incomparable capture frames.", + "status": "PASS_EXACT_SNAPSHOT_SUPPORT_AND_SINGLE_CONE_EXCLUSION", + "test_input": "X=JY; all 480 helper and eight private inputs are zero" +} diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/check_snapshot_flag_cut.py b/research/actual-query-information-bounds/payload/lanes/cover-algebra/check_snapshot_flag_cut.py new file mode 100644 index 0000000000..5a4e6668cc --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/check_snapshot_flag_cut.py @@ -0,0 +1,118 @@ +"""Verify one exact cut bound for a shared monotone cache network.""" + +from fractions import Fraction +from hashlib import sha256 +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +FLAG = [243, 249, 311, 132, 131, 489, 442, 405, 178] +SNAPSHOT = "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c" +INTERFACE = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" +CORE = "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877" + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def exact_rank(matrix): + pivots = {} + for row in matrix: + row = [Fraction(value) for value in row] + for index, old in sorted(pivots.items()): + scale = row[index] + row = [a-scale*b for a, b in zip(row, old)] + index = next((i for i, value in enumerate(row) if value), None) + if index is not None: + scale = row[index] + pivots[index] = [value/scale for value in row] + return len(pivots) + + +def binary_pivots(basis, coordinates): + pivots = {} + for vector in basis: + vector = coordinates[vector] + for index, old in sorted(pivots.items()): + if vector >> index & 1: + vector ^= old + if vector: + index = (vector & -vector).bit_length()-1 + pivots[index] = vector + return set(pivots) + + +def main(): + coordinates = {0: 0} + for index, vector in enumerate(FLAG): + require(vector not in coordinates, "The flag vectors are dependent") + coordinates.update({old ^ vector: bits | 1 << index + for old, bits in tuple(coordinates.items())}) + require(len(coordinates) == 512, "The flag is not a binary basis") + interface_raw = (HERE.parent / "circuit-interface/INTERFACE.json").read_bytes() + require(sha256(interface_raw).hexdigest() == INTERFACE, "The interface pin differs") + data = json.loads(interface_raw) + labels = data["ports"] + R = [[Fraction(row.get(str(p), "0")) for p in range(112)] for row in data["R"]] + shells = [[] for _ in range(9)] + for p, label in enumerate(labels): + dual = sum(((label & vector).bit_count() % 2) << i + for i, vector in enumerate(FLAG)) + require(dual != 0, "A nonzero port has zero dual coordinates") + shells[dual.bit_length()-1].append(p) + ranks = [exact_rank([[row[p] for p in shell] for row in R]) for shell in shells] + require(ranks == [0, 1, 1, 2, 8, 6, 8, 8, 8], "The exact shell ranks differ") + snapshot_raw = gzip.decompress((HERE.parent / "history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz").read_bytes()) + require(sha256(snapshot_raw).hexdigest() == SNAPSHOT, "The snapshot pin differs") + source = json.loads(snapshot_raw) + frame_pivots = [binary_pivots(basis, coordinates) for basis in source["frames"]] + require(all(len(pivots) == len(basis) for pivots, basis in zip(frame_pivots, source["frames"])), + "A frame basis is dependent") + # Check the support separation for every possible permitted port at each frame. + support_tests = 0 + for basis, pivots in zip(source["frames"], frame_pivots): + for i in pivots: + for p in shells[i]: + support_tests += 1 + require(any((labels[p] & vector).bit_count() % 2 for vector in basis), + "A shell port can enter its cut without a native edge") + core_raw = gzip.decompress((HERE.parent / "circuit-interface/CENTRE-FREE-PROGRAMS.json.gz").read_bytes()) + require(sha256(core_raw).hexdigest() == CORE, "The core pin differs") + edges = set() + for event in json.loads(core_raw)["backward"]: + if event[0] != "climb": + continue + _, _, wire, before, after, cost = event + old, new = frame_pivots[before], frame_pivots[after] + require(old <= new, "A retained edge is not monotone in the flag cuts") + require(len(new-old) == cost, "The cut charge differs from native rank") + edges.add((before, after, cost)) + review = HERE / "SNAPSHOT-SUPPORT-REVIEW.json" + dependency = json.loads(review.read_bytes()) + require(dependency["status"] == "PASS_EXACT_SNAPSHOT_SUPPORT_AND_SINGLE_CONE_EXCLUSION", + "The exact support review is absent") + require(dependency["inputs"]["snapshot_decompressed_sha256"] == SNAPSHOT, + "The support review uses another snapshot source") + result = { + "status": "PASS_SHARED_MONOTONE_CACHE_DAG_LOWER_BOUND_42", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "sources": {"snapshot_decompressed_sha256": SNAPSHOT, "interface_sha256": INTERFACE, + "core_decompressed_sha256": CORE, + "support_review_sha256": sha256(review.read_bytes()).hexdigest()}, + "flag_basis": FLAG, "shells": shells, "exact_shell_ranks": ranks, + "rank_sum": sum(ranks), "retained_edge_count": len(edges), + "frame_shell_support_tests": support_tests, + "scope": "Same-content monotone frame networks, arbitrary scalar sharing and all snapshot times. This bound does not prove64 or optimality.", + "not_checked": ["A constructive merged cache network", "Internal native-child cuts", "A changed core", "Logical address re-gauging", "A complete supplier invoice"], + } + output = HERE / "SNAPSHOT-FLAG-CUT.json" + output.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(json.dumps({key: value for key, value in result.items() if key != "shells"}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_movable_rank8_cuts.py b/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_movable_rank8_cuts.py new file mode 100644 index 0000000000..ce823fcd4b --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_movable_rank8_cuts.py @@ -0,0 +1,179 @@ +"""Review the movable rank-eight cuts and their FULL extensions.""" + +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent +SNAPSHOT_PIN = '3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c' +INTERFACE_PIN = '5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3' +CERT_PIN = '62c3b26274ef80a75bbc90b680ceeed9ed24fb158fd7db32594995859c875951' +PROOF_PIN = '9e8ebc108a758883e9811798900bbaa7c42ffa90ac960953a7596d3427f50708' + + +def require(value, message): + if not value: + raise ValueError(message) + + +def span(basis): + values = {0} + for v in basis: + values |= {x ^ v for x in tuple(values)} + require(len(values) == 1 << len(basis), 'A frame basis is dependent') + return values + + +def add(row, other, factor): + for j, x in other.items(): + value = row.get(j, 0) + factor * x + if value: + row[j] = value + else: + row.pop(j, None) + + +def minor(R, ports): + pivots = {} + selected = [] + for port in sorted(ports): + vector = [R[i][port] for i in range(8)] + for p, row in sorted(pivots.items()): + value = vector[p] + vector = [x - value * y for x, y in zip(vector, row)] + p = next((i for i, x in enumerate(vector) if x), None) + if p is not None: + value = vector[p] + pivots[p] = [x / value for x in vector] + selected.append(port) + require(len(selected) == 8, 'A source test does not have rank eight') + matrix = [[R[i][p] for p in selected] for i in range(8)] + determinant = F(1) + for j in range(8): + p = next(i for i in range(j, 8) if matrix[i][j]) + if p != j: + matrix[p], matrix[j] = matrix[j], matrix[p] + determinant = -determinant + value = matrix[j][j] + determinant *= value + matrix[j] = [x / value for x in matrix[j]] + for i in range(j + 1, 8): + value = matrix[i][j] + matrix[i] = [x - value * y for x, y in zip(matrix[i], matrix[j])] + require(determinant != 0, 'Zero source minor') + return {'ports': selected, 'determinant': str(determinant)} + + +def main(): + raw = gzip.decompress((LANES / 'history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz').read_bytes()) + require(sha256(raw).hexdigest() == SNAPSHOT_PIN, 'Snapshot pin') + data = json.loads(raw) + interface_raw = (LANES / 'circuit-interface/INTERFACE.json').read_bytes() + require(sha256(interface_raw).hexdigest() == INTERFACE_PIN, 'Interface pin') + labels = json.loads(interface_raw)['ports'] + proof_raw = (LANES / 'history-encoding/MOVABLE-RANK8-CUTS.md').read_bytes() + certificate_raw = (LANES / 'history-encoding/MOVABLE-FULL-RANK-CUTS.json').read_bytes() + require(sha256(proof_raw).hexdigest() == PROOF_PIN, 'Proof pin') + require(sha256(certificate_raw).hexdigest() == CERT_PIN, 'Certificate pin') + certificate = json.loads(certificate_raw) + require({case['merge_frame'] for case in certificate['merges']} == {983, 991} + and len(certificate['merges']) == 2, 'The two merge cases differ') + frames = data['frames'] + spaces = [span(U) for U in frames] + require(len(frames[1]) == 9, 'FULL frame differs') + R = [[F(row.get(str(p), 0)) for p in range(112)] for row in data['R']] + final = [{int(j): F(x) for j, x in row.items()} for row in data['final_rows']] + for p in range(112): + expected = {p: F(1)} + for q in range(112): + value = sum(row[p] * row[q] for row in R) / 4 - (p == q) + if value: + expected[112 + q] = value + require(final[p] == expected, 'A completed X row differs from X-JY') + by_frame = {} + for _, _, _, frame, rowid in data['intervals']: + by_frame.setdefault(frame, set()).add(rowid) + reduced = {} + + def observation_support(frame): + support = set() + for rowid in by_frame.get(frame, ()): + if rowid not in reduced: + row = {int(j): F(x) for j, x in data['rows'][rowid].items()} + for j in list(row): + if j < 112: + add(row, final[j], -row[j]) + reduced[rowid] = {j - 112 for j, x in row.items() if 112 <= j < 224 and x} + support |= reduced[rowid] + return support + + require(not observation_support(1), 'A FULL snapshot is nonzero on the test family') + reports = [] + for case in certificate['merges']: + merge = case['merge_frame'] + require(len(frames[merge]) == 8, 'Merge rank differs') + nodes = [u for u in range(len(frames)) if spaces[u] <= spaces[merge]] + require(nodes == case['contained_frames'], 'The complete contained frame set differs') + edges = [(u, v) for u in nodes for v in nodes if spaces[u] < spaces[v]] + hasse = {(u, v, len(frames[v]) - len(frames[u])) for u, v in edges + if not any(spaces[u] < spaces[w] < spaces[v] for w in nodes)} + require(hasse == {tuple(edge) for edge in case['hasse_edges']}, 'The Hasse graph differs') + require(len(edges) == case['all_inclusion_edges_checked'], 'The direct inclusion count differs') + supports = {} + for u in nodes: + allowed = {p for p, q in enumerate(labels) + if all((q & v).bit_count() % 2 == 0 for v in frames[u])} + supports[u] = observation_support(u) + require(supports[u] <= allowed, 'An actual snapshot violates the support premise') + minors = [] + tests = [] + for test in case['source_tests']: + ports = set(test['ports']) + require(len(ports) == len(test['ports']) and ports <= set(range(112)), 'A source test repeats or exceeds the ports') + minors.append(minor(R, ports)) + tests.append(ports) + maximal = {u for u in nodes if all(any((labels[p] & v).bit_count() % 2 for v in frames[u]) for p in ports)} + require(maximal == set(test['maximal_inside_frames']), 'A maximal support cut differs') + cuts = [] + require(len(case['cuts']) == 7, 'There must be seven cuts') + for cut in case['cuts']: + inside = set(cut['inside_frames']) + test = tests[cut['test']] + require(inside <= set(nodes) and merge in inside, 'Cut node scope differs') + require(all(not supports[u].intersection(test) for u in inside), 'A cut contains a nonzero free observation') + require(all(u not in inside or v in inside for u, v in edges), 'A cut is not upward closed') + entered = [i for i, (u, v, _) in enumerate(case['hasse_edges']) if u not in inside and v in inside] + require(entered == cut['entering_edges'], 'The stated entering edges differ') + cuts.append(inside) + charges = [sum(u not in cut and v in cut for cut in cuts) for u, v in edges] + require(all(charge <= len(frames[v]) - len(frames[u]) for charge, (u, v) in zip(charges, edges)), 'A direct edge is overcharged') + extended = [cut | {1} for cut in cuts] + [{1}] + full_edges = edges + [(u, 1) for u in nodes] + full_charges = [sum(u not in cut and v in cut for cut in extended) for u, v in full_edges] + require(all(charge <= len(frames[v]) - len(frames[u]) for charge, (u, v) in zip(full_charges, full_edges)), 'The FULL extension overcharges an edge') + reports.append({'merge_frame': merge, 'contained_frames': len(nodes), + 'all_internal_edges': len(edges), 'hasse_edges': len(hasse), + 'source_test_minors': minors, 'internal_cuts': 7, + 'extended_cuts': 8, 'extended_edges': len(full_edges), + 'extended_charge_histogram': dict(sorted(Counter(full_charges).items())), + 'bound_per_query_dimension': 8, + 'bound_for_all_eight_queries': 64}) + report = {'status': 'PASS_INDEPENDENT_MOVABLE_RANK8_CUTS', + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'reviewed_proof_sha256': PROOF_PIN, 'reviewed_certificate_sha256': CERT_PIN, + 'snapshot_decompressed_sha256': SNAPSHOT_PIN, 'interface_sha256': INTERFACE_PIN, + 'cases': reports, 'exact_snapshot_rows_reduced': len(reduced), + 'scope': 'At least8k native rank for any k-dimensional centre-query output at FULL when every proper frame is an actual subframe of one chosen V in{983,991}. Branches may bypass V. All snapshot times, frame zero, and arbitrary scalar sharing are granted.', + 'not_checked': ['Cross-cone networks', 'Synthetic intermediate frames', 'A global all-frame bound', 'Chronological native recipes', 'Complete supplier pricing']} + (HERE / 'MOVABLE-RANK8-CUTS-REVIEW.json').write_text(json.dumps(report, indent=2, sort_keys=True) + '\n') + print(report['status']) + print('Both contained cones pass all edge charges, including direct completion to FULL; bound8k.') + + +if __name__ == '__main__': + main() diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_query_moments.py b/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_query_moments.py new file mode 100644 index 0000000000..ec43368242 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_query_moments.py @@ -0,0 +1,91 @@ +"""Check the exact moment arithmetic and the finite source contractions.""" + +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import json + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent +PINS = { + "QUERY-MOMENTS.md": "91121028d7f084d3c1d53a16ca8a3634ce4ede59fcab31c9a74c4a221c7d75e5", + "check_query_fourth_moment.py": "e7ff30dfdc23dd929599c05aa037a082060906021d5e9a40e9f586e680d0449e", + "QUERY-FOURTH-MOMENT.json": "df32110bbd285e3036bdb2082e3307b24edc7515953cab7a1b3b6b684adc1e66", + "check_query_fifth_moment.py": "2eee310e2db3593d4844e9806be695c869d0c101e881d677b5429232beb0e0a4", + "QUERY-FIFTH-MOMENT.json": "562d05a6f830f88d36efc148f81a01f3dfa95afbcab8195a9b5add02a5fdb742", +} + + +def need(value, message): + if not value: + raise ValueError(message) + + +def main(): + for name, expected in PINS.items(): + need(sha256((LANES / "temporal-reuse" / name).read_bytes()).hexdigest() == expected, "A source pin differs: " + name) + source_path = LANES / "circuit-interface/INTERFACE.json" + source = json.loads(source_path.read_text()) + a = [0, 7, 20, 27, 36, 46, 57, 111] + t = [21, 37, 47, 76, 81, 87, 92, 110] + ordinary = [p for p in range(112) if p not in a + t] + roots = [[Q(row.get(str(p), 0)) for row in source["R"]] for p in ordinary] + dot = lambda x, y: sum((v * w for v, w in zip(x, y)), Q()) + need(all(dot(v, v) == 4 for v in roots), "A column norm differs") + need(all(sum((v[i] * v[j] for v in roots), Q()) == 48 * int(i == j) for i in range(8) for j in range(8)), "The ordinary Gram differs") + products = [[dot(x, y) for y in roots] for x in roots] + need(all(sum(bool(v) for v in row) == 45 for row in products), "The supported degree differs") + off = [products[p][q] for p in range(96) for q in range(96) if p != q and products[p][q]] + need(len(off) == 4224 and set(map(abs, off)) == {Q(2)}, "The off-diagonal root products differ") + fourth_numerator = 8 * 192**2 + sum(16 * x * x for x in off) + need(Q(fourth_numerator, 48**4) == Q(23, 216), "The alternating contraction differs") + # The reviewed finite route check says that all fifth-order matches have s=t. + # Contract those terms directly, without its coefficient-table implementation. + fifth_numerator = sum((192 * products[r][r]**3 for r in range(96)), Q()) + fifth_numerator += sum((64 * x * x for x in off), Q()) + need(fifth_numerator == 2260992 and Q(fifth_numerator, 48**5) == Q(23, 2592), "The fifth contraction differs") + fifth = json.loads((LANES / "temporal-reuse/QUERY-FIFTH-MOMENT.json").read_text()) + need(fifth["supported_triples"] == 194400 and fifth["matched_group_terms"] == 4320 and fifth["identity_matches"] == 96, "The finite match receipt differs") + patterns = fifth["match_equality_patterns"] + need(patterns == {"(False, True, False)": 4224, "(True, True, True)": 96}, "The match classification differs") + m = [Q(96), Q(72), Q(120), Q(244), Q(1649, 3), Q(47467, 36)] + # The fourth-moment word count follows cyclic idempotence and singleton deletion. + k = 9 + m4 = 8*k + 4*k*(k-1) + Q(23, 216)*k*(k-1) + m4 += Q(k*(k-1)*(k-2), 3) + Q(k*(k-1)*(k-2)*(k-3), 216) + need(m4 == m[4], "The fourth word count differs") + v1, v2 = m[1], m[2] + h11, h12, h22 = m[2:5] + determinant = h11*h22 - h12*h12 + bound4 = (v1*v1*h22 - 2*v1*v2*h12 + v2*v2*h11) / determinant + need(bound4 == Q(4104, 73), "The optimal quadratic Cauchy bound differs") + need((h22*v1-h12*v2) / (-h12*v1+h11*v2) == -Q(13, 4), "The fourth optimizing polynomial differs") + weighted = [9*m[i] - m[i+1] for i in range(1, 5)] + v1, v2, h22 = weighted[0], weighted[1], weighted[3] + h11, h12 = weighted[1:3] + determinant = h11*h22 - h12*h12 + bound5 = (m[1] + (v1*v1*h22 - 2*v1*v2*h12 + v2*v2*h11) / determinant) / 9 + need(bound5 == Q(15560, 273), "The weighted quadratic bound differs") + need((h22*v1-h12*v2) / (-h12*v1+h11*v2) == -Q(19, 6), "The fifth optimizing polynomial differs") + moment = [bound5] + m[1:] + need(all(moment[i+3] - Q(73, 6)*moment[i+2] + Q(1459, 48)*moment[i+1] - Q(273, 16)*moment[i] == 0 for i in range(3)), "The extremal measure recurrence differs") + mass9 = (moment[2] - Q(19, 6)*moment[1] + Q(91, 48)*moment[0]) / Q(2611, 48) + mean = (moment[1] - 9*mass9) / (bound5-mass9) + need(mass9 == Q(8, 7833) and 1 < mean < 2 and 0 < bound5 < 96, "The extremal masses are not positive") + # The two remaining nodes are (19 +/- 2 sqrt(22))/12. + need(7**2 < 88 < 19**2 and 5**2 < 88 < 17**2, "The node intervals differ") + result = { + "status": "PASS_INDEPENDENT_QUERY_MOMENT_PROOF_AND_ARITHMETIC_REVIEW", + "source_pins": PINS, + "matrix_source_sha256": sha256(source_path.read_bytes()).hexdigest(), + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "checks": {"ordinary_columns": 96, "off_diagonal_support": len(off), "fourth_contraction": str(Q(fourth_numerator, 48**4)), "fifth_contraction": str(Q(fifth_numerator, 48**5)), "rank4": str(bound4), "rank5": str(bound5), "whole_fields": 57, "eight_field_cohorts": 8, "positive_measure_attains_first_five_moments": True}, + "scope": "Independent proof review and exact arithmetic. The frozen finite route-support enumerations are inspected dependencies; this review does not rerun or replace them. The capacity statement uses the full fixed-source regular-cover payload module. No changing-source, native-child, cache construction, or supplier claim." + } + (HERE / "QUERY-MOMENTS-REVIEW.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_query_support_distance.py b/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_query_support_distance.py new file mode 100644 index 0000000000..c5eff8c791 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_query_support_distance.py @@ -0,0 +1,87 @@ +"""Rebuild the exact source-distance facts without producer imports.""" + +from collections import defaultdict +from hashlib import sha256 +from itertools import product +from math import comb +from pathlib import Path +import gzip +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent + + +def require(value, message): + if not value: + raise ValueError(message) + + +def main(): + raw = (LANES / 'circuit-interface/INTERFACE.json').read_bytes() + require(sha256(raw).hexdigest() == '5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3', 'The interface pin differs') + source = json.loads(raw) + rows = [[int(row.get(str(p), '0')) for p in range(112)] for row in source['R']] + columns = list(zip(*rows)) + groups = defaultdict(list) + for column in columns: + support = tuple(i for i, value in enumerate(column) if value) + require(len(support) == 4, 'A column has the wrong support') + groups[support].append(column) + require(len(groups) == 14 and all(len(block) == 8 for block in groups.values()), 'The quartet sizes differ') + for support, block in groups.items(): + expected = {(1,) + signs for signs in product((-1, 1), repeat=3)} + found = {tuple(column[i] * column[support[0]] for i in support) for column in block} + require(found == expected, 'The exact sign set differs') + zero_bound = [0] + [2 * (comb(t, t // 2) // 2) for t in range(1, 5)] + # Count full four-sign patterns first, then identify opposite patterns. + table = [0] + [(16 - zero_bound[t] * 2 ** (4 - t)) // 2 for t in range(1, 5)] + require(table == [0, 8, 4, 6, 5], 'The antichain table differs') + minima = {} + all_bounds = {} + for signs in product((0, 1), repeat=8): + count = sum(signs) + if count == 0: + continue + bound = sum(table[sum(signs[i] for i in block)] for block in groups) + minima[count] = min(minima.get(count, bound), bound) + all_bounds[str(sum(value << i for i, value in enumerate(signs)))] = bound + require(minima == {1: 56, 2: 76, 3: 78, 4: 53, 5: 73, 6: 75, 7: 77, 8: 70}, 'A support minimum differs') + attaining = [sum(sum(a * b for a, b in zip(vector, col)) != 0 for col in columns) for vector in columns] + require(attaining == [53] * 112, 'The attained distance differs') + snap_raw = gzip.decompress((LANES / 'history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz').read_bytes()) + require(sha256(snap_raw).hexdigest() == '3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c', 'The snapshot pin differs') + maxima = {} + for U in json.loads(snap_raw)['frames']: + support = sum(all((q & v).bit_count() % 2 == 0 for v in U) for q in source['ports']) + maxima[len(U)] = max(maxima.get(len(U), 0), support) + require([maxima[r] for r in range(2, 9)] == [20, 10, 8, 8, 4, 2, 1], 'The frame support maxima differ') + path = LANES / 'history-encoding/QUERY-SUPPORT-DISTANCE.json' + producer = json.loads(path.read_bytes()) + require(all_bounds == producer['all_255_coefficient_support_bounds'], 'The independent support table differs') + proof = LANES / 'history-encoding/QUERY-SUPPORT-DISTANCE.md' + result = { + 'status': 'PASS_INDEPENDENT_QUERY_SUPPORT_DISTANCE_53_REVIEW', + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'proof_sha256': sha256(proof.read_bytes()).hexdigest(), + 'source_checker_sha256': sha256((LANES / 'history-encoding/check_query_support_distance.py').read_bytes()).hexdigest(), + 'source_receipt_sha256': sha256(path.read_bytes()).hexdigest(), + 'interface_sha256': sha256(raw).hexdigest(), 'snapshot_decompressed_sha256': sha256(snap_raw).hexdigest(), + 'quartet_count': len(groups), 'nonzero_table': table, 'support_size_minima': minima, + 'attaining_directions': 112, 'actual_frame_support_maxima': maxima, + 'proof_review': [ + 'A generic real projection keeps each nonzero coefficient nonzero and preserves every complex zero sum.', + 'Positive equal-sum subsets form an antichain. Opposite zero sign patterns give the even count bound.', + 'A scalar coefficient code with distance at least three remains injective after any two coordinate deletions.', + 'For block fields, choose a linear section of the surjective reconstruction map. Its kd-dimensional image has block distance at least three.', + ], + 'scope': 'A k-dimensional query span needs at least k+2 birth fields when each has source support at most20. This does not price a multilevel shared network.', + 'not_rerun': ['The full scalar core', 'The snapshot producer', 'A native cache program'], + 'findings': [], + } + (HERE / 'QUERY-SUPPORT-DISTANCE-REVIEW.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\n') + print(result['status']) + + +if __name__ == '__main__': + main() diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_rank5_union_cuts.py b/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_rank5_union_cuts.py new file mode 100644 index 0000000000..146f01ee90 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_rank5_union_cuts.py @@ -0,0 +1,177 @@ +"""Review the twelve rank-five query spaces and their unit-weight cuts.""" + +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent +SNAPSHOT_PIN = '3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c' +INTERFACE_PIN = '5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3' +CERTIFICATE_PIN = 'caf4ea536cc79ec7cd585b9f3d4714efc86874785cf463dc215d0158caff5607' +PROOF_PIN = 'd85d71839a600f7d8d0cb511530ca2d1169f0efa543f8c342d2b2cbfe9396629' +EXPECTED = {630, 631, 632, 633, 635, 637, 734, 735, 736, 737, 739, 741} + + +def require(value, message): + if not value: + raise ValueError(message) + + +def add(row, other, factor): + for j, value in other.items(): + new = row.get(j, 0) + factor * value + if new: + row[j] = new + else: + row.pop(j, None) + + +class Span: + def __init__(self): + self.rows = {} + + def reduce(self, row): + row = dict(row) + for pivot, old in sorted(self.rows.items()): + if pivot in row: + add(row, old, -row[pivot]) + return row + + def insert(self, row): + row = self.reduce(row) + if row: + pivot = min(row) + value = row[pivot] + self.rows[pivot] = {j: x / value for j, x in row.items()} + + +def bitspan(basis): + values = {0} + for v in basis: + values |= {x ^ v for x in tuple(values)} + return values + + +def rank(rows): + span = Span() + for row in rows: + span.insert(row) + return len(span.rows) + + +def main(): + raw = gzip.decompress((LANES / 'history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz').read_bytes()) + require(sha256(raw).hexdigest() == SNAPSHOT_PIN, 'Snapshot pin') + source = json.loads(raw) + interface_raw = (LANES / 'circuit-interface/INTERFACE.json').read_bytes() + require(sha256(interface_raw).hexdigest() == INTERFACE_PIN, 'Interface pin') + labels = json.loads(interface_raw)['ports'] + certificate_raw = (LANES / 'history-encoding/RANK5-UNION-CUTS.json').read_bytes() + require(sha256(certificate_raw).hexdigest() == CERTIFICATE_PIN, 'Certificate pin') + proof_raw = (LANES / 'history-encoding/LOW-BIRTH-UNION-CUTS.md').read_bytes() + require(sha256(proof_raw).hexdigest() == PROOF_PIN, 'Reviewed proof pin') + certificate = json.loads(certificate_raw) + cases = certificate['merges'] + require({case['merge_frame'] for case in cases} == EXPECTED and len(cases) == 12, 'Twelve distinct cases') + frames = source['frames'] + spaces = [bitspan(U) for U in frames] + final = [{int(j): F(x) for j, x in row.items()} for row in source['final_rows']] + R = [{int(j): F(x) for j, x in row.items()} for row in source['R']] + for p in range(112): + expected = {p: F(1)} + for q in range(112): + value = sum(row.get(p, 0) * row.get(q, 0) for row in R) / 4 - (p == q) + if value: + expected[112 + q] = value + require(final[p] == expected, 'A complete X row differs') + helpers = {j for j in range(224, 704) if source['final_frames'][j] == 1} + require(len(helpers) == 402 and all(final[j] == {j: F(1)} for j in helpers), 'The free helper baselines differ') + by_frame = {} + for _, _, _, frame, rowid in source['intervals']: + by_frame.setdefault(frame, set()).add(rowid) + reduced = {} + reports = [] + for case in cases: + merge = case['merge_frame'] + require(len(frames[merge]) == 5, 'Merge dimension') + nodes = sorted(u for u in by_frame if frames[u] and spaces[u] <= spaces[merge]) + edges = {(u, v) for u in nodes for v in nodes if spaces[u] < spaces[v]} + require(edges == {tuple(edge) for edge in case['edges']}, 'The complete actual edge set differs') + targets = [] + for coefficients in case['query_coefficients']: + row = {} + for i, value in coefficients.items(): + add(row, R[int(i)], F(value)) + targets.append(row) + require(len(targets) == rank(targets) == 5, 'Independent target rows') + observations = Span() + support_tests = 0 + for u in nodes: + allowed = {p for p, q in enumerate(labels) if all((q & v).bit_count() % 2 == 0 for v in frames[u])} + for rowid in by_frame[u]: + if rowid not in reduced: + row = {int(j): F(x) for j, x in source['rows'][rowid].items()} + for j in list(row): + if j < 112: + add(row, final[j], -row[j]) + reduced[rowid] = {j: x for j, x in row.items() if j not in helpers} + row = reduced[rowid] + require({j - 112 for j in row if 112 <= j < 224} <= allowed, 'An annihilating-input support differs') + observations.insert(row) + support_tests += 1 + require(all(not observations.reduce({112 + p: x for p, x in row.items()}) for row in targets), 'A target row is absent') + residuals = [observations.reduce({112 + p: x for p, x in row.items()}) for row in R] + require(8 - rank(residuals) == 5, 'Exact maximal query overlap differs') + + positive = [cut for cut in case['cuts'] if F(cut['weight'])] + require(len(positive) == 5 and all(F(cut['weight']) == 1 for cut in positive), 'Five unit-weight cuts') + cuts = [] + for cut in positive: + characters = set(cut['characters']) + ports = {p for p, q in enumerate(labels) + if sum(((q & v).bit_count() % 2) << i for i, v in enumerate(frames[merge])) in characters} + require(ports == set(cut['source_ports']), 'Source character classes differ') + inside = {u for u in nodes + if all(any((labels[p] & v).bit_count() % 2 for v in frames[u]) for p in ports)} + stated_inside = set(cut['inside_frames']) + require(stated_inside <= inside and merge in stated_inside, 'A cut admits a nonzero observation') + require(all(u not in stated_inside or v in stated_inside for u, v in edges), 'A cut is not upward closed') + demand = rank([{p: value for p, value in row.items() if p in ports} for row in targets]) + require(demand == cut['demand'] == 5, 'A target restriction is not injective') + cuts.append(stated_inside) + charges = [] + for u, v in sorted(edges): + charge = sum(u not in inside and v in inside for inside in cuts) + cost = len(frames[v]) - len(frames[u]) + require(charge <= cost, 'A native edge is overcharged') + charges.append(charge) + require(F(case['internal_bound']) == 25 and case['completion_bound'] == 20, 'The reported bound differs') + reports.append({'merge_frame': merge, 'exact_query_overlap': 5, + 'actual_nodes': len(nodes), 'actual_edges': len(edges), + 'support_tests': support_tests, 'positive_cuts': 5, + 'every_positive_cut_rank': 5, 'internal_bound_per_query': 5, + 'completion_bound_per_query': 4, 'total_bound_per_query': 9, + 'edge_charge_histogram': {str(c): charges.count(c) for c in sorted(set(charges))}}) + report = { + 'status': 'PASS_INDEPENDENT_RANK5_UNION_CUT_REVIEW', + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'snapshot_decompressed_sha256': SNAPSHOT_PIN, + 'interface_sha256': INTERFACE_PIN, + 'reviewed_certificate_sha256': sha256(certificate_raw).hexdigest(), + 'reviewed_proof_sha256': PROOF_PIN, + 'cases': reports, + 'scope': 'Every subspace of the exact maximal five-query space at each of the twelve listed rank-five frames costs at least nine rank units per query in the actual positive-frame common-merge network. Same-content monotone transport and no new observations after the merge are required. All source times are granted.', + 'not_checked': ['Other merge frames and the other displayed-space certificates in the proof', 'Synthetic intermediate frames', 'Cross-merge sharing', + 'Chronological native recipes', 'A global64 bound', 'Supplier pricing'], + } + (HERE / 'RANK5-UNION-CUTS-REVIEW.json').write_text(json.dumps(report, indent=2, sort_keys=True) + '\n') + print(report['status']) + print('Twelve exact five-query overlaps; five injective unit-weight cuts each; lower cost9k.') + + +if __name__ == '__main__': + main() diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_snapshot_support.py b/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_snapshot_support.py new file mode 100644 index 0000000000..76964357cf --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/review_snapshot_support.py @@ -0,0 +1,165 @@ +"""Check the snapshot support law with exact integer arithmetic.""" + +from collections import Counter +from fractions import Fraction +from hashlib import sha256 +from math import lcm +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +SNAPSHOT_PIN = "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c" +INTERFACE_PIN = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" +PRIME = 65521 + + +def require(value, message): + if not value: + raise ValueError(message) + + +def determinant(matrix): + """Use exact elimination on the selected eight-column minor.""" + rows = [[Fraction(x) for x in row] for row in matrix] + result = Fraction(1) + for col in range(len(rows)): + pivot = next((j for j in range(col, len(rows)) if rows[j][col]), None) + if pivot is None: + return Fraction(0) + if pivot != col: + rows[col], rows[pivot] = rows[pivot], rows[col] + result = -result + value = rows[col][col] + result *= value + for j in range(col + 1, len(rows)): + scale = rows[j][col] / value + for k in range(col + 1, len(rows)): + rows[j][k] -= scale * rows[col][k] + return result + + +def select_minor(matrix, columns): + """Select columns over a finite field, then check their exact minor.""" + size = len(matrix) + pivots = {} + selected = [] + for column in columns: + row = [matrix[k][column] % PRIME for k in range(size)] + for k, pivot in sorted(pivots.items()): + factor = row[k] + row = [(a - factor*b) % PRIME for a, b in zip(row, pivot)] + leading = next((k for k, value in enumerate(row) if value), None) + if leading is not None: + scale = pow(row[leading], -1, PRIME) + pivots[leading] = [value*scale % PRIME for value in row] + selected.append(column) + if len(selected) == size: + break + require(len(selected) == size, "An excluded-column block has deficient rank") + value = determinant([[row[p] for p in selected] for row in matrix]) + require(value != 0, "The selected rational minor is zero") + return selected, str(value) + + +def main(): + snapshot_path = HERE.parent / "history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz" + raw = gzip.decompress(snapshot_path.read_bytes()) + require(sha256(raw).hexdigest() == SNAPSHOT_PIN, "The snapshot pin differs") + data = json.loads(raw) + interface_path = HERE.parent / "circuit-interface/INTERFACE.json" + interface_raw = interface_path.read_bytes() + require(sha256(interface_raw).hexdigest() == INTERFACE_PIN, "The interface pin differs") + interface = json.loads(interface_raw) + labels = interface["ports"] + R = [[int(Fraction(row.get(str(j), "0"))) for j in range(112)] + for row in data["R"]] + require(R == [[int(Fraction(row.get(str(j), "0"))) for j in range(112)] + for row in interface["R"]], "The root matrices differ") + require(all(Fraction(v).denominator == 1 for row in data["R"] for v in row.values()), + "A root coefficient is not an integer") + require([[sum(a*b for a, b in zip(R[i], R[j])) for j in range(8)] + for i in range(8)] == [[56*int(i == j) for j in range(8)] for i in range(8)], + "The root Gram differs") + J4 = [{q: 4*int(p == q)-sum(row[p]*row[q] for row in R) + for q in range(112)} for p in range(112)] + J4 = [{q: value for q, value in row.items() if value} for row in J4] + reduced = [] + for item in data["rows"]: + row = {int(k): Fraction(value) for k, value in item.items() if int(k) < 224} + denominator = lcm(*(value.denominator for value in row.values())) + output = {} + for k, value in row.items(): + coefficient = int(value*denominator) + source = J4[k] if k < 112 else {k-112: 4} + for q, entry in source.items(): + output[q] = output.get(q, 0) + coefficient*entry + reduced.append({q: value for q, value in output.items() if value}) + failures = [] + full_nonzero = [] + support_checks = 0 + for first, last, wire, frame, row in data["intervals"]: + basis = data["frames"][frame] + for port in reduced[row]: + support_checks += 1 + if any((labels[port] & vector).bit_count() % 2 for vector in basis): + failures.append([first, last, wire, frame, row, port]) + if frame == 1 and reduced[row]: + full_nonzero.append(row) + require(not failures, "A snapshot violates the exact support law") + require(not full_nonzero, "A FULL snapshot remains nonzero on the test input") + minors = [] + for frame, basis in enumerate(data["frames"]): + if not 0 < len(basis) < 9: + continue + excluded = [p for p, q in enumerate(labels) + if any((q & v).bit_count() % 2 for v in basis)] + columns, value = select_minor(R, excluded) + minors.append({"frame": frame, "columns": columns, "determinant": value}) + normals = [42, 7, 25, 52, 82, 127, 97, 76] + require(all([n] not in data["frames"] for n in normals), "A normal line is an actual frame") + require(all({p for p, value in enumerate(R[k]) if value} + == {p for p, q in enumerate(labels) if (q & n).bit_count() % 2 == 0} + for k, n in enumerate(normals)), "The normal support relation differs") + line_minors = [] + for vector in range(1, 512): + excluded = [p for p, q in enumerate(labels) if (q & vector).bit_count() % 2] + omit = normals.index(vector) if vector in normals else None + selected_rows = [k for k in range(8) if k != omit] + columns, value = select_minor([R[k] for k in selected_rows], excluded) + if omit is not None: + require(all(R[omit][p] == 0 for p in excluded), "A normal line has the wrong kernel") + line_minors.append({"line": vector, "rank": len(selected_rows), + "rows": selected_rows, "columns": columns, + "determinant": value}) + source_proof = HERE.parent / "history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md" + source_receipt = HERE.parent / "history-encoding/SNAPSHOT-CONE-OBSTRUCTION.json" + result = { + "status": "PASS_EXACT_SNAPSHOT_SUPPORT_AND_SINGLE_CONE_EXCLUSION", + "inputs": {"snapshot_decompressed_sha256": SNAPSHOT_PIN, + "interface_sha256": INTERFACE_PIN, + "reviewed_source_proof_sha256": sha256(source_proof.read_bytes()).hexdigest(), + "reviewed_source_receipt_sha256": sha256(source_receipt.read_bytes()).hexdigest()}, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "rows": len(reduced), "intervals": len(data["intervals"]), + "nonzero_port_incidence_checks": support_checks, + "proper_frame_minor_count": len(minors), + "minor_determinants": dict(Counter(item["determinant"] for item in minors)), + "excluded_column_minors": minors, + "all_511_line_minors": line_minors, + "line_rank_counts": dict(Counter(item["rank"] for item in line_minors)), + "normal_lines_absent": normals, + "test_input": "X=JY; all 480 helper and eight private inputs are zero", + "scope": "One nonzero birth frame and all later containing frames. This does not exclude a merged network with incomparable capture frames.", + "phase_scope": "Scalar rows are read in the canonical view. Non-FULL views after event 17605 require the supplied endpoint monomial adapter.", + "not_checked": ["The full snapshot producer replay", "A new native cache word", "Chronological branching synthesis", "A complete supplier invoice"], + } + output = HERE / "SNAPSHOT-SUPPORT-REVIEW.json" + output.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(json.dumps({k: v for k, v in result.items() + if k not in {"excluded_column_minors", "all_511_line_minors"}}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/payload/lanes/cover-algebra/verify_algebra.py b/research/actual-query-information-bounds/payload/lanes/cover-algebra/verify_algebra.py new file mode 100644 index 0000000000..cebca25849 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/cover-algebra/verify_algebra.py @@ -0,0 +1,248 @@ +"""Check exact relations between the routed centre projections.""" + +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import json + + +INTERFACE_SHA256 = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def dot(a, b): + return (a & b).bit_count() & 1 + + +def chart_basis(q): + zero = next(i for i in range(9) if not ((q >> i) & 1)) + v = q ^ (1 << zero) + out = [] + for i in range(9): + x = 1 << i + if zero and ((x & 1) != ((x >> zero) & 1)): + x ^= 1 | (1 << zero) + out.append(x ^ (v if dot(v, x) else 0)) + require(out[0] == q, "The first chart vector is not the port") + require(all(dot(a, b) == (i == j) + for i, a in enumerate(out) for j, b in enumerate(out)), + "A chart basis is not orthogonal") + return out + + +def route_column(x, stage, basis): + if not stage: + return x + offset = 9 + 8 * (stage - 1) + out = x & ~((1 << 9) - 1 | ((1 << 8) - 1) << offset) + out ^= basis[0] if dot(x, basis[0]) else 0 + for i, v in enumerate(basis[1:]): + out ^= 1 << (offset + i) if dot(x, v) else 0 + out ^= v if (x >> (offset + i)) & 1 else 0 + return out + + +def act(matrix, x): + out = 0 + while x: + bit = x & -x + out ^= matrix[bit.bit_length() - 1] + x ^= bit + return out + + +def mul(a, b): + return tuple(act(a, x) for x in b) + + +def packed(matrix): + return b"".join(x.to_bytes(3, "little") for x in matrix) + + +def gram(columns): + return [[sum(x * y for x, y in zip(a, b)) for b in columns] + for a in columns] + + +def sparse_corner(a, products, row=0): + out = Counter() + for i in range(112): + if not a[row][i]: + continue + for j in range(112): + value = a[row][i] * a[i][j] * a[j][row] + if value: + out[products[i, j]] += value + return {g: value for g, value in out.items() if value} + + +def sixth_moment(a, routes, products): + # The coefficient at each group element is a sum of rank-one matrices. + # Store their two endpoint indices and integer coefficients. + coefficients = {} + numerator = 0 + for i in range(112): + for j in range(112): + if not a[i][j]: + continue + left = products[i, j] + for k in range(112): + scale = a[i][j] * a[j][k] + if not scale: + continue + key = packed(mul(left, routes[k])) + old = coefficients.setdefault(key, []) + numerator += 16 * scale * scale + numerator += 2 * scale * sum( + value * a[i][u] * a[k][v] for u, v, value in old) + old.append((i, k, scale)) + return Q(numerator, 56 ** 6), { + "group_elements": len(coefficients), + "walks": sum(map(len, coefficients.values())), + "collision_distribution": dict(sorted(Counter(map(len, coefficients.values())).items())), + } + + +def run(interface, with_sixth_moment=False): + raw = interface.read_bytes() + require(sha256(raw).hexdigest() == INTERFACE_SHA256, "The interface source pin changed") + data = json.loads(raw) + ports = data["ports"] + columns = [tuple(int(data["R"][r].get(str(i), "0")) for r in range(8)) + for i in range(112)] + a = gram(columns) + require(all(sum(columns[i][r] * columns[i][s] for i in range(112)) == + 56 * (r == s) for r in range(8) for s in range(8)), "R R^T") + require(Counter(v for row in a for v in row) == + {0: 6608, 2: 3920, -2: 1904, 4: 112}, "The Gram entry counts") + require(all(not a[i][j] or i == j or not dot(ports[i], ports[j]) + for i in range(112) for j in range(112)), "The edge orthogonality") + bases = [chart_basis(q) for q in ports] + routes = [tuple(route_column(1 << i, 1, basis) for i in range(17)) + for basis in bases] + identity = tuple(1 << i for i in range(17)) + require(all(mul(g, g) == identity for g in routes), "A route is not an involution") + products = {(i, j): mul(routes[i], routes[j]) + for i in range(112) for j in range(112) if a[i][j]} + collisions = {} + for pair, g in products.items(): + collisions.setdefault(g, []).append(pair) + require(Counter(map(len, collisions.values())) == {1: 5824, 112: 1}, + "The edge products are not distinct") + require(collisions[identity] == [(i, i) for i in range(112)], + "An edge product is the identity") + # Check the kernel and image certificates of every nonidentity local block. + for (i, j), g in products.items(): + if i == j: + continue + local = tuple(x & 511 for x in g[:9]) + require(act(local, ports[j]) == 0, "The local kernel certificate") + require(all(not dot(ports[i], x) for x in local), "The local image certificate") + require(len({act(local, x) for x in range(512)}) == 256, "The local block rank") + + corner = sparse_corner(a, products) + g01 = products[0, 1] + require(corner[g01] == 16, "The isoclinic witness") + left_commutator = Counter() + for i in range(112): + if a[0][i]: + left_commutator[products[i, 0]] += a[0][i] ** 2 + left_commutator[products[0, i]] -= a[0][i] ** 2 + require(left_commutator[g01] == -4, "The commutator witness") + conjugated = {mul(mul(routes[0], g), routes[0]): value + for g, value in corner.items()} + defect = {g: corner.get(g, 0) - conjugated.get(g, 0) + for g in corner.keys() | conjugated.keys() + if corner.get(g, 0) != conjugated.get(g, 0)} + require(bool(defect), "The braid obstruction did not hold") + witness = min(defect) + + # The coefficient of identity defines the normalized trace on a regular cover. + second_numerator = sum(a[i][j] ** 2 for i in range(112) for j in range(112)) + second_numerator *= 16 + second_numerator += 16 * sum(a[i][j] ** 2 + for i in range(112) for j in range(112) if i != j) + moment1 = Q(112 * 16, 56 ** 2) + moment2 = Q(second_numerator, 56 ** 4) + require((moment1, moment2) == (Q(4, 7), Q(27, 343)), "The trace moments") + difference_second = 16 - 2 * moment1 + difference_fourth = 16 - 4 * moment1 + 2 * moment2 + rank_bound = difference_second ** 2 / difference_fourth + require(rank_bound == Q(2912, 183), "The rank bound") + + star_checks = 0 + identity73 = tuple(1 << i for i in range(73)) + for basis in bases: + stages = [identity73] + [tuple(route_column(1 << i, s, basis) for i in range(73)) + for s in range(1, 9)] + for s in range(1, 9): + for t in range(s + 1, 9): + expected = list(identity73) + for k in range(8): + i, j = 9 + 8 * (s - 1) + k, 9 + 8 * (t - 1) + k + expected[i], expected[j] = expected[j], expected[i] + require(mul(mul(stages[s], stages[t]), stages[s]) == tuple(expected), + "The star-transposition relation") + star_checks += 1 + + result = { + "status": "PASS_EXACT_ROUTED_PROJECTION_ALGEBRA", + "interface_sha256": INTERFACE_SHA256, + "source_base": data["base"], + "arithmetic": "Integer group coefficients and Fraction", + "representation": "Full binary orthogonal matrices; no phase specialization", + "gram_entry_distribution": dict(sorted(Counter(v for row in a for v in row).items())), + "distinct_nonidentity_edge_products": 5824, + "star_transposition_checks": star_checks, + "corner_port": ports[0], + "noncommutation_witness": { + "group_columns": list(g01), + "coefficient_in_commutator_P0_P1_corner_0_0": str(Q(-4, 56 ** 2)), + }, + "nonisoclinic_witness": { + "group_columns": list(g01), + "coefficient_in_P0_P1_P0_corner_0_0": str(Q(16, 56 ** 3)), + "coefficient_in_any_scalar_multiple_of_P0": "0", + }, + "nonbraid_witness": { + "group_columns": list(witness), + "coefficient_in_P0_P1_P0_minus_P1_P0_P1_corner_0_0": str(Q(defect[witness], 56 ** 3)), + "coefficient_in_K0_K1_K0_minus_K1_K0_K1_corner_0_0": str(Q(-14 ** 3 * defect[witness], 56 ** 3)), + }, + "normalized_trace_P0": "8", + "normalized_trace_P0_P1": str(moment1), + "normalized_trace_P0_P1_squared": str(moment2), + "normalized_trace_P0_minus_P1_squared": str(difference_second), + "normalized_trace_P0_minus_P1_fourth_power": str(difference_fourth), + "common_range_dimension_upper_bound_per_cover_element": "8/183", + "equal_J_subspace_codimension_lower_bound_per_cover_element": str(rank_bound), + "scope": "Exact group-algebra relations and a full-cover dimension bound. No changed supplier, paid router, or kappa claim.", + } + if with_sixth_moment: + moment3, details = sixth_moment(a, routes, products) + result["normalized_trace_P0_P1_cubed"] = str(moment3) + result["sixth_moment_calculation"] = details + h3 = (moment1 * moment3 - moment2 ** 2) / (moment1 - 2 * moment2 + moment3) + result["common_range_dimension_upper_bound_from_third_moment"] = str(h3) + result["equal_J_subspace_codimension_lower_bound_from_third_moment"] = str(16 - 2 * h3) + result["isoclinic_braid_third_moment_required"] = str((1 + Q(13, 196)) * moment2 - Q(13, 196) * moment1) + return result + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--interface", type=Path, required=True) + parser.add_argument("--out", type=Path, required=True) + parser.add_argument("--sixth-moment", action="store_true") + args = parser.parse_args() + result = run(args.interface, args.sixth_moment) + args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(result["status"]) + print("edge_products=5824 TL=false commute=false braid=false") + print("trace_PQ=4/7 trace_PQPQ=27/343 common_J_codimension>=2912/183") diff --git a/research/actual-query-information-bounds/payload/lanes/encoded-controller/CONTROLLER-CHECKS.json b/research/actual-query-information-bounds/payload/lanes/encoded-controller/CONTROLLER-CHECKS.json new file mode 100644 index 0000000000..ac1f93a8a5 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/encoded-controller/CONTROLLER-CHECKS.json @@ -0,0 +1,63 @@ +{ + "actual_controller_uses_each_stage_once": true, + "all_nonzero_pairs_change_to_orthogonal_ports": true, + "centre_free_nonzero_port_pairs": 5824, + "empty_paths_preserve_xy_side": true, + "external_block_other_stage_checks": 57344, + "external_block_pair_checks": 12544, + "external_displacement_rank_distribution": { + "0": 112, + "1": 100, + "2": 4474, + "3": 6140, + "4": 1718 + }, + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "not_claimed": [ + "An obstruction to bridges in the full completed-frame stabilizer.", + "An obstruction to repeated stages or a changed endpoint encoding.", + "An admitted algebraic-coefficient compiler.", + "A new supplier or kappa bound." + ], + "old_controller_identity_checked": true, + "rank_bill": { + "centre_free_local": 5522, + "free_coefficient_arithmetic_granted_for_this_screen": true, + "local_data": 1792, + "local_helpers": 3730, + "maximum_productive_mass_including_ideal_helper_hosting": 28126, + "old_local": 5586, + "seven_calls_paid": 38654, + "unavoidable_excess_in_this_fixed_chart_realization": 10528 + }, + "repeated_stage_escape": { + "inverse_pair_word_is_identity": true, + "moved_external_coordinates": [ + 0, + 1, + 2, + 3 + ], + "port_indices": [ + 1, + 0 + ], + "port_values": [ + 19, + 11 + ] + }, + "single_pass_endpoint_witness": { + "actual": "The same X bank, port p, and class d receives zero after the fixed terminal exchange.", + "input": "One X bank, one port p, one cover class d, one nonzero native vector.", + "required": "The full invertible native transform of that nonzero input.", + "scope": "One call per stage, intermediate port-preserving and cover-preserving bridges that preserve X/Y side, fixed endpoint frames and terminal exchange." + }, + "source_base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "source_pins": { + "slots/local/CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219", + "slots/local/LOCAL-CHECKS.json": "2b8b1891a736598010232bfb26abc31973b265a53a2009a3fcfd9138b5ecadb4", + "t16/global/base/split-centres/GLOBAL-TEMPLATE.json.gz": "a179dad87651aba340a5a8ddbcd86a8e757cad87b8a1f8bad48106fbecd38518" + }, + "status": "PASS_SINGLE_PASS_CHART_PREMISES_AND_FIXED_CHART_BILL" +} diff --git a/research/actual-query-information-bounds/payload/lanes/encoded-controller/CONTROLLER.md b/research/actual-query-information-bounds/payload/lanes/encoded-controller/CONTROLLER.md new file mode 100644 index 0000000000..ccebde0918 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/encoded-controller/CONTROLLER.md @@ -0,0 +1,202 @@ +# Controller consequences of the centre-free interface + +This note uses base `bce54fb3f895cbe5cd4c0eb477c3afeed100190f` and the +centre-free scalar interface in the adjacent circuit-interface lane. It does +not admit a new supplier. It gives a proof for a restricted controller class +and prices a repeated-chart realization of the seven-shear identity. + +## 1. The native endpoint that the controller must meet + +Let `Q` be the diagonal operator whose port `p`, cover class `d` component is +the native line operator `C_(d q_p)` to tensor power lambda. Let `F_s` be the +full native operator on the first `9+8s` axes, transported by `d`. The exact +stage phase corrections in the pinned `DATA-PHASES.json` give these boundary +frames: + +* At entry: `(Q,I)` on the X and Y banks. +* After stage s: `(F_s,F_s Q^-1)` on the active X and Y banks. +* After all idle work: `(F_8,F_8 Q^-1)` on every data pair. + +Write `D_s` for the port-dependent cover router from the actual controller. +For s greater than zero, its port component is the involution `rho_s(q_p)`. +This involution fixes `q_p`, exchanges its eight-dimensional orthogonal +complement in the first nine axes with the new external block `E_s`, and +fixes all other external blocks. `D_0=I`. + +The abstract local shear therefore uses + + K_s = D_s^-1 J D_s, J = I - R^T R/4. + +This is a statement about the scalar content in the actual moving frames. +It does not replace all the `K_s` by one matrix J. + +Let C be the product of the abstract local shears and intermediate bridges, +before the terminal operation. In the physical coordinates its endpoint is + + diag(F_8,F_8 Q^-1) C diag(Q^-1,I). + +The prescribed terminal operation first translates Y by `Q^2`, then uses +`W=[[0,I],[-I,0]]`. Since every line operator commutes with `F_8`, the final +physical map, before the fixed full-cover phase correction, is + + F_8 diag(Q,I) W C diag(Q^-1,I). + +Thus the required full native transform on every original data family is +equivalent to `C=W^-1`. A free terminal bank exchange alone does not meet this +equation. Its input frames differ, and the factors Q remain in the equation. + +## 2. A single-pass obstruction for the retained bridge class + +The following hypotheses define the claim. + +1. Each stage is used at most once on each path through the controller. +2. Every intermediate bridge preserves each port and cover class and maps + X banks to X banks and Y banks to Y banks. Its coefficients and its mixing + among banks on the same side can be arbitrary. +3. The entry frames, final frames, and terminal operation are those in + Section 1. There is only one stage-zero local call on a path. + +The actual nine-stage recipe has these properties. The claim permits changes +to its scalar coefficients and same-side bank bridges. It does not cover +arbitrary physical bank exchanges, port changes, or completed-frame routers. + +**Theorem.** Under these hypotheses, no controller made only from the +centre-free local shears can perform the required native transform. + +**Proof.** Each column of R has squared norm four. Hence every diagonal entry +of J is zero. Each nonzero entry `J[q,p]` changes the port. Its two ports are +orthogonal in the binary native geometry. + +For s greater than zero, let `B_p:F_2^8 -> q_p^perp` be the orthogonal basis +map used by `rho_s(q_p)`. A nonzero entry in `K_s` has cover permutation + + g_s(q,p) = rho_s(q) rho_s(p), q != p. + +This permutation does not fix `E_s` pointwise. If it did, multiplication by +`rho_s(q)` would give `B_p v=B_q v` for all v. The two orthogonal complements +would be equal. Their perpendicular lines, and thus their nonzero binary +vectors p and q, would be equal. This is a contradiction. + +Expand a controller matrix entry as a sum over paths. If a path uses a +nonidentity term from stage s greater than zero, all other factors on that +path fix `E_s` pointwise: other stages act on other external blocks, and the +allowed bridges do not change the cover. The pointwise stabilizer of `E_s` +is a group. A product with exactly one factor outside that group cannot be +the identity. Thus this path cannot contribute to the identity cover +permutation. + +A path with no positive-stage local term can use only the stage-zero local +term. A single such term changes its port, since J has zero diagonal. A path +with no local term remains on the same X/Y side. It follows that every +same-port, same-cover coefficient from X to Y, or from Y to X, is zero. +`W^-1` has nonzero coefficients there. Therefore `C != W^-1`. + +For a physical witness, place a nonzero native vector in one X bank at one +port and cover class, and set the other data to zero. The same X bank, port, +and cover class receives zero after the fixed terminal exchange. The required +full native transform has a nonzero value there because it is invertible. +The diagonal native phase factors do not change the port or cover class. +This proves failure of the full normalized endpoint, not only of a chosen +scalar coefficient. QED. + +The finite verifier checks all 12,544 port pairs, all 5,824 nonzero J entries, +the external-block premise, and the actual controller recipe. The group +argument proves the statement for all paths and all tensor powers. Finite +enumeration of the full orthogonal group is not used. + +## 3. What a repeated chart makes possible + +The previous theorem has a real escape. If a stage is repeated, a port path +`p -> q -> p` can have cover permutation + + rho_s(p) rho_s(q) rho_s(q) rho_s(p) = I. + +In fact `J^2+12J-13I=0`. The root lane found a seven-shear word that equals W +at both eigenvalues of J, and the bounds-review lane checked it independently +in an exact cubic quotient ring. The scalar identity can be placed in a +single native chart without treating frame transitions as free. + +In that chart let F be the full nine-dimensional native operator, and put + + A=diag(I,Q^-1), B=diag(Q^-1,I), M(t)=F A U(tJ) B. + +The upper-shear variant `U(tJ)` is obtained from the backward orientation by +scalar conjugation. For this algebraic statement, grant exact arithmetic in +the coefficient field. The current dyadic compiler does not yet implement +those fixed algebraic coefficients. + +The native bridge + + V=B^-1 W A^-1=diag(Q^2,I) W + +is a signed bank exchange and a port-dependent translation. It has rank zero. +All C line operators commute with F. Thus inserting V between seven calls +gives + + M_7 V M_6 V ... V M_1 + = F^7 A (S_7 W S_6 W ... W S_1) B. + +If the verified alternating seven-shear coefficients are +`(a,b,c,d,c,b,a)`, choose all seven S factors to be upper shears, with +coefficients `(a,-b,c,-d,c,-b,a)`. The parenthesized product is `-W`. +Since `F^2` and `Q^2` are translations, one final rank-zero bridge converts +the result into F on both data banks. This is an exact native block identity +for every tensor power, conditional on the local scaled shear interface. +It gives one full nine-dimensional transform, rather than seven fresh +eight-dimensional advances. + +## 4. The fixed-chart bill + +The pinned provider has local rank mass + + 5586 = 1792 data + 3730 helper + 64 centre. + +The centre-free provider has rank mass 5522. Seven calls therefore cost +38,654 rank units. They perform a full rank-nine transform on 224 data +families, for data mass 2,016. Even if every helper residual is usefully +hosted, their useful helper mass is at most `7*3730=26110`. The total useful +mass is at most 28,126. The excess is 10,528 rank units. + +This count grants coefficient arithmetic, all bridges, and perfect helper +hosting for free. It already rules out a positive rank deficit for this +fixed-chart realization. Additional scalar, precision, storage, or routing +charges cannot fix it. This is not a lower bound for all controllers that +repeat stages. + +## 5. Next construction questions + +The retained bridge class is smaller than the legal physical router class. +At boundary s, a router that preserves `U_s` is legal on X. A sufficient +condition on a Y router is that it also transports the new port line to the +old one. This condition is not necessary. The actual Y frame is +`H_s(q)=U_s intersect q-perp`. A Y-only router can preserve this hyperplane +while mixing its missing line with unused future directions. The old +controller names that missing line, but this label does not itself prove +that a new controller must preserve it. Such routers invalidate the +pointwise-stabilizer proof above. The cover-algebra lane is checking their +exact phases and their use in a construction. + +There is also a legal full-boundary correction. Normalize every final Y bank +by Q, apply the inverse abstract controller at the common full frame, and +normalize every X bank by Q. Orthogonal cover routing at that full frame has +only the known phase correction. This costs one rank-one line transform per +data family: 896 units per replica, versus 576 removed centre units. It loses +the old 320-unit deficit. A lower-dimensional syndrome correction could be +better; the residual-syndrome lane is checking that question. + +No claim here excludes those two construction routes. + +## Reproduction + +From the workspace root, run: + +```sh +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/encoded-controller/verify_controller.py \ + --repo worktrees/k5-centre-sharing \ + --interface work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json \ + --out work/centre-encoding-campaign-20261014/lanes/encoded-controller/CONTROLLER-CHECKS.json +``` + +Expected status: `PASS_SINGLE_PASS_CHART_PREMISES_AND_FIXED_CHART_BILL`. +No full supplier replay, algebraic-coefficient compilation, or exponent +calculation is claimed. 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zK|8LY9oK9k)IzB9*XOS=n>9tWY}L-5BGMHy(-kt2UMAAZO!cx-y{v}zxz!nLpe^P5 zGd+jRl>JH(J4K{g+-%$3mBAW{Q+8)Cv}RE>XuqOC;PHM%gan1co{hquQwaN05vu() zTB6g_0cHSzhdJY(*Wj|o_mHFK#l=96JQp=Y{2K_ zmlm;*zU`EQuQbelT z_GQ5>!KB)4CzsL-z*K-~e`ScCB1Ve%vfP?rW-4U?DH~u;jv3iE^;fofhDdcgzAU#S zm{hyNfRqU^3t)E2=41#= 3 * 1024**3, + "At least 3 GiB of free disk space is required") + import sympy + manifest = load(PACKAGE / "SOURCE-MANIFEST.json") + for entry in manifest["files"]: + require(sha(PACKAGE / entry["path"]) == entry["sha256"], + "A source hash differs: " + entry["path"]) + output.mkdir() + work = output / "work" + shutil.copytree(PACKAGE / "payload", work) + lanes = work / "lanes" + frozen = PACKAGE / "payload/lanes" + report = { + "status": "RUNNING", + "python": sys.version, + "sympy": sympy.__version__, + "source_manifest_sha256": sha(PACKAGE / "SOURCE-MANIFEST.json"), + "replay_sha256": sha(Path(__file__)), + "source_files_checked": len(manifest["files"]), + "checks": [], + "omitted": [ + "The optional sixth-moment extension of the cover theorem", + "Search and LP routines used to find cut certificates", + "A new native-phase sweep or complete supplier replay", + "An application to the 22 October 2026 selected frontier", + ], + } + env = dict(os.environ) + env.update(OMP_NUM_THREADS="1", OPENBLAS_NUM_THREADS="1", MKL_NUM_THREADS="1", + VECLIB_MAXIMUM_THREADS="1", NUMEXPR_NUM_THREADS="1", PYTHONDONTWRITEBYTECODE="1") + provenance_changes = [] + + def expected(relative, updates=None): + result = load(frozen / relative) + for key, value in (updates or {}).items(): + provenance_changes.append({"receipt": relative, "field": key, + "historical": result[key], "portable": value}) + result[key] = value + return result + + cases = [] + binding = load(frozen / "temporal-reuse/SPECTRAL-BOUND-REVIEW.json")["source_reconstruction"] + binding["status"] = "PASS_REVERSE_SOURCE_MATRIX_BINDING" + cases.append(("source-matrix", "temporal-reuse/check_source_matrix.py", [], + "temporal-reuse/SOURCE-MATRIX-BINDING.json", binding)) + cases.append(("fourth-moment", "temporal-reuse/check_query_fourth_moment.py", [], + "temporal-reuse/QUERY-FOURTH-MOMENT.json", expected("temporal-reuse/QUERY-FOURTH-MOMENT.json"))) + cases.append(("fifth-moment", "temporal-reuse/check_query_fifth_moment.py", [], + "temporal-reuse/QUERY-FIFTH-MOMENT.json", expected("temporal-reuse/QUERY-FIFTH-MOMENT.json"))) + moment_pins = {name: sha(frozen / "temporal-reuse" / name) for name in + ("QUERY-MOMENTS.md", "check_query_fourth_moment.py", "QUERY-FOURTH-MOMENT.json", + "check_query_fifth_moment.py", "QUERY-FIFTH-MOMENT.json")} + cases.append(("moment-review", "cover-algebra/review_query_moments.py", [], + "cover-algebra/QUERY-MOMENTS-REVIEW.json", + expected("cover-algebra/QUERY-MOMENTS-REVIEW.json", { + "source_pins": moment_pins, + "checker_sha256": sha(frozen / "cover-algebra/review_query_moments.py")}))) + cases.append(("complete-snapshot-rows", "circuit-interface/snapshot-audit/review_snapshot_rows.py", [], + "circuit-interface/snapshot-audit/SNAPSHOT-ROWS-REVIEW.json", + expected("circuit-interface/snapshot-audit/SNAPSHOT-ROWS-REVIEW.json", { + "reviewer_sha256": sha(frozen / "circuit-interface/snapshot-audit/review_snapshot_rows.py")}))) + for name, script, receipt in [ + ("snapshot-cones", "history-encoding/check_snapshot_cone_obstruction.py", "history-encoding/SNAPSHOT-CONE-OBSTRUCTION.json"), + ("snapshot-support-review", "cover-algebra/review_snapshot_support.py", "cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json"), + ("support-distance", "history-encoding/check_query_support_distance.py", "history-encoding/QUERY-SUPPORT-DISTANCE.json"), + ("support-distance-review", "cover-algebra/review_query_support_distance.py", "cover-algebra/QUERY-SUPPORT-DISTANCE-REVIEW.json"), + ("global-cut-42", "cover-algebra/check_snapshot_flag_cut.py", "cover-algebra/SNAPSHOT-FLAG-CUT.json"), + ("global-cut-42-review", "history-encoding/review_snapshot_flag_cut.py", "history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.json"), + ("rank5-cuts-review", "cover-algebra/review_rank5_union_cuts.py", "cover-algebra/RANK5-UNION-CUTS-REVIEW.json"), + ("rank8-cuts-review", "cover-algebra/review_movable_rank8_cuts.py", "cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.json"), + ]: + cases.append((name, script, [], receipt, expected(receipt))) + algebra = expected("cover-algebra/ALGEBRA.json") + for key in ("normalized_trace_P0_P1_cubed", "sixth_moment_calculation", + "common_range_dimension_upper_bound_from_third_moment", + "equal_J_subspace_codimension_lower_bound_from_third_moment", + "isoclinic_braid_third_moment_required"): + del algebra[key] + cases.append(("cover-algebra", "cover-algebra/verify_algebra.py", + ["--interface", "{lanes}/circuit-interface/INTERFACE.json", "--out", "{lanes}/cover-algebra/ALGEBRA.json"], + "cover-algebra/ALGEBRA.json", algebra)) + cases.append(("cover-review", "source-domain/review_cover.py", + ["--source-dir", "{work}/upstream", "--campaign", "{work}", "--out", "{lanes}/source-domain/COVER-REVIEW.json"], + "source-domain/COVER-REVIEW.json", expected("source-domain/COVER-REVIEW.json"))) + cases.append(("residual", "residual-syndrome/verify_residual.py", + ["--source-dir", "{work}/upstream", "--interface", "{lanes}/circuit-interface/INTERFACE.json", "--out", "{lanes}/residual-syndrome/RESIDUAL.json"], + "residual-syndrome/RESIDUAL.json", expected("residual-syndrome/RESIDUAL.json"))) + cases.append(("residual-review", "residual-syndrome/review/independent_residual.py", [], + "residual-syndrome/review/INDEPENDENT-RECEIPT.json", expected("residual-syndrome/review/INDEPENDENT-RECEIPT.json"))) + report["portable_receipt_provenance_changes"] = provenance_changes + started = time.monotonic() + try: + for name, script, arguments, receipt, target in cases: + require(shutil.disk_usage(output).free >= 3 * 1024**3, + "Free disk space fell below 3 GiB") + command = [sys.executable, "-I", "-O", "-B", str(lanes / script)] + command += [arg.format(work=work, lanes=lanes) for arg in arguments] + begin = time.monotonic() + run = subprocess.run(command, cwd=work, env=env, text=True, capture_output=True) + (output / (name + ".log")).write_text(run.stdout + run.stderr) + require(run.returncode == 0, name + " failed; inspect its log") + actual = load(lanes / receipt) + require(canonical(actual) == canonical(target), name + " receipt differs") + report["checks"].append({"name": name, "status": actual["status"], + "seconds": round(time.monotonic() - begin, 3), + "receipt": "work/lanes/" + receipt, + "receipt_sha256": sha(lanes / receipt), + "exact_typed_json_match": True}) + print(name + ": " + actual["status"], flush=True) + (output / "REPLAY.json").write_text(json.dumps(report, indent=2, sort_keys=True) + "\n") + report["status"] = "PASS_ACTUAL_QUERY_INFORMATION_BOUNDS_PACKAGE" + except Exception as error: + report["status"] = "FAIL" + report["error"] = str(error) + raise + finally: + report["seconds"] = round(time.monotonic() - started, 3) + (output / "REPLAY.json").write_text(json.dumps(report, indent=2, sort_keys=True) + "\n") + print(report["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/validation/REPLAY.json b/research/actual-query-information-bounds/validation/REPLAY.json new file mode 100644 index 0000000000..e5d4eb9e70 --- /dev/null +++ b/research/actual-query-information-bounds/validation/REPLAY.json @@ -0,0 +1,185 @@ +{ + "checks": [ + { + "exact_typed_json_match": true, + "name": "source-matrix", + "receipt": "work/lanes/temporal-reuse/SOURCE-MATRIX-BINDING.json", + "receipt_sha256": "b3661339df9a160a078bf3c26fbe23bb1d389d5b3411ce63f0db6b4309bd3870", + "seconds": 0.166, + "status": "PASS_REVERSE_SOURCE_MATRIX_BINDING" + }, + { + "exact_typed_json_match": true, + "name": "fourth-moment", + "receipt": "work/lanes/temporal-reuse/QUERY-FOURTH-MOMENT.json", + "receipt_sha256": "df32110bbd285e3036bdb2082e3307b24edc7515953cab7a1b3b6b684adc1e66", + "seconds": 5.145, + "status": "PASS_ACTUAL_QUERY_FOURTH_MOMENT" + }, + { + "exact_typed_json_match": true, + "name": "fifth-moment", + "receipt": "work/lanes/temporal-reuse/QUERY-FIFTH-MOMENT.json", + "receipt_sha256": "562d05a6f830f88d36efc148f81a01f3dfa95afbcab8195a9b5add02a5fdb742", + "seconds": 7.271, + "status": "PASS_ACTUAL_QUERY_FIFTH_MOMENT" + }, + { + "exact_typed_json_match": true, + "name": "moment-review", + "receipt": "work/lanes/cover-algebra/QUERY-MOMENTS-REVIEW.json", + "receipt_sha256": "479289a3444327e49d6c50619074c5dc596463b82d1ec4826a1e664f8ba1af23", + "seconds": 0.225, + "status": "PASS_INDEPENDENT_QUERY_MOMENT_PROOF_AND_ARITHMETIC_REVIEW" + }, + { + "exact_typed_json_match": true, + "name": "complete-snapshot-rows", + "receipt": "work/lanes/circuit-interface/snapshot-audit/SNAPSHOT-ROWS-REVIEW.json", + "receipt_sha256": "099dd4a8e7c5b48eb9536c20c5812c875dbefb9dee819204c75650da67cb9cdd", + "seconds": 3.458, + "status": "PASS_INDEPENDENT_BACKWARD_SNAPSHOT_ROWS" + }, + { + "exact_typed_json_match": true, + "name": "snapshot-cones", + "receipt": "work/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.json", + "receipt_sha256": "35698700474f2309a4eea2f192a5afbd2f42f580a7e0e510a0bb5687a87fdc2d", + "seconds": 4.341, + "status": "PASS_EXACT_SNAPSHOT_CONE_OBSTRUCTION" + }, + { + "exact_typed_json_match": true, + "name": "snapshot-support-review", + "receipt": "work/lanes/cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json", + "receipt_sha256": "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7", + "seconds": 2.378, + "status": "PASS_EXACT_SNAPSHOT_SUPPORT_AND_SINGLE_CONE_EXCLUSION" + }, + { + "exact_typed_json_match": true, + "name": "support-distance", + "receipt": "work/lanes/history-encoding/QUERY-SUPPORT-DISTANCE.json", + "receipt_sha256": "6c22878f6259772183263ae192422f8089113a11629662aee31fd82cea4824ce", + "seconds": 0.273, + "status": "PASS_EXACT_QUERY_SUPPORT_MINIMUM_53" + }, + { + "exact_typed_json_match": true, + "name": "support-distance-review", + "receipt": "work/lanes/cover-algebra/QUERY-SUPPORT-DISTANCE-REVIEW.json", + "receipt_sha256": "720824f618aadb2b8d5c2e56709157009e3b8915eef2119c856ba7f478ea0050", + "seconds": 0.274, + "status": "PASS_INDEPENDENT_QUERY_SUPPORT_DISTANCE_53_REVIEW" + }, + { + "exact_typed_json_match": true, + "name": "global-cut-42", + "receipt": "work/lanes/cover-algebra/SNAPSHOT-FLAG-CUT.json", + "receipt_sha256": "2c001f0336c1f930a41eace304e957eb5da354edc56c4c9b0449bf253d65fb25", + "seconds": 0.295, + "status": "PASS_SHARED_MONOTONE_CACHE_DAG_LOWER_BOUND_42" + }, + { + "exact_typed_json_match": true, + "name": "global-cut-42-review", + "receipt": "work/lanes/history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.json", + "receipt_sha256": "07f77e4bf9837a2b486fc89e56dc01eeaa0443a778eae9c600cc483b64162ab1", + "seconds": 0.397, + "status": "PASS_INDEPENDENT_SHARED_SNAPSHOT_FLAG_BOUND_42" + }, + { + "exact_typed_json_match": true, + "name": "rank5-cuts-review", + "receipt": "work/lanes/cover-algebra/RANK5-UNION-CUTS-REVIEW.json", + "receipt_sha256": "d9dd35aa3fe97fa7c76afd2054725925527a4a604e7d4a6bd11b7ae8e957d076", + "seconds": 1.216, + "status": "PASS_INDEPENDENT_RANK5_UNION_CUT_REVIEW" + }, + { + "exact_typed_json_match": true, + "name": "rank8-cuts-review", + "receipt": "work/lanes/cover-algebra/MOVABLE-RANK8-CUTS-REVIEW.json", + "receipt_sha256": "d75fe3bd9f3c9391aed01368af37a3f56792ad95bcdefe21bbd4cbf0bdc2de50", + "seconds": 2.959, + "status": "PASS_INDEPENDENT_MOVABLE_RANK8_CUTS" + }, + { + "exact_typed_json_match": true, + "name": "cover-algebra", + "receipt": "work/lanes/cover-algebra/ALGEBRA.json", + "receipt_sha256": "a7fb6baa7afb90df77db94c80023144a5be3ae78db1aa6272adf7fb761b44b55", + "seconds": 2.801, + "status": "PASS_EXACT_ROUTED_PROJECTION_ALGEBRA" + }, + { + "exact_typed_json_match": true, + "name": "cover-review", + "receipt": "work/lanes/source-domain/COVER-REVIEW.json", + "receipt_sha256": "7cfc5263852b72710f21152b234c5b2ad57ad68120bb6b4f989a442e453b1a25", + "seconds": 5.334, + "status": "PASS_INDEPENDENT_73D_COVER_TRACE_REVIEW" + }, + { + "exact_typed_json_match": true, + "name": "residual", + "receipt": "work/lanes/residual-syndrome/RESIDUAL.json", + "receipt_sha256": "e819f407bd7269a0505b1ceca70150825e8e2673321293fadccc20860887a8d2", + "seconds": 0.626, + "status": "PASS_SELECTED_CONTROLLER_RESIDUAL_FACTORIZATION" + }, + { + "exact_typed_json_match": true, + "name": "residual-review", + "receipt": "work/lanes/residual-syndrome/review/INDEPENDENT-RECEIPT.json", + "receipt_sha256": "5657cd2219337f897d7f018f8d81f470878f66dd8662897ac501665fa8bfb810", + "seconds": 26.699, + "status": "PASS_INDEPENDENT_RESIDUAL_ALGEBRA_REVIEW" + } + ], + "omitted": [ + "The optional sixth-moment extension of the cover theorem", + "Search and LP routines used to find cut certificates", + "A new native-phase sweep or complete supplier replay", + "An application to the 22 October 2026 selected frontier" + ], + "portable_receipt_provenance_changes": [ + { + "field": "source_pins", + "historical": { + "QUERY-FIFTH-MOMENT.json": "d346e38c1dc323d3304c94e7faf14384ac7970bb7b7775c49749a90a509fa0e9", + "QUERY-FOURTH-MOMENT.json": "df32110bbd285e3036bdb2082e3307b24edc7515953cab7a1b3b6b684adc1e66", + "QUERY-MOMENTS.md": "91121028d7f084d3c1d53a16ca8a3634ce4ede59fcab31c9a74c4a221c7d75e5", + "check_query_fifth_moment.py": "bea72f2bafab8cc38142557d6d3a1bee5f4db1f9a2a75668fce146ca6ebba4f0", + "check_query_fourth_moment.py": "c22539e007c763b2d92d2932c4d84080ccda8549774d6be8b7705575a03a253f" + }, + "portable": { + "QUERY-FIFTH-MOMENT.json": "562d05a6f830f88d36efc148f81a01f3dfa95afbcab8195a9b5add02a5fdb742", + "QUERY-FOURTH-MOMENT.json": "df32110bbd285e3036bdb2082e3307b24edc7515953cab7a1b3b6b684adc1e66", + "QUERY-MOMENTS.md": "91121028d7f084d3c1d53a16ca8a3634ce4ede59fcab31c9a74c4a221c7d75e5", + "check_query_fifth_moment.py": 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+ "source_manifest_sha256": "7b01de4de8e46f22f641be44afaed8e10af8a0a141341a0436b05fa3ff662c87", + "status": "PASS_ACTUAL_QUERY_INFORMATION_BOUNDS_PACKAGE", + "sympy": "1.14.0" +} diff --git a/research/publication-reviews/actual-query-information-bounds/REVIEW.json b/research/publication-reviews/actual-query-information-bounds/REVIEW.json new file mode 100644 index 0000000000..ab7b5934a8 --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/REVIEW.json @@ -0,0 +1,240 @@ +{ + "claims_reviewed": [ + { + "claim": "Fixed-source 57 whole fields and 64 whole-cohort fields", + "exact_rank_ratio": "15560/273", + "hypotheses": "Nine actual queries of one fixed source on the full regular cover module tensor an honest unitary payload representation; exact stage charts and complete field capacity.", + "sharpness_scope": "The stated continuous positive moment problem only." + }, + { + "claim": "Exact scalar query support distance 53 and snapshot bound m>=k+2", + "hypotheses": "The actual eight rows and stated rank-at-least-two birth-frame support bound of 20 ports; linear reconstruction with no extra source reads." + }, + { + "claim": "One-cone obstruction for all 1002 positive proper actual frames", + "hypotheses": "The declared free observations and completed X/helper baselines; unchanged Y is not a free terminal observation; no incomparable-cone capture." + }, + { + "claim": "Global shared monotone bound 42", + "hypotheses": "The same-content monotone linear model, all inside free observations, and every allowed edge charged under the exact cut weights." + }, + { + "claim": "Structured rank-five bound 9k and rank-eight bound 8k", + "hypotheses": "The stated contained-frame common-merge model; the rank-eight case uses one cone from 983 or 991 and the FULL extension charges direct completion edges." + }, + { + "claim": "Residual rank 72|G|-d and proper-stage rank 8|S||G|", + "hypotheses": "The exact historical nine-stage bank controller, routed centre-free interface, and full regular cover representation; no commutation of routed projections." + }, + { + "claim": "72 residual arrays per replica and 1152 across 16 replicas", + "hypotheses": "A complete residual encoding channel, the cover bound d<=8|G|/183, and a payload tensor that multiplies rank and complete-array capacity equally; native application keeps the local lift and global endpoint normal form as explicit premises." + } + ], + "cold_replay": { + "check_count": 17, + "checks": [ + { + "exact_typed_json_match": true, + "name": "source-matrix", + "receipt": "work/lanes/temporal-reuse/SOURCE-MATRIX-BINDING.json", + "receipt_sha256": "b3661339df9a160a078bf3c26fbe23bb1d389d5b3411ce63f0db6b4309bd3870", + "seconds": 0.154, + "status": "PASS_REVERSE_SOURCE_MATRIX_BINDING" + }, + { + "exact_typed_json_match": true, + "name": "fourth-moment", + "receipt": "work/lanes/temporal-reuse/QUERY-FOURTH-MOMENT.json", + "receipt_sha256": 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"work/lanes/source-domain/COVER-REVIEW.json", + "receipt_sha256": "7cfc5263852b72710f21152b234c5b2ad57ad68120bb6b4f989a442e453b1a25", + "seconds": 4.029, + "status": "PASS_INDEPENDENT_73D_COVER_TRACE_REVIEW" + }, + { + "exact_typed_json_match": true, + "name": "residual", + "receipt": "work/lanes/residual-syndrome/RESIDUAL.json", + "receipt_sha256": "e819f407bd7269a0505b1ceca70150825e8e2673321293fadccc20860887a8d2", + "seconds": 0.355, + "status": "PASS_SELECTED_CONTROLLER_RESIDUAL_FACTORIZATION" + }, + { + "exact_typed_json_match": true, + "name": "residual-review", + "receipt": "work/lanes/residual-syndrome/review/INDEPENDENT-RECEIPT.json", + "receipt_sha256": "5657cd2219337f897d7f018f8d81f470878f66dd8662897ac501665fa8bfb810", + "seconds": 18.28, + "status": "PASS_INDEPENDENT_RESIDUAL_ALGEBRA_REVIEW" + } + ], + "command": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/autonomous-kappa-run/venv/bin/python -I -O -B /private/tmp/actual-query-information-bounds-independent-20261022/package/replay.py --output /private/tmp/actual-query-information-bounds-independent-20261022/replay", + "git_network_or_external_campaign_source_used": false, + "one_python_child_at_a_time": true, + "python": "3.14.7 (main, Aug 5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]", + "receipt": "cold-replay/REPLAY.json", + "receipt_sha256": "f46154487e1d0eed171f370e220fecf72c42cb04bf4026ec02712a4d09d27b83", + "seconds": 46.329, + "status": "PASS_ACTUAL_QUERY_INFORMATION_BOUNDS_PACKAGE", + "sympy": "1.14.0", + "working_directory": "/private/tmp" + }, + "excluded_conclusions": [ + "Universal native, circuit, or storage lower bounds", + "Peak workspace lower bound", + "A new chronological cache or capture word", + "Finite-precision, ownership, tape-cost, or complete recursive-cost result", + "A kappa improvement or selected-frontier change" + ], + "not_run": [ + "Optional sixth-moment extension", + "Cut-certificate search and LP searches", + "Fresh complete native phase or supplier replay", + "Application to the changed PR4470 construction", + "GitHub link-target, rendered PR description, and published-readback checks" + ], + "open_material_findings": [], + "package": "packages/actual-query-information-bounds", + "package_manifest_sha256": "7317a4956c2d734d4a7376d252f12a8543ba5d7977572ea3c17758c74e9f8aca", + "resolved_findings": [ + { + "corrected_file_sha256": "898388f738b6857e176831629d03a18734beca2d3732a15c1e80081e6c366ad0", + "file": "PROOF.md", + "finding": "The residual summary assigned dimension d to ker(V). The correct space is ker(V*).", + "frozen_source_or_executable_change_required": false, + "resolution": "The producer corrected the new summary before this freeze. The full source proof was correct.", + "section": "5" + } + ], + "review_actions": { + "commit": false, + "merge": false, + "package_or_frozen_source_edits": false, + "pull_request": false, + "push": false + }, + "review_date": "2026-10-22", + "review_text": "REVIEW.md", + "review_text_sha256": "d77c24c6afb660eac5879b5fb1d39d4fc545db7b43f251fd008105b58d70e9ac", + "reviewed_file_hashes": "REVIEWED-PACKAGE-HASHES.json", + "reviewed_file_hashes_sha256": "563b1143175c374e94744701e76bcd133193bd0235a49ed79b7266eec90ad54e", + "reviewed_files_including_manifest": 110, + "reviewer": "OpenAI Codex independent agent tagged_reset_package", + "schema": 1, + "source_and_replay_audit": "SOURCE-AND-REPLAY-CHECKS.json", + "source_and_replay_audit_sha256": "bf9a05f09f521b56e8eae989e1dce84ac1cad00e6a8715ff3aacec273d1be4f5", + "source_binding": { + "all_eight_portable_adaptations_compared_with_frozen_originals": true, + "all_four_bundled_archive_members_byte_exact": true, + "historical_source_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "local_package_document_links_checked": 44, + "mathematical_operations_unchanged_by_portability_edits": true, + "review_record_local_links_checked": 3, + "reviewed_package_unchanged": true, + "source_matrix_extraction_reviewed": true + }, + "status": "ACCEPT_SCOPED_ACTUAL_QUERY_INFORMATION_BOUNDS_PACKAGE" +} diff --git a/research/publication-reviews/actual-query-information-bounds/REVIEW.md b/research/publication-reviews/actual-query-information-bounds/REVIEW.md new file mode 100644 index 0000000000..0e355076de --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/REVIEW.md @@ -0,0 +1,147 @@ +# Independent review of the actual query information bounds + +Result: accept the package in its stated scopes. No material finding +remains after the summary correction below. This review does not accept +a universal circuit, native-cost, or storage lower bound. + +The reviewed `PACKAGE-MANIFEST.json` has SHA-256 +`7317a4956c2d734d4a7376d252f12a8543ba5d7977572ea3c17758c74e9f8aca`. +It lists 109 files; the manifest itself is a 110th file. All listed +hashes and sizes match. The package stayed unchanged during the cold +replay. [REVIEWED-PACKAGE-HASHES.json](REVIEWED-PACKAGE-HASHES.json) +binds every reviewed file, including the manifest. + +## Resolved finding + +The first new summary of the residual theorem said that the kernel of +V has dimension d. The correct space is `ker(V*)`. The source proof +already had the correct statement. The producer changed the summary +before the reviewed freeze. No executable or frozen source change was +needed. The corrected proof hash is +`898388f738b6857e176831629d03a18734beca2d3732a15c1e80081e6c366ad0`. + +## Mathematical review + +The fixed-source theorem uses the full logical module `C[G] tensor W`. +It does not use only constant payloads. The right regular action has +trace zero on a nonidentity group element. An honest unitary payload +action can be removed by the fieldwise change `f(d) -> V_d f(d)`. +Thus all trace and field-capacity factors include `dim(W)`. The actual +chart binding uses the complete linear and quadratic phase forms. +This binding remains distinct from a new complete native phase audit. + +The positive-singleton rule is valid: all other factors fix that +stage's fresh block pointwise. If the full product is the identity, +the one remaining factor must also fix it. The actual port bases then +force equal port indices. The factor is exactly `4/48=1/12`. +The fourth- and fifth-order contractions, cyclic reductions, weighted +Cauchy calculation, and positive four-atom moment witness give +`rank(S)/N >= 15560/273`. This implies 57 whole fields, or 64 when +storage is restricted to whole eight-field cohorts. Sharpness is only +for the stated continuous moment problem. The theorem requires nine +queries of one fixed source and cannot be applied directly to changing +controller sources. + +The support distance proof applies to every nonzero complex scalar +combination of the eight actual rows. A generic real projection keeps +the nonzero coefficients and preserves each zero signed sum. Equal-sum +subsets of positive coefficients form an antichain. The resulting +quartet bounds and all 255 support cases give 53, and all 112 stated +root directions attain 53. The snapshot bound uses the separate +support limit of 20 ports for each eligible birth field. For block +fields, a linear section of the reconstruction map gives a code of +dimension `kd`; deleting two field blocks is injective. This proves +`m>=k+2` under that support premise, with no extra source reads. It +does not price a multilevel shared network. + +The one-cone argument uses the valid test inputs `X=JY`, with every +helper and private input zero. All granted observations and completed +X/helper baselines vanish on the excluded-port test. The exact query +minor has rank eight for each of the 1,002 positive proper actual +frames. Thus no nonzero required query lies in that one cone. The +argument does not grant the unchanged Y bank as a free terminal +observation, and it does not cover captures from incomparable cones. + +The general cut lemma follows by induction through a finite causal +linear circuit. It includes every free observation inside the cut +and charges re-entry. Nonnegative weights can be summed only after +checking every allowed edge. The global flag argument gives 42 in the +same-content monotone model. It does not sum eight separate tree +bounds. The twelve rank-five certificates give `9k` only in their +specified contained-frame model, with a common merge and no later +observation. The rank-eight certificates give `8k` for proper frames +inside one chosen cone, 983 or 991. Their FULL extension correctly +charges all direct completion edges. Neither cone can be combined +with the other without a new edge and observation check. The package +does not claim a global bound of 64. + +The residual factorization preserves chronology and does not commute +the routed projections. The nine bank rows have one relation with +every coefficient nonzero. The space `ker(V*)` is identified with the +common routed image, and the form of `4I-L` there is `-47/14` times its stated +inner product. Its nonsingularity excludes further rank loss. Thus +the full residual rank is `72|G|-d`; every proper omitted-stage set S +has rank `8|S||G|`. The separate cover calculation gives +`d<=8|G|/183`, so the full residual channel needs 72 whole arrays per +replica, or 1,152 across all 16 replicas. Tensoring the logical source +and its field capacity by the signal space preserves these normalized +counts. The native application remains conditional on the included +local lift and global endpoint normal form. The result is a channel +dimension bound, not a bound on peak workspace, native children, or +a computation with later source reads. + +## Source and execution checks + +I compared all eight portable adaptations with their hash-pinned +originals. The edits change only source loading, the corresponding +source hashes, and one CLI argument name. The extracted source-matrix +routine retains the reviewed reverse propagation. No mathematical +operation changed. The original versions are retained in `frozen/`. + +I read the historical archive from the exact Git object at +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`, verified all 19,299,540 +bytes against SHA-256 +`22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754`, +and checked all four bundled members. Each is the unique regular +archive member at the stated path, and each matches byte for byte. +All 44 local links in the new package documents resolve. + +The package was copied to a fresh directory under `/private/tmp`. +Its full portable command ran from `/private/tmp`, with one Python +child process at a time. The runtime was Python 3.14.7 with SymPy +1.14.0. All 17 checks passed in 46.329 seconds: + +```text +PASS_ACTUAL_QUERY_INFORMATION_BOUNDS_PACKAGE +``` + +The run rebuilt the source matrix and all 712-input snapshot rows, +enumerated the 194,400 fifth-order triples, checked all support and +cut certificates, repeated the independent 73-axis cover calculation, +and ran the separate exact residual algebra. Every complete JSON +receipt matched its declared target, including JSON types. The only +removed comparison fields are the five explicitly named optional +sixth-moment fields. Source-hash changes are recorded separately. + +The replay used no Git, network, or external campaign source. Git was +used only for the separate source audit. The evidence is in +[SOURCE-AND-REPLAY-CHECKS.json](SOURCE-AND-REPLAY-CHECKS.json) and +[cold-replay/REPLAY.json](cold-replay/REPLAY.json). + +## Remaining limits + +No material dependency gap remains for the scoped algebraic claims. +The inherited local native lift and controller endpoint normal form +are explicit application premises; this review does not establish +them through a fresh native supplier replay. It does not repeat the +optional sixth-moment extension, cut searches, or LP searches. It +does not establish a new cache, a chronological capture word, ownership, +finite precision, tape cost, or a complete recursive invoice. + +The package retains the historical source and states that applicability +to the changed PR4470 construction is unproved. No kappa improvement +or selected-frontier change follows. Link-target checks on GitHub, +the final PR description, its rendered Markdown, and the published +readback remain the coordinator's publication work. This review made +no commit, push, PR, merge, or frozen-source edit. OpenAI Codex supplied +this independent agent review; it is not a human review. diff --git a/research/publication-reviews/actual-query-information-bounds/REVIEWED-PACKAGE-HASHES.json b/research/publication-reviews/actual-query-information-bounds/REVIEWED-PACKAGE-HASHES.json new file mode 100644 index 0000000000..cc3d29ef2d --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/REVIEWED-PACKAGE-HASHES.json @@ -0,0 +1,112 @@ +{ + "NOTICE.md": "40e1cf742e31b0146f7dfb506871651fbce1545ed1e9b6d73926bc1cce8eca79", + "PACKAGE-MANIFEST.json": "7317a4956c2d734d4a7376d252f12a8543ba5d7977572ea3c17758c74e9f8aca", + "PROOF.md": "898388f738b6857e176831629d03a18734beca2d3732a15c1e80081e6c366ad0", + "README.md": "a98ded794a2cdbe18a02e31498623ed95f69ae7e9efb5931e866c4d61797f3f4", + "SOURCE-MANIFEST.json": "7b01de4de8e46f22f641be44afaed8e10af8a0a141341a0436b05fa3ff662c87", + "SOURCE-PINS.md": "a4e6f3dc661683546a3f2d1472b5081e0a10de9ba4129a2e60e441983a806736", + "VALIDATION.md": 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2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]", + "replay_sha256": "a0126b2e906045d5f905e8103424fc63f585453b58e2eca7541b7337e34d01b6", + "seconds": 46.329, + "source_files_checked": 84, + "source_manifest_sha256": "7b01de4de8e46f22f641be44afaed8e10af8a0a141341a0436b05fa3ff662c87", + "status": "PASS_ACTUAL_QUERY_INFORMATION_BOUNDS_PACKAGE", + "sympy": "1.14.0" +} From 0a1e553b57afd588dc3c26b9f7e5f937bb821098 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Thu, 22 Oct 2026 12:55:10 -0500 Subject: [PATCH 2/4] Include pinned files excluded by repository ignore rules --- .../validation/logs/complete-snapshot-rows.log | 2 ++ .../validation/logs/cover-algebra.log | 3 +++ .../validation/logs/cover-review.log | 2 ++ .../validation/logs/fifth-moment.log | 1 + .../validation/logs/fourth-moment.log | 1 + .../validation/logs/global-cut-42-review.log | 1 + .../validation/logs/global-cut-42.log | 1 + .../validation/logs/moment-review.log | 1 + .../validation/logs/rank5-cuts-review.log | 2 ++ .../validation/logs/rank8-cuts-review.log | 2 ++ .../validation/logs/residual-review.log | 1 + .../validation/logs/residual.log | 3 +++ .../validation/logs/snapshot-cones.log | 1 + .../validation/logs/snapshot-support-review.log | 1 + .../validation/logs/source-matrix.log | 1 + .../validation/logs/support-distance-review.log | 1 + .../validation/logs/support-distance.log | 1 + 17 files changed, 25 insertions(+) create mode 100644 research/actual-query-information-bounds/validation/logs/complete-snapshot-rows.log create mode 100644 research/actual-query-information-bounds/validation/logs/cover-algebra.log create mode 100644 research/actual-query-information-bounds/validation/logs/cover-review.log create mode 100644 research/actual-query-information-bounds/validation/logs/fifth-moment.log create mode 100644 research/actual-query-information-bounds/validation/logs/fourth-moment.log create mode 100644 research/actual-query-information-bounds/validation/logs/global-cut-42-review.log create mode 100644 research/actual-query-information-bounds/validation/logs/global-cut-42.log create mode 100644 research/actual-query-information-bounds/validation/logs/moment-review.log create mode 100644 research/actual-query-information-bounds/validation/logs/rank5-cuts-review.log create mode 100644 research/actual-query-information-bounds/validation/logs/rank8-cuts-review.log create mode 100644 research/actual-query-information-bounds/validation/logs/residual-review.log create mode 100644 research/actual-query-information-bounds/validation/logs/residual.log create mode 100644 research/actual-query-information-bounds/validation/logs/snapshot-cones.log create mode 100644 research/actual-query-information-bounds/validation/logs/snapshot-support-review.log create mode 100644 research/actual-query-information-bounds/validation/logs/source-matrix.log create mode 100644 research/actual-query-information-bounds/validation/logs/support-distance-review.log create mode 100644 research/actual-query-information-bounds/validation/logs/support-distance.log diff --git a/research/actual-query-information-bounds/validation/logs/complete-snapshot-rows.log b/research/actual-query-information-bounds/validation/logs/complete-snapshot-rows.log new file mode 100644 index 0000000000..563cbf4936 --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/complete-snapshot-rows.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_BACKWARD_SNAPSHOT_ROWS +{"constant_intervals": 16687, "distinct_frame_row_support_checks": 16023, "exact_nonzero_support_coefficients": 98056, "interval_endpoint_checks": 24199, "last_original_private_event": 8702, "reviewer_sha256": "c8a72435ce0dc8c8f2c387f2ce24bc3e900f9559d3fdc824e4fc4ee4055921fc"} diff --git a/research/actual-query-information-bounds/validation/logs/cover-algebra.log b/research/actual-query-information-bounds/validation/logs/cover-algebra.log new file mode 100644 index 0000000000..8d625c556b --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/cover-algebra.log @@ -0,0 +1,3 @@ +PASS_EXACT_ROUTED_PROJECTION_ALGEBRA +edge_products=5824 TL=false commute=false braid=false +trace_PQ=4/7 trace_PQPQ=27/343 common_J_codimension>=2912/183 diff --git a/research/actual-query-information-bounds/validation/logs/cover-review.log b/research/actual-query-information-bounds/validation/logs/cover-review.log new file mode 100644 index 0000000000..8c088d2e8b --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/cover-review.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_73D_COVER_TRACE_REVIEW +routes73=896 trace_PQ=4/7 trace_PQPQ=27/343 rank>=2912/183>896/73 diff --git a/research/actual-query-information-bounds/validation/logs/fifth-moment.log b/research/actual-query-information-bounds/validation/logs/fifth-moment.log new file mode 100644 index 0000000000..fcc2adef5d --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/fifth-moment.log @@ -0,0 +1 @@ +{"status": "PASS_ACTUAL_QUERY_FIFTH_MOMENT", "m5": "47467/36", "rank_per_cover": "15560/273", "whole_fields": 57, "moment_relaxation_is_sharp": true} diff --git a/research/actual-query-information-bounds/validation/logs/fourth-moment.log b/research/actual-query-information-bounds/validation/logs/fourth-moment.log new file mode 100644 index 0000000000..b6d74b8343 --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/fourth-moment.log @@ -0,0 +1 @@ +{"status": "PASS_ACTUAL_QUERY_FOURTH_MOMENT", "nine_chart_moments": ["72", "120", "244", "1649/3"], "rank_per_cover": "4104/73", "whole_fields": 57, "eight_field_cohorts": 8} diff --git a/research/actual-query-information-bounds/validation/logs/global-cut-42-review.log b/research/actual-query-information-bounds/validation/logs/global-cut-42-review.log new file mode 100644 index 0000000000..19ade876c7 --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/global-cut-42-review.log @@ -0,0 +1 @@ +{"candidate_proof_sha256": "f550ecd52133f7fb856538abf6ed7ef9241577bf309f7268cd4610b8c12735df", "candidate_receipt_sha256": "2c001f0336c1f930a41eace304e957eb5da354edc56c4c9b0449bf253d65fb25", "checked_frames": 1004, "checked_native_edges": 2880, "checker_sha256": "e52355cbedf49346d2e27271fa999e68d66ae9b3d00980477d8750b66b0fc919", "controls": {"one_unit_native_undercharge_rejected": true, "reversed_shell_failures": 6293}, "exact_gram_ranks": [0, 1, 1, 2, 8, 6, 8, 8, 8], "flag": [243, 249, 311, 132, 131, 489, 442, 405, 178], "native_rank_lower_bound": 42, "not_checked": ["A positive cache circuit", "Native phase recipes for new edges", "Changed address codes", "Global supplier cost"], "proof_checks": ["Pivot-set inclusion for arbitrary nested frames", "Whole-array dimension in each cut inequality", "No separate-tree assumption in the cut sum"], "scope": "Same-content monotone frame DAGs with scalar sharing. No 64 bound or construction is proved.", "separation_checks": 23279, "shell_sizes": [0, 1, 1, 2, 8, 7, 11, 22, 60], "sources": {"core": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877", "interface": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", "snapshot": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", "support_review": "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7"}, "status": "PASS_INDEPENDENT_SHARED_SNAPSHOT_FLAG_BOUND_42"} diff --git a/research/actual-query-information-bounds/validation/logs/global-cut-42.log b/research/actual-query-information-bounds/validation/logs/global-cut-42.log new file mode 100644 index 0000000000..0519fcc6ea --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/global-cut-42.log @@ -0,0 +1 @@ +{"checker_sha256": "b49857d0005b19880309c2790378fe1b956a5ada092b94a4814d2bc016ab1b28", "exact_shell_ranks": [0, 1, 1, 2, 8, 6, 8, 8, 8], "flag_basis": [243, 249, 311, 132, 131, 489, 442, 405, 178], "frame_shell_support_tests": 23279, "not_checked": ["A constructive merged cache network", "Internal native-child cuts", "A changed core", "Logical address re-gauging", "A complete supplier invoice"], "rank_sum": 42, "retained_edge_count": 2880, "scope": "Same-content monotone frame networks, arbitrary scalar sharing and all snapshot times. This bound does not prove64 or optimality.", "sources": {"core_decompressed_sha256": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877", "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", "snapshot_decompressed_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", "support_review_sha256": "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7"}, "status": "PASS_SHARED_MONOTONE_CACHE_DAG_LOWER_BOUND_42"} diff --git a/research/actual-query-information-bounds/validation/logs/moment-review.log b/research/actual-query-information-bounds/validation/logs/moment-review.log new file mode 100644 index 0000000000..5c7573d5ea --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/moment-review.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_QUERY_MOMENT_PROOF_AND_ARITHMETIC_REVIEW diff --git a/research/actual-query-information-bounds/validation/logs/rank5-cuts-review.log b/research/actual-query-information-bounds/validation/logs/rank5-cuts-review.log new file mode 100644 index 0000000000..2131474cdb --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/rank5-cuts-review.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_RANK5_UNION_CUT_REVIEW +Twelve exact five-query overlaps; five injective unit-weight cuts each; lower cost9k. diff --git a/research/actual-query-information-bounds/validation/logs/rank8-cuts-review.log b/research/actual-query-information-bounds/validation/logs/rank8-cuts-review.log new file mode 100644 index 0000000000..e82cf8224c --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/rank8-cuts-review.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_MOVABLE_RANK8_CUTS +Both contained cones pass all edge charges, including direct completion to FULL; bound8k. diff --git a/research/actual-query-information-bounds/validation/logs/residual-review.log b/research/actual-query-information-bounds/validation/logs/residual-review.log new file mode 100644 index 0000000000..cfde96036b --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/residual-review.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_RESIDUAL_ALGEBRA_REVIEW diff --git a/research/actual-query-information-bounds/validation/logs/residual.log b/research/actual-query-information-bounds/validation/logs/residual.log new file mode 100644 index 0000000000..eddc318bed --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/residual.log @@ -0,0 +1,3 @@ +PASS_SELECTED_CONTROLLER_RESIDUAL_FACTORIZATION +proper_subsets=independent residual_rank=72|G|-common_image_dimension +native_supplier_or_kappa_claim=false diff --git a/research/actual-query-information-bounds/validation/logs/snapshot-cones.log b/research/actual-query-information-bounds/validation/logs/snapshot-cones.log new file mode 100644 index 0000000000..b90d5c52e8 --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/snapshot-cones.log @@ -0,0 +1 @@ +{"actual_positive_proper_frames": 1002, "distinct_frame_row_pairs": 16023, "exact_nonzero_support_coefficients": 98056, "status": "PASS_EXACT_SNAPSHOT_CONE_OBSTRUCTION"} diff --git a/research/actual-query-information-bounds/validation/logs/snapshot-support-review.log b/research/actual-query-information-bounds/validation/logs/snapshot-support-review.log new file mode 100644 index 0000000000..1f3f900e3a --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/snapshot-support-review.log @@ -0,0 +1 @@ +{"checker_sha256": "b605064b4be17fd2ceb6825fe01cd6b813abd3351ad499dd6c5b4fa4947a52ba", "inputs": {"interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", "reviewed_source_proof_sha256": "be9575e1cac8706c42fddff243f435935e098d197edaf7f8689352c93b7e3961", "reviewed_source_receipt_sha256": "35698700474f2309a4eea2f192a5afbd2f42f580a7e0e510a0bb5687a87fdc2d", "snapshot_decompressed_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c"}, "intervals": 16687, "line_rank_counts": {"7": 8, "8": 503}, "minor_determinants": {"-16": 1, "-32": 126, "-48": 2, "-64": 45, "32": 790, "64": 38}, "nonzero_port_incidence_checks": 104088, "normal_lines_absent": [42, 7, 25, 52, 82, 127, 97, 76], "not_checked": ["The full snapshot producer replay", "A new native cache word", "Chronological branching synthesis", "A complete supplier invoice"], "phase_scope": "Scalar rows are read in the canonical view. Non-FULL views after event 17605 require the supplied endpoint monomial adapter.", "proper_frame_minor_count": 1002, "rows": 12271, "scope": "One nonzero birth frame and all later containing frames. This does not exclude a merged network with incomparable capture frames.", "status": "PASS_EXACT_SNAPSHOT_SUPPORT_AND_SINGLE_CONE_EXCLUSION", "test_input": "X=JY; all 480 helper and eight private inputs are zero"} diff --git a/research/actual-query-information-bounds/validation/logs/source-matrix.log b/research/actual-query-information-bounds/validation/logs/source-matrix.log new file mode 100644 index 0000000000..4dbe4b4d77 --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/source-matrix.log @@ -0,0 +1 @@ +PASS_REVERSE_SOURCE_MATRIX_BINDING diff --git a/research/actual-query-information-bounds/validation/logs/support-distance-review.log b/research/actual-query-information-bounds/validation/logs/support-distance-review.log new file mode 100644 index 0000000000..38f29e443c --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/support-distance-review.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_QUERY_SUPPORT_DISTANCE_53_REVIEW diff --git a/research/actual-query-information-bounds/validation/logs/support-distance.log b/research/actual-query-information-bounds/validation/logs/support-distance.log new file mode 100644 index 0000000000..ca89dafae8 --- /dev/null +++ b/research/actual-query-information-bounds/validation/logs/support-distance.log @@ -0,0 +1 @@ +{"attaining_old_root_directions": 112, "checker_sha256": "d9bff383c911653f17087849203f3a64dc4d511f27f6a243bbfa7f3d175d9a09", "consequence": "A k-dimensional query space needs at least k+2 rank-at-least-two birth fields in one common span.", "controls": {"duplicate_sign_pattern_rejected": true, "excessive_quartet_bound_rejected": true}, "frame_allowed_port_histogram": {"0": {"112": 1}, "1": {"48": 7, "52": 112, "56": 1}, "2": {"20": 168}, "3": {"8": 152, "10": 16}, "4": {"0": 14, "6": 51, "8": 8}, "5": {"4": 16, "6": 5, "8": 6}, "6": {"2": 16, "4": 152}, "7": {"2": 152}, "8": {"0": 14, "1": 112}, "9": {"0": 1}}, "lower_bounds_by_nonzero_coefficient_count": {"1": 56, "2": 76, "3": 78, "4": 53, "5": 73, "6": 75, "7": 77, "8": 70}, "minimum_source_port_support": 53, "nonzero_per_quartet_lower_bounds": [0, 8, 4, 6, 5], "not_claimed": ["A native rank lower bound of 64 for shared networks", "A constructive cache network", "A full supplier improvement"], "sources": {"independent_support_review_sha256": "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7", "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", "snapshot_decompressed_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c"}, "status": "PASS_EXACT_QUERY_SUPPORT_MINIMUM_53"} From 8be1acaf2d4648cd9903cd76987a939596c81b7e Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Thu, 22 Oct 2026 13:36:53 -0500 Subject: [PATCH 3/4] Add chronological cache criterion and separate-tree rank bound --- .../ANNEX-MANIFEST.json | 82 + .../chronological-cache-paths/PROOF.md | 38 + .../chronological-cache-paths/PUBLICATION.md | 7 + .../chronological-cache-paths/README.md | 24 + .../chronological-cache-paths/REVIEW.json | 15 + .../chronological-cache-paths/REVIEW.md | 53 + .../chronological-cache-paths/SOURCES.json | 41 + .../chronological-cache-paths/TASK.json | 9 + .../chronological-cache-paths/VALIDATION.json | 35 + .../lanes/circuit-interface/INTERFACE.json | 1441 + .../CHRONOLOGICAL-CACHE-PATHS.md | 242 + .../SNAPSHOT-SUPPORT-REVIEW.json | 26836 ++++++++++++++++ .../cover-algebra/review_snapshot_support.py | 165 + .../BACKWARD-SNAPSHOT-INTERVALS.json.gz | Bin 0 -> 414717 bytes .../SNAPSHOT-CONE-OBSTRUCTION.json | 21549 +++++++++++++ .../SNAPSHOT-CONE-OBSTRUCTION.md | 129 + .../chronological-cache-paths/replay.py | 72 + .../validation/normal.log | 1 + .../validation/optimized.log | 1 + 19 files changed, 50740 insertions(+) create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/ANNEX-MANIFEST.json create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/PROOF.md create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/PUBLICATION.md create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/README.md create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/REVIEW.json create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/REVIEW.md create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/SOURCES.json create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/TASK.json create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/VALIDATION.json create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/circuit-interface/INTERFACE.json create mode 100644 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create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/validation/normal.log create mode 100644 research/actual-query-information-bounds/annexes/chronological-cache-paths/validation/optimized.log diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/ANNEX-MANIFEST.json b/research/actual-query-information-bounds/annexes/chronological-cache-paths/ANNEX-MANIFEST.json new file mode 100644 index 0000000000..b1bfe51c16 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/ANNEX-MANIFEST.json @@ -0,0 +1,82 @@ +{ + "appendix": "chronological-cache-paths", + "files": { + "PROOF.md": { + "bytes": 1967, + "sha256": "d38c1ead02a527076a3355b317048c719125daa00ad15953f17915a5b9c97863" + }, + "PUBLICATION.md": { + "bytes": 676, + "sha256": "fbad8effff89056dc3d7021827184b8103ab034a6b537754a0bbe0089f873ff2" + }, + "README.md": { + "bytes": 1109, + "sha256": 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1357, + "sha256": "fb55d12399a64df3cb5d8c96265267861886248a64b73de702fad3a67ecd7fde" + }, + "validation/optimized.log": { + "bytes": 1357, + "sha256": "fb55d12399a64df3cb5d8c96265267861886248a64b73de702fad3a67ecd7fde" + } + }, + "frozen_input_files": 7, + "schema": "accepted-support-proof-appendix-v1", + "scope": "Fixed-path permitted-ring module criterion and native-rank bound 8 for one scalar monotone output tree; 64 only for eight separately paid trees.", + "total_bytes_excluding_manifest": 1101902, + "total_files_excluding_manifest": 18 +} diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/PROOF.md b/research/actual-query-information-bounds/annexes/chronological-cache-paths/PROOF.md new file mode 100644 index 0000000000..3b76bbc7d8 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/PROOF.md @@ -0,0 +1,38 @@ +# Fixed cache paths and scalar merge trees + +This appendix adopts two results from the unchanged +[chronological cache proof](frozen/lanes/cover-algebra/CHRONOLOGICAL-CACHE-PATHS.md). +It gives no new complete kappa bound. + +For a fixed chronological path, a fixed read schedule, and supplied exact +native transitions, the accessible logical rows are exactly the module +generated by the available snapshot rows over the permitted coefficient +ring. The cache must start at zero in an owned field that may be cleared. +A rational solution need not be a dyadic solution. Final unchanged X and +restored-helper rows may be used for cleanup. All query cleanups must finish +before the first X repair if they use those endpoint rows. + +Consider one scalar-content rooted tree whose edges move into containing +frames. Grant every snapshot time. An edge costs at least its frame dimension +increase. At a node v, let I_v be the intersection of its descendant leaf +frames. Codimension subadditivity and induction give + +```text +cost below v >= dim(U_v) - dim(I_v). +``` + +The actual snapshot support law shows that every output row is supported +on ports perpendicular to I_root. The exact line minors show that a nonzero +centre query has a source-support annihilator of dimension at most one. +With FULL dimension nine, the tree therefore costs at least eight units of +native rank. Eight separately paid trees cost at least 64. + +These bounds do not add across shared paid edges. They do not prove a global +64 bound for a shared multi-output network. Logical address changes, changed +core calls, and cuts inside native children are outside the tree model. +The general cut proof and stronger numerical network certificates in the +parent package remain separate results. + +The [independent review](REVIEW.md) checks the proof. The appendix replay +checks the existing exact snapshot support and line-minor certificate. It +does not construct a native cache or prove a complete storage schedule. diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/PUBLICATION.md b/research/actual-query-information-bounds/annexes/chronological-cache-paths/PUBLICATION.md new file mode 100644 index 0000000000..1087880ebd --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/PUBLICATION.md @@ -0,0 +1,7 @@ +The [cache-path appendix](PROOF.md) adds an exact permitted-ring criterion for a fixed read path and an independently reviewed native-rank lower bound of eight for one nonzero query in the stated scalar monotone merge-tree model. The bound 64 applies only to eight separately paid trees. It does not establish a global 64 bound for a shared multi-output network. The unchanged support checker passes in normal Python and with `-O`; no native cache is constructed. + +```sh +python3 -I -B research/actual-query-information-bounds/annexes/chronological-cache-paths/replay.py --out /tmp/chronological-cache-paths-replay +``` + +Expected final line: `PASS_SCOPED_SUPPORT_PROOF_REPLAY`. diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/README.md b/research/actual-query-information-bounds/annexes/chronological-cache-paths/README.md new file mode 100644 index 0000000000..eb88b0d59e --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/README.md @@ -0,0 +1,24 @@ +# Scoped support appendix + +[PROOF.md](PROOF.md) states the accepted result and its limits. +[REVIEW.md](REVIEW.md) gives the separate independent proof review. +The original files under `frozen/` are unchanged and are bound by +[SOURCES.json](SOURCES.json). Historical review status is retained. + +Use Python 3.10 or later and the standard library. Run from this appendix +with a new output directory: + +```sh +python3 -I -B replay.py --out /tmp/chronological-cache-paths-replay +``` + +The runner uses fresh copies, one process at a time. It runs normal Python +and Python with `-O`. Both complete receipts must match exact bytes. +The final line is `PASS_SCOPED_SUPPORT_PROOF_REPLAY`. +[VALIDATION.json](VALIDATION.json) records the independent publication run. +The replay does not prove the full native or recursive supplier contract. + +This appendix preserves campaign work and uses substantial OpenAI Codex +assistance. Its new proof review is a separate agent calculation, not an +independent human review. The parent package retains the upstream source +credit and license. This appendix makes no complete kappa claim. diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/REVIEW.json b/research/actual-query-information-bounds/annexes/chronological-cache-paths/REVIEW.json new file mode 100644 index 0000000000..f6c491efd6 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/REVIEW.json @@ -0,0 +1,15 @@ +{ + "accepted_proof_wrapper_sha256": "d38c1ead02a527076a3355b317048c719125daa00ad15953f17915a5b9c97863", + "claim": "Fixed-path permitted-ring module criterion and native-rank bound 8 for one scalar monotone output tree; 64 only for eight separately paid trees.", + "complete_kappa_improvement": false, + "independent_review": "REVIEW.md", + "native_or_recursive_admission": false, + "normal_optimized_complete_receipts_match": true, + "original_inputs_unchanged": true, + "remaining_publication_check": "Coordinator review of actual appendix files, final package link verification, GitHub rendering and readback.", + "review_sha256": "766e29a5133cb1c08c39356d738ccf5f7a11199b55fb1bc92841ad7aeca0f092", + "source_manifest_sha256": "1f8a707234438332ea54fcbc3ccaa70b7c0fc3ea6ca9cd5b0fbfec3f31ae09d1", + "status": "ACCEPT_SCOPED_SUPPORT_APPENDIX", + "target_package": "actual-query-information-bounds", + "validation_sha256": "7e232925ae6a8833e41a9bd9b5a9c30d8c88d8bbc1bd57ae475486c7422cca6d" +} diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/REVIEW.md b/research/actual-query-information-bounds/annexes/chronological-cache-paths/REVIEW.md new file mode 100644 index 0000000000..7d9e6cc6e3 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/REVIEW.md @@ -0,0 +1,53 @@ +# Independent review of the cache path and tree proof + +Verdict: accept the fixed-path module criterion and the one-output scalar +merge-tree bound as a scoped appendix. This is a new independent proof +review of the existing text. It does not change the historical receipts. +The reviewer read the workspace PR-DESCRIPTION-STANDARD.md. + +For a path with a supplied exact transition T_V T_U^-1, a transition changes +the physical frame and preserves the logical row. Each scalar read adds a +permitted-ring multiple of its snapshot row. Induction proves necessity of +the module condition. The coefficients of any module representation give +the sequence of ADDs and prove sufficiency for the stated fixed schedule. +Owned clearable cache fields, the supplied native recipes, and the declared +read times are premises. This does not clear an arbitrary borrowed field +without an account of its old contents. + +The endpoint term dE is valid only while those rows retain their recorded +values. Completing all eight cleanups before the first X repair provides +that invariant. The telescoping rank cost is a conditional identity for +edges that have the stated cost; it is not an existence proof for a path. + +The tree induction is correct for every finite rooted tree. At a k-child +node, the child costs plus incoming edges give +k*dim(U_v)-sum_j dim(I_j). Each I_j lies inside U_v. Subadditivity of +codimension bounds this below by dim(U_v)-dim(intersection_j I_j). +A snapshot at an internal node can be treated as an extra zero-length leaf. +Scalar cancellation cannot add a source port outside the union of leaf +supports. Every such support lies in I_root perpendicular. + +The 511 line certificates imply that a nonzero query row can annihilate +only one binary line. On each of the eight special normal lines, the +excluded-column matrix has a one-dimensional left kernel generated by one +row of R. Two distinct such rows are independent because R R^T=56I. +Thus two independent annihilator lines are impossible. The rank cost is +at least 9-1=8. The factor eight for eight outputs requires disjoint paid +trees. A shared subexpression cannot be charged again by this proof. + +The source support checker was read and rerun in fresh copies in normal +Python and with -O. Both complete output files match the retained receipt +byte for byte. It checks 12,271 rows, 16,687 intervals, 104,088 nonzero port +incidences, all 1,002 proper actual frame minors, and all 511 line minors. +It selects minor columns modulo a prime, then evaluates each determinant +over the rationals. Its conclusions therefore do not rely on a failed +finite-field search. The full snapshot producer is not rerun here; the +parent query package retains and replays that separate source audit. + +The older exploratory path screen is not needed for either accepted proof. +The shared-network formulation and cut inequality are sound, but the parent +package already gives their broader independent review and exact global +42 certificate. The tree bound remains useful because it applies to one +nonzero output and distinguishes separate output trees from shared DAGs. +No current selected source, native cache construction, owner schedule, +precision claim, or complete supplier price is admitted by this appendix. diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/SOURCES.json b/research/actual-query-information-bounds/annexes/chronological-cache-paths/SOURCES.json new file mode 100644 index 0000000000..73702ee1f3 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/SOURCES.json @@ -0,0 +1,41 @@ +{ + "frozen_files": { + "lanes/circuit-interface/INTERFACE.json": { + "bytes": 23232, + "sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "source": "work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json" + }, + "lanes/cover-algebra/CHRONOLOGICAL-CACHE-PATHS.md": { + "bytes": 9805, + "sha256": "419bb67187d4edeead01d564d7f239f351f4d906c9b6f73e585ec51d2a730c7c", + "source": "work/centre-encoding-campaign-20261014/lanes/cover-algebra/CHRONOLOGICAL-CACHE-PATHS.md" + }, + "lanes/cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json": { + "bytes": 333522, + "sha256": "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7", + "source": "work/centre-encoding-campaign-20261014/lanes/cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json" + }, + "lanes/cover-algebra/review_snapshot_support.py": { + "bytes": 8113, + "sha256": "b605064b4be17fd2ceb6825fe01cd6b813abd3351ad499dd6c5b4fa4947a52ba", + "source": "work/centre-encoding-campaign-20261014/lanes/cover-algebra/review_snapshot_support.py" + }, + "lanes/history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz": { + "bytes": 414717, + "sha256": "a15fbfcb758cb77b5b044963d771ac6baf4ff9d155e6c46f47bac3694b1fc17f", + "source": "work/centre-encoding-campaign-20261014/lanes/history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz" + }, + "lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.json": { + "bytes": 289400, + "sha256": "35698700474f2309a4eea2f192a5afbd2f42f580a7e0e510a0bb5687a87fdc2d", + "source": "work/centre-encoding-campaign-20261014/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.json" + }, + "lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md": { + "bytes": 5433, + "sha256": "be9575e1cac8706c42fddff243f435935e098d197edaf7f8689352c93b7e3961", + "source": "work/centre-encoding-campaign-20261014/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md" + } + }, + "schema": "support-proof-appendix-sources-v1", + "scope": "Unchanged proof and check inputs. Historical receipts retain their original status." +} diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/TASK.json b/research/actual-query-information-bounds/annexes/chronological-cache-paths/TASK.json new file mode 100644 index 0000000000..5f716dc58a --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/TASK.json @@ -0,0 +1,9 @@ +{ + "arguments": [], + "expected": "frozen/lanes/cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json", + "id": "chronological-cache-paths", + "location": "workspace", + "receipt": "lanes/cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json", + "scope": "Exact snapshot support, 1002 cone minors, and 511 line minors. The separate proof review checks the fixed-path module and scalar merge-tree arguments. No full snapshot producer or shared-network solution is replayed.", + "script": "lanes/cover-algebra/review_snapshot_support.py" +} diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/VALIDATION.json b/research/actual-query-information-bounds/annexes/chronological-cache-paths/VALIDATION.json new file mode 100644 index 0000000000..83f0525be4 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/VALIDATION.json @@ -0,0 +1,35 @@ +{ + "appendix": "chronological-cache-paths", + "comparison": "Both complete receipt files match exact bytes.", + "runner_sha256": "c5b6abbe8d9704adfaea980c77f4f34fee78ae2367bf1e2e88bed59ca79b7697", + "runs": [ + { + "command": [ + "/opt/homebrew/opt/python@3.14/bin/python3.14", + "-I", + "-B", + "/private/tmp/chronological-cache-paths-review-20261022-a/normal/lanes/cover-algebra/review_snapshot_support.py" + ], + "elapsed_seconds": 1.522, + "exit_code": 0, + "mode": "normal", + "receipt_sha256": "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7" + }, + { + "command": [ + "/opt/homebrew/opt/python@3.14/bin/python3.14", + "-I", + "-B", + "-O", + "/private/tmp/chronological-cache-paths-review-20261022-a/optimized/lanes/cover-algebra/review_snapshot_support.py" + ], + "elapsed_seconds": 1.539, + "exit_code": 0, + "mode": "optimized", + "receipt_sha256": "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7" + } + ], + "scope": "Exact snapshot support, 1002 cone minors, and 511 line minors. The separate proof review checks the fixed-path module and scalar merge-tree arguments. 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Native endpoint mixing and a changed controller are not admitted.", + "status": "PASS_CENTRE_FREE_SCALAR_INTERFACE", + "target_endpoint": "T_q = F C_q^-1; distinct q have distinct frames", + "word_sha256": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c" +} diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/cover-algebra/CHRONOLOGICAL-CACHE-PATHS.md b/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/cover-algebra/CHRONOLOGICAL-CACHE-PATHS.md new file mode 100644 index 0000000000..2f2ec3fd2b --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/cover-algebra/CHRONOLOGICAL-CACHE-PATHS.md @@ -0,0 +1,242 @@ +# Chronological cache paths and merged query flows + +A fixed path has an exact linear-algebra test. The retained backward word +fails a stronger single-cone test. A scalar merge tree that produces one +nonzero centre query costs at least eight units of native rank. This last +bound does not add across outputs that share paid operations. + +No construction below improves the complete supplier. A merged network +with several outputs remains open. + +## 1. Native and scalar contracts + +Let `T_U` be the exact canonical operator for frame `U`. A snapshot at +event `t` and frame `U` has physical value `T_U a z`, where `a` is its +row on the 712 arbitrary input fields. The coefficient ring is the +dyadic rationals. The same statements over a larger coefficient field +give relaxations, not a dyadic implementation. + +A permitted cache transition from `U` to `V` must supply the exact +operator `T_V T_U^-1`, including its global phase and monomial maps. +Subspace inclusion alone is not a native recipe. In particular, an +alternating complement can prevent an assumed orthonormal embedding. +The transition cost is the rank of its supplied native children. + +The cache starts at exact zero. Its initial arbitrary contents are +cleared. At a matching frame, a scalar ADD from a snapshot changes its +logical row from `a` to `a+c b`. A supplied transition changes the frame +and leaves that logical row unchanged. These statements hold on all +arrays, including arrays that are not tensor products. + +For a path `U_0,...,U_m=FULL`, assign each snapshot read a time within its +recorded availability interval. These read times and transition times +must be in chronological order. If read coefficients are `c_i`, the +final physical value is + +\[ +T_{\rm FULL}\sum_i c_i a_i z. \tag{1} +\] + +Thus the scalar module spanned by the available snapshot rows is the +exact set of logical rows that this path can form. This gives a necessary +and sufficient test for a fixed path, fixed read schedule, and supplied +native transitions. A rational solution is insufficient when its +coefficients are outside the permitted ring. + +Let `E` contain the unchanged FULL X outputs and the restored FULL helper +outputs. A target query `q` can be cleaned at exit if + +\[ +q=\sum_i c_i a_i+dE. \tag{2} +\] + +After the cache reaches FULL, add the `dE` terms. For eight queries, +complete all eight cleanups before the first X repair. Then subtract +`K` times the clean cache from X. This order preserves the endpoint rows +used in (2). A different order needs a separate invariant. + +If each supplied edge costs `dim(V)-dim(U)`, one buffer costs +`9-dim(U_0)` along the path. Eight buffers on one path cost eight times +that amount. This is a conditional cost identity. It does not prove that +such a path has the required observations. + +## 2. Exact retained-source test + +The source is `history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz`, with +decompressed SHA256 +`3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c`. +It has 12,271 exact rows and 16,687 intervals. Our independent checker +`review_snapshot_support.py` reads that payload and the pinned +`circuit-interface/INTERFACE.json`. It imports no source producer. + +The checker substitutes the valid test input + +\[ +x=Jy,\qquad h=0,\qquad c=0. +\] + +All 480 helper inputs are zero in this test. No helper is assumed clean +in a proposed circuit. Every completed X row and every restored helper +row vanishes on this input family. + +For every snapshot at frame `U`, exact integer arithmetic verifies + +\[ +\operatorname{supp}(a_U)\subseteq +S_U:=\{p:q_p\perp U\}. \tag{3} +\] + +The check includes 104,088 nonzero port incidences, counted once per +availability interval. The source checker counts distinct frame/row +pairs instead; this accounts for the different total. + +For every one of the 1,002 positive proper actual frames, our checker +selects and evaluates a nonzero exact eight-column minor of + +\[ +R_{E_U},\qquad E_U=\{p:q_p\not\perp U\}. \tag{4} +\] + +On inputs supported in `E_U`, all snapshots in frames containing `U` +are zero, while `Ry` is arbitrary. Therefore no nonzero centre-query +combination can be formed from that cone, even with all read times +granted and all final X and helper rows granted. Exact phases cannot +change a zero input. This proves the source cone theorem in its stated +scope. + +The eight normal lines are absent from the actual rank-one frames. A +cache can start empty in a new normal-line frame, but its first nonzero +snapshot is still at an actual frame. A subsequent monotone path then +lies in the cone of that actual frame. + +A separate exploratory screen used the 2,880 distinct retained native +climb edges. It found 6,068 rank-two-to-FULL paths. Over `GF(65521)`, every +path had zero query intersection after quotient by the 112 completed-X +rows and 402 FULL helper baselines. It granted every snapshot time at +each path node. This screen is not used as a rational impossibility +certificate; the exact support argument above gives the stronger result. + +## 3. The support annihilator of a query + +The independent checker also tests all 511 nonzero binary lines. It +gives exact nonzero minors for each rank claim: + +\[ +\operatorname{rank}R_{\{p:q_p\cdot v=1\}}= +\begin{cases} +7,&v\in\{42,7,25,52,82,127,97,76\},\\ +8,&\text{otherwise}. +\end{cases} \tag{5} +\] + +At normal `n_k`, row `k` is zero on the excluded columns. A nonzero +seven-column minor on the other rows proves that this is the entire +left kernel. Hence a nonzero query row `aR` has a source-support +annihilator of dimension at most one. If that dimension is one, the +line is `n_k` and `aR` is proportional to row `k` of `R`. + +Two independent query rows have trivial common annihilator. This does +not by itself give a rank-weighted network cost bound. + +## 4. A scalar monotone merge-tree bound + +Consider one rooted tree. Each edge carries one scalar-content field +from a child frame into a containing parent frame. Each leaf forms an +arbitrary scalar combination of granted snapshots in its frame. At a +merge, form a scalar linear combination of the incoming fields. The +root frame is FULL. Each edge has native cost at least its dimension +increase. This model permits cancellations and grants all read times. +It excludes address changes to the logical content and paid +subexpressions shared with a second output tree. + +For a node `v`, let `I_v` be the intersection of its descendant leaf +frames. The total cost below `v` is at least + +\[ +\dim U_v-\dim I_v. \tag{6} +\] + +For a leaf this is zero. Suppose `v` has `k` children. The induction +hypothesis and the `k` incoming edge costs give the lower bound + +\[ +k\dim U_v-\sum_{j=1}^k\dim I_j. +\] + +All `I_j` are subspaces of `U_v`. Codimension subadditivity gives + +\[ +\sum_j\dim I_j-\dim\bigcap_j I_j +\leq(k-1)\dim U_v, +\] + +which proves (6). A new snapshot added at an internal node can be +represented by a zero-length leaf in that node's frame, so the proof +also covers such reads. + +Every leaf row is supported on ports perpendicular to `I_root`. +The same is true after every scalar cancellation. If the final row is +a nonzero centre query, (5) gives `dim(I_root)<=1`. Thus the cost is at +least `9-1=8`. Eight separate trees cost at least 64. This conclusion +requires separate paid trees. It is not a bound for a shared +multi-output DAG, a different core, or cuts inside native children. + +## 5. Exact formulation for a shared network + +A time-expanded network node specifies an exact frame and an event cut. +It has a matrix `O_v` of available snapshot rows. Every native edge has +a supplied same-content recipe and an integer field capacity `c_e`. +Let `B_e` be the matrix of logical rows carried by that edge. + +A proposed network is a scalar certificate if, at each node, every +outgoing row is in the permitted-ring module generated by its incoming +rows and `O_v`. At FULL, the eight rows of `RY` must be in the module +generated by incoming rows and the unchanged endpoint rows `E`. +Explicit coefficient matrices for these inclusions give a circuit by +COPY, ADD, and CLEAR on owned fields. A storage schedule must preserve +each incoming field until its last use. The native cost is + +\[ +\sum_e c_e\,\operatorname{cost}(e). \tag{7} +\] + +Conversely, any linear cache circuit in this model gives such row +matrices. This is an exact algebraic formulation. It does not remove +the native recipe, timing, storage, coefficient, or complete-cost +obligations. + +There is a useful necessary cut inequality over any coefficient field. +Let `Omega` be a set of nodes containing the output. Let `S_Omega` be +the span of all observations at those nodes and the granted endpoint +rows. Then + +\[ +\operatorname{rank}(Q+S_\Omega)-\operatorname{rank}S_\Omega +\leq \sum_{e:\,e\text{ enters }\Omega}c_e. \tag{8} +\] + +Indeed, all information used inside the cut is generated by these +observations and the incoming edge rows. The inequality holds even +when the cut is not closed under the time order. + +Nonnegative cut weights give a cost lower bound if, for each edge, the +sum of weights of cuts that it enters is at most that edge's cost. +This gives a precise route to a shared-network lower-bound certificate. +No cut family with total bound 64 is supplied here. The scalar-tree +proof must not be used in place of that missing certificate. + +## 6. Reproduction and limits + +Run the independent exact check with: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/cover-algebra/review_snapshot_support.py +``` + +It writes `SNAPSHOT-SUPPORT-REVIEW.json`, with all 1,002 frame minors and +all 511 line minors. The result is +`PASS_EXACT_SNAPSHOT_SUPPORT_AND_SINGLE_CONE_EXCLUSION`. + +The check did not rerun the full snapshot producer or a new native +cache word. The source proof was inspected. No actual shared-network +solution, global owner assignment, or full supplier invoice is claimed. diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json b/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json new file mode 100644 index 0000000000..df5238431c --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json @@ -0,0 +1,26836 @@ +{ + "all_511_line_minors": [ + { + "columns": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ], + "determinant": "32", + "line": 1, + "rank": 8, + "rows": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7 + ] + }, + { + "columns": [ + 0, + 1, + 2, + 3, + 4, + 5, + 25, + 31 + ], + "determinant": "-32", + "line": 2, + "rank": 8, + "rows": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7 + ] + }, + { + "columns": [ + 6, + 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16687, + "line_rank_counts": { + "7": 8, + "8": 503 + }, + "minor_determinants": { + "-16": 1, + "-32": 126, + "-48": 2, + "-64": 45, + "32": 790, + "64": 38 + }, + "nonzero_port_incidence_checks": 104088, + "normal_lines_absent": [ + 42, + 7, + 25, + 52, + 82, + 127, + 97, + 76 + ], + "not_checked": [ + "The full snapshot producer replay", + "A new native cache word", + "Chronological branching synthesis", + "A complete supplier invoice" + ], + "phase_scope": "Scalar rows are read in the canonical view. Non-FULL views after event 17605 require the supplied endpoint monomial adapter.", + "proper_frame_minor_count": 1002, + "rows": 12271, + "scope": "One nonzero birth frame and all later containing frames. This does not exclude a merged network with incomparable capture frames.", + "status": "PASS_EXACT_SNAPSHOT_SUPPORT_AND_SINGLE_CONE_EXCLUSION", + "test_input": "X=JY; all 480 helper and eight private inputs are zero" +} diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/cover-algebra/review_snapshot_support.py b/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/cover-algebra/review_snapshot_support.py new file mode 100644 index 0000000000..76964357cf --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/cover-algebra/review_snapshot_support.py @@ -0,0 +1,165 @@ +"""Check the snapshot support law with exact integer arithmetic.""" + +from collections import Counter +from fractions import Fraction +from hashlib import sha256 +from math import lcm +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +SNAPSHOT_PIN = "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c" +INTERFACE_PIN = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" +PRIME = 65521 + + +def require(value, message): + if not value: + raise ValueError(message) + + +def determinant(matrix): + """Use exact elimination on the selected eight-column minor.""" + rows = [[Fraction(x) for x in row] for row in matrix] + result = Fraction(1) + for col in range(len(rows)): + pivot = next((j for j in range(col, len(rows)) if rows[j][col]), None) + if pivot is None: + return Fraction(0) + if pivot != col: + rows[col], rows[pivot] = rows[pivot], rows[col] + result = -result + value = rows[col][col] + result *= value + for j in range(col + 1, len(rows)): + scale = rows[j][col] / value + for k in range(col + 1, len(rows)): + rows[j][k] -= scale * rows[col][k] + return result + + +def select_minor(matrix, columns): + """Select columns over a finite field, then check their exact minor.""" + size = len(matrix) + pivots = {} + selected = [] + for column in columns: + row = [matrix[k][column] % PRIME for k in range(size)] + for k, pivot in sorted(pivots.items()): + factor = row[k] + row = [(a - factor*b) % PRIME for a, b in zip(row, pivot)] + leading = next((k for k, value in enumerate(row) if value), None) + if leading is not None: + scale = pow(row[leading], -1, PRIME) + pivots[leading] = [value*scale % PRIME for value in row] + selected.append(column) + if len(selected) == size: + break + require(len(selected) == size, "An excluded-column block has deficient rank") + value = determinant([[row[p] for p in selected] for row in matrix]) + require(value != 0, "The selected rational minor is zero") + return selected, str(value) + + +def main(): + snapshot_path = HERE.parent / "history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz" + raw = gzip.decompress(snapshot_path.read_bytes()) + require(sha256(raw).hexdigest() == SNAPSHOT_PIN, "The snapshot pin differs") + data = json.loads(raw) + interface_path = HERE.parent / "circuit-interface/INTERFACE.json" + interface_raw = interface_path.read_bytes() + require(sha256(interface_raw).hexdigest() == INTERFACE_PIN, "The interface pin differs") + interface = json.loads(interface_raw) + labels = interface["ports"] + R = [[int(Fraction(row.get(str(j), "0"))) for j in range(112)] + for row in data["R"]] + require(R == [[int(Fraction(row.get(str(j), "0"))) for j in range(112)] + for row in interface["R"]], "The root matrices differ") + require(all(Fraction(v).denominator == 1 for row in data["R"] for v in row.values()), + "A root coefficient is not an integer") + require([[sum(a*b for a, b in zip(R[i], R[j])) for j in range(8)] + for i in range(8)] == [[56*int(i == j) for j in range(8)] for i in range(8)], + "The root Gram differs") + J4 = [{q: 4*int(p == q)-sum(row[p]*row[q] for row in R) + for q in range(112)} for p in range(112)] + J4 = [{q: value for q, value in row.items() if value} for row in J4] + reduced = [] + for item in data["rows"]: + row = {int(k): Fraction(value) for k, value in item.items() if int(k) < 224} + denominator = lcm(*(value.denominator for value in row.values())) + output = {} + for k, value in row.items(): + coefficient = int(value*denominator) + source = J4[k] if k < 112 else {k-112: 4} + for q, entry in source.items(): + output[q] = output.get(q, 0) + coefficient*entry + reduced.append({q: value for q, value in output.items() if value}) + failures = [] + full_nonzero = [] + support_checks = 0 + for first, last, wire, frame, row in data["intervals"]: + basis = data["frames"][frame] + for port in reduced[row]: + support_checks += 1 + if any((labels[port] & vector).bit_count() % 2 for vector in basis): + failures.append([first, last, wire, frame, row, port]) + if frame == 1 and reduced[row]: + full_nonzero.append(row) + require(not failures, "A snapshot violates the exact support law") + require(not full_nonzero, "A FULL snapshot remains nonzero on the test input") + minors = [] + for frame, basis in enumerate(data["frames"]): + if not 0 < len(basis) < 9: + continue + excluded = [p for p, q in enumerate(labels) + if any((q & v).bit_count() % 2 for v in basis)] + columns, value = select_minor(R, excluded) + minors.append({"frame": frame, "columns": columns, "determinant": value}) + normals = [42, 7, 25, 52, 82, 127, 97, 76] + require(all([n] not in data["frames"] for n in normals), "A normal line is an actual frame") + require(all({p for p, value in enumerate(R[k]) if value} + == {p for p, q in enumerate(labels) if (q & n).bit_count() % 2 == 0} + for k, n in enumerate(normals)), "The normal support relation differs") + line_minors = [] + for vector in range(1, 512): + excluded = [p for p, q in enumerate(labels) if (q & vector).bit_count() % 2] + omit = normals.index(vector) if vector in normals else None + selected_rows = [k for k in range(8) if k != omit] + columns, value = select_minor([R[k] for k in selected_rows], excluded) + if omit is not None: + require(all(R[omit][p] == 0 for p in excluded), "A normal line has the wrong kernel") + line_minors.append({"line": vector, "rank": len(selected_rows), + "rows": selected_rows, "columns": columns, + "determinant": value}) + source_proof = HERE.parent / "history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md" + source_receipt = HERE.parent / "history-encoding/SNAPSHOT-CONE-OBSTRUCTION.json" + result = { + "status": "PASS_EXACT_SNAPSHOT_SUPPORT_AND_SINGLE_CONE_EXCLUSION", + "inputs": {"snapshot_decompressed_sha256": SNAPSHOT_PIN, + "interface_sha256": INTERFACE_PIN, + "reviewed_source_proof_sha256": sha256(source_proof.read_bytes()).hexdigest(), + "reviewed_source_receipt_sha256": sha256(source_receipt.read_bytes()).hexdigest()}, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "rows": len(reduced), "intervals": len(data["intervals"]), + "nonzero_port_incidence_checks": support_checks, + "proper_frame_minor_count": len(minors), + "minor_determinants": dict(Counter(item["determinant"] for item in minors)), + "excluded_column_minors": minors, + "all_511_line_minors": line_minors, + "line_rank_counts": dict(Counter(item["rank"] for item in line_minors)), + "normal_lines_absent": normals, + "test_input": "X=JY; all 480 helper and eight private inputs are zero", + "scope": "One nonzero birth frame and all later containing frames. This does not exclude a merged network with incomparable capture frames.", + "phase_scope": "Scalar rows are read in the canonical view. Non-FULL views after event 17605 require the supplied endpoint monomial adapter.", + "not_checked": ["The full snapshot producer replay", "A new native cache word", "Chronological branching synthesis", "A complete supplier invoice"], + } + output = HERE / "SNAPSHOT-SUPPORT-REVIEW.json" + output.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(json.dumps({k: v for k, v in result.items() + if k not in {"excluded_column_minors", "all_511_line_minors"}}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz b/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/history-encoding/BACKWARD-SNAPSHOT-INTERVALS.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..9011ba4b63bc130352155843f605450c233865bc GIT binary patch literal 414717 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"excluded_count": 110, + "frame": 981, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 259, + 135, + 67, + 33, + 18, + 12 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 982, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 129, + 64, + 33, + 17, + 9, + 5, + 3 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 983, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 132, + 64, + 32, + 16, + 12, + 2, + 1 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 984, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 320, + 131, + 33, + 18, + 8, + 4 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 985, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 130, + 64, + 32, + 18, + 8, + 4, + 1 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 986, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 129, + 64, + 33, + 16, + 8, + 4, + 2 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 987, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 262, + 135, + 70, + 33, + 18, + 12 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 988, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 320, + 134, + 32, + 18, + 12, + 1 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 989, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 263, + 131, + 67, + 33, + 18, + 12 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 990, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 260, + 128, + 64, + 32, + 16, + 12, + 2, + 1 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 991, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 257, + 128, + 64, + 33, + 17, + 9, + 5, + 3 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 992, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 259, + 192, + 33, + 18, + 8, + 4 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 993, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 257, + 128, + 64, + 33, + 16, + 8, + 4, + 2 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 994, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 258, + 128, + 64, + 32, + 18, + 8, + 4, + 1 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 995, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 263, + 134, + 70, + 33, + 18, + 12 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 996, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 262, + 192, + 32, + 18, + 12, + 1 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 997, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 64, + 33, + 17, + 8, + 4, + 3 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 998, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 64, + 32, + 18, + 10, + 6, + 1 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 999, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 65, + 32, + 16, + 9, + 4, + 3 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 1000, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 66, + 34, + 16, + 8, + 6, + 1 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 1001, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 65, + 32, + 17, + 8, + 5, + 2 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 1002, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 72, + 40, + 24, + 4, + 2, + 1 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 1003, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + } + ], + "frames_by_rank": { + "1": 120, + "2": 168, + "3": 168, + "4": 73, + "5": 27, + "6": 168, + "7": 152, + "8": 126 + }, + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "interval_count": 16687, + "normal_lines": [ + 42, + 7, + 25, + 52, + 82, + 127, + 97, + 76 + ], + "normal_lines_are_absent": true, + "scope": "Single positive-birth cone, with all cone snapshots and all completed X/helper baselines. Merged incomparable cones and other protocols remain open.", + "snapshot_payload_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", + "source_pins": { + "R": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "core": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877", + "word": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219" + }, + "status": "PASS_EXACT_SNAPSHOT_CONE_OBSTRUCTION", + "support_law": "At frame U, every nonzero reduced Y coefficient has q_p perpendicular to U.", + "test_input": "X=JY; all 480 helpers and all 8 private inputs are zero", + "wrong_frame_control": { + "original_frame": 2, + "rejected": true, + "row": 3382, + "source_port": 35, + "wrong_line": 50 + } +} diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md b/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md new file mode 100644 index 0000000000..09ba0af502 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/frozen/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md @@ -0,0 +1,129 @@ +# An exact obstruction for one monotone snapshot cone + +The backward clean-J word has no nonzero centre query in a single positive +snapshot cone. This result covers all 1,002 positive proper frames in the +actual word. It permits every recorded snapshot in that cone, without a +time constraint. Thus time order is not the obstruction in this model. + +This result does not cover a network that merges captures from different +cones. It also does not cover new internal cuts inside a native child, new +changes to the core, or transitions between incomparable frames. + +## Source and exact check + +`BACKWARD-SNAPSHOT-INTERVALS.json.gz` records the complete rational scalar +rows on 712 input coordinates. Its uncompressed SHA256 is +`3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c`. +The producer is `emit_snapshot_intervals.py`. It checks every scalar frame +access and every native frame transition. It also checks the final map + +\[ + (x,y,h,c)\longmapsto(x-Jy,y,h,0),\qquad + J=I-R^TR/4. +\] + +There are 12,271 distinct rows, 16,687 availability intervals, and 1,004 +native frames. An interval `[a,b,j,f,r]` states that row `r` of wire `j` +is available after each event from `a` through `b`, inclusive, with frame +index `f`. The recorded boundary range is 8,106 through 24,913. + +The scalar content uses the canonical frame coordinates. Before event +17,606, these are the literal native frames after the entry adapters. +After that event, a non-FULL field needs its specified inverse exit +monomial to expose that canonical view. This theorem grants those views. +It makes no claim that they are free in a constructive word. A zero +formal row is zero in both views, which is all that this proof needs. + +Run the exact certificate with: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/history-encoding/check_snapshot_cone_obstruction.py +``` + +The result is `PASS_EXACT_SNAPSHOT_CONE_OBSTRUCTION`. The checker uses +rational arithmetic. It checks 16,023 distinct frame/row pairs and 98,056 +nonzero reduced coefficients. For each of the 1,002 positive proper +frames, it emits an eight-column minor with a nonzero exact determinant. +The receipt is `SNAPSHOT-CONE-OBSTRUCTION.json`. + +The two controls reject a wrong frame for a nonzero source coefficient +and a repeated column in a query minor. No sampled rank or numerical +tolerance is used in this certificate. + +## Support identity + +Write the old port labels as \(q_p\in\mathbb F_2^9\), for +\(0\leq p<112\). Use the following valid family of inputs: + +\[ + x=Jy,\qquad h=0,\qquad c=0. +\] + +Here all 480 helper inputs are zero. This includes the 78 helpers whose +final frame is not FULL. This choice is an input for an impossibility +proof. It is not a clean-helper assumption for a proposed construction. +On this family, all completed X fields and all final helper fields vanish. + +For each actual snapshot in a frame \(U\), its remaining source row has +the form + +\[ + \sum_{p:q_p\perp U} a_p y_p. \tag{1} +\] + +The checker proves (1) directly from every exact row. It substitutes +\(x=Jy\), deletes the zero helper and private inputs, and checks the +support of each remaining coefficient. This includes data snapshots, +not only helper snapshots. + +Fix an actual positive proper frame \(U\), and set + +\[ + E_U=\{p:q_p\not\perp U\}. +\] + +The exact minor certificate proves + +\[ + \operatorname{rank} R_{E_U}=8. \tag{2} +\] + +The eight normal lines \(42,7,25,52,82,127,97,76\) do not contradict (2). +Row \(k\) of \(R\) is supported exactly on the ports perpendicular to +normal \(n_k\). But none of these normal lines is an actual rank-one +frame. The actual rank-one frames consist of the 112 old port lines and +eight even lines. Their absence and the normal support identity are both +checked exactly. + +## Cone theorem + +For an actual positive proper frame \(U\), its snapshot cone consists of +all recorded frames \(V\) such that \(U\subseteq V\). Grant every +snapshot in that cone, without a time constraint. Also grant every final +X and helper field, with arbitrary linear operations on those granted +fields. + +No nonzero scalar combination of the eight completed centre queries +\(F_9 R y\) can be formed from these observations. + +To prove the statement, restrict \(y\) to the coordinates in \(E_U\). +If \(V\supseteq U\), then \(q_p\perp V\) implies +\(q_p\perp U\). Thus (1) makes every snapshot in the cone zero. +The final X and helper fields are also zero. Every linear operation on +these observations is zero, with every native phase and address map. +But (2) allows \(Ry\) to take any value in eight dimensions. Since +\(F_9\) is invertible, the required nonzero query cannot be zero on all +these inputs. This is a contradiction. + +In particular, a cache that starts at zero, first captures content in a +positive actual frame, and then follows only increasing native frames +cannot produce a centre query. The same conclusion holds for any number +of caches restricted to that one cone. Allowing all cone snapshots is +stronger than any one chronological path. A cache that starts empty in +an unrecorded smaller frame must still make its first nonzero capture +in an actual frame; the theorem then applies from that frame onward. + +The theorem does not rule out a cache with earlier nonzero captures from +an incomparable frame. That is the precise remaining escape for a +merged snapshot network. It gives no lower bound for such a network, +for a different core, or for the complete supplier. diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/replay.py b/research/actual-query-information-bounds/annexes/chronological-cache-paths/replay.py new file mode 100644 index 0000000000..46a081958d --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/replay.py @@ -0,0 +1,72 @@ +"""Replay one support appendix in fresh source copies.""" + +import argparse +from hashlib import sha256 +import json +import os +from pathlib import Path +import shutil +import subprocess +import sys +import time + + +def digest(path): + return sha256(path.read_bytes()).hexdigest() + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + package = Path(__file__).resolve().parent + config = json.loads((package/"TASK.json").read_text()) + manifest = json.loads((package/"SOURCES.json").read_text()) + + def verify(): + for rel, record in manifest["frozen_files"].items(): + path = package/"frozen"/rel + if digest(path) != record["sha256"] or path.stat().st_size != record["bytes"]: + raise ValueError("Frozen source differs: "+rel) + + verify() + output = args.out.resolve() + output.mkdir(parents=True, exist_ok=False) + runs = [] + env = dict(os.environ, OPENBLAS_NUM_THREADS="1", OMP_NUM_THREADS="1", + MKL_NUM_THREADS="1", VECLIB_MAXIMUM_THREADS="1") + for mode in ("normal", "optimized"): + workspace = output/mode + shutil.copytree(package/"frozen", workspace) + (workspace/"results").mkdir(exist_ok=True) + script = (package if config["location"] == "package" else workspace)/config["script"] + command = [sys.executable, "-I", "-B"] + if mode == "optimized": + command.append("-O") + command.append(str(script)) + command.extend(v.format(workspace=str(workspace)) for v in config["arguments"]) + start = time.monotonic() + result = subprocess.run(command, cwd=workspace, env=env, + capture_output=True, text=True) + (output/(mode+".log")).write_text(result.stdout+result.stderr) + if result.returncode: + raise RuntimeError("Child failed: "+mode) + receipt = workspace/config["receipt"] + if receipt.read_bytes() != (package/config["expected"]).read_bytes(): + raise ValueError("Receipt bytes differ: "+mode) + runs.append({"mode": mode, "command": command, "exit_code": 0, + "receipt_sha256": digest(receipt), + "elapsed_seconds": round(time.monotonic()-start, 3)}) + print("PASS", mode, config["id"], flush=True) + verify() + receipt = {"status": "PASS_SCOPED_SUPPORT_PROOF_REPLAY", "appendix": config["id"], + "runs": runs, "source_manifest_sha256": digest(package/"SOURCES.json"), + "runner_sha256": digest(Path(__file__)), + "comparison": "Both complete receipt files match exact bytes.", + "scope": config["scope"]} + (output/"REPLAY.json").write_text(json.dumps(receipt, indent=2, sort_keys=True)+"\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/validation/normal.log b/research/actual-query-information-bounds/annexes/chronological-cache-paths/validation/normal.log new file mode 100644 index 0000000000..1f3f900e3a --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/validation/normal.log @@ -0,0 +1 @@ +{"checker_sha256": "b605064b4be17fd2ceb6825fe01cd6b813abd3351ad499dd6c5b4fa4947a52ba", "inputs": {"interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", "reviewed_source_proof_sha256": "be9575e1cac8706c42fddff243f435935e098d197edaf7f8689352c93b7e3961", "reviewed_source_receipt_sha256": "35698700474f2309a4eea2f192a5afbd2f42f580a7e0e510a0bb5687a87fdc2d", "snapshot_decompressed_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c"}, "intervals": 16687, "line_rank_counts": {"7": 8, "8": 503}, "minor_determinants": {"-16": 1, "-32": 126, "-48": 2, "-64": 45, "32": 790, "64": 38}, "nonzero_port_incidence_checks": 104088, "normal_lines_absent": [42, 7, 25, 52, 82, 127, 97, 76], "not_checked": ["The full snapshot producer replay", "A new native cache word", "Chronological branching synthesis", "A complete supplier invoice"], "phase_scope": "Scalar rows are read in the canonical view. Non-FULL views after event 17605 require the supplied endpoint monomial adapter.", "proper_frame_minor_count": 1002, "rows": 12271, "scope": "One nonzero birth frame and all later containing frames. This does not exclude a merged network with incomparable capture frames.", "status": "PASS_EXACT_SNAPSHOT_SUPPORT_AND_SINGLE_CONE_EXCLUSION", "test_input": "X=JY; all 480 helper and eight private inputs are zero"} diff --git a/research/actual-query-information-bounds/annexes/chronological-cache-paths/validation/optimized.log b/research/actual-query-information-bounds/annexes/chronological-cache-paths/validation/optimized.log new file mode 100644 index 0000000000..1f3f900e3a --- /dev/null +++ b/research/actual-query-information-bounds/annexes/chronological-cache-paths/validation/optimized.log @@ -0,0 +1 @@ +{"checker_sha256": "b605064b4be17fd2ceb6825fe01cd6b813abd3351ad499dd6c5b4fa4947a52ba", "inputs": {"interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", "reviewed_source_proof_sha256": "be9575e1cac8706c42fddff243f435935e098d197edaf7f8689352c93b7e3961", "reviewed_source_receipt_sha256": "35698700474f2309a4eea2f192a5afbd2f42f580a7e0e510a0bb5687a87fdc2d", "snapshot_decompressed_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c"}, "intervals": 16687, "line_rank_counts": {"7": 8, "8": 503}, "minor_determinants": {"-16": 1, "-32": 126, "-48": 2, "-64": 45, "32": 790, "64": 38}, "nonzero_port_incidence_checks": 104088, "normal_lines_absent": [42, 7, 25, 52, 82, 127, 97, 76], "not_checked": ["The full snapshot producer replay", "A new native cache word", "Chronological branching synthesis", "A complete supplier invoice"], "phase_scope": "Scalar rows are read in the canonical view. Non-FULL views after event 17605 require the supplied endpoint monomial adapter.", "proper_frame_minor_count": 1002, "rows": 12271, "scope": "One nonzero birth frame and all later containing frames. This does not exclude a merged network with incomparable capture frames.", "status": "PASS_EXACT_SNAPSHOT_SUPPORT_AND_SINGLE_CONE_EXCLUSION", "test_input": "X=JY; all 480 helper and eight private inputs are zero"} From cb102a57254748651ce16aa4454bb611f6380e53 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Thu, 22 Oct 2026 14:20:14 -0500 Subject: [PATCH 4/4] Add source geometry and actual operator-query lower bounds --- .gitattributes | 3 + .../source-geometry/ANNEX-MANIFEST.json | 405 + .../source-geometry/ARCHIVE-CHECK.json | 27 + .../annexes/source-geometry/NOTICE.md | 71 + .../source-geometry/PARENT-SNAPSHOT.json | 524 + .../annexes/source-geometry/PORTABILITY.json | 105 + .../annexes/source-geometry/PORTABILITY.patch | 263 + .../annexes/source-geometry/README.md | 226 + .../annexes/source-geometry/SOURCES.json | 463 + .../annexes/source-geometry/VALIDATION.md | 43 + .../centre-mixing-review/REVIEW.json | 13363 +++++++++++++++ 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No native-child, scratch, supplier, or kappa improvement." +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/ARCHIVE-CHECK.json b/research/actual-query-information-bounds/annexes/source-geometry/ARCHIVE-CHECK.json new file mode 100644 index 0000000000..304f9af1c1 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/ARCHIVE-CHECK.json @@ -0,0 +1,27 @@ +{ + "archive_bytes": 6095634, + "archive_original_path": "worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz", + "archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "runtime_scope": "The portable replay checks the parent member bytes. It does not require the full archive.", + "status": "PASS_EXACT_OLD_ARCHIVE_AND_PARENT_MEMBERS", + "unique_regular_members": [ + { + "archive_member": "candidate/strict/global/base/providers/gauge44/CANONICAL-WORD.json.gz", + "bytes": 84805, + "parent_path": "payload/upstream/CANONICAL-WORD.json.gz", + "sha256": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219" + }, + { + "archive_member": "candidate/strict/global/base/providers/gauge44/LOCAL-PROGRAMS.json.gz", + "bytes": 209318, + "parent_path": "payload/upstream/LOCAL-PROGRAMS.json.gz", + "sha256": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a" + }, + { + "archive_member": "candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json", + "bytes": 814141, + "parent_path": "payload/upstream/DATA-PHASES.json", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + } + ] +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/NOTICE.md b/research/actual-query-information-bounds/annexes/source-geometry/NOTICE.md new file mode 100644 index 0000000000..9aade8ecda --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/NOTICE.md @@ -0,0 +1,71 @@ +# Source and license notice + +The campaign results and new publication files use the repository's +Apache-2.0 license. A copy is in [notices/LICENSE](notices/LICENSE). +Original source text, notices, and receipts are unchanged. OpenAI Codex +assisted the proofs, exact checks, separate agent reviews, and packaging. +No independent human review or formal proof assistant verification is +claimed. + +The root and history-encoding lanes supplied the support geometry. The +controller-followthrough lane supplied the structured centre rows and +full-null source family. The oblique-native lane supplied the mixed-source +unit criterion and complete cut inventory. The root supplied the residue +argument. The coherent-port lane supplied the centre restriction and its +integer certificate. The bridge-review lane supplied the independent +interval audit, physical support proof, ring clarification, and two-basis +explanation. The independent-review lane checked the support spaces. The +schur-selection lane supplied the source/response-span theorem. The +source-domain lane independently reconstructed its source and checked the +line and plane certificates. The interface-proof lane checked the initial +factorizations. These roles refer to the recorded AI-agent work. + +The historical line source and phase data use the parent package's +unchanged source members and notices. The parent +[source record](../../SOURCE-PINS.md) and [notice](../../NOTICE.md) retain +the supplier, controller, compiler, and owner credit. The archive used by +the historical query-span review has SHA256 +`f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6`. +Its three consumed members are byte-equal to the parent members. The new +[archive check](ARCHIVE-CHECK.json) records that comparison. + +The clean core derives from +[PR #3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133), at +`51eb9c4ee9e4722010d308aa3309e039d3940cc2`, and the byte-equal provider +words in [PR #3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148), +at `f2927a4b8afcf0701a6b945e14f30de1d94f5176`. The retained +[notice](notices/PR3133-NOTICE) and [credits](notices/PR3133-CREDITS.md) +credit dcharb78 for the coupled folds and preserve the earlier lineage. +The exact PR #3148 README credits Jeremy Diviney for packing exchange, +integration, and verification. No author is inferred from a submitter. +The [source readback](evidence/source-verification/NATIVE-SOURCE-VERIFICATION.json) +and [notice readback](evidence/source-verification/PROVIDER-NOTICE-VERIFICATION.json) +retain the immutable object and hash checks made before this extraction. + +The logical warp definition comes from +[PR #2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588), at +`8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`. Its +[notice](notices/PR2588-NOTICE) credits Cinna Davis, Rohan Arun, Jeremy +Kothe, and named predecessors for their stated contributions. This annex +reads the unchanged definition as source evidence. It does not rerun the +native recipe compiler or claim authorship of that compiler. + +The 56-plane matching comes from +[PR #1825](https://github.com/CrocSwap/integer-mult-bounds/pull/1825), at +`d16fb8936795ff101e4d2f63cfdc6a25066ebabf`. Its retained +[README](frozen/lanes/interface-proof/github-refresh-20261014-1155/pr1825_readme.md) +and [exact readback](frozen/lanes/interface-proof/github-refresh-20261014-1155/pr1825_readme.json) +preserve the selected-lineage and earlier discussion credit and identify +OpenAI Codex research-agent preparation. The retained +[certificate](frozen/lanes/schur-selection/plane-repair/sources/PR1825-CERTIFICATE.json) +and [proof](frozen/lanes/schur-selection/plane-repair/sources/PR1825-PROOF.md) +are source evidence for the matching. No human author is inferred from +the PR submitter. No separate source-specific license notice was present +in the bounded saved PR #1825 record; the repository license and original +credit text are retained. + +The predecessor's binary factorization, scalar-price screen, and route +claims are not new claims of this annex. The query-span checker verifies +the consumed matching, exact plane operators, and source minors directly. +Other results mentioned by the frozen source files remain context unless +the README lists them as executed checks. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/PARENT-SNAPSHOT.json b/research/actual-query-information-bounds/annexes/source-geometry/PARENT-SNAPSHOT.json new file mode 100644 index 0000000000..b304658f76 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/PARENT-SNAPSHOT.json @@ -0,0 +1,524 @@ +{ + "excluded_new_annex": "annexes/source-geometry", + "file_count": 129, + "files": { + "NOTICE.md": { + "bytes": 2203, + "sha256": "40e1cf742e31b0146f7dfb506871651fbce1545ed1e9b6d73926bc1cce8eca79" + }, + "PACKAGE-MANIFEST.json": { + "bytes": 19932, + "sha256": "7317a4956c2d734d4a7376d252f12a8543ba5d7977572ea3c17758c74e9f8aca" + }, + "PROOF.md": { + "bytes": 10470, + "sha256": 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"PASS_CENTRE_SUPPORT_GEOMETRY", + "frozen_script": "frozen/root/check_centre_support_geometry_20261018.py", + "function_count": 3, + "name": "centre-support-producer", + "non_main_function_AST_equal": true, + "original_sha256": "99582e42007012d31dcddc14e05da8c5aac75c1f3b546c00ef0fcf0169f081b2", + "portable_script": "portable/centre-support-producer.py", + "portable_sha256": "87968c0d45b7194742feec2df265457058d0853193333c49e1148069a2329519", + "receipts": [ + "frozen/root/CENTRE-SUPPORT-GEOMETRY-20261018.json" + ] + }, + { + "allowed_edits": "Input root, explicit output CLI, output destinations; query-span archive loading uses exact parent members.", + "expected_status": "PASS_INDEPENDENT_CENTRE_SUPPORT_GEOMETRY", + "frozen_script": "frozen/lanes/independent-review-20261017/centre-support-review-20261018/check_support.py", + "function_count": 3, + "name": "centre-support-review", + "non_main_function_AST_equal": true, + "original_sha256": "a8c8e4ee762d5052414f44d2060745c1cc74d47d241c379ee1bdc58fe5aac8b8", + "portable_script": "portable/centre-support-review.py", + "portable_sha256": "e2785466e186ad51ddc3c9f2335f4f441206531e7b2dbf61e5cb080ba23c8c46", + "receipts": [ + "frozen/lanes/independent-review-20261017/centre-support-review-20261018/CHECKS.json" + ] + }, + { + "allowed_edits": "Input root, explicit output CLI, output destinations; query-span archive loading uses exact parent members.", + "expected_status": "PASS_DYADIC_QUERY_SEPARATION", + "frozen_script": "frozen/root/check_dyadic_query_separation_20261018.py", + "function_count": 6, + "name": "dyadic-producer", + "non_main_function_AST_equal": true, + "original_sha256": "b4ed000b5b600944f614b86ae7a88ac55af8eac3213e6827ed211a2630ccd342", + "portable_script": "portable/dyadic-producer.py", + "portable_sha256": "f949b92e3672c1b854f584c46c3ec36664db38c5cd0dfa80767c2d41996d4130", + "receipts": [ + "frozen/root/DYADIC-QUERY-SEPARATION-20261018.json" + ] + }, + { + "allowed_edits": "Input root, explicit output CLI, output destinations; query-span archive loading uses exact parent members.", + "expected_status": "PASS_INDEPENDENT_DYADIC_QUERY_SEPARATION", + "frozen_script": "frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/check_review.py", + "function_count": 16, + "name": "dyadic-review", + "non_main_function_AST_equal": true, + "original_sha256": "d7f2338efcd0c006f02fcab0bc36f83557fa38c7070c420a7b4a405b91452af5", + "portable_script": "portable/dyadic-review.py", + "portable_sha256": "bdc237dd266102fa99170aab0d309c3f03894924875f5a8a79d198d6fbd02548", + "receipts": [ + "frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/REVIEW.json" + ] + }, + { + "allowed_edits": "Input root, explicit output CLI, output destinations; query-span archive loading uses exact parent members.", + "expected_status": "PASS_INDEPENDENT_NATIVE_CENTRE_REVIEW", + "frozen_script": "frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/check_review.py", + "function_count": 14, + "name": "centre-mixing-review", + "non_main_function_AST_equal": true, + "original_sha256": "e1ee26d24acd2c894596c7f0672239e5d2ec02bc54734006f76db3c1b062f84a", + "portable_script": "portable/centre-mixing-review.py", + "portable_sha256": "2bcfa8a1ebf3464700453023b89ec7060a39dc6e5794510bec1d1dc2b19c3dcb", + "receipts": [ + "frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/REVIEW.json", + "frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/TWO-BASES.json" + ] + }, + { + "allowed_edits": "Input root, explicit output CLI, output destinations; query-span archive loading uses exact parent members.", + "expected_status": "PASS_EXACT_QUERY_SOURCE_SPANS", + "frozen_script": "frozen/lanes/schur-selection/plane-repair/check_query_span.py", + "function_count": 2, + "name": "query-span-producer", + "non_main_function_AST_equal": true, + "original_sha256": "bcc8bb5482c76578014512d51dd5d650d4bf13d6546b29e355ae01bec8a07811", + "portable_script": "portable/query-span-producer.py", + "portable_sha256": "0bc0a07bf80fac3c06d920859f3097a65a29f8718bd987b3cdea37249cc415d5", + "receipts": [ + "frozen/lanes/schur-selection/plane-repair/QUERY-SPAN.json" + ] + }, + { + "allowed_edits": "Input root, explicit output CLI, output destinations; query-span archive loading uses exact parent members.", + "expected_status": "PASS_INDEPENDENT_QUERY_SPAN_SOURCE_AND_CERTIFICATE", + "frozen_script": "frozen/lanes/source-domain/query-span-review/review_query_span.py", + "function_count": 3, + "name": "query-span-review", + "non_main_function_AST_equal": true, + "original_sha256": "f13d88dffbe36b9d6e349786fd368343fd57f46766e839ca52d3cf46f7c82184", + "portable_script": "portable/query-span-review.py", + "portable_sha256": "268ac2938b8282e030578f8bd50d83635e8cf7da60e972cee93155f238624f19", + "receipts": [ + "frozen/lanes/source-domain/query-span-review/REVIEW.json" + ] + } + ], + "receipt_metadata_exception": "Only checker_sha256 can differ, and it must equal the executing portable script hash.", + "schema": "source-geometry-portability-v1" +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/PORTABILITY.patch b/research/actual-query-information-bounds/annexes/source-geometry/PORTABILITY.patch new file mode 100644 index 0000000000..675f04dd9d --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/PORTABILITY.patch @@ -0,0 +1,263 @@ +--- frozen/root/check_centre_support_geometry_20261018.py ++++ portable/centre-support-producer.py +@@ -9,7 +9,15 @@ + from pathlib import Path + + +-HERE = Path(__file__).resolve().parent ++import argparse ++ ++ANNEX = Path(__file__).resolve().parents[1] ++PARENT = ANNEX.parents[1] ++parser = argparse.ArgumentParser(description=__doc__) ++parser.add_argument("--out", required=True) ++OUT = Path(parser.parse_args().out).resolve() ++OUT.mkdir(parents=True, exist_ok=True) ++HERE = ANNEX / "frozen" / 'root' + LANES = HERE.parent / "lanes" + SOURCES = { + "directions": ( +@@ -124,7 +132,7 @@ + "or general query lower bound is claimed." + ), + } +- target = HERE / "CENTRE-SUPPORT-GEOMETRY-20261018.json" ++ target = OUT / "CENTRE-SUPPORT-GEOMETRY-20261018.json" + target.write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(receipt["status"]) + +--- frozen/lanes/independent-review-20261017/centre-support-review-20261018/check_support.py ++++ portable/centre-support-review.py +@@ -6,7 +6,15 @@ + import gzip + import json + +-HERE = Path(__file__).resolve().parent ++import argparse ++ ++ANNEX = Path(__file__).resolve().parents[1] ++PARENT = ANNEX.parents[1] ++parser = argparse.ArgumentParser(description=__doc__) ++parser.add_argument("--out", required=True) ++OUT = Path(parser.parse_args().out).resolve() ++OUT.mkdir(parents=True, exist_ok=True) ++HERE = ANNEX / "frozen" / 'lanes/independent-review-20261017/centre-support-review-20261018' + CAMPAIGN = HERE.parents[2] + LANES = CAMPAIGN/'lanes' + ROOT = CAMPAIGN/'root' +@@ -111,7 +119,7 @@ + 'method': 'Explicit primal XOR closure; independent RREF nullspace equations; exact set intersections; complete multipartite graph proof.', + 'scope': 'One direct capture per row with single unwarped carriers on monotone source-subspace chains. Pair coding violates this carrier premise.', + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest()} +- (HERE/'CHECKS.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') ++ (OUT/'CHECKS.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(result['status']) + + +--- frozen/root/check_dyadic_query_separation_20261018.py ++++ portable/dyadic-producer.py +@@ -7,7 +7,15 @@ + import json + + +-HERE = Path(__file__).resolve().parent ++import argparse ++ ++ANNEX = Path(__file__).resolve().parents[1] ++PARENT = ANNEX.parents[1] ++parser = argparse.ArgumentParser(description=__doc__) ++parser.add_argument("--out", required=True) ++OUT = Path(parser.parse_args().out).resolve() ++OUT.mkdir(parents=True, exist_ok=True) ++HERE = ANNEX / "frozen" / 'root' + CORE = HERE.parent / "lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz" + CORE_PIN = "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa" + A = [0, 7, 20, 27, 36, 46, 57, 111] +@@ -120,7 +128,7 @@ + "matched_section_stack_rank": 8, + "scope": "Source information rank and exact representation choice; no native child bound or supplier claim.", + } +- destination = HERE / "DYADIC-QUERY-SEPARATION-20261018.json" ++ destination = OUT / "DYADIC-QUERY-SEPARATION-20261018.json" + destination.write_text(json.dumps(receipt, indent=2) + "\n", encoding="utf-8") + print(receipt["status"]) + +--- frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/check_review.py ++++ portable/dyadic-review.py +@@ -7,7 +7,15 @@ + from pathlib import Path + + +-HERE = Path(__file__).resolve().parent ++import argparse ++ ++ANNEX = Path(__file__).resolve().parents[1] ++PARENT = ANNEX.parents[1] ++parser = argparse.ArgumentParser(description=__doc__) ++parser.add_argument("--out", required=True) ++OUT = Path(parser.parse_args().out).resolve() ++OUT.mkdir(parents=True, exist_ok=True) ++HERE = ANNEX / "frozen" / 'lanes/bridge-review-20261017/dyadic-query-separation-review-20261018' + CAMPAIGN = HERE.parents[2] + PINS = { + "root/DYADIC-QUERY-SEPARATION-20261018.md": "664f430efd099f35cbc7c2abc8025968c03020707027857d2882daa51a065a1a", +@@ -290,7 +298,7 @@ + "actual_source": actual, "routed_operator_fixture": routed, "formal_full_null": full_null, + "universal_proof": "Residue row relation times D forces beta=0 because MD is a unit; full residue rank of B forces alpha=0. A nonzero residue minor lifts to the fraction field.", + "scope": "Fixed linear observations on the full underlying field space, with arbitrary postprocessing. No native-child, bit-packing, arbitrary nonlinear-encoding or complete supplier lower bound."} +- (HERE / "REVIEW.json").write_text(json.dumps(out, sort_keys=True, indent=2) + "\n") ++ (OUT / "REVIEW.json").write_text(json.dumps(out, sort_keys=True, indent=2) + "\n") + print(out["status"]) + print(json.dumps({"rank": 16, "matched_rank": 8, "MD_nonidentity_cases": 24, "routed_rank": 32, + "null_family_uses_MD_identity": False}, sort_keys=True)) +--- frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/check_review.py ++++ portable/centre-mixing-review.py +@@ -8,7 +8,15 @@ + from pathlib import Path + + +-HERE = Path(__file__).resolve().parent ++import argparse ++ ++ANNEX = Path(__file__).resolve().parents[1] ++PARENT = ANNEX.parents[1] ++parser = argparse.ArgumentParser(description=__doc__) ++parser.add_argument("--out", required=True) ++OUT = Path(parser.parse_args().out).resolve() ++OUT.mkdir(parents=True, exist_ok=True) ++HERE = ANNEX / "frozen" / 'lanes/bridge-review-20261017/centre-mixing-review-20261018' + LANES = HERE.parents[1] + CORE = LANES / "new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz" + CUTS = LANES / "oblique-native-20261017/interior-cut/ALL-CUT-EDGES.json.gz" +@@ -399,7 +407,7 @@ + equations.append((t, s, row)) + need(len(equations) == 6608, "Every forbidden off-diagonal pair") + two_bases = two_basis_certificate(r, ports) +- (HERE/"TWO-BASES.json").write_text(json.dumps(two_bases, indent=2, sort_keys=True)+"\n") ++ (OUT/"TWO-BASES.json").write_text(json.dumps(two_bases, indent=2, sort_keys=True)+"\n") + by_pair = {(t, s): row for t, s, row in equations} + matrix = [[by_pair[tuple(pair)][j] for j in cert["centre_entry_columns"]] + for pair in cert["independent_pairs"]] +@@ -420,7 +428,7 @@ + exact_kernel="scalar multiples of I8", dense_rank_seven_failures=len(failures), + negative_controls=["dense rank-seven projection", "duplicate certificate row"], + checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest()) +- (HERE/"REVIEW.json").write_text(json.dumps(report, indent=2, sort_keys=True)+"\n") ++ (OUT/"REVIEW.json").write_text(json.dumps(report, indent=2, sort_keys=True)+"\n") + print(report["status"], "determinant", det, flush=True) + + +--- frozen/lanes/schur-selection/plane-repair/check_query_span.py ++++ portable/query-span-producer.py +@@ -3,10 +3,17 @@ + from hashlib import sha256 + from pathlib import Path + import json +-import tarfile + + +-HERE = Path(__file__).resolve().parent ++import argparse ++ ++ANNEX = Path(__file__).resolve().parents[1] ++PARENT = ANNEX.parents[1] ++parser = argparse.ArgumentParser(description=__doc__) ++parser.add_argument("--out", required=True) ++OUT = Path(parser.parse_args().out).resolve() ++OUT.mkdir(parents=True, exist_ok=True) ++HERE = ANNEX / "frozen" / 'lanes/schur-selection/plane-repair' + ROOT = HERE.parents[4] + INTERFACE_PIN = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" + PLANE_PIN = "f55bd0e7b81a15b6526ca3056ef3bf1bbf57b13137699e71a374f4cf8f55f794" +@@ -24,17 +31,16 @@ + + + def main(): +- raw = (HERE.parents[1] / "circuit-interface/INTERFACE.json").read_bytes() ++ raw = (PARENT / "payload/lanes/circuit-interface/INTERFACE.json").read_bytes() + need(sha256(raw).hexdigest() == INTERFACE_PIN, "Actual eight centre rows") + interface = json.loads(raw) + rows = [[int(row.get(str(p),0)) for p in range(112)] for row in interface["R"]] + need(len(rows) == 8, "Eight required centre outputs") + need([[sum(rows[i][p]*rows[j][p] for p in range(112)) for j in range(8)] for i in range(8)] + == [[56*int(i == j) for j in range(8)] for i in range(8)], "Actual row Gram") +- archive = ROOT / "worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz" +- need(sha256(archive.read_bytes()).hexdigest() == ARCHIVE_PIN, "Selected source archive") +- with tarfile.open(archive) as source: +- phase = source.extractfile("candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json").read() ++ archive_record = json.loads((ANNEX / "ARCHIVE-CHECK.json").read_bytes()) ++ need(archive_record["archive_sha256"] == ARCHIVE_PIN, "Historical archive binding") ++ phase = (PARENT / "payload/upstream/DATA-PHASES.json").read_bytes() + need(sha256(phase).hexdigest() == PHASE_PIN, "Actual line labels") + labels = [r["q"] for r in sorted(json.loads(phase)["recipes"],key=lambda r:r["port"])] + need(len(labels) == len(set(labels)) == 112 and all(labels), "Distinct nonzero actual line labels") +@@ -79,7 +85,7 @@ + "plane_endpoint_functional":"normalized trace minus constant-character expectation", + "plane_endpoint_value_at_tensor_depth_lambda":"2^(-lambda)-1", + "scope":"Exact scalar input spans for plain-input operator matrices, plus proof-based all-depth extension. This is a payload-query count bound under scalar free gates, not a native-child or rank-zero-map lower bound for the full supplier."} +- (HERE / "QUERY-SPAN.json").write_text(json.dumps(result,indent=2,sort_keys=True)+"\n") ++ (OUT / "QUERY-SPAN.json").write_text(json.dumps(result,indent=2,sort_keys=True)+"\n") + print(result["status"]) + print(json.dumps({k:result[k] for k in ("line_scalar_input_rank","plane_scalar_input_rank","plane_minor_determinant_in_matching_order","plane_character_sum_checks")},sort_keys=True)) + +--- frozen/lanes/source-domain/query-span-review/review_query_span.py ++++ portable/query-span-review.py +@@ -6,10 +6,17 @@ + import gzip + import json + from pathlib import Path +-import tarfile + + +-HERE = Path(__file__).resolve().parent ++import argparse ++ ++ANNEX = Path(__file__).resolve().parents[1] ++PARENT = ANNEX.parents[1] ++parser = argparse.ArgumentParser(description=__doc__) ++parser.add_argument("--out", required=True) ++OUT = Path(parser.parse_args().out).resolve() ++OUT.mkdir(parents=True, exist_ok=True) ++HERE = ANNEX / "frozen" / 'lanes/source-domain/query-span-review' + LANES = HERE.parents[1] + ROOT = LANES.parents[2] + PACKET = LANES / "schur-selection/plane-repair" +@@ -53,14 +60,13 @@ + need(sha256((PACKET / name).read_bytes()).hexdigest() == pin, "Frozen packet: " + name) + certificate = json.loads((PACKET / "QUERY-SPAN.json").read_bytes()) + planes = json.loads((PACKET / "PLANE-INVOLUTION.json").read_bytes())["planes"] +- path = ROOT / "worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz" +- need(sha256(path.read_bytes()).hexdigest() == ARCHIVE, "Selected source archive") ++ archive_record = json.loads((ANNEX / "ARCHIVE-CHECK.json").read_bytes()) ++ need(archive_record["archive_sha256"] == ARCHIVE, "Historical archive binding") + source = {} +- with tarfile.open(path) as archive: +- for key, (name, pin) in MEMBERS.items(): +- raw = archive.extractfile(name).read() +- need(sha256(raw).hexdigest() == pin, "Selected member: " + key) +- source[key] = json.loads(gzip.decompress(raw) if name.endswith(".gz") else raw) ++ for key, (name, pin) in MEMBERS.items(): ++ raw = (PARENT / "payload/upstream" / Path(name).name).read_bytes() ++ need(sha256(raw).hexdigest() == pin, "Selected member: " + key) ++ source[key] = json.loads(gzip.decompress(raw) if name.endswith(".gz") else raw) + word, program, phases = [source[key] for key in MEMBERS] + rows = [{i: Fraction(1)} if i < 112 else {} for i in range(712)] + count = 0 +@@ -86,7 +92,7 @@ + else: + raise ValueError("The original centre boundary is absent") + matrix = [[rows[centre].get(p, 0) for p in range(112)] for centre in word["centers"]] +- interface_raw = (LANES / "circuit-interface/INTERFACE.json").read_bytes() ++ interface_raw = (PARENT / "payload/lanes/circuit-interface/INTERFACE.json").read_bytes() + need(sha256(interface_raw).hexdigest() == certificate["interface_sha256"], "Accepted interface pin") + interface = json.loads(interface_raw) + expected = [[Fraction(row.get(str(p), "0")) for p in range(112)] for row in interface["R"]] +@@ -177,7 +183,7 @@ + grammar="Every non-scalar payload map is counted, including rank-zero address maps; scalar initial and final contracts are required.", + controls=["Exact reversed-orientation moved-character sign differs."], + not_certified=["Native-child lower bound", "Native-cost bound", "Changed source interface", "Supplier or kappa improvement"]) +- (HERE / "REVIEW.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n", encoding="utf-8") ++ (OUT / "REVIEW.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n", encoding="utf-8") + print(result["status"]) + print(json.dumps({key: result[key] for key in ("source_scalar_events_replayed", "exact_Fourier_columns", + "separating_functional_column_checks", "exact_block_minor_determinant")})) diff --git a/research/actual-query-information-bounds/annexes/source-geometry/README.md b/research/actual-query-information-bounds/annexes/source-geometry/README.md new file mode 100644 index 0000000000..6979b25ec5 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/README.md @@ -0,0 +1,226 @@ +# Source geometry and payload-query limits + +This annex preserves four reviewed results about source access. They give +exact support geometry, a conditional direct-capture bound, an observation +rank separation, a scalar centre restriction, and payload-query bounds. +They improve no complete kappa calculation. The four gate and interface +classes are different. Their bounds must not be added as one cost invoice. + +The parent package and its chronological-cache annex keep all 129 original +files unchanged. [PARENT-SNAPSHOT.json](PARENT-SNAPSHOT.json) binds those +bytes. This annex has its own [manifest](ANNEX-MANIFEST.json), +[source record](SOURCES.json), and [portable edits](PORTABILITY.patch). +All original proofs and prior reviews remain unchanged under `frozen`. + +## Eight support spaces and a direct-capture bound + +The [source proof](frozen/root/CENTRE-SUPPORT-GEOMETRY-20261018.md) and +[independent review](frozen/lanes/independent-review-20261017/centre-support-review-20261018/REVIEW.md) +give eight rank-seven binary support spaces. The four equal-space pairs +are `{0,5}`, `{1,6}`, `{2,7}`, and `{3,4}`. Distinct spaces meet in rank +six. All four meet in rank five and span the rank-eight hyperplane +perpendicular to 45. The shared-port graph is `K_(2,2,2,2)`. Each edge +has two ports, and each of the 48 used ports occurs in two rows. + +Assume one unwarped carrier per original source value, an increasing +subspace chain on each carrier, and one direct common-frame capture per +complete row. The frame must contain that row's support. No extra carrier, +stored partial query, or operator-valued source code can supply a term. +Then at most two captures have rank seven. The sum of the eight capture +ranks is at least `2*7+6*8=62`. + +This is a conditional bound, not a construction at 62. The pair code uses +two coded carriers and violates the premise. The theorem does not price +scalar work or prove a lower bound for arbitrary native query words. +Both the producer calculation and the independent XOR-closure calculation +are rerun. Their exact [certificate](frozen/root/CENTRE-SUPPORT-GEOMETRY-20261018.json) +and [review receipt](frozen/lanes/independent-review-20261017/centre-support-review-20261018/CHECKS.json) +are retained. + +## Dyadic unit logs require sixteen fixed observation fields + +The [residue proof](frozen/root/DYADIC-QUERY-SEPARATION-20261018.md) and +[independent proof review](frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/REVIEW.md) +use `BD=cI`, full residue rank of `B`, zero residue of `c`, and a two-sided +unit `MD` over the coefficient ring. A row relation in `[B;M]`, multiplied +by `D`, first forces its `M` coefficients to zero and then its `B` +coefficients to zero. Thus the stack has rank `2r`. Over an integral +domain, a nonzero residue minor also gives rank `2r` over the fraction +field. + +The actual eight-centre matrices have `BD=13I` and a dyadic invertible +eight-column minor of `B`. Every dyadic `M` with dyadic unit `MD` gives +stack rank sixteen. The +[mixed-source unit criterion](frozen/lanes/oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md) +and [full-null terminal family](frozen/lanes/controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md) +fix the application. Completed X and retired selected Y vanish on that +family. The only further observation of retired ordinary Y is a fixed +linear map `N`. Required outputs force +`ker N` to lie in `ker B` intersect `ker M`, even with nonlinear +postprocessing. Total observation rank is therefore at least sixteen +complete fields. This is not a bound on simultaneous scratch storage. + +For `M=B/13`, the stack has rank eight and `MD=I` over the rationals. +With the invertible `B` minor, a unit log with stack rank eight exists +over the coefficient ring exactly when 13 is invertible there. The +normalized choice with `MD=I` is uniquely `B/13`. Allowing denominators +coprime to 13 does not remove this obstruction. + +For finite routed arrays with `ell` scalar coordinates per field, the +rank is `16*ell` if the ordered identities and Gaussian-dyadic two-sided +inverses hold after flattening. The map `i -> 5` in `F_13` is used. The +executed noncommuting two-coordinate route test is a fixture, not a full +native or global route replay. The annex implements no odd division, +cheap old-stage query, target scatter, or complete decoder. Arbitrary +nonlinear encodings, extra observations, changed output partitions, and +packing on a bounded finite domain are outside this observation theorem. + +Both source and independent checks are rerun. They check 64 perturbed +sections, 24 logs with nonidentity unit `MD`, the explicit stack minor +`1/8`, the route fixture of rank 32, and the ordered full-null algebra. +The [review receipt](frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/REVIEW.json) +records controls for the unit, residue-rank, zero-residue, and null-family +hypotheses. Historical review-pending text remains unchanged; the retained +independent review supplies the later status. + +## Fixed native support forces a scalar centre matrix + +The [all-cut proof](frozen/lanes/oblique-native-20261017/interior-cut/ALL-CUT-SUPPORT.md), +[physical support proof](frozen/lanes/coherent-port/centre-mixing-20261018/MIXING.md), +and [independent review](frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/REVIEW.md) +fix the actual native paths and require equal physical views at scalar +accesses. The first class retains the source computation and Y scalar +tail. It permits one-way equal-frame source-to-Y insertions or gain +changes, with the stated raw-I helper entry correction. The second, +separately reviewed class fixes the exterior and all wrappers. It permits +scalar rewiring only in the canonical interval from cut 7502 to cut +17249, subject to the support induction and the endpoint contract. +Neither class permits arbitrary edits through physical wrappers. + +Let `R` be the actual eight-row matrix and `K=R^T/4`. If the retained +response and a constant scalar centre matrix give +`E+KAR=diag(d_0,...,d_111) tensor I`, support gives 6,608 off-diagonal +equations on all 64 entries of `A`. A 63-row minor has determinant +`-2^71=-2361183241434822606848`. Their kernel is exactly `A=cI8`. +The diagonal support witness then gives `d_p=c` at every port. +Over the rational or Gaussian rational field, a nonzero clean diagonal +response therefore needs centre rank eight in this class. A factorization +through seven constant scalar centre channels fails. + +The independent checker rebuilds both complete interval inventories and +the 4,276 products. It checks all 640 original columns, helper and owned +outputs, native frame conditions, physical-view restrictions, and private +zero-buffer lifetimes. It computes the determinant by rational elimination. +The [two-basis proof](frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/TWO-BASES.md) +uses two actual eight-port bases with a connected overlap graph. Its +nonzero overlaps are `+1/2` or `-1/2`, so the scalar-equation conclusion +also holds over a commutative ring in which two is a unit. The +[peer check](frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/PEER-CHECK.md) +covers that explanation and the bounded canonical interval extension. + +The physical support witness applies at every positive tensor depth and +does not assume independence of formal warp words. The frozen producer's +`check_support.py` composes histories in forward list order. All consumed +X histories have length at most one, so this does not alter its result. +The executed independent checker uses reverse order and checks that length +limit. A future packet with longer histories must change the producer loop. + +This replay does not run the producer inventory, modular existing-site +rank check, or their source emitters. Their source and historical receipts +are retained. The independent interval replay is the decisive completeness +check. The dense rank-seven projection fails 2,534 equations, a duplicate +certificate row has zero determinant, and a second orthogonal basis pair +with two graph components fails the connectedness premise. + +Changed native paths, arbitrary wrappers, unequal physical views, changed +query or scatter spaces, and operator-valued centre entries are outside +these results. No bound on all native encodings follows. + +## Plain-input payload queries have source rank 112 + +The [query-span theorem](frozen/lanes/schur-selection/plane-repair/QUERY-SPAN.md) +and [independent source review](frozen/lanes/source-domain/query-span-review/REVIEW.md) +use scalar free gates `B tensor I`, scalar initial and final interfaces, +and queries `I+uQv` with scalar `u,v`. Singular scalar gates, COPY, CLEAR, +borrowed fields, feedback, and query reuse are allowed. Every non-scalar +payload map must count, including a rank-zero address permutation. +An `r`-direction block query counts `r` times. + +After `c` queries, both a scalar response-column factorization and a scalar +source-row factorization have width at most `c`. Applying any collection +of operator functionals that kill the identity bounds the simultaneous +column and row spans by `c`. The ordered proof does not require commuting +payload operators or invertible intermediate scalar gates. + +For the actual line-centre query and the proposed matched-plane query, +the scalar source rank is 112 although there are eight output fields. +Exact functionals isolate the line columns or the matched two-column +blocks. The plane minor in matching order has determinant eight. The +same bound holds at every positive tensor depth by compression to fixed +constant characters. A separate mixed-plane endpoint on `n` fields needs +at least `n` payload queries: normalized trace minus constant-character +expectation gives `2^(-lambda)-1` on each plane. A common negative +eigenspace is not required. + +Both producer and independent checks are rerun. The independent check +reconstructs R from 10,851 historical scalar events, checks 28,672 exact +plane Fourier columns and 802,816 functional contributions, and verifies +all 56 pair Grams and the determinant. It rejects reversed plane +orientation. The retained [handoff](frozen/lanes/schur-selection/HANDOFF.md) +records the completed review and supersedes the proof's old review-pending +sentence without changing its bytes. + +These are payload-query counts, not native-child, native-rank, or scratch +bounds. A source with an existing port-dependent phase code has a changed +input contract. The theorem does not charge that code again. At depth one, +one rank-zero translation and scalar work can form a line phase. The +annex neither prices such implementations nor reruns the separate plane +route construction. + +## Reproduction, sources, and open costs + +Use Python 3.11 or later, its standard library, one process, and at least +3 GiB of free disk space. Keep the complete parent package at its published +relative paths. Use a new output directory: + +```sh +python3 -I -O -B research/actual-query-information-bounds/annexes/source-geometry/replay.py --out /tmp/source-geometry-replay +``` + +Expected final line: + +```text +PASS_SOURCE_GEOMETRY_ANNEX +``` + +The seven checks run serially and compare every JSON value and type with +the historical receipts. Only an explicit checker-hash field changes to +the portable checker hash. The driver verifies all annex and original +parent bytes before and after execution. It needs no Git, external tool, +network, numerical library, or solver. [ARCHIVE-CHECK.json](ARCHIVE-CHECK.json) +binds the historical archive to the exact parent members used at runtime. +The portable replay does not copy or reload the complete archive. + +The publication base is `b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`. +Its selected result is the conditional joint-helper result in +[PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470), with +kappa `60403/20000000`. These results use their historical actual source +packets and the parent's historical `bce54fb3f895cbe5cd4c0eb477c3afeed100190f` +source. No transfer to that newer selected construction is proved. +[NOTICE.md](NOTICE.md) retains the predecessor roles, exact source pins, +license records, and AI disclosures. + +Open next questions: + +1. Price a changed source representation and all required reads, scatters, + address operations, and restoration. These results do not supply that + complete physical invoice. +2. For an eight-observation log, implement the required inversion of 13 + under an exact arithmetic and endpoint contract. Prove the remaining + old-stage query, complete decoder, and recursive precision bounds. +3. For a proposed escape from the centre restriction, state the new + wrapper, support, native-path, or operator-valued interface. Check it + against its own source model before deriving a cost. +4. Convert a payload-query count to a native cost only with an explicit + contract that accounts for rank-zero maps and prior input encoding. + The present annex supplies no supplier moment or complete kappa gain. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/SOURCES.json b/research/actual-query-information-bounds/annexes/source-geometry/SOURCES.json new file mode 100644 index 0000000000..9cda86ee98 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/SOURCES.json @@ -0,0 +1,463 @@ +{ + "files": { + "evidence/source-verification/NATIVE-SOURCE-VERIFICATION.json": { + "bytes": 4860, + "original_path": "work/centre-encoding-campaign-20261014/publication-wrap-20261022/packages/centre-metric-encoders/evidence/NATIVE-SOURCE-VERIFICATION.json", + "role": "Prior exact external source readback", + "sha256": "26c8f75ce5d07a7cf8eb4de87fc8a86c192c1631e0e7d5fdb9b44ccee642c9ba" + }, + 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unchanged." +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/VALIDATION.md b/research/actual-query-information-bounds/annexes/source-geometry/VALIDATION.md new file mode 100644 index 0000000000..1806d34cfe --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/VALIDATION.md @@ -0,0 +1,43 @@ +# Executed validation + +The seven listed checks passed with Python 3.14.7 in normal mode and with +`-O`. The normal run took 3.175434 seconds. The optimized run took 2.877606 +seconds. Each run used one child process at a time and the Python standard +library. The driver required at least 3 GiB of free disk space. + +```text +PASS_CENTRE_SUPPORT_GEOMETRY +PASS_INDEPENDENT_CENTRE_SUPPORT_GEOMETRY +PASS_DYADIC_QUERY_SEPARATION +PASS_INDEPENDENT_DYADIC_QUERY_SEPARATION +PASS_INDEPENDENT_NATIVE_CENTRE_REVIEW +PASS_EXACT_QUERY_SOURCE_SPANS +PASS_INDEPENDENT_QUERY_SPAN_SOURCE_AND_CERTIFICATE +PASS_SOURCE_GEOMETRY_ANNEX +``` + +The [normal receipt](evidence/replay-normal.json) and +[optimized receipt](evidence/replay-optimized.json) record each check, +timing, and typed JSON comparison. Both runs used the +[pre-receipt manifest](evidence/replay-input-manifest.json). That manifest +contains the same executed scripts and frozen sources as the final annex +manifest; the final manifest also contains this validation record and the +saved outputs. The eight actual optimized JSON outputs are retained under +`evidence/optimized-receipts`. The only receipt field allowed to change is +`checker_sha256`, which must equal the executing portable script's hash. + +Both runs verified all 129 parent and cache-annex files before and after +execution. The extraction also compared all 72 copied source and notice +files with their exact local originals. No original file changed. The +portable edits preserve every non-main function AST. The seven main +functions change input/output paths only. Two archive readers now load +the exact parent members, whose old whole-archive binding is recorded +separately. The complete differences are in `PORTABILITY.patch`. + +This annex did not run the parent package or cache-annex mathematics. +It did not rerun the mixing producer inventory, modular existing-site +rank checker, cut source emitters, native recipe generator, plane route +generator, odd-grid implementation, or a complete supplier. Their results +must not be reported as fresh checks. The independent mixing interval +replay checked the full retained cut product set and physical premises. +The prior reviews remain separate from the fresh publication review. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/evidence/optimized-receipts/centre-mixing-review/REVIEW.json b/research/actual-query-information-bounds/annexes/source-geometry/evidence/optimized-receipts/centre-mixing-review/REVIEW.json new file mode 100644 index 0000000000..a15e0b2994 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/evidence/optimized-receipts/centre-mixing-review/REVIEW.json @@ -0,0 +1,13363 @@ +{ + "checker_sha256": "2bcfa8a1ebf3464700453023b89ec7060a39dc6e5794510bec1d1dc2b19c3dcb", + "core_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "dense_rank_seven_failures": 2534, + "determinant": "-2361183241434822606848", + "exact_kernel": "scalar multiples of I8", + "forbidden_pairs": 6608, + "inventory_decompressed_sha256": "18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418", + "negative_controls": [ + "dense rank-seven projection", + "duplicate certificate row" + ], + "producer_pins": { + "coherent-port/centre-mixing-20261018/MIXING.json": "1a55e02768ad814b1441bfc616244a083ca3776007dcc0a370820059b83bdf11", + "coherent-port/centre-mixing-20261018/MIXING.md": "e8ac0be5c3bd03cf853e9cb5718325d1f401eb1fc68d68869843ac6ded408903", + "coherent-port/centre-mixing-20261018/SUPPORT.json": "251e656ce50b87f21149915d73b5c07d968d62aff2f47ccf2e1566cc5d6c756a", + "coherent-port/centre-mixing-20261018/check_mixing.py": "fe017063d3b5bad93bf2f884813576e169d59daad1c5aec8051001e0a3476dc7", + "coherent-port/centre-mixing-20261018/check_support.py": "82d608f7220d9959925c2990fd717b028a2fce47fcf41ee9f061d0687c32f97c", + "new-native-recipes-20261017/sources/bw_adapters.py": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce", + 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no native child bound or supplier claim." +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/evidence/optimized-receipts/dyadic-review/REVIEW.json b/research/actual-query-information-bounds/annexes/source-geometry/evidence/optimized-receipts/dyadic-review/REVIEW.json new file mode 100644 index 0000000000..e1822bc13c --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/evidence/optimized-receipts/dyadic-review/REVIEW.json @@ -0,0 +1,183 @@ +{ + "actual_source": { + "B_rank_mod_13": 8, + "controls": [ + "M=B has MD=13I and rank-eight stack", + "Missing B residue rank", + "Missing zero residue of c", + "Matched coefficients have no residue at 13" + ], + "explicit_minor_determinant": "1/8", + "explicit_minor_ports": [ + 1, + 2, + 3, + 4, + 5, + 6, + 8, + 12, + 21, + 37, + 47, + 76, + 81, + 87, + 92, + 110 + ], + "matched_rank_over_Q": 8, + "nonidentity_MD_cases": [ + { + "MD_is_identity": false, + "case": 0, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 1, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 2, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 3, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 4, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 5, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 6, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 7, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 8, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 9, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 10, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 11, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 12, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 13, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 14, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 15, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 16, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 17, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 18, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 19, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 20, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 21, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 22, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 23, + "stack_rank_mod_13": 16 + } + ], + "stack_rank_mod_13": 16 + }, + "checker_sha256": "bdc237dd266102fa99170aab0d309c3f03894924875f5a8a79d198d6fbd02548", + "core_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "formal_full_null": { + "all_pair_counts": "The future inputs and all visible outputs are zero; the only nonzero next-bank bridge is -v+v.", + "operator_relations": [ + "Qq=I", + "qQ=I" + ], + "unit_factorization": "diag(I,-MD)", + "uses_BD_identity_for_null_family": false, + "uses_MD_identity": false, + "wrong_original_b_control": true + }, + "routed_operator_fixture": { + "coordinates_per_field": 2, + "noncommuting_routes": true, + "query_rank_mod_13": 32, + "scope": "An actual-B Gaussian-unit conjugation fixture; the general finite-operator version follows from the residue proof, not a new native route replay." + }, + "scope": "Fixed linear observations on the full underlying field space, with arbitrary postprocessing. No native-child, bit-packing, arbitrary nonlinear-encoding or complete supplier lower bound.", + "source_pins": { + "lanes/controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md": "50ce523e083f70556cc62694219da94b684cc898f3d5e358767fcc40dd77e4bc", + "lanes/oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md": "1a4d715e089773a9063fba88d5b83ec770bb5eb6ed501bc8f96b290c19b08401", + "root/DYADIC-QUERY-SEPARATION-20261018.json": "e66d5c311490c06973bf604d207fb5cf7a9cd4800c0cea049623c3b5e2369732", + "root/DYADIC-QUERY-SEPARATION-20261018.md": "664f430efd099f35cbc7c2abc8025968c03020707027857d2882daa51a065a1a", + "root/check_dyadic_query_separation_20261018.py": "b4ed000b5b600944f614b86ae7a88ac55af8eac3213e6827ed211a2630ccd342" + }, + "status": "PASS_INDEPENDENT_DYADIC_QUERY_SEPARATION", + "universal_proof": "Residue row relation times D forces beta=0 because MD is a unit; full residue rank of B forces alpha=0. A nonzero residue minor lifts to the fraction field." +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/evidence/optimized-receipts/query-span-producer/QUERY-SPAN.json b/research/actual-query-information-bounds/annexes/source-geometry/evidence/optimized-receipts/query-span-producer/QUERY-SPAN.json new file mode 100644 index 0000000000..99a99bfe32 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/evidence/optimized-receipts/query-span-producer/QUERY-SPAN.json @@ -0,0 +1,1364 @@ +{ + "archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "input_fields": 112, + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "line_pivot_functionals": [ + { + "centre_row": 0, + "pivot": 1, + "port": 0, + "q": 11 + }, + { + "centre_row": 1, + "pivot": 1, + "port": 1, + "q": 19 + }, + { + "centre_row": 0, + "pivot": 1, + "port": 2, + "q": 35 + }, + { + "centre_row": 1, 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No supplier or complete-kappa claim.", + "source_core_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "source_inventory_decompressed_sha256": "18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418" +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/PEER-CHECK.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/PEER-CHECK.md new file mode 100644 index 0000000000..b5f972036d --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/PEER-CHECK.md @@ -0,0 +1,31 @@ +# Peer check of the new proof extensions + +The agent `coherent_port_encoding` checked the two additions made by +this reviewer. This is a separate mathematical check by an AI agent. +It is not a claim of human review. The original producer packets remain +unchanged. + +For the bounded scalar-rewiring extension, the peer read `REVIEW.md` and +checked the literal program after cut 17249. There are no scalar writes +to Y after that cut. The canonical interval has scalar gates, nested +climbs, and warps. The peer accepted the support induction with the +stated fixed exterior and with the prefix condition at cut 7502. The +independent checker now verifies these two cut indices, the prefix +condition, and the suffix condition directly. Arbitrary edits through +the physical adapters remain excluded. + +For the two-basis proof, the peer independently checked the two actual +eight-port Gram matrices, all binary within-basis dot products, the +overlap entries, and the graph. It reported Gram matrices `4I`, overlap +entries `0,+2,-2` before division by four, and a connected graph with +16 vertices and 32 edges. It accepted the proof without a symmetry +assumption and the commutative-ring extension when two is a unit. + +The peer also confirmed that the current producer's source X histories +have length at most one. Its forward-list composition loop therefore +does not change this packet's result. A future packet with longer +histories must apply the operators in reverse list order. + +The primary exact evidence is in `REVIEW.json`, `TWO-BASES.json`, and +`PRODUCER-REPLAY.json`. This note records the peer's proof review and +does not replace that evidence. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/PRODUCER-REPLAY.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/PRODUCER-REPLAY.json new file mode 100644 index 0000000000..eba93af8b9 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/PRODUCER-REPLAY.json @@ -0,0 +1,37 @@ +[ + { + "output": "ALL-CUT-EDGES.json", + "output_equal": true, + "sha256": "4c7429f07d3b331ddc0e9b530937e48e3d2e4006353aeb163f82a87c07012570", + "source": "oblique-native-20261017/interior-cut/inventory_new_edges.py", + "source_unchanged": true + }, + { + "output": "ALL-CUT-EDGES.json.gz", + "output_equal": true, + "sha256": 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"zero_buffer": 182 + }, + "history_lengths": { + "0": 9558, + "1": 1880 + }, + "interval_overlaps": 7838, + "source_intervals": 8957, + "target_frame_checks": 1030, + "target_intervals": 1054 + } + }, + "status": "PASS_INDEPENDENT_NATIVE_CENTRE_REVIEW", + "two_basis_certificate": { + "components": [ + [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15 + ] + ], + "core_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "disconnected_control_components": [ + [ + 0, + 1, + 3, + 6, + 11, + 12, + 13, + 14 + ], + [ + 2, + 4, + 5, + 7, + 8, + 9, + 10, + 15 + ] + ], + "disconnected_control_ports": [ + 21, + 37, + 47, + 76, + 81, + 87, + 92, + 110 + ], + "exact_common_diagonal_algebra": "scalar multiples of I8", + "left_ports": [ + 0, + 7, + 20, + 27, + 36, + 46, + 57, + 111 + ], + "overlap_denominator": 4, + "overlap_numerator": [ + [ + 2, + 2, + 0, + 0, + 2, + 2, + 0, + 0 + ], + [ + 0, + -2, + 2, + 0, + 0, + 2, + -2, + 0 + ], + [ + 0, + 0, + -2, + 2, + 0, + 0, + -2, + 2 + ], + [ + 0, + 0, + 2, + 0, + 2, + -2, + 0, + 2 + ], + [ + 0, + 2, + 2, + 2, + -2, + 0, + 0, + 0 + ], + [ + -2, + 2, + 0, + -2, + 0, + 0, + -2, + 0 + ], + [ + -2, + 0, + 0, + 0, + 0, + 2, + 2, + 2 + ], + [ + -2, + 0, + 0, + 2, + 2, + 0, + 0, + -2 + ] + ], + "right_ports": [ + 3, + 6, + 18, + 21, + 89, + 92, + 105, + 109 + ], + "spanning_tree": [ + [ + 0, + 8 + ], + [ + 0, + 9 + ], + [ + 0, + 12 + ], + [ + 0, + 13 + ], + [ + 8, + 5 + ], + [ + 8, + 6 + ], + [ + 8, + 7 + ], + [ + 9, + 1 + ], + [ + 9, + 4 + ], + [ + 12, + 3 + ], + [ + 5, + 11 + ], + [ + 5, + 14 + ], + [ + 6, + 15 + ], + [ + 1, + 10 + ], + [ + 11, + 2 + ] + ] + } +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/REVIEW.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/REVIEW.md new file mode 100644 index 0000000000..f986dcfda6 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/REVIEW.md @@ -0,0 +1,235 @@ +# Independent review of the centre-matrix restriction + +The all-cut result passes independent review for the stated fixed-source +class. The physical support proof is valid. It does not need independence +of formal warp words. The exact equations constrain all 64 entries of the +centre matrix. Their kernel is `A=c I8`. + +The source inventory is complete for its declared equal-frame one-way +insertion grammar. A separate interval method gives the same 4,276 +products. The exact 63-row determinant is `-2^71`. No claim about a new +supplier, total native-child lower bound, precision bound, or complete +kappa improvement follows from this result. + +## Inputs and reproduction + +The reviewed producer packets are: + +- `oblique-native-20261017/interior-cut/ALL-CUT-SUPPORT.md`, its inventory, + and `FRAME-SUPPORT.json`; +- `coherent-port/centre-mixing-20261018/MIXING.md`, `SUPPORT.json`, and + their checkers; +- the actual clean core with decompressed SHA256 + `a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa`; +- the logical monomial definition in + `new-native-recipes-20261017/sources/bw_adapters.py`. + +The review receipt pins the producer files. The freeze file pins this +review and both checkers. The reviewer imported no producer code in the +independent checker. Run from the workspace root: + +```text +python3 -I -B -O work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/centre-mixing-review-20261018/check_review.py +python3 -I -B work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/centre-mixing-review-20261018/replay_producers.py +``` + +The first command must print `PASS_INDEPENDENT_NATIVE_CENTRE_REVIEW` and +the determinant `-2361183241434822606848`. The second repeats the producer +checks. It redirects only their declared output writes into the review +directory and requires byte equality with the frozen outputs. It must +print `ALL_PRODUCER_OUTPUTS_BYTE_EQUAL`. + +## Independent derivation + +Let `q_s` be the actual odd binary label of source port `s`. Put the +computational-basis vector `|q_s>` in that source. Put zero in every +other source and in every Y, helper, and owned input. This is a legal +test input to an operation required to work for arbitrary borrowed state. + +At a canonical cut, write `F` for a field's current binary subspace. +The logical content has support in `F` under the following conditions: + +1. Its initial support is in its initial frame. +2. Every scalar ADD has equal source and target frames. A SCALE cannot + change support. A CLEAR gives zero support in its declared new frame. +3. A native climb has nested frames `F_old` contained in `F_new`. Its + logical content is unchanged; only its physical representation changes. +4. A logical monomial has an address map that sends `F_old` into `F_new`. + +These conditions preserve the support statement by induction. They do +not require one-way scalar gates, an unchanged Y tail, or independent +operator words. Arbitrary complex phases on the supported addresses do +not change the argument. + +For the actual current core, all 3,507 climbs are strict inclusions with +the declared rank difference. Each of the 240 signed warp occurrences +has address map `G` or `G^-1` and sends its old frame onto its new frame. +The source definition is `perm(G)` followed by a diagonal phase. Thus it +has no affine translation. Both providers have the required properties, +although their actual `G` matrices differ. + +The initial X frame contains `q_s`. The final canonical Y frame at port +`t` is contained in `q_t`-perp. Therefore, if `q_t dot q_s=1`, the final +Y content has zero coefficient at `q_s`. Equivalently, every retained +response operator in the declared class satisfies + +```text + = 0 when q_t dot q_s = 1. +``` + +This is a computational-basis statement, not a Fourier-character +statement. It remains true when different warp words have the same +physical operator or when sums of warp operators cancel. For a positive +tensor depth, use `(q_s,0,...,0)` as the input label. The address maps +fix zero in each other tensor factor. Thus the same witness works at +every tensor depth at least one. No claim at tensor depth zero is needed. + +For the fixed-source producer class, the independent checker also +verifies the support statement directly at every source interval. It +uses actual signed binary matrices in the correct operator order. It +checks the frame containment for each reverse Y-tail interval. Thus the +proof does not rest only on the general induction. + +## Complete cut and adapter audit + +The independent checker first replays all 640 formal input columns. It +checks every scalar frame, all native changes, the full clean-J endpoint, +all 408 arbitrary helper outputs, the owned outputs, and all 91 private +zero-buffer lifetimes. It then builds maximal constant intervals for +each source row and frame. A separate reverse pass builds constant +intervals for each remaining Y-tail column and frame. It joins the two +interval lists by overlap at the same frame. + +For each provider this gives 8,957 source intervals, 1,054 target +intervals, and 7,838 nonempty interval intersections. Their product set +is exactly the supplied set of 4,276 products. This method covers each +of the 23,389 literal cuts, including the initial and final cuts, without +using the producer's change-event enumeration. The producer replay +separately reproduces its 267,854 pair visits and its compressed payload +byte for byte. The two visit counts measure different enumerations. + +The independent support pass checks 11,438 distinct source/frame terms, +including 1,880 terms with a nonempty warp word. It checks 1,030 distinct +target/frame pairs. These counts cover all source and tail intervals, +not only the product representatives. + +Adapter events require care. A physical view change must not be ignored +when a new scalar read is admitted. The current replay finds 317 helper +view changes with an X-dependent branch. Every one is a `new_to_old` +adapter at FULL. No X-dependent helper branch passes through a proper- +frame residual wrapper. No Y frame is FULL. These FULL helper branches +therefore cannot give an extra one-way X-to-Y response through an +equal-frame scalar read. The fixed source branches at proper helper +wrappers are zero. The owned fields carry no X branch, and each private +Z field has frame FULL. These facts justify the omitted source types in +the supplied inventory for this obstruction. + +The result does not treat access inside an atomic wrapper as an ordinary +cut. It does not identify two physical views merely because a stale +canonical frame number is equal. Source and target must have the same +actual canonical view at an admitted scalar gate. Before the entry +adapters the X fields do not match Y's zero frame. After the exit +adapters only FULL sources can have an X branch in a changed view, and +they do not match a Y field. This covers the fixed one-way class without +assuming that exit adapters act as identities on physical arrays. + +There is a useful wider, explicit class. Keep the exterior prefix, +entry adapters, exit adapters, and exterior suffix fixed. Between the +last entry adapter and the first exit adapter, allow any scalar edits +that keep all current native frame changes and that satisfy the four +support conditions above. This includes changes to the source and Y +scalar subwords and Y-to-source feedback. The support induction still +holds. In the current event indexing this canonical section starts at +cut 7502 and ends at cut 17249. The resulting circuit must still meet +its endpoint and restoration contract. This wider statement does not +cover arbitrary edits through the physical wrapper boundaries. + +## Full centre matrix and its consequence + +Let `R` be the actual eight-row integer matrix and `K=R^T/4`. Consider +any constant scalar 8-by-8 matrix `A`. Suppose the retained response and +the centre response give a clean diagonal map: + +```text +E + K A R = diag(d_0,...,d_111) tensor I. +``` + +Here `E` can initially be a sum of actual operator words. Apply the +matrix-entry functional from the support proof to each off-diagonal +pair with `q_t dot q_s=1`. Its value on `E_ts` is zero. Its value on the +payload identity is one. Hence + +```text +R[:,t]^T A R[:,s] = 0. +``` + +There are 6,608 such pairs. They are equations on all 64 entries of `A`; +no symmetry or diagonal form is imposed. The supplied 63 pairs with the +column for `A[7,7]` removed have determinant `-2^71`. The independent +checker computes this by rational Gaussian elimination, rather than +the producer's integer Bareiss elimination. It also checks directly that +`I8` satisfies every one of the 6,608 equations. Thus the exact kernel +over the rationals or Gaussian rationals is `span(I8)`. Since the minor +is a power of two, the same linear-equation conclusion holds over any +commutative coefficient ring in which two is a unit. + +There is also an analytic proof using two actual orthogonal port bases. +Their overlap graph is connected, and every nonzero overlap is a dyadic +unit. A matrix diagonal in both bases must then be scalar. The separate +`TWO-BASES.md` gives the general criterion and the 16-port witness. +`TWO-BASES.json` gives its exact overlap matrix and a spanning tree. This +explains the rank-63 result without using a large elimination. + +Each column of `R` has squared norm four. Each port label is odd. The +same support witness at `s=t` therefore gives `d_s=c` when `A=cI8`. +Consequently every nonzero clean diagonal response in this family has +the form + +```text +A = c I8, d_0 = ... = d_111 = c, E = c (I-KR) tensor I. +``` + +Over the rational or Gaussian rational field, a nonzero `cI8` has rank +eight. A factorization through seven scalar centre channels has rank at +most seven. It cannot give the required nonzero diagonal response. +Allowing odd denominators does not alter this obstruction. + +The negative example `A=I8-ones(8,8)/8` has rank seven and has a nonzero +`KAR` diagonal at every port. It nevertheless fails 2,534 forbidden-pair +equations. This checks the distinction between a diagonal test and the +full centre-matrix condition. Duplicating a certificate row makes the +independently computed determinant zero. + +## Limits and one checker qualification + +The physical support proof and the integer minor establish a theorem +for the stated circuit class. The event inventory establishes that the +current native words meet its hypotheses. A finite inventory by itself +would not prove the theorem for changed native paths. + +The result does not exclude an invertible off-diagonal retained response, +a port matching with orthogonal source and target labels, a changed +centre query or scatter space, a native inverse hop, a new address map +that fails the support condition, a mixed-view physical operation, or +operator-valued centre entries. Each escape needs its own access, +restoration, and complete cost analysis. In particular, this result is +not a lower bound of eight new native children for every possible +encoding. + +One producer detail must not be generalized without a correction. +The source histories are stored with the outermost operator first. +Generic composition must therefore apply their linear maps in reverse +list order. The frozen `check_support.py` applies them in list order. +Every X history in its consumed inventory has length zero or one, so +the current checked result is unchanged. The independent checker uses +reverse order and confirms this length bound for all relevant source +intervals. A future packet with longer X histories must change that +loop. This is not a material finding against the frozen result. + +No frozen producer file was edited. No PR, push, commit, or publication +was made. The user continues to require explicit permission before a +PR. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. +The work builds on the current core, the oblique-native cut inventory, +the coherent-port centre certificate, and the prior native frame work. +OpenAI Codex assisted this independent review. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/TWO-BASES.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/TWO-BASES.json new file mode 100644 index 0000000000..34b2bf1756 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/TWO-BASES.json @@ -0,0 +1,221 @@ +{ + "components": [ + [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15 + ] + ], + "core_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "disconnected_control_components": [ + [ + 0, + 1, + 3, + 6, + 11, + 12, + 13, + 14 + ], + [ + 2, + 4, + 5, + 7, + 8, + 9, + 10, + 15 + ] + ], + "disconnected_control_ports": [ + 21, + 37, + 47, + 76, + 81, + 87, + 92, + 110 + ], + "exact_common_diagonal_algebra": "scalar multiples of I8", + "left_ports": [ + 0, + 7, + 20, + 27, + 36, + 46, + 57, + 111 + ], + "overlap_denominator": 4, + "overlap_numerator": [ + [ + 2, + 2, + 0, + 0, + 2, + 2, + 0, + 0 + ], + [ + 0, + -2, + 2, + 0, + 0, + 2, + -2, + 0 + ], + [ + 0, + 0, + -2, + 2, + 0, + 0, + -2, + 2 + ], + [ + 0, + 0, + 2, + 0, + 2, + -2, + 0, + 2 + ], + [ + 0, + 2, + 2, + 2, + -2, + 0, + 0, + 0 + ], + [ + -2, + 2, + 0, + -2, + 0, + 0, + -2, + 0 + ], + [ + -2, + 0, + 0, + 0, + 0, + 2, + 2, + 2 + ], + [ + -2, + 0, + 0, + 2, + 2, + 0, + 0, + -2 + ] + ], + "right_ports": [ + 3, + 6, + 18, + 21, + 89, + 92, + 105, + 109 + ], + "spanning_tree": [ + [ + 0, + 8 + ], + [ + 0, + 9 + ], + [ + 0, + 12 + ], + [ + 0, + 13 + ], + [ + 8, + 5 + ], + [ + 8, + 6 + ], + [ + 8, + 7 + ], + [ + 9, + 1 + ], + [ + 9, + 4 + ], + [ + 12, + 3 + ], + [ + 5, + 11 + ], + [ + 5, + 14 + ], + [ + 6, + 15 + ], + [ + 1, + 10 + ], + [ + 11, + 2 + ] + ] +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/TWO-BASES.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/TWO-BASES.md new file mode 100644 index 0000000000..44ab9b4f7f --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/TWO-BASES.md @@ -0,0 +1,109 @@ +# A two-basis proof of centre rigidity + +The scalar centre restriction has a short algebraic explanation. Two +sets of eight actual ports suffice. The proof permits every entry of +the centre matrix to vary. It does not assume that the matrix is +symmetric. + +## General criterion + +Let `V` and `W` be invertible square matrices over a field. Set +`H=V^-1 W`. Form a bipartite graph with one vertex for each column of +`V` and one for each column of `W`. Join vertices `i` and `j` when +`H[i,j]` is nonzero. + +The vector space of linear maps diagonal in both bases has dimension +equal to the number of connected components of this graph. In +particular, a connected graph forces every such map to be `cI`. + +To prove this, write a common diagonal map as + +```text +A V = V diag(lambda), A W = W diag(mu). +``` + +Since `W=V H`, these equations give + +```text +diag(lambda) H = H diag(mu). +``` + +On every edge, `lambda_i=mu_j`. Thus all labels in one connected +component are equal. Conversely, choose one scalar for each component. +Assign this scalar to each vertex in that component. Every entry of +the last matrix equation then holds. These assignments give all the +common diagonal maps and are independent. + +The same proof works over a commutative ring if `V` and `W` are +invertible and every nonzero entry of `H` is a unit. In that case the +common diagonal module is free, with one generator per component. +The unit condition is needed to infer equality from +`(lambda_i-mu_j) H[i,j]=0`. + +## The actual 16-port certificate + +Use the current integer matrix `R` from the clean core with decompressed +SHA256 `a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa`. +Set + +```text +P = [0, 7, 20, 27, 36, 46, 57, 111] +Q = [3, 6, 18, 21, 89, 92, 105, 109] +V = R[:,P], W = R[:,Q]. +``` + +Exact substitution gives `V^T V=W^T W=4I`. All actual binary port +labels within either set have dot product one, including the distinct +pairs. The forbidden-pair equations therefore say that both `V^T A V` +and `W^T A W` are diagonal. Since the Gram matrices are `4I`, this is +equivalent to `A` being diagonal in both bases. + +Here `H=V^T W/4` is one half of the following integer matrix: + +```text + 1 1 0 0 1 1 0 0 + 0 -1 1 0 0 1 -1 0 + 0 0 -1 1 0 0 -1 1 + 0 0 1 0 1 -1 0 1 + 0 1 1 1 -1 0 0 0 +-1 1 0 -1 0 0 -1 0 +-1 0 0 0 0 1 1 1 +-1 0 0 1 1 0 0 -1 +``` + +Its bipartite support graph is connected. `TWO-BASES.json` gives a +15-edge spanning tree on its 16 vertices. Every nonzero overlap is +`1/2` or `-1/2`. Thus the common diagonal module is exactly `cI` +over every commutative coefficient ring in which two is a unit. + +This proves the scalar-I restriction directly from two orthogonal +bases. The independent `-2^71` determinant check remains a separate +certificate for the same restriction. The two-basis proof uses 112 +within-basis off-diagonal equations; the determinant uses 63 equations +from the larger list. Neither proof assumes that `A` is diagonal in +the original coordinate basis. + +## Why the graph hypothesis matters + +Keep `V` and instead use the actual basis with port list + +```text +[21, 37, 47, 76, 81, 87, 92, 110]. +``` + +It also has Gram matrix `4I`, and all its within-basis binary dot +products are one. But its overlap graph with `V` has two components, +each with four vertices from either basis. Those two basis constraints +alone allow two independent scalar blocks. The checker verifies this +case. Thus the conclusion does not follow merely from having two +orthogonal bases; the connection between them is decisive. + +The linear-algebra criterion is elementary. The contribution here is +its exact application to the current port geometry and to the physical +support restriction. This is an explanation of the obstruction, not +an additional supplier construction or a cost improvement. A changed +query or scatter space must be checked against its own basis graph. + +OpenAI Codex assisted this derivation. The producer cut proof and the +coherent-port integer certificate supplied the starting result. No +frozen producer artifact was changed. No publication was made. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/check_review.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/check_review.py new file mode 100644 index 0000000000..c54232e82c --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/check_review.py @@ -0,0 +1,428 @@ +"""Check the centre restriction from the native fields and cut intervals.""" + +from collections import Counter, defaultdict +from fractions import Fraction as Q +from hashlib import sha256 +import gzip +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +CORE = LANES / "new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz" +CUTS = LANES / "oblique-native-20261017/interior-cut/ALL-CUT-EDGES.json.gz" +CERT = LANES / "coherent-port/centre-mixing-20261018/SUPPORT.json" +PINS = { + "coherent-port/centre-mixing-20261018/MIXING.md": "e8ac0be5c3bd03cf853e9cb5718325d1f401eb1fc68d68869843ac6ded408903", + "coherent-port/centre-mixing-20261018/check_support.py": "82d608f7220d9959925c2990fd717b028a2fce47fcf41ee9f061d0687c32f97c", + "coherent-port/centre-mixing-20261018/SUPPORT.json": "251e656ce50b87f21149915d73b5c07d968d62aff2f47ccf2e1566cc5d6c756a", + "coherent-port/centre-mixing-20261018/check_mixing.py": "fe017063d3b5bad93bf2f884813576e169d59daad1c5aec8051001e0a3476dc7", + "coherent-port/centre-mixing-20261018/MIXING.json": "1a55e02768ad814b1441bfc616244a083ca3776007dcc0a370820059b83bdf11", + "oblique-native-20261017/interior-cut/ALL-CUT-SUPPORT.md": "758f8750a833ba08b44d9fe1df555f747eef62bd53302993bca6cdae7769d431", + "oblique-native-20261017/interior-cut/FRAME-SUPPORT.json": "6d9e1de85b7a2492bcef42514da240d74b81559c738aedac54cf65169a5a3fb5", + "oblique-native-20261017/interior-cut/check_frame_support.py": "3a81e98c83e418408eb7490771867a11f491a6af403820ad722c43a51026b508", + "oblique-native-20261017/interior-cut/inventory_new_edges.py": "6d77e20d6ef1a10951b7abeaa65852fad9161cc3b48e82d538a9748c3c9cc786", + "new-native-recipes-20261017/sources/bw_adapters.py": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce", +} + + +def need(test, label): + if not test: + raise ValueError(label) + + +def read_gzip(path, pin): + raw = gzip.decompress(path.read_bytes()) + need(sha256(raw).hexdigest() == pin, str(path.name) + " input pin") + return json.loads(raw) + + +def add(left, right, value=Q(1)): + for key, coefficient in right.items(): + result = left.get(key, Q(0)) + value * coefficient + if result: + left[key] = result + else: + left.pop(key, None) + + +def lin(columns, value): + answer = 0 + for j, column in enumerate(columns): + if value >> j & 1: + answer ^= column + return answer + + +def inverse(columns): + # Solve nine binary systems. Do not use a 512-value inverse table. + rows = [sum(((columns[j] >> i) & 1) << j for j in range(9)) | (1 << (9+i)) + for i in range(9)] + for j in range(9): + pivot = next((k for k in range(j, 9) if rows[k] >> j & 1), None) + need(pivot is not None, "Invertible binary warp") + rows[pivot], rows[j] = rows[j], rows[pivot] + for k in range(9): + if k != j and rows[k] >> j & 1: + rows[k] ^= rows[j] + return [sum(((rows[i] >> (9+j)) & 1) << i for i in range(9)) for j in range(9)] + + +def space(vectors): + result = {0} + for value in vectors: + result |= {x ^ value for x in result} + need(len(result) == 1 << len(vectors), "Independent frame basis") + return result + + +def row_key(row, allowed): + return tuple(sorted((s, word, c.numerator, c.denominator) + for (s, word), c in row.items() if s not in allowed or word)) + + +def tail_key(row): + return tuple(sorted((t, c.numerator, c.denominator) for t, c in row.items())) + + +def add_interval(out, field, start, end, frame, value): + if start < end and value: + out.append((field, start, end, frame, value)) + + +def replay_sources(item, centre_rows): + word, events = item["canonical"], item["programs"]["forward"] + size = len(word["start"]) + sources = set(range(112)) | set(range(224, size)) + allowed = {p for p in range(224, size) if word["start"][p] == 0} + rows = {p: {(p, ()): Q(1)} for p in range(size+8)} + frames = dict(enumerate(word["start"] + [0]*8)) + keys = {p: row_key(rows[p], allowed) for p in sources} + starts = {p: 0 for p in sources} + intervals, views, counts = [], [], Counter() + spaces = [space(vectors) for vectors in word["frames"]] + canonical_start = events.index(["phase", "A"]) + canonical_end = events.index(["phase", "exit_adapters"]) + need((canonical_start, canonical_end) == (7502, 17249), "Actual canonical interval") + need(all(e[0] in ("scalar", "climb", "warp", "phase") + for e in events[canonical_start:canonical_end]), "No wrapper inside the canonical interval") + maps = {record["op"]: record["G_columns"] for record in word["warps"]} + maps.update({-k: inverse(v) for k, v in list(maps.items())}) + for s in range(112): + need(word["ports"][s] in spaces[frames[s]], "Initial X line") + need(all((v & word["ports"][s]).bit_count() % 2 == 0 + for v in spaces[word["final"][112+s]]), "Final Y hyperplane") + + def slot(value): + return value[1] if value[0] == "L" else size+value[1] if value[0] == "C" else ("Z", value[1]) + + for pos, event in enumerate(events): + tag, changed = event[0], None + if pos == canonical_start: + for field, row in rows.items(): + if isinstance(field, int) and field < 112: + need(row == {(field, ()): Q(1)}, "The exterior prefix preserves each X input") + else: + need(not any(s < 112 for s, _ in row), "The exterior prefix has no other X branch") + counts[tag] += 1 + if tag == "scalar": + gate, frame = event[1:] + op, target = gate[0], slot(gate[1]) + if pos >= canonical_end: + need(not (isinstance(target, int) and 112 <= target < 224), "The exterior suffix makes no Y write") + old_frame = frames.get(target) + if op == "clear": + rows[target], frames[target] = {}, frame + else: + need(frames[target] == frame, "Literal scalar target frame") + if op == "scale": + q = Q(*gate[2:4]) + rows[target] = {k: q*v for k, v in rows[target].items() if q*v} + else: + source = slot(gate[2]) + need(source != target and frames[source] == frame, "Literal scalar source frame") + if op == "copy": + rows[target] = dict(rows[source]) + else: + need(op == "add", "Known scalar operation") + need(not (isinstance(source, int) and 112 <= source < 224) + or isinstance(target, int) and 112 <= target < 224, + "No Y feedback to fixed sources") + add(rows[target], rows[source], Q(*gate[3:5])) + changed = target + elif tag == "climb": + target, old_frame, new, rank = event[2:6] + need(frames[target] == old_frame and spaces[old_frame] < spaces[new], "Nested positive climb") + need(len(word["frames"][new]) - len(word["frames"][old_frame]) == rank, "Exact climb rank") + frames[target], changed = new, target + elif tag == "warp": + target, op, old_frame, new = slot(event[1]), event[2], event[3], event[4] + need(frames[target] == old_frame, "Literal warp input frame") + need({lin(maps[op], v) for v in spaces[old_frame]} == spaces[new], "Actual warp frame image") + updated = {} + for (s, history), coefficient in rows[target].items(): + history = history[1:] if history and history[0] == -op else (op,) + history + add(updated, {(s, history): coefficient}) + rows[target], frames[target], changed = updated, new, target + elif tag == "zero_buffer": + target = ("Z", event[2]) + if event[1] == "alloc": + need(target not in rows, "Private buffer allocation") + rows[target], frames[target] = {}, 1 + else: + need(not rows[target], "Private buffer return") + del rows[target], frames[target] + elif tag in ("adapter", "residual_adapter"): + target = event[2] + x_terms = [(s, history) for s, history in rows[target] if s < 112] + if x_terms: + views.append({"event": pos, "kind": event[:2], "field": target, + "frame": frames[target], "X_terms": len(x_terms)}) + if target >= 224: + need(tag == "adapter" and event[1] == "new_to_old" and frames[target] == 1, + "Every X-dependent helper view change is at FULL") + else: + need(tag == "phase", "Known event kind") + if changed in sources: + new_key = row_key(rows[changed], allowed) + if new_key != keys[changed] or frames[changed] != old_frame: + add_interval(intervals, changed, starts[changed], pos+1, old_frame, keys[changed]) + starts[changed], keys[changed] = pos+1, new_key + if tag == "scalar" and isinstance(changed, int) and changed >= size: + need(not any(s < 112 for s, _ in rows[changed]), "Owned fields have no X input branch") + for field in sources: + add_interval(intervals, field, starts[field], len(events)+1, frames[field], keys[field]) + need([frames[p] for p in range(size)] == word["final"], "All final frames") + for p in range(size): + if not 112 <= p < 224: + need(rows[p] == {(p, ()): Q(1)}, "Every fixed source and helper restores") + else: + target = p-112 + goal = {(p, ()): Q(1), (target, ()): Q(1)} + for row in centre_rows: + add(goal, {(s, ()): value for s, value in row.items()}, -row.get(target, Q(0))/4) + need(rows[p] == goal, "Exact clean-J response on every arbitrary input") + need(not rows[size] and all(rows[size+p] == {(size+p, ()): Q(1)} for p in range(1, 8)), "Owned endpoint") + return intervals, views, dict(counts), [canonical_start, canonical_end] + + +def replay_tails(item): + word, events = item["canonical"], item["programs"]["forward"] + rows = [{t: Q(1)} for t in range(112)] + frames = word["final"][112:224].copy() + ends = [len(events)+1]*112 + intervals = [] + for pos in range(len(events)-1, -1, -1): + event, changed = events[pos], None + if event[0] == "climb" and 112 <= event[2] < 224: + changed = event[2]-112 + old_key, old_frame = tail_key(rows[changed]), frames[changed] + need(old_frame == event[4], "Reverse Y frame") + frames[changed] = event[3] + elif event[0] == "scalar": + gate = event[1] + if gate[1][0] == "L" and 112 <= gate[1][1] < 224: + target = gate[1][1]-112 + if gate[0] == "scale": + changed = target + old_key, old_frame = tail_key(rows[changed]), frames[changed] + rows[target] = {k: Q(*gate[2:4])*v for k, v in rows[target].items()} + elif gate[0] == "add" and gate[2][0] == "L" and 112 <= gate[2][1] < 224: + changed = gate[2][1]-112 + old_key, old_frame = tail_key(rows[changed]), frames[changed] + add(rows[changed], rows[target], Q(*gate[3:5])) + elif event[0] == "warp": + need(not (event[1][0] == "L" and 112 <= event[1][1] < 224), "No Y warp") + if changed is not None: + new_key = tail_key(rows[changed]) + if new_key != old_key or frames[changed] != old_frame: + add_interval(intervals, changed, pos+1, ends[changed], old_frame, old_key) + ends[changed] = pos+1 + for target in range(112): + add_interval(intervals, target, 0, ends[target], frames[target], tail_key(rows[target])) + need(rows == [{t: Q(1)} for t in range(112)] and frames == [0]*112, "Y scalar subword is identity") + return intervals + + +def join_intervals(source, target): + groups = defaultdict(list) + for kind, intervals in enumerate((source, target)): + for index, (_, lo, hi, frame, value) in enumerate(intervals): + groups[frame].append((lo, 1, kind, index, value)) + groups[frame].append((hi, 0, kind, index, value)) + products, overlaps = set(), 0 + for events in groups.values(): + active = [{}, {}] + for _, start, kind, index, value in sorted(events): + if not start: + del active[kind][index] + continue + for other in active[1-kind].values(): + products.add((value, other) if kind == 0 else (other, value)) + overlaps += 1 + active[kind][index] = value + return products, overlaps + + +def determinant_fraction(matrix): + rows = [[Q(x) for x in row] for row in matrix] + det = Q(1) + for j in range(len(rows)): + pivot = next((k for k in range(j, len(rows)) if rows[k][j]), None) + if pivot is None: + return Q(0) + if pivot != j: + rows[pivot], rows[j] = rows[j], rows[pivot] + det = -det + value = rows[j][j] + det *= value + rows[j] = [x/value for x in rows[j]] + for k in range(j+1, len(rows)): + value = rows[k][j] + if value: + rows[k] = [x-value*y for x, y in zip(rows[k], rows[j])] + return det + + +def two_basis_certificate(r, ports): + left = [0, 7, 20, 27, 36, 46, 57, 111] + right = [3, 6, 18, 21, 89, 92, 105, 109] + disconnected = [21, 37, 47, 76, 81, 87, 92, 110] + + def gram(a, b): + return [[sum(r[k][s]*r[k][t] for k in range(8)) for t in b] for s in a] + + def check_basis(fields): + need(gram(fields, fields) == [[4*int(i == j) for j in range(8)] for i in range(8)], + "Actual orthogonal centre basis") + need(all((ports[s] & ports[t]).bit_count() % 2 for s in fields for t in fields), + "All within-basis pairs have binary dot one") + + def components(matrix): + neighbours = {i: set() for i in range(16)} + for i in range(8): + for j in range(8): + if matrix[i][j]: + neighbours[i].add(8+j) + neighbours[8+j].add(i) + groups, tree = [], [] + unseen = set(range(16)) + while unseen: + seed = min(unseen) + group, queue = {seed}, [seed] + unseen.remove(seed) + for node in queue: + for next_node in sorted(neighbours[node] & unseen): + unseen.remove(next_node) + group.add(next_node) + queue.append(next_node) + tree.append([node, next_node]) + groups.append(sorted(group)) + return groups, tree + + for fields in (left, right, disconnected): + check_basis(fields) + numerator = gram(left, right) + need(all(x in (-2, 0, 2) for row in numerator for x in row), "Every overlap is zero or a dyadic unit") + groups, tree = components(numerator) + need(len(groups) == 1 and len(tree) == 15, "Connected two-basis graph") + control_groups, _ = components(gram(left, disconnected)) + need(len(control_groups) == 2 and all(len(group) == 8 for group in control_groups), + "A real disconnected basis pair has two scalar blocks") + return dict(core_decompressed_sha256="a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + left_ports=left, right_ports=right, overlap_denominator=4, + overlap_numerator=numerator, components=groups, spanning_tree=tree, + disconnected_control_ports=disconnected, disconnected_control_components=control_groups, + exact_common_diagonal_algebra="scalar multiples of I8") + + +def main(): + for path, pin in PINS.items(): + need(sha256((LANES/path).read_bytes()).hexdigest() == pin, "Pinned producer file " + path) + core = read_gzip(CORE, "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa") + cuts = read_gzip(CUTS, "18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418") + cert = json.loads(CERT.read_text()) + supplied = set() + for product in cuts["products"]: + source = tuple(sorted((s, tuple(sign*op[1] for op, sign in history), num, den) + for s, history, num, den in cuts["source_rows"][product["source_row"]]["constrained"])) + tail = tuple(tuple(x) for x in cuts["tail_columns"][product["tail_column"]]) + supplied.add((source, tail)) + reports = {} + centre_rows = [{int(k): Q(v) for k, v in row.items()} for row in core["R"]] + for name, item in core["providers"].items(): + sources, views, counts, canonical_cuts = replay_sources(item, centre_rows) + tails = replay_tails(item) + actual, overlaps = join_intervals(sources, tails) + need(actual == supplied, "Independent interval inventory equals the supplied product set") + word = item["canonical"] + spaces = [space(vectors) for vectors in word["frames"]] + maps = {record["op"]: record["G_columns"] for record in word["warps"]} + maps.update({-k: inverse(v) for k, v in list(maps.items())}) + checks, history_lengths = set(), Counter() + for _, _, _, frame, row in sources: + for s, history, _, _ in row: + if s >= 112 or (frame, s, history) in checks: + continue + checks.add((frame, s, history)) + value = word["ports"][s] + for op in reversed(history): + value = lin(maps[op], value) + need(value in spaces[frame], "Actual X term support at every source interval") + history_lengths[len(history)] += 1 + tail_checks = set() + for _, _, _, frame, row in tails: + for t, _, _ in row: + if (frame, t) not in tail_checks: + tail_checks.add((frame, t)) + need(all((x & word["ports"][t]).bit_count() % 2 == 0 for x in spaces[frame]), + "Every reverse tail frame is inside the target hyperplane") + reports[name] = dict(source_intervals=len(sources), target_intervals=len(tails), + interval_overlaps=overlaps, distinct_products=len(actual), + actual_X_term_frame_checks=len(checks), history_lengths=dict(history_lengths), + target_frame_checks=len(tail_checks), event_counts=counts, + canonical_rewiring_cuts=canonical_cuts, + X_dependent_view_changes=views) + print(name, len(actual), "products from", overlaps, "interval overlaps", flush=True) + r = [[int(row.get(str(p), 0)) for p in range(112)] for row in core["R"]] + need([[sum(r[a][p]*r[b][p] for p in range(112)) for b in range(8)] for a in range(8)] + == [[56*int(a == b) for b in range(8)] for a in range(8)], "Actual full centre Gram matrix") + ports = core["providers"]["base"]["canonical"]["ports"] + equations = [] + for t in range(112): + need(sum(r[a][t]**2 for a in range(8)) == 4 and ports[t].bit_count() % 2, "Each port is odd and each R column has norm four") + for s in range(112): + if t != s and (ports[t] & ports[s]).bit_count() % 2: + row = [r[a][t]*r[b][s] for a in range(8) for b in range(8)] + need(sum(row[9*a] for a in range(8)) == 0, "Scalar identity satisfies all constraints") + equations.append((t, s, row)) + need(len(equations) == 6608, "Every forbidden off-diagonal pair") + two_bases = two_basis_certificate(r, ports) + (HERE/"TWO-BASES.json").write_text(json.dumps(two_bases, indent=2, sort_keys=True)+"\n") + by_pair = {(t, s): row for t, s, row in equations} + matrix = [[by_pair[tuple(pair)][j] for j in cert["centre_entry_columns"]] + for pair in cert["independent_pairs"]] + need(len(matrix) == 63 and cert["centre_entry_columns"] == list(range(63)), "Full centre matrix certificate") + det = determinant_fraction(matrix) + need(det == -(1 << 71), "Independent rational determinant") + projection = [Q(a == b)-Q(1, 8) for a in range(8) for b in range(8)] + failures = [(t, s) for t, s, row in equations if sum(x*y for x, y in zip(row, projection))] + need(failures, "Dense rank-seven projection is rejected") + duplicated = [row[:] for row in matrix] + duplicated[-1] = duplicated[0][:] + need(determinant_fraction(duplicated) == 0, "Duplicate certificate row is rejected") + report = dict(status="PASS_INDEPENDENT_NATIVE_CENTRE_REVIEW", producer_pins=PINS, + core_decompressed_sha256="a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + inventory_decompressed_sha256="18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418", + providers=reports, forbidden_pairs=len(equations), determinant=str(det), + two_basis_certificate=two_bases, + exact_kernel="scalar multiples of I8", dense_rank_seven_failures=len(failures), + negative_controls=["dense rank-seven projection", "duplicate certificate row"], + checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest()) + (HERE/"REVIEW.json").write_text(json.dumps(report, indent=2, sort_keys=True)+"\n") + print(report["status"], "determinant", det, flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/producer-replay/ALL-CUT-EDGES.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/producer-replay/ALL-CUT-EDGES.json new file mode 100644 index 0000000000..9ed6e7aab3 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/producer-replay/ALL-CUT-EDGES.json @@ -0,0 +1,9 @@ +{ + 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The original rational equation matrix has nullity one." +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/producer-replay/SUPPORT.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/producer-replay/SUPPORT.json new file mode 100644 index 0000000000..4f82fdc9e4 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/producer-replay/SUPPORT.json @@ -0,0 +1,352 @@ +{ + "centre_entry_columns": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 22, + 23, + 24, + 25, + 26, + 27, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 36, + 37, + 38, + 39, + 40, + 41, + 42, + 43, + 44, + 45, + 46, + 47, + 48, + 49, + 50, + 51, + 52, + 53, + 54, + 55, + 56, + 57, + 58, + 59, + 60, + 61, + 62 + ], + "checker_sha256": "82d608f7220d9959925c2990fd717b028a2fce47fcf41ee9f061d0687c32f97c", + "exact_centre_kernel": "span(I8)", + "forbidden_offdiagonal_pairs": 6608, + "independent_pairs": [ + [ + 0, + 7 + ], + [ + 0, + 8 + ], + [ + 0, + 9 + ], + [ + 0, + 10 + ], + [ + 0, + 11 + ], + [ + 0, + 16 + ], + [ + 0, + 26 + ], + [ + 1, + 6 + ], + [ + 1, + 8 + ], + [ + 1, + 9 + ], + [ + 1, + 10 + ], + [ + 1, + 11 + ], + [ + 1, + 12 + ], + [ + 1, + 25 + ], + [ + 2, + 6 + ], + [ + 2, + 7 + ], + [ + 2, + 9 + ], + [ + 2, + 10 + ], + [ + 2, + 11 + ], + [ + 2, + 13 + ], + [ + 2, + 25 + ], + [ + 3, + 6 + ], + [ + 3, + 7 + ], + [ + 3, + 8 + ], + [ + 3, + 10 + ], + [ + 3, + 11 + ], + [ + 3, + 12 + ], + [ + 3, + 25 + ], + [ + 4, + 6 + ], + [ + 4, + 7 + ], + [ + 4, + 8 + ], + [ + 4, + 9 + ], + [ + 4, + 11 + ], + [ + 4, + 12 + ], + [ + 4, + 25 + ], + [ + 5, + 6 + ], + [ + 5, + 7 + ], + [ + 5, + 8 + ], + [ + 5, + 9 + ], + [ + 5, + 10 + ], + [ + 5, + 12 + ], + [ + 5, + 25 + ], + [ + 6, + 1 + ], + [ + 6, + 2 + ], + [ + 6, + 3 + ], + [ + 6, + 4 + ], + [ + 6, + 5 + ], + [ + 6, + 16 + ], + [ + 6, + 26 + ], + [ + 7, + 0 + ], + [ + 7, + 2 + ], + [ + 8, + 0 + ], + [ + 9, + 0 + ], + [ + 10, + 0 + ], + [ + 11, + 0 + ], + [ + 12, + 1 + ], + [ + 12, + 3 + ], + [ + 12, + 4 + ], + [ + 12, + 5 + ], + [ + 12, + 7 + ], + [ + 12, + 17 + ], + [ + 12, + 25 + ], + [ + 13, + 2 + ] + ], + "input_pins": { + "core_decompressed": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "inventory_decompressed": "18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418", + "logical_warp_source": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce" + }, + "integer_minor_determinant": "-2361183241434822606848", + "provider_checks": { + "base": { + "forbidden_spatial_diagonal_controls": 648, + "nonempty_source_words": 1160, + "source_terms": 6920, + "tail_incidences": 8856 + }, + "extra": { + "forbidden_spatial_diagonal_controls": 648, + "nonempty_source_words": 1160, + "source_terms": 6920, + "tail_incidences": 8856 + } + }, + "rank_seven_projection": "I8 - ones(8,8)/8", + "rank_seven_projection_diagonal_counts": { + "1": 42, + "1/2": 14, + "7/8": 56 + }, + "scope": "The supplied all-cut inventory, with its complete current native source states and unchanged Y tail. Actual monomial phases do not alter the spatial support witness. Inventory completeness is a separate source dependency.", + "status": "PASS_SPATIAL_SUPPORT_AND_INTEGER_MINOR" +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/replay_producers.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/replay_producers.py new file mode 100644 index 0000000000..cf3b12eeb6 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/replay_producers.py @@ -0,0 +1,56 @@ +"""Repeat the producer checks without writing to their frozen paths.""" + +from hashlib import sha256 +import json +from pathlib import Path +import runpy +import sys +from unittest.mock import patch + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +OUTPUT = HERE / "producer-replay" +JOBS = [ + ("oblique-native-20261017/interior-cut/inventory_new_edges.py", ["ALL-CUT-EDGES.json", "ALL-CUT-EDGES.json.gz"]), + ("oblique-native-20261017/interior-cut/check_frame_support.py", ["FRAME-SUPPORT.json"]), + ("coherent-port/centre-mixing-20261018/check_support.py", ["SUPPORT.json"]), + ("coherent-port/centre-mixing-20261018/check_mixing.py", ["MIXING.json"]), +] + + +def main(): + OUTPUT.mkdir(exist_ok=True) + sys.path.insert(0, str(LANES / "oblique-native-20261017/interior-cut")) + receipts = [] + write_text, write_bytes = Path.write_text, Path.write_bytes + for name, outputs in JOBS: + source = LANES / name + pins = {output: sha256((source.parent/output).read_bytes()).hexdigest() for output in outputs} + + def destination(path): + if path.parent != source.parent or path.name not in outputs: + raise ValueError("Undeclared producer write: " + str(path)) + return OUTPUT / path.name + + def redirect_text(path, *args, **kwargs): + return write_text(destination(path), *args, **kwargs) + + def redirect_bytes(path, *args, **kwargs): + return write_bytes(destination(path), *args, **kwargs) + + with patch.object(Path, "write_text", redirect_text), patch.object(Path, "write_bytes", redirect_bytes): + runpy.run_path(str(source), run_name="__main__") + for output in outputs: + original = sha256((source.parent/output).read_bytes()).hexdigest() + actual = sha256((OUTPUT/output).read_bytes()).hexdigest() + if original != pins[output] or actual != original: + raise ValueError("Producer output mismatch: " + output) + receipts.append(dict(source=name, output=output, sha256=actual, + source_unchanged=True, output_equal=True)) + (HERE/"PRODUCER-REPLAY.json").write_text(json.dumps(receipts, indent=2, sort_keys=True)+"\n") + print("ALL_PRODUCER_OUTPUTS_BYTE_EQUAL", flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/FREEZE.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/FREEZE.json new file mode 100644 index 0000000000..e88ea0b8ac --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/FREEZE.json @@ -0,0 +1,35 @@ +{ + "accepted_scope": "Universal residue-field rank separation, the actual dyadic application, the finite Gaussian routed-operator version, and the general-M null family in the fixed linear observation class.", + "additional_corollary": "With an invertible B minor, a unit log with stack rank r exists exactly when c is a unit in the coefficient ring. For c=13, the normalized rank-eight log is uniquely B/13; M=B moves the division to the decoder.", + "core_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "date": "2026-10-18", + "files": { + "REVIEW.json": "d80060946c13e5a2c997396c5c53b33e555732fdba74e4cc9b547cd72b65579f", + "REVIEW.md": "dc1d2d56c4210bc049051c72c7cf0aa2e19dbef65b01eb06d9424181af393e1c", + "check_review.py": "d7f2338efcd0c006f02fcab0bc36f83557fa38c7070c420a7b4a405b91452af5" + }, + "limits": [ + "Information rank, not a native-child or simultaneous-storage lower bound", + "Fixed linear observations, not arbitrary nonlinear queries or bounded-domain packing", + "Physical query access, scatter, phases, recursive costs and a complete supplier remain open" + ], + "pr_standard": "/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md", + "publication": "No PR, push, commit or publication was performed.", + "source_pins": { + "lanes/controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md": "50ce523e083f70556cc62694219da94b684cc898f3d5e358767fcc40dd77e4bc", + "lanes/oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md": "1a4d715e089773a9063fba88d5b83ec770bb5eb6ed501bc8f96b290c19b08401", + "root/DYADIC-QUERY-SEPARATION-20261018.json": "e66d5c311490c06973bf604d207fb5cf7a9cd4800c0cea049623c3b5e2369732", + "root/DYADIC-QUERY-SEPARATION-20261018.md": "664f430efd099f35cbc7c2abc8025968c03020707027857d2882daa51a065a1a", + "root/check_dyadic_query_separation_20261018.py": "b4ed000b5b600944f614b86ae7a88ac55af8eac3213e6827ed211a2630ccd342" + }, + "status": "FROZEN_INDEPENDENT_THEOREM_REVIEW", + "validation": { + "actual_stack_minor_determinant": "1/8", + "full_null_relations": [ + "qQ=I", + "Qq=I" + ], + "nonidentity_MD_fixtures": 24, + "routed_two_coordinate_stack_rank": 32 + } +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/REVIEW.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/REVIEW.json new file mode 100644 index 0000000000..3e7eb3ccd7 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/REVIEW.json @@ -0,0 +1,183 @@ +{ + "actual_source": { + "B_rank_mod_13": 8, + "controls": [ + "M=B has MD=13I and rank-eight stack", + "Missing B residue rank", + "Missing zero residue of c", + "Matched coefficients have no residue at 13" + ], + "explicit_minor_determinant": "1/8", + "explicit_minor_ports": [ + 1, + 2, + 3, + 4, + 5, + 6, + 8, + 12, + 21, + 37, + 47, + 76, + 81, + 87, + 92, + 110 + ], + "matched_rank_over_Q": 8, + "nonidentity_MD_cases": [ + { + "MD_is_identity": false, + "case": 0, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 1, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 2, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 3, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 4, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 5, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 6, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 7, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 8, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 9, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 10, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 11, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 12, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 13, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 14, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 15, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 16, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 17, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 18, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 19, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 20, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 21, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 22, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 23, + "stack_rank_mod_13": 16 + } + ], + "stack_rank_mod_13": 16 + }, + "checker_sha256": "d7f2338efcd0c006f02fcab0bc36f83557fa38c7070c420a7b4a405b91452af5", + "core_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "formal_full_null": { + "all_pair_counts": "The future inputs and all visible outputs are zero; the only nonzero next-bank bridge is -v+v.", + "operator_relations": [ + "Qq=I", + "qQ=I" + ], + "unit_factorization": "diag(I,-MD)", + "uses_BD_identity_for_null_family": false, + "uses_MD_identity": false, + "wrong_original_b_control": true + }, + "routed_operator_fixture": { + "coordinates_per_field": 2, + "noncommuting_routes": true, + "query_rank_mod_13": 32, + "scope": "An actual-B Gaussian-unit conjugation fixture; the general finite-operator version follows from the residue proof, not a new native route replay." + }, + "scope": "Fixed linear observations on the full underlying field space, with arbitrary postprocessing. No native-child, bit-packing, arbitrary nonlinear-encoding or complete supplier lower bound.", + "source_pins": { + "lanes/controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md": "50ce523e083f70556cc62694219da94b684cc898f3d5e358767fcc40dd77e4bc", + "lanes/oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md": "1a4d715e089773a9063fba88d5b83ec770bb5eb6ed501bc8f96b290c19b08401", + "root/DYADIC-QUERY-SEPARATION-20261018.json": "e66d5c311490c06973bf604d207fb5cf7a9cd4800c0cea049623c3b5e2369732", + "root/DYADIC-QUERY-SEPARATION-20261018.md": "664f430efd099f35cbc7c2abc8025968c03020707027857d2882daa51a065a1a", + "root/check_dyadic_query_separation_20261018.py": "b4ed000b5b600944f614b86ae7a88ac55af8eac3213e6827ed211a2630ccd342" + }, + "status": "PASS_INDEPENDENT_DYADIC_QUERY_SEPARATION", + "universal_proof": "Residue row relation times D forces beta=0 because MD is a unit; full residue rank of B forces alpha=0. A nonzero residue minor lifts to the fraction field." +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/REVIEW.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/REVIEW.md new file mode 100644 index 0000000000..f5f105c5ee --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/REVIEW.md @@ -0,0 +1,276 @@ +# Independent review of dyadic query separation + +The universal query-separation theorem passes this review. The actual +eight-centre B matrix has full row rank modulo 13. Every dyadic M for +which MD has a dyadic two-sided inverse therefore gives a stack `[B;M]` +of rank sixteen. The full-null family applies to general M; it does not +require MD=I. The matched choice M=B/13 has rank eight and MD=I. + +This is a theorem about the rank of fixed linear observations in the +stated output partition. Postprocessing may be nonlinear. The theorem +does not bound native children, concurrent scratch fields, arbitrary +nonlinear encodings, or packing on one bounded finite input domain. It +does not prove that the old-stage B query is cheap or physically available. + +## Sources and independent method + +The producer source is +[DYADIC-QUERY-SEPARATION-20261018.md](../../../root/DYADIC-QUERY-SEPARATION-20261018.md), +SHA256 `664f430efd099f35cbc7c2abc8025968c03020707027857d2882daa51a065a1a`. +The source criterion is +[UNIT-COMPLETION.md](../../oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md), +and the terminal class is +[MINOR-LOG-SOURCE-ACCESS.md](../../controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md). +All proof and checker pins are in [REVIEW.json](REVIEW.json). + +The independent checker reads the actual R entries from the pinned +decompressed `CLEAN-J-PROGRAMS.json.gz` payload, SHA256 +`a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa`. +It derives the selected inverse by exact elimination. It then derives B +and D and checks the actual minor inverses. It imports no producer module. +Its modular rank check builds a column basis instead of using the +producer's row reduction. + +The exact actual sparse stack has a nonzero 16-by-16 minor with columns + +```text +[1,2,3,4,5,6,8,12,21,37,47,76,81,87,92,110] +``` + +and determinant 1/8. The checker also checks 24 different logs for which +MD is a nonidentity dyadic unit. Thus the independent examples are not +limited to sections with MD=I. A Gaussian two-coordinate route fixture +uses noncommuting unit routes and has stack rank 32 after reduction. +The finite fixture is not a replay of the complete global native schedule. + +## Residue proof and rank lift + +Let R be a commutative ring with a unital map phi to a field k. Suppose +B is r by n, D is n by r, and M is r by n, all over R. Assume + +```text +BD=cI, phi(c)=0, +rank_k phi(B)=r, +MD is a unit in Mat_r(R). +``` + +Apply phi entrywise. Since a matrix inverse over R maps to its inverse +over k, `phi(MD)` is invertible. If + +```text +alpha phi(B)+beta phi(M)=0, +``` + +right multiplication by `phi(D)` gives `beta phi(MD)=0`. Hence beta +is zero. The full row rank of `phi(B)` then makes alpha zero. This +proves row rank 2r over k and also implies `n>=2r`. It does not assume +MD is identity, that B and M commute, or that R is a field. + +For the fraction-field conclusion, assume R is an integral domain. +Some 2r-by-2r determinant has nonzero image under phi. Its determinant +over R is therefore nonzero. The same determinant remains nonzero in +the fraction field. Thus the stack has rank 2r there. In fact this +step needs no extra property of a residue map beyond the stated ring +homomorphism and integral-domain hypothesis. + +Both hypotheses have a role. If MD is only invertible over Q, choose +M=B in the actual example. Then MD=13I, but `[B;M]` has rank eight. +If full residue rank of B is dropped, the scalar example B=13, D=M=1 +has a unit MD and a rank-one stack. If the condition phi(c)=0 is +dropped, B=D=M=1 gives the same failure. These are failures of the +weakened hypotheses, not exceptions to the theorem. + +## Binding to the actual canonical and routed matrices + +Use the actual selected minor +`A=[0,7,20,27,36,46,57,111]` and ordinary minor +`T=[21,37,47,76,81,87,92,110]`. Direct calculation gives + +```text +B=R_A^-1 R_U, +D=R_U^T (R_A^-1)^T, +BD=13I. +``` + +The inverse of B restricted to T and the inverse of D restricted to T +are both dyadic. The checker verifies both orders of each inverse. +Reducing the B minor modulo 13 preserves its inverse. Thus B has full +row rank eight over F_13. This proves the actual application for every +dyadic M with a dyadic unit MD, without an enumeration of all M. + +For finite routed arrays, let each field have ell complex coordinates. +Flatten every ordered operator to its complete finite matrix over +`Z[i,1/2]`. The map + +```text +i -> 5, 1/2 -> 7, integers -> F_13 +``` + +is well defined, because `5^2=-1` and `2*7=1` in F_13. Every proved +Gaussian-dyadic inverse maps to an inverse. The complete identities +`BD=13I` and the inverse-minor identities therefore give the hypotheses +with r replaced by 8ell and n by 104ell. The stack has rank 16ell. + +This argument uses the full finite matrices. A ring of ell-by-ell +operators is not itself being called a field. Flattening puts the rank +argument over the commutative scalar residue field. No Q, frame change, +or port route moves through B, D, or M. If an intended physical map +does not have the stated ordered identities and Gaussian-dyadic +inverses, it has not met the theorem's hypotheses. + +## The source unit condition for general MD + +The mixed-source part of the local map, in source variables beta=qb +and v, is + +```text +w=-D beta-v+DMv, +d=Mv. +``` + +The invertible output changes `f0=-w+Dd` and `g=d-Mf0` give + +```text +f0=v+D beta, +g=-MD beta. +``` + +The input change from `(beta,v)` to `(beta,v+D beta)` is invertible. +After component reordering, the source map is therefore equivalent +to `diag(I,-MD)`. That map is a unit exactly when MD is a two-sided +unit. This proves the criterion over the ordered operator ring as +well as over a field. A zero-kernel test alone would not prove this +ring-level statement. + +## Full-null family for arbitrary M + +Let q=Q^-1, and choose an arbitrary ordinary vector v. Put all later +pair inputs to zero. For pair zero, set + +```text +original x_U=(I-DB)v, +original y_U=DBv, +Qa=-Mv, +original b=-QBv+qMv. +``` + +The first full shear gives incoming ordinary Y equal to v. Since +`a=-qMv`, its selected source value becomes `-QBv`. Thus the backward +call gives + +```text +d=Qa+Mv=0, +h=q(-QBv)+Bv=0, +w=(I-DB)v-v+D(0-q(-QBv))=0. +``` + +These cancellations use only qQ=I and Qq=I. They do not use MD=I, +MD invertibility, or BD=13I. The independent checker verifies this +in free operator words with only those two inverse relations. It +also rejects removal of the original-b term qMv. + +Every selected exchange acts on zeros. The raw or corrected forward +call leaves retired ordinary Y equal to v. The bridge to the next +ordinary bank is `-v+v=0`. Every later pair and the final completed-X +triangle therefore remain zero, for every pair count. + +The required original selected data and ordinary source values include +`-Mv` and `DBv`. Their destination fields are zero on this family. +The terminal obtains all other information about v only through the +fixed linear observation Nv. If Nv=0, these destination outputs must +match the zero-input outputs. Hence Mv=0 and DBv=0. Over Q or Q(i), +BD=13I makes D injective, so DBv=0 is equivalent to Bv=0. Therefore + +```text +ker N is contained in ker B intersect ker M. +``` + +For finite vector spaces, this condition is equivalent to a linear +factorization `[B;M]=LN`. Define L on the image of N by `L(Nv)=[B;M]v`; +the kernel condition makes it well defined. Extend L to the observation +space. It follows that `rank N>=rank[B;M]`. This proof permits arbitrary +nonlinear postprocessing of N: postprocessing cannot distinguish two +inputs with the same N value. + +If N returns q complete fields of ell coordinates, its rank is at most +qell. Thus q must be at least sixteen for a dyadic-unit log. Cross-pair +queries do not help this family: restrict N to the first ordinary bank. +The count is total independent observation rank. It is not a claim +that sixteen scratch fields must be live at the same time. + +The argument does not require recovery of every coordinate of v from N. +The retained ordinary Y can keep its unobserved contents and receive +known corrections. The displayed kernel condition is a necessary source +condition; it does not prove a full decoder. If the underlying inputs +are Gaussian dyadic, a finite rational kernel witness can be cleared +of denominators and scaled by a power of two. It then gives admissible +dyadic witnesses in a uniform all-precision model. The argument is not +a lower bound for precision-dependent packing of one bounded finite set. + +## Exact odd division and a sharper consequence + +For M=B/13, the equation MD=I holds and the stack has rank eight over +the fraction field. Its rank is exactly eight because B has an invertible +minor. This M lies outside the dyadic ring, and its entries cannot be +reduced modulo 13. The independent checker verifies both facts. The +existing common-grid theorem supplies exact division by 13 only under +its exact-child, all-numeric-stream root conversion, arbitrary-borrowed +input, binary-guard, and final dyadic-endpoint conditions. + +The argument has a stronger coefficient-ring consequence. Suppose B +has an invertible r-column minor over an integral domain R, BD=cI +with nonzero c, and `[B;M]` has fraction-field rank r. Then + +```text +M=T B, +T=M_minor (B_minor)^-1 lies in Mat_r(R), +MD=cT. +``` + +If MD is a unit over R, then `T(MD)^-1` is in Mat_r(R), and c times +this matrix is identity. A diagonal entry therefore gives an inverse +of c in R. Conversely, if c is a unit, M=B/c has MD=I and stack rank r. +Thus a unit log with only r independent query rows exists exactly when +c is a unit in the coefficient ring. + +For the actual construction, an eight-query unit log consequently +requires inversion of 13. Rational divisions with denominators coprime +to 13 leave the residue map intact and still force sixteen queries. +In particular, division by three alone does not resolve this query +obstruction. Under the normalization MD=I, the rank-eight choice is +uniquely M=B/13. More generally it is `M=K B/13` for a unit K=MD. + +This also gives a scheduling alternative. In the ring with 13 inverted, +one may take the dyadic initial log M=B, leave K=13I, and use +`K^-1=I/13` in the general source-code formulas. This moves the odd +normalization from the initial log to the decoder. It does not remove +the required B query or establish a cheaper physical implementation. + +## Reproduction and status + +Run from the workspace root: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/check_review.py +``` + +Expected status: + +```text +PASS_INDEPENDENT_DYADIC_QUERY_SEPARATION +``` + +The independent checker passed. The producing checker and receipt were +pinned and read; this review did not rerun its entry point because that +entry point writes the frozen producer receipt. No material defect was +found in the stated theorem. The coefficient-ring characterization above +is a direct consequence proved in this review. + +The cheap implementation of the remaining old-stage query, target +scatter, phases, recursive admission, complete decoder, and supplier +moment remain open. No native-child lower bound or kappa result follows. +This review used substantial OpenAI Codex assistance. + +No PR, push, or publication commit is authorized. Before a future PR +description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/check_review.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/check_review.py new file mode 100644 index 0000000000..145f285f7e --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/check_review.py @@ -0,0 +1,300 @@ +"""Review the residue-field query theorem on the actual centre matrices.""" + +from fractions import Fraction as Q +from hashlib import sha256 +import gzip +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +CAMPAIGN = HERE.parents[2] +PINS = { + "root/DYADIC-QUERY-SEPARATION-20261018.md": "664f430efd099f35cbc7c2abc8025968c03020707027857d2882daa51a065a1a", + "root/check_dyadic_query_separation_20261018.py": "b4ed000b5b600944f614b86ae7a88ac55af8eac3213e6827ed211a2630ccd342", + "root/DYADIC-QUERY-SEPARATION-20261018.json": "e66d5c311490c06973bf604d207fb5cf7a9cd4800c0cea049623c3b5e2369732", + "lanes/oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md": "1a4d715e089773a9063fba88d5b83ec770bb5eb6ed501bc8f96b290c19b08401", + "lanes/controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md": "50ce523e083f70556cc62694219da94b684cc898f3d5e358767fcc40dd77e4bc", +} +CORE = "lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz" +CORE_RAW_PIN = "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa" +A = [0, 7, 20, 27, 36, 46, 57, 111] +T = [21, 37, 47, 76, 81, 87, 92, 110] +U = [p for p in range(112) if p not in A] +P = 13 + + +def require(ok, label): + if not ok: + raise ValueError(label) + + +def eye(n): + return [[Q(i == j) for j in range(n)] for i in range(n)] + + +def tr(a): + return [list(c) for c in zip(*a)] + + +def mm(a, b): + out = [[Q(0) for _ in b[0]] for _ in a] + for i, row in enumerate(a): + for k, value in enumerate(row): + if value: + for j, right in enumerate(b[k]): + if right: + out[i][j] += value * right + return out + + +def inverse(a): + n = len(a) + rows = [list(row) + unit for row, unit in zip(a, eye(n))] + for j in range(n): + pivot = next((k for k in range(j, n) if rows[k][j]), None) + require(pivot is not None, "Invertible exact minor") + rows[j], rows[pivot] = rows[pivot], rows[j] + value = rows[j][j] + rows[j] = [x / value for x in rows[j]] + for k in range(n): + if k != j: + value = rows[k][j] + rows[k] = [x - value * y for x, y in zip(rows[k], rows[j])] + return [row[n:] for row in rows] + + +def dyadic(a): + return all(x.denominator & (x.denominator - 1) == 0 for row in a for x in row) + + +def mod(a): + out = [] + for row in a: + values = [] + for x in row: + x = Q(x) + require(x.denominator % P != 0, "The coefficient has a defined residue") + values.append(x.numerator * pow(x.denominator, -1, P) % P) + out.append(values) + return out + + +def pivots(a): + # Build a column basis, instead of reducing the source matrix by rows. + basis = {} + chosen = [] + for j, col in enumerate(zip(*a)): + v = list(col) + for pivot, b in sorted(basis.items()): + value = v[pivot] + v = [(x - value * y) % P for x, y in zip(v, b)] + pivot = next((k for k, value in enumerate(v) if value), None) + if pivot is not None: + inv = pow(v[pivot], -1, P) + basis[pivot] = [x * inv % P for x in v] + chosen.append(j) + return chosen + + +def determinant(a): + rows = [list(r) for r in a] + det = Q(1) + for j in range(len(rows)): + pivot = next((k for k in range(j, len(rows)) if rows[k][j]), None) + if pivot is None: + return Q(0) + if pivot != j: + rows[j], rows[pivot] = rows[pivot], rows[j] + det *= -1 + v = rows[j][j] + det *= v + for k in range(j + 1, len(rows)): + c = rows[k][j] / v + for col in range(j + 1, len(rows)): + rows[k][col] -= c * rows[j][col] + return det + + +def actual_matrices(): + for path, pin in PINS.items(): + require(sha256((CAMPAIGN / path).read_bytes()).hexdigest() == pin, path) + raw = gzip.decompress((CAMPAIGN / CORE).read_bytes()) + require(sha256(raw).hexdigest() == CORE_RAW_PIN, "Actual clean-core payload pin") + core = json.loads(raw) + r = [[Q(row.get(str(p), 0)) for p in range(112)] for row in core["R"]] + ra = [[row[p] for p in A] for row in r] + ru = [[row[p] for p in U] for row in r] + rai = inverse(ra) + b = mm(rai, ru) + d = mm(tr(ru), tr(rai)) + require(dyadic(b) and dyadic(d), "Actual graphs are dyadic") + require(mm(b, d) == [[13 * x for x in row] for row in eye(8)], "Actual BD=13I") + dt = [d[U.index(p)] for p in T] + dti = inverse(dt) + bt = [[row[U.index(p)] for p in T] for row in b] + bti = inverse(bt) + require(dyadic(dti) and dyadic(bti), "Actual source and query minors are dyadic units") + require(mm(dt, dti) == mm(dti, dt) == eye(8), "Both ordinary inverse-minor orders") + require(mm(bt, bti) == mm(bti, bt) == eye(8), "Both B inverse-minor orders") + m = [[Q(0) for _ in U] for _ in A] + for i in range(8): + for j, p in enumerate(T): + m[i][U.index(p)] = dti[i][j] + require(mm(m, d) == eye(8), "Sparse starting section") + return b, d, m + + +def log_checks(b, d, m): + require(len(pivots(mod(b))) == 8, "B has full row rank modulo 13") + cols = pivots(mod(b + m)) + require(len(cols) == 16, "Independent source stack modulo 13") + minor = [[row[j] for j in cols] for row in b + m] + det = determinant(minor) + require(det and mod([[det]])[0][0], "Explicit minor lifts to a nonzero rational determinant") + ker = eye(104) + projection = mm(d, m) + ker = [[x - y for x, y in zip(row, sub)] for row, sub in zip(ker, projection)] + require(mm(ker, d) == [[0] * 8 for _ in U], "Exact kernel projector rows") + cases = [] + last = None + for case in range(24): + unit = eye(8) + a, j = case % 8, (case + 1) % 8 + unit[a][a] = Q(2) if case % 2 else Q(1, 2) + unit[a][j] = Q((-1) ** case, 2 ** (case % 3)) + unit_inv = inverse(unit) + require(unit != eye(8) and dyadic(unit_inv) and mm(unit, unit_inv) == mm(unit_inv, unit) == eye(8), "Nonidentity dyadic unit K") + candidate = mm(unit, m) + for row in range(8): + krow = ker[(17 * case + 9 * row + 1) % 104] + coefficient = Q(1 + case % 5, 2 ** (row % 3)) + candidate[row] = [x + coefficient * y for x, y in zip(candidate[row], krow)] + require(mm(candidate, d) == unit, "MD can be a general unit, not only identity") + require(len(pivots(mod(b + candidate))) == 16, "Every general-unit fixture has rank 16") + cases.append({"case": case, "MD_is_identity": False, "stack_rank_mod_13": 16}) + last = candidate + matched = [[x / 13 for x in row] for row in b] + require(mm(matched, d) == eye(8) and all(13 * x == y for row, base in zip(matched, b) for x, y in zip(row, base)), "Matched exact section and row dependence") + require(not dyadic(matched), "Matched section leaves the dyadic ring") + try: + mod(matched) + except ValueError: + pass + else: + raise ValueError("The matched coefficient must not have a mod-13 residue") + require(len(pivots(mod(b + b))) == 8 and mm(b, d) != eye(8), "A rationally invertible MD alone is insufficient") + require(len(pivots([[0], [1]])) == 1, "B=13,D=M=1 defeats the conclusion without full residue rank") + require(len(pivots([[1], [1]])) == 1, "B=D=M=1 defeats the conclusion when c survives reduction") + return last, {"B_rank_mod_13": 8, "stack_rank_mod_13": 16, + "explicit_minor_ports": [U[j] for j in cols], "explicit_minor_determinant": str(det), + "nonidentity_MD_cases": cases, "matched_rank_over_Q": 8, + "controls": ["M=B has MD=13I and rank-eight stack", "Missing B residue rank", "Missing zero residue of c", "Matched coefficients have no residue at 13"]} + + +def mm_mod(a, b): + columns = list(zip(*b)) + return [[sum(x * y for x, y in zip(row, col)) % P for col in columns] for row in a] + + +def route(index): + # This is the residue of L(b) U(i*a), a Gaussian-dyadic unit. + a, b = (index % 7) + 1, (index % 5) + 1 + ia = 5 * a % P + forward = [[1, ia], [b, (1 + b * ia) % P]] + back = [[(1 + b * ia) % P, -ia % P], [-b % P, 1]] + require(mm_mod(forward, back) == mm_mod(back, forward) == [[1, 0], [0, 1]], "Gaussian unit route and its inverse") + return forward, back + + +def lift(a, target_routes, source_routes): + out = [[0] * (2 * len(a[0])) for _ in range(2 * len(a))] + for i, row in enumerate(a): + left = target_routes[i][1] + for j, x in enumerate(row): + block = mm_mod(left, source_routes[j][0]) + for s in range(2): + for t in range(2): + out[2 * i + s][2 * j + t] = x * block[s][t] % P + return out + + +def routed_check(b, d, m): + require((5 * 5 + 1) % P == 0 and 2 * 7 % P == 1, "Gaussian dyadic residue i->5, 1/2->7") + eroutes = [route(3 * j + 1) for j in range(8)] + uroutes = [route(5 * j + 2) for j in range(104)] + require(mm_mod(eroutes[0][0], uroutes[0][0]) != mm_mod(uroutes[0][0], eroutes[0][0]), "The fixture uses noncommuting routes") + br = lift(mod(b), eroutes, uroutes) + dr = lift(mod(d), uroutes, eroutes) + mr = lift(mod(m), eroutes, uroutes) + require(mm_mod(br, dr) == [[0] * 16 for _ in range(16)], "Routed BD reduces to zero with the exact order") + require(len(pivots(mm_mod(mr, dr))) == 16, "Routed MD is a unit") + require(len(pivots(br)) == 16 and len(pivots(br + mr)) == 32, "Routed two-coordinate stack has rank 32") + return {"coordinates_per_field": 2, "query_rank_mod_13": 32, "noncommuting_routes": True, + "scope": "An actual-B Gaussian-unit conjugation fixture; the general finite-operator version follows from the residue proof, not a new native route replay."} + + +def full_null_check(): + zero, v, beta = {}, {(): 1}, {("beta",): 1} + + def add(a, b, coefficient=1): + out = dict(a) + for word, value in b.items(): + out[word] = out.get(word, 0) + coefficient * value + if not out[word]: + del out[word] + return out + + def apply(op, a): + out = {} + for word, value in a.items(): + term = (op,) + word + if len(term) >= 2 and term[:2] in [("Q", "q"), ("q", "Q")]: + term = term[2:] + out[term] = out.get(term, 0) + value + return {word: value for word, value in out.items() if value} + + bv, mv = apply("B", v), apply("M", v) + dbv = apply("D", bv) + original_u = add(v, dbv, -1) + qa = add(zero, mv, -1) + a = apply("q", qa) + original_b = add(apply("Q", bv), apply("q", mv), -1) + original_b = {word: -value for word, value in original_b.items()} + incoming_v = add(dbv, original_u) + incoming_b = add(original_b, a) + d = add(qa, apply("M", incoming_v)) + h = add(apply("q", incoming_b), apply("B", incoming_v)) + w = add(add(original_u, incoming_v, -1), apply("D", add(d, apply("q", incoming_b), -1))) + require(incoming_v == v and d == h == w == zero, "Full-null family without any MD or BD relation") + require(add(add(zero, incoming_v, -1), v) == zero, "The next ordinary bridge cancels for every pair count") + bad_b = add(zero, apply("Q", bv), -1) + require(add(apply("q", add(bad_b, a)), bv) != zero, "The original-b qMv term is necessary") + source_w = add(add(zero, apply("D", beta), -1), add(apply("D", mv), v, -1)) + source_d = mv + f0 = add(add(zero, source_w, -1), apply("D", source_d)) + g = add(source_d, apply("M", f0), -1) + require(f0 == add(v, apply("D", beta)) and g == add(zero, apply("M", apply("D", beta)), -1), "General MD unit-criterion factorization") + return {"operator_relations": ["Qq=I", "qQ=I"], "uses_MD_identity": False, + "uses_BD_identity_for_null_family": False, "unit_factorization": "diag(I,-MD)", + "wrong_original_b_control": True, "all_pair_counts": "The future inputs and all visible outputs are zero; the only nonzero next-bank bridge is -v+v."} + + +def main(): + b, d, m = actual_matrices() + candidate, actual = log_checks(b, d, m) + routed = routed_check(b, d, candidate) + full_null = full_null_check() + out = {"status": "PASS_INDEPENDENT_DYADIC_QUERY_SEPARATION", "source_pins": PINS, + "core_decompressed_sha256": CORE_RAW_PIN, "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "actual_source": actual, "routed_operator_fixture": routed, "formal_full_null": full_null, + "universal_proof": "Residue row relation times D forces beta=0 because MD is a unit; full residue rank of B forces alpha=0. A nonzero residue minor lifts to the fraction field.", + "scope": "Fixed linear observations on the full underlying field space, with arbitrary postprocessing. No native-child, bit-packing, arbitrary nonlinear-encoding or complete supplier lower bound."} + (HERE / "REVIEW.json").write_text(json.dumps(out, sort_keys=True, indent=2) + "\n") + print(out["status"]) + print(json.dumps({"rank": 16, "matched_rank": 8, "MD_nonidentity_cases": 24, "routed_rank": 32, + "null_family_uses_MD_identity": False}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/MIXING.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/MIXING.json new file mode 100644 index 0000000000..7b45a22083 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/MIXING.json @@ -0,0 +1,13740 @@ +{ + "admissible_basis": [ + [ + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 1, + 0, + 0, + 0, + 0, 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The original rational equation matrix has nullity one." +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/MIXING.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/MIXING.md new file mode 100644 index 0000000000..710f48fbe8 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/MIXING.md @@ -0,0 +1,180 @@ +# Scalar centre mixing in the retained native word + +The retained response grammar does not permit a rank-seven scalar centre +map with a nonzero diagonal data response. This result permits all 64 +entries of the centre map to vary. It is not limited to deletion of one +centre coordinate. + +The result does not give a lower bound for a changed native word. It does +not exclude scalar gates between unequal physical frames, a changed source +code, new native hops, or a new centre query or scatter space. + +## 1. Source and question + +Use the two providers in `new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz`. +The decompressed SHA256 is +`a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa`. +There are 112 data ports in each bank. The exact source matrices satisfy + +\[ +R\in\mathbb Z^{8\times112},\qquad K=R^T/4,\qquad RK=14I_8. +\] + +The clean cross response is \(J=I-KR\). Each diagonal entry of \(KR\) +is one. Let \(A\) be an arbitrary constant scalar \(8\times8\) matrix. +The proposed centre response is \(KAR\). A fixed scalar factor on each +port can give an ideal shear only if a retained response \(E\) satisfies + +\[ +E+KAR=\operatorname{diag}(d_0,\ldots,d_{111}),\qquad d_p\ne0. \tag{1} +\] + +A factorization through seven scalar centre channels has +\(\operatorname{rank}A\le7\). The calculation below permits such a +factorization without charging for its access. Thus a failure here is not +caused by an assumption that centre mixing is free. + +The first test retains the source and helper computation, the Y-only +scalar word, and all native events. It changes only gains on existing +non-Y-to-Y ADDs. It permits arbitrary initial-I-helper entry corrections. +All other helper terms and all nonempty operator words must cancel. + +The second test permits new one-way equal-frame ADDs at every cut in the +supplied `ALL-CUT-EDGES.json.gz` inventory. The source computation and the +Y-only tail remain fixed. No Y-to-source feedback is added. The inventory +has 4,276 products from 267,854 source/target pair checks. Its completeness +and physical cut admission are source dependencies. This packet checks +the supplied products; it does not create a stronger owner contract. + +## 2. Exact existing-site certificate + +`check_mixing.py` imports no producer. It replays each full clean word on +all 640 input columns. It checks scalar frames, native frame changes, +the source identity, all 408 arbitrary helper outputs, and the exact +clean-J data map. C0 is cleared. C1 through C7 retain their arbitrary +inputs in this source core. + +The program builds the source row and remaining Y-tail column for each +existing cross ADD. There are 825 active site variables. Add the 64 +entries of \(A\). The exact rational system has 13,900 equations and +889 variables. Its rank modulo 1,000,003 is 888. `MIXING.json` records +the independent row keys and pivot columns for both providers. + +The original cross gains, together with \(A=I_8\), satisfy every equation +over the rationals. A nonzero minor modulo a prime is also nonzero over +the rationals. Therefore the exact rational nullspace has dimension one. +Every solution has + +\[ +A=cI_8. \tag{2} +\] + +This rank argument does not restrict the denominators in a proposed +rational solution. In particular, division by an odd integer does not +change the result. The first certificate uses coefficientwise cancellation +in the formal operator-word model. The next certificate removes that +restriction for the supplied all-cut products. + +## 3. Spatial support of the actual monomial words + +Write \(q_p\in\mathbb F_2^9\) for the actual odd label of port \(p\). +At a listed cut, let \(F\) be its current native frame subspace. For each +source term from X port \(s\), let \(W\) be its ordered logical warp word. +The source definition `new-native-recipes-20261017/sources/bw_adapters.py` +defines each warp as a monomial \(K_G\) with linear address part \(G\). +Its quadratic phase can be nonzero. A negative occurrence has linear +part \(G^{-1}\). + +The checker composes these signed linear maps in event order. It checks + +\[ +W_{\rm lin}q_s\in F, +\qquad F\subseteq q_t^\perp \tag{3} +\] + +for each final target \(t\) in the remaining scalar Y tail. Both providers +pass 6,920 source-term checks and 8,856 source/target incidences. These +counts include 1,160 nonempty source words. They do not discard the actual +warp terms. + +Suppose \(q_t\cdot q_s=1\). Equation (3) implies +\(W_{\rm lin}q_s\ne q_s\). In the computational basis, + +\[ +\langle q_s|W|q_s\rangle=0. \tag{4} +\] + +Every monomial phase is irrelevant to this zero. Equation (4) remains true +after any scalar sum of these terms. Thus an identity operator on the +payload cannot appear in this source/target response. This argument does +not assume that distinct warp words are linearly independent. + +The same witness works at every tensor depth \(\lambda\ge1\). Use the +input label \((q_s,0,\ldots,0)\). A linear warp fixes each zero column and +fails to fix the first column. This is a spatial-basis argument. It is not +a Fourier-character or constant-payload argument. + +It follows that every solution of (1) must satisfy + +\[ +R_{:,t}^{\,T} A R_{:,s}=0 +\quad\text{if }t\ne s\text{ and }q_t\cdot q_s=1. \tag{5} +\] + +## 4. A small integer certificate + +There are 6,608 pairs in (5). `SUPPORT.json` gives 63 of them. Delete the +column for \(A_{7,7}\) from their coefficient matrix. The resulting +\(63\times63\) integer matrix has determinant + +\[ +-2361183241434822606848=-2^{71}. \tag{6} +\] + +The checker computes this determinant by exact integer elimination. It +also checks that \(I_8\) satisfies all 6,608 equations exactly. Hence the +kernel of (5) is precisely (2). This conclusion holds over the rationals +and the Gaussian rationals. The power-of-two minor also gives the same +kernel over coefficient rings in which two is a unit, for these scalar +equations. + +If \(c\ne0\), \(cI_8\) has rank eight. If \(c=0\), the diagonal response +in (1) is zero: the support argument also excludes each same-port scalar +response, since every \(q_p\) is odd. Therefore no rank-seven \(A\) +solves (1) in this grammar. + +A concrete test shows why a nonzero diagonal is not sufficient. The +dyadic rank-seven projection + +\[ +A=I_8-\mathbf1\mathbf1^T/8 +\] + +gives diagonal entries of \(KAR\) equal to 1 on 42 ports, 7/8 on 56 ports, +and 1/2 on 14 ports. All are nonzero. The matrix fails the off-diagonal +conditions (5). + +## 5. Reproduction and limits + +Run from the repository root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/coherent-port/centre-mixing-20261018/check_mixing.py +python3 -I -B work/centre-encoding-campaign-20261014/lanes/coherent-port/centre-mixing-20261018/check_support.py +``` + +The first command gives quotient rank 63 and exact rational nullity one +for each provider. The second command gives +`PASS_SPATIAL_SUPPORT_AND_INTEGER_MINOR` and determinant `-2^71` in decimal. +The first checker uses assertions and rejects `-O`. + +`probe_all_cuts.py` is a separate modular check of the supplied inventory. +It finds product-space rank 3,740 and centre-quotient rank 63. The proof +in Sections 3–4 does not use a rational lift of that modular basis. + +This result does not test a changed centre query dictionary, a changed +centre scatter space, arbitrary operator-valued centre entries, unequal- +frame physical gates, changed native paths, or global encoded endpoints. +It does not give a native-child lower bound for those larger grammars. +It supplies no complete controller, all-size cost, precision result, or +improvement in the multiplication exponent. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/SUPPORT.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/SUPPORT.json new file mode 100644 index 0000000000..4f82fdc9e4 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/SUPPORT.json @@ -0,0 +1,352 @@ +{ + "centre_entry_columns": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 22, + 23, + 24, + 25, + 26, + 27, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 36, + 37, + 38, + 39, + 40, + 41, + 42, + 43, + 44, + 45, + 46, + 47, + 48, + 49, + 50, + 51, + 52, + 53, + 54, + 55, + 56, + 57, + 58, + 59, + 60, + 61, + 62 + ], + "checker_sha256": "82d608f7220d9959925c2990fd717b028a2fce47fcf41ee9f061d0687c32f97c", + "exact_centre_kernel": "span(I8)", + "forbidden_offdiagonal_pairs": 6608, + "independent_pairs": [ + [ + 0, + 7 + ], + [ + 0, + 8 + ], + [ + 0, + 9 + ], + [ + 0, + 10 + ], + [ + 0, + 11 + ], + [ + 0, + 16 + ], + [ + 0, + 26 + ], + [ + 1, + 6 + ], + [ + 1, + 8 + ], + [ + 1, + 9 + ], + [ + 1, + 10 + ], + [ + 1, + 11 + ], + [ + 1, + 12 + ], + [ + 1, + 25 + ], + [ + 2, + 6 + ], + [ + 2, + 7 + ], + [ + 2, + 9 + ], + [ + 2, + 10 + ], + [ + 2, + 11 + ], + [ + 2, + 13 + ], + [ + 2, + 25 + ], + [ + 3, + 6 + ], + [ + 3, + 7 + ], + [ + 3, + 8 + ], + [ + 3, + 10 + ], + [ + 3, + 11 + ], + [ + 3, + 12 + ], + [ + 3, + 25 + ], + [ + 4, + 6 + ], + [ + 4, + 7 + ], + [ + 4, + 8 + ], + [ + 4, + 9 + ], + [ + 4, + 11 + ], + [ + 4, + 12 + ], + [ + 4, + 25 + ], + [ + 5, + 6 + ], + [ + 5, + 7 + ], + [ + 5, + 8 + ], + [ + 5, + 9 + ], + [ + 5, + 10 + ], + [ + 5, + 12 + ], + [ + 5, + 25 + ], + [ + 6, + 1 + ], + [ + 6, + 2 + ], + [ + 6, + 3 + ], + [ + 6, + 4 + ], + [ + 6, + 5 + ], + [ + 6, + 16 + ], + [ + 6, + 26 + ], + [ + 7, + 0 + ], + [ + 7, + 2 + ], + [ + 8, + 0 + ], + [ + 9, + 0 + ], + [ + 10, + 0 + ], + [ + 11, + 0 + ], + [ + 12, + 1 + ], + [ + 12, + 3 + ], + [ + 12, + 4 + ], + [ + 12, + 5 + ], + [ + 12, + 7 + ], + [ + 12, + 17 + ], + [ + 12, + 25 + ], + [ + 13, + 2 + ] + ], + "input_pins": { + "core_decompressed": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "inventory_decompressed": "18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418", + "logical_warp_source": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce" + }, + "integer_minor_determinant": "-2361183241434822606848", + "provider_checks": { + "base": { + "forbidden_spatial_diagonal_controls": 648, + "nonempty_source_words": 1160, + "source_terms": 6920, + "tail_incidences": 8856 + }, + "extra": { + "forbidden_spatial_diagonal_controls": 648, + "nonempty_source_words": 1160, + "source_terms": 6920, + "tail_incidences": 8856 + } + }, + "rank_seven_projection": "I8 - ones(8,8)/8", + "rank_seven_projection_diagonal_counts": { + "1": 42, + "1/2": 14, + "7/8": 56 + }, + "scope": "The supplied all-cut inventory, with its complete current native source states and unchanged Y tail. Actual monomial phases do not alter the spatial support witness. Inventory completeness is a separate source dependency.", + "status": "PASS_SPATIAL_SUPPORT_AND_INTEGER_MINOR" +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/check_mixing.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/check_mixing.py new file mode 100644 index 0000000000..f93d928d38 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/check_mixing.py @@ -0,0 +1,309 @@ +#!/usr/bin/env python3 +"""Check all scalar centre maps against the supplied response space.""" + +import ast +import gzip +import hashlib +import json +from fractions import Fraction +from pathlib import Path + + +if not __debug__: + raise RuntimeError("Run without -O; this checker uses assertions.") + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SPACE = LANES / "oblique-native-20261017/interior-cut/RESPONSE-SPACE.json" +CUT = LANES / "new-core-transfer-20261017/CUT-PROBE.json" +CORE = LANES / "new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz" +PRIME = 1000003 + + +def digest(path): + return hashlib.sha256(path.read_bytes()).hexdigest() + + +def mod(value): + value = Fraction(value) + return value.numerator * pow(value.denominator, -1, PRIME) % PRIME + + +def add(dst, src, factor): + for key, value in src.items(): + result = (dst.get(key, 0) + factor * value) % PRIME + if result: + dst[key] = result + else: + dst.pop(key, None) + + +def insert(basis, row): + row = dict(row) + while row: + pivot = min(row) + if pivot not in basis: + factor = pow(row[pivot], -1, PRIME) + basis[pivot] = {key: value * factor % PRIME + for key, value in row.items()} + return True + add(row, basis[pivot], -row[pivot]) + return False + + +def reduce_by(basis, row): + row = dict(row) + result = {} + while row: + pivot = min(row) + if pivot not in basis: + result[pivot] = row.pop(pivot) + else: + add(row, basis[pivot], -row[pivot]) + return result + + +def nullspace(basis, size): + result = [] + for free in range(size): + if free in basis: + continue + row = {free: 1} + for pivot, equation in sorted(basis.items(), reverse=True): + value = -sum(c * row.get(k, 0) + for k, c in equation.items() if k != pivot) % PRIME + if value: + row[pivot] = value + result.append([row.get(k, 0) for k in range(size)]) + return result + + +def exact_add(dst, src, factor): + for key, value in src.items(): + result = dst.get(key, 0) + factor * value + if result: + dst[key] = result + else: + dst.pop(key, None) + + +def y_port(field): + return field[1] - 112 if field[0] == "L" and 112 <= field[1] < 224 else None + + +def original_equations(item, r): + word, program = item["canonical"], item["programs"]["forward"] + n = len(word["start"]) + columns = [{i: Fraction(1)} for i in range(112)] + tails = {} + for position in range(len(program) - 1, -1, -1): + event = program[position] + if event[0] != "scalar": + continue + op = event[1] + target = y_port(op[1]) + if op[0] == "add": + source = y_port(op[2]) + assert source is None or target is not None + if target is not None: + if source is None: + tails[position] = dict(columns[target]) + else: + exact_add(columns[source], columns[target], Fraction(*op[3:5])) + elif target is not None: + assert op[0] == "scale" + columns[target] = {key: Fraction(*op[2:4]) * value + for key, value in columns[target].items()} + assert columns == [{i: 1} for i in range(112)] + fields = [("L", i) for i in range(n)] + [("C", i) for i in range(8)] + state = {field: {(field, ()): Fraction(1)} for field in fields} + frames = {("L", i): f for i, f in enumerate(word["start"])} + frames.update({("C", i): 0 for i in range(8)}) + allowed = {("L", i) for i in range(224, n) if word["start"][i] == 0} + sources = {} + zero = set() + for position, event in enumerate(program): + tag = event[0] + if tag == "scalar": + op, frame = event[1:] + target = tuple(op[1]) + if op[0] == "clear": + state[target], frames[target] = {}, frame + else: + assert frames[target] == frame + if op[0] == "scale": + state[target] = {key: Fraction(*op[2:4]) * value + for key, value in state[target].items()} + else: + source = tuple(op[2]) + assert frames[source] == frame and source != target + if position in tails: + sources[position] = dict(state[source]) + if op[0] == "copy": + state[target] = dict(state[source]) + else: + assert op[0] == "add" + exact_add(state[target], state[source], Fraction(*op[3:5])) + elif tag == "climb": + target = ("L", event[2]) + assert frames[target] == event[3] + assert len(word["frames"][event[4]]) - len(word["frames"][event[3]]) == event[5] + frames[target] = event[4] + elif tag == "warp": + target, symbol = tuple(event[1]), event[2] + assert y_port(target) is None and frames[target] == event[3] + frames[target] = event[4] + state[target] = { + (source, history[:-1] if history and history[-1] == -symbol + else history + (symbol,)): value + for (source, history), value in state[target].items()} + elif tag == "zero_buffer": + target = ("Z", event[2]) + if event[1] == "alloc": + assert target not in zero + state[target], frames[target] = {}, 1 + zero.add(target) + else: + assert target in zero and not state[target] + zero.remove(target) + else: + assert tag in ("phase", "adapter", "residual_adapter") + assert not zero + assert [frames["L", i] for i in range(n)] == word["final"] + assert all(frames["C", i] == 0 for i in range(8)) + assert not state["C", 0] + assert all(state["C", i] == {(("C", i), ()): 1} for i in range(1, 8)) + for p in range(112): + assert state["L", p] == {(("L", p), ()): 1} + goal = {(("L", 112+p), ()): Fraction(1), (("L", p), ()): Fraction(1)} + for row in r: + for s, value in row.items(): + exact_add(goal, {(("L", s), ()): value}, -row.get(p, 0) / 4) + assert state["L", 112+p] == goal + assert all(state["L", p] == {(("L", p), ()): 1} for p in range(224, n)) + active = sorted(pos for pos, source in sources.items() + if any(field not in allowed or history for field, history in source)) + equations = {} + for col, pos in enumerate(active): + for t, tc in tails[pos].items(): + for (field, history), sc in sources[pos].items(): + if field in allowed and not history: + continue + if field[0] == "L" and field[1] < 112 and not history: + if t == field[1]: + continue + key = ("data", t, field[1]) + else: + key = ("other", t, field, history) + exact_add(equations.setdefault(key, {}), {col: tc * sc}, 1) + for a in range(8): + for b in range(8): + col = len(active) + 8*a + b + for t, tc in r[a].items(): + for s, sc in r[b].items(): + if t != s: + exact_add(equations.setdefault(("data", t, s), {}), + {col: tc * sc / 4}, 1) + witness = [Fraction(*program[pos][1][3:5]) for pos in active] + witness += [Fraction(a == b) for a in range(8) for b in range(8)] + assert all(sum(value*witness[col] for col, value in row.items()) == 0 + for row in equations.values()) + x_warp_terms = sum(field[0] == "L" and field[1] < 112 and bool(history) + for pos in active for field, history in sources[pos]) + return active, equations, witness, x_warp_terms + + +def main(): + assert digest(SPACE) == "320e25fec5c0f52285aa2e945b2e0f30d43e2504de207595b0f35ec93bab7337" + assert digest(CUT) == "78c9c2f87d0ae5c345e5ae467f94a92f94c97d618b3011e436c0dc94c3b15cbc" + supplied = json.loads(SPACE.read_text()) + source = json.loads(CUT.read_text()) + r = [{int(k): Fraction(v) for k, v in row.items()} + for row in source["base"]["center_R"]] + assert source["base"]["center_R"] == source["extra"]["center_R"] + basis = {} + for item in supplied["directions"]: + row = {ast.literal_eval(k): v % PRIME for k, v in item["effect"].items()} + assert not any(t == s for t, s in row) + assert insert(basis, row) + assert len(basis) == 413 + equations = {} + sizes = [] + for a in range(8): + for b in range(8): + row = {(t, s): mod(tc * sc / 4) + for t, tc in r[a].items() for s, sc in r[b].items() if t != s} + remainder = reduce_by(basis, row) + sizes.append(len(remainder)) + for key, value in remainder.items(): + equations.setdefault(key, {})[8 * a + b] = value + print("centre row", a, "complete", flush=True) + constraints = {} + for key in sorted(equations): + insert(constraints, equations[key]) + kernels = nullspace(constraints, 64) + print("quotient rank", len(constraints), "kernel dimension", len(kernels), flush=True) + identity = [int(a == b) for a in range(8) for b in range(8)] + assert kernels == [identity] + data = gzip.decompress(CORE.read_bytes()) + assert hashlib.sha256(data).hexdigest() == "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa" + core = json.loads(data) + original_reports = {} + first_equations = None + for name, item in core["providers"].items(): + active, native_equations, witness, x_warp_terms = original_equations(item, r) + assert active == supplied["active_sites"] + native_basis = {} + selected_rows = [] + for key in sorted(native_equations): + if insert(native_basis, {col: mod(value) for col, value in native_equations[key].items()}): + selected_rows.append(key) + assert len(native_basis) == len(active) + 63 == 888 + kernel = nullspace(native_basis, len(active) + 64) + assert len(kernel) == 1 and kernel[0] == [mod(value) for value in witness] + if first_equations is not None: + assert native_equations == first_equations + first_equations = native_equations + data_site_basis, data_combined_basis = {}, {} + for key in sorted(native_equations): + if key[0] != "data": + continue + equation = {col: mod(value) for col, value in native_equations[key].items()} + insert(data_site_basis, {col: value for col, value in equation.items() if col < len(active)}) + insert(data_combined_basis, equation) + original_reports[name] = { + "variables": len(active) + 64, + "equations": len(native_equations), + "rank_mod_prime": len(native_basis), + "exact_rational_witness": "The original clean-J cross-site coefficients and A=I8.", + "exact_rational_nullity": 1, + "scalar_frame_checks": True, + "all_input_column_checks": len(item["canonical"]["start"]) + 8, + "source_X_warp_term_count": x_warp_terms, + "plain_data_site_rank": len(data_site_basis), + "plain_data_combined_rank": len(data_combined_basis), + "pivot_columns": sorted(native_basis), + "independent_equation_keys": selected_rows, + } + print(name, "original equation rank", len(native_basis), "exact nullity 1", flush=True) + result = { + "inputs": {str(SPACE.relative_to(LANES)): digest(SPACE), + str(CUT.relative_to(LANES)): digest(CUT)}, + "prime": PRIME, + "response_dimension": len(basis), + "centre_parameter_count": 64, + "quotient_rank": len(constraints), + "admissible_basis": [ + [[x if x <= PRIME // 2 else x - PRIME for x in v[8*a:8*a+8]] + for a in range(8)] for v in kernels], + "elementary_residual_sizes": [sizes[8*a:8*a+8] for a in range(8)], + "original_equation_checks": original_reports, + "clean_core_decompressed_sha256": hashlib.sha256(data).hexdigest(), + "scope": "Constant scalar centre maps and existing cross sites, with coefficientwise formal operator-word cancellation. The original rational equation matrix has nullity one." + } + (HERE / "MIXING.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/check_support.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/check_support.py new file mode 100644 index 0000000000..18a07f2242 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/coherent-port/centre-mixing-20261018/check_support.py @@ -0,0 +1,185 @@ +#!/usr/bin/env python3 +"""Check the spatial support witness and a 63-equation integer minor.""" + +import gzip +import hashlib +import json +from collections import Counter +from fractions import Fraction +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +CORE = LANES / "new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz" +INVENTORY = LANES / "oblique-native-20261017/interior-cut/ALL-CUT-EDGES.json.gz" +WARP_SOURCE = LANES / "new-native-recipes-20261017/sources/bw_adapters.py" +PRIME = 1000003 + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def read(path, pin): + raw = gzip.decompress(path.read_bytes()) + need(hashlib.sha256(raw).hexdigest() == pin, "Input pin: " + path.name) + return json.loads(raw) + + +def linear(columns, vector): + out = 0 + for bit, column in enumerate(columns): + if vector >> bit & 1: + out ^= column + return out + + +def inverse(columns): + values = [linear(columns, x) for x in range(512)] + need(len(set(values)) == 512, "Every warp map is invertible") + back = {value: x for x, value in enumerate(values)} + return [back[1 << bit] for bit in range(9)] + + +def contains(vectors, vector): + basis = {} + for value in vectors: + while value: + bit = value.bit_length() - 1 + if bit not in basis: + basis[bit] = value + break + value ^= basis[bit] + while vector: + bit = vector.bit_length() - 1 + if bit not in basis: + return False + vector ^= basis[bit] + return True + + +def independent(basis, row): + row = dict(row) + while row: + pivot = min(row) + if pivot not in basis: + scale = pow(row[pivot], -1, PRIME) + basis[pivot] = {key: value*scale % PRIME for key, value in row.items()} + return True + scale = row[pivot] + for key, value in basis[pivot].items(): + result = (row.get(key, 0) - scale*value) % PRIME + if result: + row[key] = result + else: + row.pop(key, None) + return False + + +def determinant(matrix): + matrix = [list(row) for row in matrix] + sign, previous = 1, 1 + for i in range(len(matrix)-1): + pivot_row = next(j for j in range(i, len(matrix)) if matrix[j][i]) + if pivot_row != i: + matrix[i], matrix[pivot_row] = matrix[pivot_row], matrix[i] + sign = -sign + pivot = matrix[i][i] + for j in range(i+1, len(matrix)): + for k in range(i+1, len(matrix)): + value = matrix[j][k]*pivot - matrix[j][i]*matrix[i][k] + need(value % previous == 0, "Exact integer determinant division") + matrix[j][k] = value // previous + matrix[j][i] = 0 + previous = pivot + return sign*matrix[-1][-1] + + +def main(): + core_pin = "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa" + inventory_pin = "18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418" + warp_pin = "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce" + core, inventory = read(CORE, core_pin), read(INVENTORY, inventory_pin) + need(hashlib.sha256(WARP_SOURCE.read_bytes()).hexdigest() == warp_pin, + "Logical warp definition pin") + need(core["providers"]["base"]["programs"] == core["providers"]["extra"]["programs"], + "The two providers have the same event indices and frame IDs") + r = [{int(key): int(value) for key, value in row.items()} for row in core["R"]] + provider_checks = {} + for name, provider in core["providers"].items(): + word = provider["canonical"] + ports = word["ports"] + maps = {w["op"]: w["G_columns"] for w in word["warps"]} + maps.update({-key: inverse(columns) for key, columns in list(maps.items())}) + counts = Counter() + for product in inventory["products"]: + frame = word["frames"][product["frame"]] + tail = inventory["tail_columns"][product["tail_column"]] + for t, _, _ in tail: + need(all((value & ports[t]).bit_count() % 2 == 0 for value in frame), + "The cut frame lies in every final target hole") + for s, history, numerator, denominator in inventory["source_rows"][product["source_row"]]["constrained"]: + if s >= 112: + continue + need(numerator != 0 and denominator > 0, "Nonzero rational source term") + vector = ports[s] + for operator, sign in history: + need(operator[0] == "K" and sign in (-1, 1), "Forward warp word") + vector = linear(maps[sign*operator[1]], vector) + need(contains(frame, vector), "The transported source line lies in the cut frame") + counts["source_terms"] += 1 + counts["nonempty_source_words"] += bool(history) + for t, _, _ in tail: + counts["tail_incidences"] += 1 + need((ports[t] & vector).bit_count() % 2 == 0, "Physical spatial support") + if (ports[t] & ports[s]).bit_count() % 2: + need(vector != ports[s], "The forbidden spatial diagonal entry is zero") + counts["forbidden_spatial_diagonal_controls"] += 1 + provider_checks[name] = dict(counts) + ports = core["providers"]["base"]["canonical"]["ports"] + basis, pairs, all_equations = {}, [], 0 + for t in range(112): + for s in range(112): + if t == s or not (ports[t] & ports[s]).bit_count() % 2: + continue + row = {8*a+b: r[a].get(t, 0)*r[b].get(s, 0) + for a in range(8) for b in range(8) + if r[a].get(t, 0)*r[b].get(s, 0)} + need(sum(row.get(9*a, 0) for a in range(8)) == 0, "I8 is an exact solution") + all_equations += 1 + if independent(basis, {key: value % PRIME for key, value in row.items()}): + pairs.append([t, s]) + need(len(pairs) == 63, "Sixty-three independent centre equations") + columns = list(range(63)) + matrix = [[r[a].get(t, 0)*r[b].get(s, 0) + for a in range(8) for b in range(8) if 8*a+b in columns] + for t, s in pairs] + det = determinant(matrix) + need(det != 0, "The integer minor is nonzero") + diagonal_counts = Counter(str(1-Fraction(sum(row.get(p, 0) for row in r)**2, 32)) + for p in range(112)) + need(diagonal_counts == {"1": 42, "7/8": 56, "1/2": 14}, + "The rank-seven dense projection has a nonzero diagonal") + result = { + "status": "PASS_SPATIAL_SUPPORT_AND_INTEGER_MINOR", + "input_pins": {"core_decompressed": core_pin, "inventory_decompressed": inventory_pin, + "logical_warp_source": warp_pin}, + "provider_checks": provider_checks, + "forbidden_offdiagonal_pairs": all_equations, + "independent_pairs": pairs, + "centre_entry_columns": columns, + "integer_minor_determinant": str(det), + "exact_centre_kernel": "span(I8)", + "rank_seven_projection": "I8 - ones(8,8)/8", + "rank_seven_projection_diagonal_counts": dict(diagonal_counts), + "scope": "The supplied all-cut inventory, with its complete current native source states and unchanged Y tail. Actual monomial phases do not alter the spatial support witness. Inventory completeness is a separate source dependency.", + "checker_sha256": hashlib.sha256(Path(__file__).read_bytes()).hexdigest(), + } + (HERE / "SUPPORT.json").write_text(json.dumps(result, indent=2, sort_keys=True)+"\n") + print(result["status"], "determinant", det, provider_checks, flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md new file mode 100644 index 0000000000..c23f8a578b --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md @@ -0,0 +1,137 @@ +# The source query that a minor-log terminal must distinguish + +The input-minor log changes the source block into a unit. It does not +make one sparse ordinary query sufficient at the terminal. This note +gives the exact source-query condition for a stated terminal class. +It explains the difference between a sparse log and a matched log. + +## The terminal class + +Use the unweighted ordinary suffix controller, the retained full first +shear, and the input-minor backward log. Either one or two selected +backward exchanges can be used. The forward word can be raw or use +the usual selected inverse-line prefix. Use ordinary Y bridges with +coefficients -I before forward and +I after forward. + +The terminal can read all completed X and all retired selected Y. Its +only other information about retired ordinary Y is a fixed linear +query N. The terminal may then use arbitrary functions of these +observations. This includes a linear target-writing decoder and also +allows nonlinear postprocessing. The theorem does not restrict what +the terminal can write. + +The query N in the theorem is written on logical retired Y contents. +If the actual query reads a set of physical ports, its line factors are +invertible and do not change the kernel of that port projection. The +theorem does not charge an arbitrary logical N as a native operation. + +## A full-null family + +At the first backward stage write B=B_s, D=D_s, M=M_s. Assume +BD=13I and MD=I, and put H=I-DB. Let v be an arbitrary ordinary field +vector. Set all original inputs after pair zero to zero. At pair zero +choose the original inputs + + original x_U=Hv, + original y_U=DBv, + Qa=-Mv, + original b=-QBv+qMv. (1) + +The retained first shear gives incoming ordinary Y v. It also gives +effective b=original b+a=-QBv, since a=-qMv. Therefore qb=-Bv. +The input-minor backward map gives + + d=Qa+Mv=0, + h=qb+Bv=0, + w=Hv-v+D(d-qb)=0. (2) + +The second selected exchange, if present, exchanges zero values. +Both raw and corrected forward words then return ordinary Y r=v. +Their selected outputs remain zero. The next ordinary Y bridge adds +-v+r=0. Thus every later pair remains zero. The final ordinary X +triangle also remains zero. + +Consequently every completed X and retired selected Y observation is +zero on (1). The only nonzero retired ordinary bank is v at pair zero. +The statement holds for every pair count, not just one pair. + +## Necessary and sufficient separation of this family + +The terminal must return the original selected physical X value -Mv +and the original ordinary Y value DBv. Since BD=13I, D is injective. +If Nv=0, these required outputs can agree with the zero input only if + + Bv=0 and Mv=0. (3) + +Thus a necessary condition for a complete terminal in this class is + + ker N is contained in ker B intersect ker M. (4) + +Over the finite underlying field space, (4) is equivalent to the +existence of linear maps L_B,L_M such that B=L_B N and M=L_M N. +Equivalently, the row space of the stack [B;M] must lie in the row +space of N. This condition is also sufficient to distinguish all +required outputs on family (1), including original b. It is not +sufficient to decode the full controller. + +The argument still applies if N contains cross-pair source queries: +restrict N to the first retired ordinary bank. It does not apply to +a terminal that obtains other information through new native calls +on retired ordinary Y, unless that information is included in N. + +## The actual sparse minor has two independent queries + +Use the actual selected minor A and two disjoint ordinary minors T,T': + + A =[0,7,20,27,36,46,57,111], + T =[21,37,47,76,81,87,92,110], + T'=[1,6,22,28,33,49,58,109]. + +For M=(D|T)^-1 pi_T, let N_T embed D|T in T and let N_T' embed +(B|T')^-1 in T'. The actual orthogonal-minor identities give + + M N_T=I, B N_T=I, + M N_T'=0, B N_T'=I. (5) + +Hence the two block columns N_T-N_T' and N_T' form a right inverse +for the stack [M;B]. The stack has exactly 16 complete-field rows of +rank. The eight-port query pi_T cannot satisfy (4). In particular, +v=N_T' c is invisible on T, but Bv=c and the required ordinary Y +output is Dc, which is nonzero for nonzero c. + +The identities persist in the routed chart: the port-diagonal routes +can be put on each inverse minor in their actual order. This uses no +commutation of Q with the routes. + +For the matched log M=B/13, the stack [M;B] has rank eight. That log +removes the second independent query in (4). It does not make the +old-stage B query native-free. Its actual source support, line phases, +arithmetic coefficient 1/13, and implementation cost remain separate. + +## Verification and scope + +Run with one process from the workspace root: + + python3 -I -B work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_minor_log_source_access.py + +The expected status is PASS_MINOR_LOG_SOURCE_ACCESS. The checker pins +the actual R matrix, verifies all three orthogonal minors, and checks +the two right-inverse blocks in (5) with exact fractions. It checks +all eight hidden-minor witnesses for one, two, four, and eight pairs, +with one or two selected exchanges and raw or corrected forward. +The first selected input is zero in these witnesses, so the native +assignment needs only qQ=I. The general family (1) retains both Q and +q in their displayed order. + +This is an information theorem for the stated source-query class. It +is not a native child lower bound, a proof against a changed controller, +or an obstruction to a log with a different source query. In particular, +it identifies a benefit of the matched log that merits a native decoder +attempt. + +The oblique-native lane supplied the input-minor log and its unit source +block. The native-escape lane is investigating the matched log. The +controller-followthrough lane supplied the full-null family and the +query criterion. This work used OpenAI Codex under the user's direction. +No independent human review is claimed. 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z8zT-5$jhv6NA@lUeiT(y5wLfq9fzF-Toh*qeDnjfG6MP?juJd|IHr`B8 z<>!fv+}Cq-UC+3P+0YB9!0mjN+j&O}d4{}zDHZypl;0;!pUH8FveuNIt}i3XC=ie7 zh$75LVjKhDg)pFs4(aU+WLBR$JJOm1gu{$y4j;zmYFZD+5M=?0(p%|b7jHW(?R> column & 1), None) + if choice is None: + continue + slot = len(pivots) + rows[slot], rows[choice] = rows[choice], rows[slot] + for i in range(len(rows)): + if i != slot and rows[i] >> column & 1: + rows[i] ^= rows[slot] + pivots.append(column) + answer = [] + for free in range(9): + if free not in pivots: + value = 1 << free + for row, column in zip(rows, pivots): + if row >> free & 1: + value |= 1 << column + answer.append(value) + need(all(not (row & vector).bit_count() % 2 for row in equations for vector in answer), 'Nullspace equations') + return span(answer) + + +def main(): + for name, pin in PINS.items(): + need(sha256((ROOT/name).read_bytes()).hexdigest() == pin, 'Root source pin '+name) + data = [] + for relative, pin in SOURCE_PINS.items(): + raw = gzip.decompress((LANES/relative).read_bytes()) + need(sha256(raw).hexdigest() == pin, 'Actual source pin '+relative) + data.append(json.loads(raw)) + ports = [record['q'] for record in data[0]['transfers']] + need([record['port'] for record in data[0]['transfers']] == list(range(112)), 'Actual port order') + need(len(set(ports)) == 112 and all(q.bit_count() % 2 for q in ports), 'Distinct odd source lines') + supports = [set(int(p) for p, value in row.items() if F(value)) for row in data[1]['centre_rows']] + need(len(supports) == 8 and all(len(s) == 12 for s in supports), 'Eight twelve-port supports') + spaces = [span(ports[p] for p in support) for support in supports] + duals = [nullspace([ports[p] for p in support]) for support in supports] + need(all(len(s) == 128 for s in spaces) and all(len(d) == 4 for d in duals), 'Primal and dual dimensions') + wanted = [{0, 7, 42, 45}, {0, 25, 45, 52}, {0, 45, 82, 127}, {0, 45, 76, 97}, + {0, 45, 76, 97}, {0, 7, 42, 45}, {0, 25, 45, 52}, {0, 45, 82, 127}] + need(duals == wanted, 'All actual annihilator vectors') + groups = [[0, 5], [1, 6], [2, 7], [3, 4]] + group = {v: k for k, values in enumerate(groups) for v in values} + for i in range(8): + for j in range(8): + same = group[i] == group[j] + need((spaces[i] == spaces[j]) == same, 'Exact equal-space classes') + need(len(spaces[i] & spaces[j]) == (128 if same else 64), 'Exact pair intersection') + if i != j: + need(len(supports[i] & supports[j]) == (0 if same else 2), 'Complete four-partite incidence') + all_ports = set.union(*supports) + need(len(all_ports) == 48 and all(sum(p in s for s in supports) == 2 for p in all_ports), 'All source incidences') + ambient = span(ports[p] for p in all_ports) + need(ambient == {v for v in range(512) if not (v & 45).bit_count() % 2}, 'Exact common hyperplane') + common = set.intersection(*spaces) + need(len(common) == 32, 'Exact common intersection dimension') + independent = [set()] + [{i} for i in range(8)] + [set(g) for g in groups] + for chosen in independent: + need(all(not supports[i] & supports[j] for i in chosen for j in chosen if i != j), 'All compatible subsets') + certificate = json.loads((ROOT/'CENTRE-SUPPORT-GEOMETRY-20261018.json').read_bytes()) + need(certificate['query_supports'] == [sorted(s) for s in supports] + and certificate['annihilators'] == [sorted(d-{0}) for d in duals] + and certificate['equal_subspace_classes'] == groups + and sorted(certificate['maximum_independent_sets']) == sorted(groups) + and certificate['conditional_eight_query_rank_lower_bound'] == 62, 'Certificate binding') + result = {'status': 'PASS_INDEPENDENT_CENTRE_SUPPORT_GEOMETRY', 'source_pins': PINS, + 'source_decompressed_pins': SOURCE_PINS, 'support_dimensions': [7]*8, + 'equal_space_classes': groups, 'pairwise_distinct_space_intersection_dimension': 6, + 'common_space_dimension': 5, 'ambient_dimension': 8, + 'direct_schedule_lower_bound': 62, + 'method': 'Explicit primal XOR closure; independent RREF nullspace equations; exact set intersections; complete multipartite graph proof.', + 'scope': 'One direct capture per row with single unwarped carriers on monotone source-subspace chains. Pair coding violates this carrier premise.', + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest()} + (HERE/'CHECKS.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(result['status']) + + +if __name__ == '__main__': + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/interface-proof/github-refresh-20261014-1155/pr1825.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/interface-proof/github-refresh-20261014-1155/pr1825.json new file mode 100644 index 0000000000..d3c20f5557 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/interface-proof/github-refresh-20261014-1155/pr1825.json @@ -0,0 +1,47 @@ +{ + "content": [ + { + "type": "text", + "text": "Action completed." + } + ], + "structuredContent": { + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1825", + "number": 1825, + "state": "open", + "merged": false, + "mergeable": true, + "draft": false, + "body": "## Contribution\n\nThis adds one exact paired-plane decoder mechanism for the selected PR1094\ncomplex E8 port labels. A deterministic perfect matching on the 52-regular\nzero-dot-product graph assigns a shared 2-plane to each matched pair. Solving\none exact F2 system gives a global factorization of the full selected pairing\nmatrix through those planes.\n\nThe witness has 56 matched planes, 16 active queries, and B14 copy charge 126:\nnine rank-7 terms and seven rank-9 terms. The inherited plane correction\n`C_E^2 = X_(q_i+q_j)` is checked by exact Gaussian-dyadic arithmetic on all\n28,672 local computational basis cases. The changed-law exact-rational screen\nhas `a_hi = 0.003447203501` under unpaid=2 and centre charge 126.\n\nThis is a finite decoder mechanism and favorable complex-side planning screen.\nThe complete route, hosting and frame schedule, full restoration and precision\ninvoice, bit-side plane interface, and joint assembly remain open. The reported\nplanning transfer is not a new `kappa` or an integrated multiplication bound.\n\n## Provenance and distinction\n\n- Track: `recursive-interfaces`; seed: `6c563a22f0431d23354e2a3279f9b61c`.\n- Task: `coverage-law-change`, refined to symmetric matched 2-plane ports.\n- Priority revision: 3; base: `0b1cccf86e2f5132ed286a26ef0a681a495740ea`.\n- Selected record SHA-256: `10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32`.\n- PR1094 selected source and its authors retain credit for the underlying labels\n and construction. Discussion #1587 comment 18914510 established the exact\n plane-port endpoint on small instances and posed the selected-port decoder\n question. Open PR #1808 supplies a complementary budget screen but no\n 112-port decoder. This contribution gives one explicit symmetric matching\n and global factorization.\n- Prepared by an OpenAI Codex research agent with substantial OpenAI Codex\n assistance. No independent human review or formal proof assistant is claimed.\n\n## Reproduce\n\n```sh\npython3 -B research/paired-plane-port-matching-seed6c563a/verify.py\npython3 scripts/research_package.py --package research/paired-plane-port-matching-seed6c563a --check-only\npython3.12 scripts/research_package.py --package research/paired-plane-port-matching-seed6c563a\n```\n\nExpected verifier status: `PASS_PAIRED_PLANE_PORT_MATCHING`.\n", + "title": "Construction: paired plane-port decoder on selected E8 labels", + "base": "main", + "base_sha": "0b1cccf86e2f5132ed286a26ef0a681a495740ea", + "head": "research/cycle-20261014-g", + "head_sha": "d16fb8936795ff101e4d2f63cfdc6a25066ebabf", + "head_repo_id": 1417342702, + "head_repo_full_name": "1337isnot1337/integer-mult-bounds", + "merge_commit_sha": "295e78815c4d95517fa763601fc31c344bcbfc2d", + "user": { + "login": "1337isnot1337", + "name": "1337isnot1337", + "email": null, + "avatar_url": "https://avatars.githubusercontent.com/u/164028474?v=4", + "id": 164028474 + }, + "requested_reviewers": null, + "requested_team_reviewers": null, + "diff": null, + "comments": null, + "created_at": "2026-10-14T10:59:21Z", + "updated_at": "2026-10-14T10:59:21Z", + "closed_at": null, + "merged_at": null, + "commits": 1, + "changed_files": 10, + "additions": 1510, + "deletions": 0, + "display_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1825", + "display_title": "Construction: paired plane-port decoder on selected E8 labels" + }, + "isError": false +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/interface-proof/github-refresh-20261014-1155/pr1825_readme.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/interface-proof/github-refresh-20261014-1155/pr1825_readme.json new file mode 100644 index 0000000000..17535c98b8 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/interface-proof/github-refresh-20261014-1155/pr1825_readme.json @@ -0,0 +1,16 @@ +{ + "content": [ + { + "type": "text", + "text": "Action completed." + } + ], + "structuredContent": { + "content": "# Paired plane-port matching\n\nThis package gives one explicit finite decoder mechanism for the selected 112\ncomplex E8 port labels. It symmetrically pairs the labels along zero-dot-product\nedges, assigns each pair one common 2-plane, and factors the full selected\npairing matrix through those planes.\n\n## Result and evidence\n\nThe exact construction uses 56 matched planes, of which 16 have nonzero query\nmatrices. Their exact B14 copy invoice is 126: nine rank-7 terms and seven\nrank-9 terms. The verifier checks the complete 112 by 112 decoder identity,\nthe plane basis legality, and all 56 plane endpoint translations on 28,672\nlocal computational basis cases. Four negative controls fail as required.\nThe hosted application frequency of those translations remains unpriced.\n\nThe changed local profile has a certified favorable complex relaxation at\n`a_hi=0.003447203501`, with a planning transfer cap near `0.003435361112`.\nThis is a construction component and a conditional screen. It does not supply\nthe complete routed supplier, charge all hosting and interface work, establish\nthe bit-side interface, or prove a new integer-multiplication bound or\n\\(\\kappa\\).\n\nThe exact source pins, selected archive path and predecessor roles are in\n[SOURCES.json](SOURCES.json). The mathematical statement and cost limits are\nin [PROOF.md](PROOF.md); the recomputed arrays are in\n[CERTIFICATE.json](CERTIFICATE.json); the bounded task state is in\n[TASK.json](TASK.json).\n\n## Reproduce\n\nFrom the repository root:\n\n```sh\npython3 -B research/paired-plane-port-matching-seed6c563a/verify.py\npython3 scripts/research_package.py --package research/paired-plane-port-matching-seed6c563a --check-only\npython3.12 scripts/research_package.py --package research/paired-plane-port-matching-seed6c563a\n```\n\nThe package uses Python's standard library and the exact-rational ceiling\nroutine pinned in `SOURCES.json`. The generic package replay rechecks the\nselected archive and ceiling source pins before running the verifier.\n\n## Open next questions\n\n1. **Integrate the plane endpoint into the selected complex supplier.** This\n matters because the 126 copy invoice alone does not pay for route ownership,\n frame changes, hosting, full restoration, or precision. First map all 56\n planes to the selected source and target routes and count the exact address\n permutations and transitions per call. The blocker is that no complete\n plane-port supplier/compiler interface has been constructed or charged.\n2. **Construct the matching bit-side contract.** This matters because the\n complex-side relaxation cannot establish a joint multiplication improvement.\n First derive the bit-side plane-port decoder and exact copy invoice for the\n same labels. The blocker is the absence of a bit-side plane-port template or\n integrated assembly certificate.\n\n## Credit\n\nThe selected labels and underlying construction remain credited to the\nselected PR1094 lineage, whose source manifest, assembly certificate and\nmaintainer review are pinned in `SOURCES.json`. Discussion #1587 comment\n18914510 established the exact small-instance plane-port endpoint and posed\nthe selected-port decoder question. Open PR #1808 supplies a complementary\ncopy-budget screen but no 112-port decoder. This package extends that endpoint\nto a symmetric matching and global binary factorization, with an exact\nendpoint check and copy-rank invoice. It does not claim priority over the\nsmall-instance observation or general question, or independent human review.\n\nPrepared by the OpenAI Codex research agent with substantial OpenAI Codex\nassistance in modeling, exact computation, verifier implementation and\nwriting. No formal proof assistant was used for this finite certificate.\n", + "encoding": "utf-8", + "sha": "ab671cb0261b3f1753114a1d8ab2c01cc0d36fad", + "display_url": "https://github.com/1337isnot1337/integer-mult-bounds/blob/d16fb8936795ff101e4d2f63cfdc6a25066ebabf/research/paired-plane-port-matching-seed6c563a/README.md", + "display_title": "README.md" + }, + "isError": false +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/interface-proof/github-refresh-20261014-1155/pr1825_readme.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/interface-proof/github-refresh-20261014-1155/pr1825_readme.md new file mode 100644 index 0000000000..36a2e81a22 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/interface-proof/github-refresh-20261014-1155/pr1825_readme.md @@ -0,0 +1,73 @@ +# Paired plane-port matching + +This package gives one explicit finite decoder mechanism for the selected 112 +complex E8 port labels. It symmetrically pairs the labels along zero-dot-product +edges, assigns each pair one common 2-plane, and factors the full selected +pairing matrix through those planes. + +## Result and evidence + +The exact construction uses 56 matched planes, of which 16 have nonzero query +matrices. Their exact B14 copy invoice is 126: nine rank-7 terms and seven +rank-9 terms. The verifier checks the complete 112 by 112 decoder identity, +the plane basis legality, and all 56 plane endpoint translations on 28,672 +local computational basis cases. Four negative controls fail as required. +The hosted application frequency of those translations remains unpriced. + +The changed local profile has a certified favorable complex relaxation at +`a_hi=0.003447203501`, with a planning transfer cap near `0.003435361112`. +This is a construction component and a conditional screen. It does not supply +the complete routed supplier, charge all hosting and interface work, establish +the bit-side interface, or prove a new integer-multiplication bound or +\(\kappa\). + +The exact source pins, selected archive path and predecessor roles are in +[SOURCES.json](SOURCES.json). The mathematical statement and cost limits are +in [PROOF.md](PROOF.md); the recomputed arrays are in +[CERTIFICATE.json](CERTIFICATE.json); the bounded task state is in +[TASK.json](TASK.json). + +## Reproduce + +From the repository root: + +```sh +python3 -B research/paired-plane-port-matching-seed6c563a/verify.py +python3 scripts/research_package.py --package research/paired-plane-port-matching-seed6c563a --check-only +python3.12 scripts/research_package.py --package research/paired-plane-port-matching-seed6c563a +``` + +The package uses Python's standard library and the exact-rational ceiling +routine pinned in `SOURCES.json`. The generic package replay rechecks the +selected archive and ceiling source pins before running the verifier. + +## Open next questions + +1. **Integrate the plane endpoint into the selected complex supplier.** This + matters because the 126 copy invoice alone does not pay for route ownership, + frame changes, hosting, full restoration, or precision. First map all 56 + planes to the selected source and target routes and count the exact address + permutations and transitions per call. The blocker is that no complete + plane-port supplier/compiler interface has been constructed or charged. +2. **Construct the matching bit-side contract.** This matters because the + complex-side relaxation cannot establish a joint multiplication improvement. + First derive the bit-side plane-port decoder and exact copy invoice for the + same labels. The blocker is the absence of a bit-side plane-port template or + integrated assembly certificate. + +## Credit + +The selected labels and underlying construction remain credited to the +selected PR1094 lineage, whose source manifest, assembly certificate and +maintainer review are pinned in `SOURCES.json`. Discussion #1587 comment +18914510 established the exact small-instance plane-port endpoint and posed +the selected-port decoder question. Open PR #1808 supplies a complementary +copy-budget screen but no 112-port decoder. This package extends that endpoint +to a symmetric matching and global binary factorization, with an exact +endpoint check and copy-rank invoice. It does not claim priority over the +small-instance observation or general question, or independent human review. + +Prepared by the OpenAI Codex research agent with substantial OpenAI Codex +assistance in modeling, exact computation, verifier implementation and +writing. 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Native phase lowering is inherited by exact record equality from the pinned provider. No new physical phase sweep, T9 owner admission, recursive private hosting, precision guard or global moment calculation." +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/new-core-transfer-20261017/CLEAN-J-TRANSFER.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/new-core-transfer-20261017/CLEAN-J-TRANSFER.md new file mode 100644 index 0000000000..9d2274a342 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/new-core-transfer-20261017/CLEAN-J-TRANSFER.md @@ -0,0 +1,119 @@ +# Clean centre deletion on the PR3133 words + +The two PR3133 words admit a clean centre deletion. Each changed local +word has 3507 children, rank mass 5073, and a scalar bound of 164514 real +primitives. The map is `(x,y,h) -> (x,y+Jx,h)` in the forward direction +and `(x,y,h) -> (x-Jy,y,h)` in the backward direction. Here `J=I-KR`, +`K=R^T/4`, and `RK=14I`. + +This is a local result. It does not establish a new controller, owner +allocation, private hosting bound, precision bound, or complete kappa +calculation. + +## Sources and credit + +The words are the exact `FINAL-WORD` payloads from +[PR3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133), at +commit `51eb9c4ee9e4722010d308aa3309e039d3940cc2`. The local source copy +comes from the byte-equal payloads in +[PR3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148), at +commit `f2927a4b8afcf0701a6b945e14f30de1d94f5176`: + +- [Base word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/base.json.gz). +- [Extra word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/extra.json.gz). +- [PR3133 source and credit](https://github.com/CrocSwap/integer-mult-bounds/blob/51eb9c4ee9e4722010d308aa3309e039d3940cc2/research/rank7-coupled-586-588-carrier-fold/README.md). + +The word uses the PR2979 construction by Marius-Paul Dumitrean, the +declared edits from PR3015 by Jeremy Kothe, and the restore and carrier +edits from PR3042 and PR3133 by dcharb78. The source README gives the +earlier credit. The current calculation applies the prior campaign's +centre deletion and input debt correction. OpenAI Codex assisted this +calculation. It is not a maintainer review. + +## The cut changes + +There are 112 source fields, 112 target fields, and 408 arbitrary helper +fields. There are 91 separate private zero buffers. Each centre row is + + c = R x + H h. + +The new words have the same ports, R, and propagated response K as the +earlier campaign word. H changes. It has 367 nonzero coefficients on 106 +helper roles. Every one of these roles enters at frame I and leaves at +FULL. None is removed or has a proper terminal subspace. No formal warp +symbol occurs in a centre row or in the propagated centre response. + +`probe_cut.py` derives these rows from the actual A, cut, B, restore, and +cleanup gates. `INTERFACE.json` records the result. In particular, the +earlier H is not used as the new H. + +Deletion of the centre block gives + + F0(x,y,h) = (x, y + Jx - KHh, h), + B0(x,y,h) = (x - Jy, y, h + H^T R y/4). + +Use the following input corrections: + + before F0: y += K H h, + before B0: h -= H^T R y/4. + +All operands have frame I at this cut. For each query row, C0 is cleared, +the query is formed in C0, the response is added, and C0 is cleared again. +The query source remains unchanged in each direction. Thus the correction +is legal on every arbitrary helper input. It removes the complete helper +debt. It uses one serial owned field, not a new full-cover record family. + +## Full local check and invoice + +`emit_clean_j.py` emits and replays four complete words: both source +providers, in both directions. The replay uses exact rational arithmetic +over free warp symbols. It checks all 632 arbitrary live inputs and eight +arbitrary C inputs. It also checks every scalar frame, every native frame +transition, every zero-buffer lifetime, and every live endpoint frame. +All 408 helpers have the identity logical response. All 91 zero buffers +return to zero. C0 returns to zero; C1 through C7 retain their arbitrary +physical contents because no event touches them. + +| Item | Forward | Backward | +| --- | ---: | ---: | +| Source scalar bound | 158148 | 158196 | +| Deleted centre scalars | 2160 | 2208 | +| Input debt correction | 8526 | 8526 | +| Complete scalar bound | 164514 | 164514 | + +The deleted native block is exactly eight rank-eight centre children. +The retained child profile is +`{1:2433, 2:724, 3:228, 4:102, 5:20}`. Its rank mass is 5073. Each +complete word has 23388 events. All 5115 retained native records are +byte-equal to the source emitter's records: 3507 climbs, 240 warps, 978 +ordinary adapters, and 390 residual adapters. + +The helper width inventory is +`{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}`. The result makes no reduction to +the source's reserved helper or private stock. The 91 Z buffers have the +source zero-input contract; they are not arbitrary borrowed inputs. + +## Native phase dependency + +The pinned PR2588 `bw_transport.py` and `bw_emit.py` were run on both new +source words. They accept the new frame chains and replay the source maps +on all live inputs. The changed program adds only frame-I scalar gates +and removes complete private centre paths. It retains every other native +record. Therefore it introduces no new native kernel or phase recipe. + +The source PR3133 `FULL-NATIVE-RECEIPT.json` records a full phase and +wrapper replay of these same input words. That receipt is source evidence. +A fresh full Gaussian sweep was not run in this lane. The independent +review must check the applicable native and residual-adapter dependency; +the scalar replay alone does not establish physical phase correctness. + +## Reproduction + +Run the following commands with one process, from this directory: + + python3 -I -B probe_cut.py + python3 -I -B emit_clean_j.py + +The emitter reads the source-derived files in `native-original-base` and +`native-original-extra`. `FREEZE-CLEAN-J.json` records exact source and +output pins. No PR, push, or publication commit was made. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md new file mode 100644 index 0000000000..a1fc7101cb --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md @@ -0,0 +1,140 @@ +# Native recipes for the new centre-deleted core + +This lane checks the native operators for both PR3133 provider words. +The words are the byte-equal copies in PR3148. It uses the new frame and +warp data. It does not use the earlier T74 frame data. + +Fresh generation passed for both providers. Each run checked 1130 frames, +3036 directed child edges, 224 endpoint adapters, 180 signed physical warp +classes, 72 logical warp operators, and 56 residual wrapper classes. The +residual classes include 32 proper terminal pairs, of which 24 are cold. +Each source run rejected 25 wrapper mutations and 13 warp mutations. + +The fresh child and residual recipe files have the same hashes as the +authenticated PR3133 native receipt. Both literal dual runs also passed: +each checked all 180 signed classes on all 512 columns. In each provider, +172 literal dual recipes differ from the forward recipes. All literal +dual recipes have rank zero. Thus the choice of logical warp orientation +does affect the phase tables, but it does not add native children. + +The independent interpreter review is a separate calculation. The scalar +map, stock, controller, precision, and complete kappa calculation are also +separate checks. `RESULT.json` gives the generation result; `FREEZE.json` +pins its inputs, scripts, proofs, and outputs. + +## Exact operator test + +For a binary subspace U, let T_U be the canonical Clifford frame in the +pinned source. A child from U to V must implement T_V T_U^{-1}. The +generator derives its recipe from this product. It checks the full Pauli +table and the exact Gaussian dyadic image of the zero basis vector. These +two checks include the global phase. + +To see this, let A and B be unitary operators with the same action on all +Pauli generators. Then B^{-1} A commutes with every X and Z generator. An +operator that commutes with every Z generator is diagonal in the standard +basis. If it also commutes with every X generator, all diagonal entries +are equal. Thus A is a scalar multiple of B. Equality on the zero basis +vector fixes that scalar as one. The argument applies to each generated +Clifford product. It also proves equality of all positive tensor powers. + +Each child recipe has the form L C_[r] R, with R applied first. The +serialized L and R are monomial Clifford operators. For a nested frame +change, the checked r is the difference of the frame dimensions. The +physical warp product is T_V K_G^{sign} T_U^{-1}. Its checked r is zero. +The separate Gaussian matrix implementation checks every one of its 512 +columns. + +A helper that enters at E and leaves at V has residual T_V T_E^{-1}. +The recipes include the proper terminal subspaces of the new words. They +also include the cold pairs with E equal to zero. The exact wrapper test +checks R^{-1}, then the residual, then L^{-1}; the result is C_[r]. It does +not replace a proper terminal frame by FULL. + +## Literal dual warps + +The backward scalar proof uses the inverse transpose of each logical +warp. For a unitary warp K this is the entrywise conjugate of K. The +source emitter stores the same signed warp labels for both orientations. +The orientation must therefore select a physical implementation. + +There are two valid routes. The free-operator proof can establish the +endpoint identity for an arbitrary consistent choice of invertible warp +generators. The physical implementation can then use the forward K in +both orientations. Alternatively, the literal dual implementation can +use conjugate(K) in the backward orientation. This lane supplies exact +recipes for the second route as well. + +The literal dual route has a general rank-zero closure property. Let K +be a monomial Clifford operator whose nonzero entries are fourth roots of +unity. Every source K_G has this property. In a standard basis, K is an affine +permutation with a phase of the form + + i^(c + alpha.x + 2 q(x)), + +where q is a binary quadratic form. Conjugation changes this phase by +2(c + alpha.x) modulo 4. The quadratic term vanishes. After the affine +permutation, this phase is a signed Z Pauli. Thus + + conjugate(K) K^{-1} = P + +for a Pauli P. Suppose the accepted physical warp is + + W = T_V K T_U^{-1} + +and W is monomial. Then its literal dual counterpart is + + T_V conjugate(K) T_U^{-1} = (T_V P T_V^{-1}) W. + +A Clifford frame maps a Pauli to a Pauli. A Pauli is monomial. Hence the +literal dual counterpart is monomial and needs no native child. Apply the +same argument to K^{-1} for a negative signed occurrence. This proof does +not require U and V to be FULL, or require the Pauli to be diagonal after +frame conjugation. + +`generate_dual_warps.py` also checks this conclusion directly for each +signed class of each new provider. It uses the physical product +T_V conjugate(K_G)^{sign} T_U^{-1}. A separate Gaussian matrix calculation +compares all 512 columns. A wrong global phase must fail. + +## Source and credit + +The core comes from +[PR3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133), at +commit `51eb9c4ee9e4722010d308aa3309e039d3940cc2`. The byte-equal provider +words are in +[PR3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148), at +commit `f2927a4b8afcf0701a6b945e14f30de1d94f5176`: + +- [Base word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/base.json.gz). +- [Extra word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/extra.json.gz). + +The unchanged recipe sources come from +[PR2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588), at +commit `8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`: + +- [Phase compiler](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_phases.py). +- [Residual wrappers](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_adapters.py). +- [Gaussian matrix implementation](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_gauss.py). +- [Serialized warp checker](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_check_recipes.py). +- [Exact Clifford implementation](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/clifford/clifford_exact.py). + +The source files retain their original author and AI-assistance notices. +The wrapper source credits the PR458 construction. The warp source credits +Cinna Davis and PR2226. OpenAI Codex assisted this lane's driver, literal +dual calculation, proof, and local checks. The independent review is a +separate agent calculation. It is not a maintainer review. + +## Reproduction + +Use one process and the workspace Python that has NumPy: + + work/verification-venv/bin/python -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/generate_recipes.py + OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 work/verification-venv/bin/python -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/generate_dual_warps.py + python3 -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/freeze_results.py + +The first command checks every source and input pin before generation. +It runs the wrapper, phase, and serialized warp checks for each provider. +The second command checks the source and first-stage output pins before +it generates the literal dual recipes. The scripts write results only +inside this lane. No PR, push, or publication commit is part of this work. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/new-native-recipes-20261017/sources/bw_adapters.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/new-native-recipes-20261017/sources/bw_adapters.py new file mode 100644 index 0000000000..82beaa9c1d --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/new-native-recipes-20261017/sources/bw_adapters.py @@ -0,0 +1,165 @@ +"""Paid residual wrappers for entering helpers (Lemma A): generation and independent decoding. Apache-2.0. +Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. The wrapper construction follows PR #458 +(chafreaky): a helper that starts at frame E and ends at FULL has the physical residual S_E = T_FULL T_E^-1 (apply T_E^-1 first); +S_E = L_E (C_[w] x I) R_E with R_E applied first; the wrappers R_E^-1 before the whole local invocation and L_E^-1 after its +full-frame cleanup turn the residual into the coordinate factor C_[w] x I and restore the other 9 - w coordinates identically. +usage: adapters_gk.py CANONICAL-WORD.json.gz RESIDUAL-ADAPTERS.json OUT-LEMMA-A.json +Writes the recipes (generation uses clifford_exact.lower_child) and then DECODES the serialized monomials with the primitive +constructors of clifford_exact (not lower_child) and checks, for every entrance frame, that L_E^-1 S_E R_E^-1 has exactly the +tableau and zero-state vector (global phase included) of fourier(9, range(w)); mutated recipes (wrong phase, swapped sides, wrong +translation, wrong width) must be rejected.""" +if not __debug__: + raise RuntimeError('assertions must remain enabled') # every check of this stage is an assert +import copy, gzip, json, sys +from pathlib import Path +# Package-path adaptation only; the exact wrapper mathematics is unchanged. +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE / 'vendor/clifford')) # BW: the pinned vendor531 clifford_exact (byte copy) +sys.path.insert(0, str(HERE)) +from clifford_exact import canonical_frame, lower_child, fourier, diag, perm, xgate, Op, identity, transpose, inv, parity, monomial as mono_of, mv +import bw_gauss +n = 9; FULL = tuple(1 << i for i in range(n)) +def monomial_op(rec): + """decode a serialized monomial (matrix rows, quadratic rows, Z4 linear part, translation, phase)""" + out = diag(n, tuple(rec['quadratic_rows']), tuple(rec['linear_Z4'])).then(perm(n, tuple(rec['matrix_rows']))).then(xgate(n, rec['offset'])) + return out.then(Op(n, identity(n), [('phase', rec['phase'])])) +def S_of(U, END=FULL): + # HPE: a helper that starts at E=U and ends at END has residual T_END T_E^-1 (END = FULL is the inherited case) + return canonical_frame(n, tuple(U)).adjoint().then(canonical_frame(n, tuple(END))) +def wrapped_ok(U, rec, END=FULL): + """exactly: L^-1 S R^-1 = C_[w] x I (apply order: R^-1, S, L^-1), w = dim END - dim E""" + w = len(END) - len(U); S = S_of(U, END); Rm = monomial_op(rec['right']); Lm = monomial_op(rec['left']) + net = Rm.adjoint().then(S).then(Lm.adjoint()); target = fourier(n, range(w)) + return rec['rank'] == w and net.tab == target.tab and net.zero_state() == target.zero_state() +def _contains(a, b): + a = list(a) + for x in b: + for y in sorted(a, reverse=True): + if x >> (y.bit_length() - 1) & 1: x ^= y + if x: return False + return True +def Kop(G_cols): + """BW: K_G = perm(G) then diag(Q), Q = I + G^-T G^-1: PR2226's monomial() and the conjugator inside clifford_exact.canonical_frame.""" + G = transpose(tuple(G_cols), n); gi = inv(G, n) + Q = tuple((1 << i) ^ sum(parity(gi_i & gi_j) << j for j, gi_j in enumerate(transpose(gi, n))) for i, gi_i in enumerate(transpose(gi, n))) + return perm(n, G).then(diag(n, Q)) +def numeric_K(G_cols): + import numpy as np + pv, ph = bw_gauss.monomial(list(G_cols), n) + N = 1 << n; re = np.zeros((N, N), dtype=np.int64); im = np.zeros((N, N), dtype=np.int64) + unit = [(1, 0), (0, 1), (-1, 0), (0, -1)] + for x in range(N): re[pv[x], x], im[pv[x], x] = unit[ph[x]] + return re, im, 0 +def warp_ok(G_cols, rec): + """BW: the serialized monomial equals PR2226's exact numpy K_G on all 512 columns (indep. decode) and its op decodes to K_G exactly.""" + m = bw_gauss.recipe_matrix(rec, n) + if not bw_gauss.equal_scaled(numeric_K(G_cols), m): return False + dec = monomial_op(rec); ref = Kop(G_cols) + return dec.tab == ref.tab and dec.zero_state() == ref.zero_state() + +def main(): + c = json.load(gzip.open(sys.argv[1])); frames = c['frames']; v = c['v'] + starts = sorted({c['start'][r] for r in range(2 * v, len(c['start'])) if c['start'][r] != 0 and c['final'][r] == 1}) + # HPE: (entrance, terminal) pairs of helpers ending at a proper subspace; key 'E:U'. Inherited words have none. + ends = sorted({(c['start'][r], c['final'][r]) for r in range(2 * v, len(c['start'])) if c['final'][r] != 1}) + # COLD-HPE: e == 0 (a cold helper, entrance = bottom, T_0 = I) is allowed: the (0, U) recipe is keyed '0:U' + assert all(len(frames[u]) < n and _contains(frames[u], frames[e]) for e, u in ends) + cold_ends = [(e, u) for e, u in ends if e == 0] + recipes = {} + for f in starts: + U = frames[f]; rec, compiled = lower_child(S_of(U)) + recipes[str(f)] = dict(frame=f, vectors=list(U), entrance_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right']) + for e, u in ends: + E, U = frames[e], frames[u]; rec, compiled = lower_child(S_of(E, U)) + recipes['%d:%d' % (e, u)] = dict(frame=e, terminal=u, vectors=list(E), terminal_vectors=list(U), entrance_rank=len(E), + terminal_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right']) + # BW: monomial recipes of the warps K_G (anticipatory dirty borrowing, PR2226): one per operator, serialized like a wrapper monomial + warp_recipes = {} + for w in c.get('warps', []): + _, rec_k = mono_of(Kop(w['G_columns'])) + warp_recipes[str(w['op'])] = dict(op=w['op'], from_frame=w['from_frame'], to_frame=w['to_frame'], G_columns=list(w['G_columns']), K=rec_k) + Path(sys.argv[2]).write_text(json.dumps(dict(status='RESIDUAL_ADAPTER_RECIPES', recipes=recipes, warps=warp_recipes), sort_keys=True, separators=(',', ':')) + '\n') + # ---- independent decode of the serialized file + data_all = json.loads(Path(sys.argv[2]).read_text()); data = data_all['recipes'] + dot = lambda a, b: bin(a & b).count('1') & 1 + detail = [] + for f in starts: + rec = data[str(f)]; U = frames[f] + assert wrapped_ok(U, rec), ('wrapper product is not C_[w] x I', f) + detail.append(dict(frame=f, entrance_rank=len(U), residual_width=n - len(U), vectors=list(U), all_even_weight=all(bin(x).count('1') % 2 == 0 for x in U), + totally_isotropic=all(dot(a, b) == 0 for a in U for b in U))) + hdetail = [] + for e, u in ends: # HPE: independent decode, residual width = dim U - dim E + rec = data['%d:%d' % (e, u)]; E, U = frames[e], frames[u] + assert wrapped_ok(E, rec, U), ('HPE wrapper product is not C_[w] x I', e, u) + hdetail.append(dict(frame=e, terminal=u, entrance_rank=len(E), terminal_rank=len(U), residual_width=len(U) - len(E))) + controls = [] + def reject(name, fn): + f = starts[0]; rec = copy.deepcopy(data[str(f)]); fn(rec) + if wrapped_ok(frames[f], rec): raise AssertionError('mutated wrapper accepted: ' + name) + controls.append(name) + reject('wrong global phase', lambda r: r['right'].__setitem__('phase', (r['right']['phase'] + 1) % 4)) + reject('wrong translation', lambda r: r['left'].__setitem__('offset', r['left']['offset'] ^ 1)) + reject('wrong quadratic form', lambda r: r['right'].__setitem__('quadratic_rows', [x ^ 2 if i == 0 else x for i, x in enumerate(r['right']['quadratic_rows'])]) if False else r['right']['linear_Z4'].__setitem__(0, (r['right']['linear_Z4'][0] + 2) % 4)) + reject('sides swapped', lambda r: (r.__setitem__('left', r['right']), r.__setitem__('right', r['left']))) + reject('wrong width', lambda r: r.__setitem__('rank', r['rank'] + 1)) + if ends: # HPE controls on the first (E, U) pair + e, u = next((p for p in ends if p[0] != 0), ends[0]); rec0 = data['%d:%d' % (e, u)] # COLD-HPE: an entering pair if any (= ends[0] without cold ends) + def hreject(name, ok): + if ok: raise AssertionError('HPE mutation accepted: ' + name) + controls.append(name) + hreject('hpe: U-wrapper decoded against a FULL ending', wrapped_ok(frames[e], rec0)) + hreject('hpe: width misreported as 9 - dim E', wrapped_ok(frames[e], dict(rec0, rank=n - len(frames[e])), frames[u])) + other = next(f for f in range(len(frames)) if f != u and len(frames[f]) == len(frames[u]) and _contains(frames[f], frames[e])) + hreject('hpe: wrong terminal hyperplane', wrapped_ok(frames[e], rec0, frames[other])) + fe = next(((e2, u2) for e2, u2 in ends if str(e2) in data), None) + if fe: # an entrance shared with FULL-ended helpers: R_{E,FULL} must not serve as R_{E,U} + r2 = data['%d:%d' % fe] + hreject('hpe: pre wrapper resolved to the FULL recipe R_{E,FULL}', wrapped_ok(frames[fe[0]], dict(r2, right=data[str(fe[0])]['right']), frames[fe[1]])) + hreject('hpe: wrong global phase', wrapped_ok(frames[e], dict(rec0, left=dict(rec0['left'], phase=(rec0['left']['phase'] + 1) % 4)), frames[u])) + if cold_ends: # COLD-HPE controls on the first cold pair (0, U): factor_iff_pre says only R_{0,U} itself may precede + e, u = cold_ends[0]; recc = data['%d:%d' % (e, u)]; E, U = frames[e], frames[u] + ID = dict(matrix_rows=[1 << i for i in range(n)], offset=0, quadratic_rows=[0] * n, linear_Z4=[0] * n, phase=0) + assert monomial_op(ID).tab == identity(n) # the control's wrapper really is the identity + def creject(name, ok): + if ok: raise AssertionError('cold HPE mutation accepted: ' + name) + controls.append(name) + creject('cold hpe: identity pre wrapper instead of R_{0,U}', wrapped_ok(E, dict(recc, right=ID), U)) + creject('cold hpe: identity post wrapper instead of L_{0,U}', wrapped_ok(E, dict(recc, left=ID), U)) + creject('cold hpe: no wrappers (cold FULL convention L = R = I)', wrapped_ok(E, dict(recc, left=ID, right=ID), U)) + creject('cold hpe: U-wrapper decoded against a FULL ending', wrapped_ok(E, recc)) + creject('cold hpe: width misreported as 9', wrapped_ok(E, dict(recc, rank=n), U)) + other = next(f for f in range(len(frames)) if f != u and len(frames[f]) == len(frames[u])) + creject('cold hpe: wrong terminal hyperplane', wrapped_ok(E, recc, frames[other])) + creject('cold hpe: wrong global phase', wrapped_ok(E, dict(recc, right=dict(recc['right'], phase=(recc['right']['phase'] + 1) % 4)), U)) + ent = next((p for p in ends if p[0] != 0 and p[1] == u), None) + same = lambda x, y: monomial_op(x).tab == monomial_op(y).tab and monomial_op(x).zero_state() == monomial_op(y).zero_state() + if ent and not same(data['%d:%d' % ent]['right'], recc['right']): # an entering helper ending at the same U: its R_{E,U} must not serve as R_{0,U} + creject('cold hpe: pre wrapper resolved to an entering recipe R_{E,U}', wrapped_ok(E, dict(recc, right=data['%d:%d' % ent]['right']), U)) + wdetail = [] + for w in c.get('warps', []): # BW: independent decode of every warp recipe, then mutation controls on the first warp + rec = data_all['warps'][str(w['op'])] + assert rec['G_columns'] == w['G_columns'] + assert warp_ok(w['G_columns'], rec['K']), ('warp recipe differs from the exact monomial K_G', w['op']) + wdetail.append(dict(op=w['op'], from_frame=w['from_frame'], to_frame=w['to_frame'], columns_checked=1 << n)) + if c.get('warps'): + w0 = c['warps'][0]; k0 = data_all['warps'][str(w0['op'])]['K'] + def wreject(name, ok): + if ok: raise AssertionError('warp mutation accepted: ' + name) + controls.append(name) + wreject('warp: wrong global phase', warp_ok(w0['G_columns'], dict(k0, phase=(k0['phase'] + 1) % 4))) + wreject('warp: wrong translation', warp_ok(w0['G_columns'], dict(k0, offset=k0['offset'] ^ 1))) + wreject('warp: wrong linear phase', warp_ok(w0['G_columns'], dict(k0, linear_Z4=[(k0['linear_Z4'][0] + 2) % 4] + k0['linear_Z4'][1:]))) + wreject('warp: wrong quadratic form', warp_ok(w0['G_columns'], dict(k0, quadratic_rows=[k0['quadratic_rows'][0] ^ 2, k0['quadratic_rows'][1] ^ 1] + k0['quadratic_rows'][2:]))) + wreject('warp: recipe of another operator', warp_ok(w0['G_columns'], data_all['warps'][str(c['warps'][1]['op'])]['K'])) + wreject('warp: inverse recipe used as the warp', warp_ok(w0['G_columns'], mono_of(Kop(w0['G_columns']).adjoint())[1])) + G2 = list(w0['G_columns']); G2[0] ^= G2[1] + wreject('warp: wrong G (frame-changed column)', warp_ok(G2, k0)) + sing = list(w0['G_columns']); sing[1] = sing[0] + try: Kop(sing); raise SystemExit('non-invertible G accepted') + except (AssertionError, StopIteration, ValueError): controls.append('warp: non-invertible G') + res = dict(status='PASS_RESIDUAL_WRAPPERS_ARE_EXACT', frames=len(detail), **({'hyperplane_end_pairs': hdetail} if ends else {}), **({'cold_hyperplane_end_pairs': len(cold_ends)} if cold_ends else {}), wrappers_reject=controls, all_even_weight=all(d['all_even_weight'] for d in detail), **({'warp_recipes_exact_on_all_512_columns': wdetail} if wdetail else {}), + all_totally_isotropic=all(d['totally_isotropic'] for d in detail), detail=detail) + Path(sys.argv[3]).write_text(json.dumps(res, indent=1) + '\n') + print('Lemma A (exact): L^-1 S_E R^-1 = C_[w] x I for', len(detail), 'entrance frames, global phase included;', len(controls), 'wrapper mutations rejected; all-even-weight:', res['all_even_weight']) +if __name__ == '__main__': main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/ALL-CUT-EDGES.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/ALL-CUT-EDGES.json new file mode 100644 index 0000000000..9ed6e7aab3 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/ALL-CUT-EDGES.json @@ -0,0 +1,9 @@ +{ + "all_considered_pairs": 267854, + "checker_sha256": "6d77e20d6ef1a10951b7abeaa65852fad9161cc3b48e82d538a9748c3c9cc786", + "distinct_products": 4276, + "payload_compressed_sha256": "96197487eb8ea1e0ee891b964a1e837ca81bd3dc80c527a3e5a34724c7c8fbd5", + "payload_decompressed_sha256": "18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418", + "source_rows": 2594, + "tail_columns": 300 +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/ALL-CUT-EDGES.json.gz 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Physical operator identities require separate review." +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/ALL-CUT-SUPPORT.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/ALL-CUT-SUPPORT.md new file mode 100644 index 0000000000..e95860e7e7 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/ALL-CUT-SUPPORT.md @@ -0,0 +1,106 @@ +# Scalar support at every retained native cut + +This note fixes the source computation, all native frame paths, and the +Y-to-Y scalar subword of the pinned clean forward word. It permits any +number of new X/helper-to-Y scalar ADDs at equal-frame cuts. It also +permits deletion or coefficient changes at the existing ADD sites of +that type. An arbitrary raw I-helper correction at entry is allowed. +The scalar coefficients can be rational. + +The note does not permit changes to the source computation, new native +children, operator-valued ADD coefficients, or new Y-to-Y gates. The +operator model keeps the existing warp symbols as free words and cancels +adjacent inverse symbols. A physical relation between distinct warp words +is not used. A stronger physical-character result requires a separate +proof. + +## Exact cut inventory + +The forward word has no Y-to-X or Y-to-helper ADD. Thus a new one-way ADD +does not change any later source row. Its final Y response is the outer +product of its current source row and the remaining Y scalar column. +This statement also holds for a sum of new ADDs. + +The inventory checks every cut where a source row, source frame, target +frame, or remaining Y scalar column changes. Between these events, the +possible outer products do not change. It visits 267,854 equal-frame +source/target pairs and records 4,276 distinct products. There are 2,594 +source rows and 300 remaining Y columns in the retained pools. Each +product has a concrete event index, source field, target Y field, and +frame witness. + +The source pool contains all 112 productive X fields and all 408 live +helpers. A private Z field always has the FULL frame. No Y field reaches +FULL, so a Z-to-Y ADD cannot pass the equal-frame check. The only used +owned C source contains raw I-helper terms and is cleared in the source +word. These terms are included in the allowed entry correction and do +not affect the quotient response. The other owned fields do not carry X +information. + +Two products with the same source row modulo raw I-helper terms and the +same remaining Y column are equivalent for this test. The inventory +retains one complete source row and one legal cut for each such product. +A successful construction must still price its entry correction. + +## Support invariant + +Let p_s be the actual binary label of input X_s. Let F be a recorded +transfer frame. For each empty-warp-word X_s term at that cut, the checker +verifies p_s is in F. For every final Y_t row reached by the remaining Y +column, the checker verifies F is a subspace of p_t-perp. Hence + + p_s dot p_t = 0. + +All 7,584 raw scalar source/target products pass these checks. Their union +has 5,824 distinct port pairs. Since each actual port has odd weight, +the diagonal pair s=t is forbidden. Any scalar response obtained in this +fixed free-word model has zero entries at each pair with p_s dot p_t=1. +Cancellation of nonempty words cannot change this empty-word support. + +This proves that a scalar retuning cannot change the ordinary response +to the identity, or to the identity plus a correction supported on only +eight target rows. It does not preclude a different dyadic unit response. +The separate UNIT-RESPONSE.md packet constructs such a response. + +## Full centre-matrix restriction + +Use the actual eight-row matrix R and K=R^T/4. Let A be any constant +8-by-8 rational matrix. To cancel the off-diagonal part of K A R by the +allowed scalar transfers, it is necessary that + + R_t^T A R_s = 0 + +at every distinct pair with p_s dot p_t=1. There are 6,608 such equations. +Exact rational elimination gives rank 63 on the 64 entries of A. The +one-dimensional kernel is the scalar multiples of I_8. + +Therefore seven retained centre directions cannot be made into a +nonzero diagonal response by scalar changes in this cut model. The same +restriction applies to a rank-seven constant mixer of all eight centre +directions. A rank-seven matrix is not a nonzero scalar multiple of I_8. +This is a statement about this explicit construction family, not about +all native encodings or all actual operator-valued circuits. + +## Checks and source pins + +The source core has decompressed SHA256 + a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa. +The all-cut inventory has decompressed SHA256 + 18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418. + +Run from this directory: + + OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 inventory_new_edges.py + OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 check_frame_support.py + +The second command must report +PASS_EXACT_FRAME_SUPPORT_AND_CENTRE_RIGIDITY. It uses exact fractions for +the rank-63 centre calculation. No sampled rank or numerical tolerance +is used. The file ALL-CUT-SUPPORT-FREEZE.json pins this proof, both checks, +the receipts, the cut payload, and the local replay dependency. + +The fixed-site and all-cut modular span checks in the coherent-port lane +provide separate evidence. They are not needed for the exact support and +rank argument above. The existing E8 and port-frame geometry is prior +repository work; this note binds the invariant to the current native +schedule and the stated insertion grammar. AI assistance was used. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/FRAME-SUPPORT.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/FRAME-SUPPORT.json new file mode 100644 index 0000000000..7f71c642cb --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/FRAME-SUPPORT.json @@ -0,0 +1,22 @@ +{ + "centre_mixer_constraint_rank": 63, + "centre_mixer_kernel": [ + { + "0": "1", + "18": "1", + "27": "1", + "36": "1", + "45": "1", + "54": "1", + "63": "1", + "9": "1" + } + ], + "checker_sha256": "3a81e98c83e418408eb7490771867a11f491a6af403820ad722c43a51026b508", + "forbidden_offdiagonal_equations": 6608, + "inventory_decompressed_sha256": "18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418", + "reachable_raw_scalar_pairs": 5824, + "scalar_source_target_checks": 7584, + "scope": "Fixed native source and Y frame paths with added or retuned one-way equal-frame scalar transfers, in the exact free-warp-word model. Physical operator-valued transfers, changed source circuits, and nonmonotone frame paths remain outside this result.", + "status": "PASS_EXACT_FRAME_SUPPORT_AND_CENTRE_RIGIDITY" +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/check_frame_support.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/check_frame_support.py new file mode 100644 index 0000000000..da72524679 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/check_frame_support.py @@ -0,0 +1,51 @@ +#!/usr/bin/env python3 +"""Check the scalar transfer support forced by the actual cut frames.""" +from fractions import Fraction as F +from pathlib import Path +import gzip,json +from hashlib import sha256 +import probe_readiness as p +HERE=Path(__file__).resolve().parent +raw=gzip.decompress((HERE/'ALL-CUT-EDGES.json.gz').read_bytes()) +p.need(sha256(raw).hexdigest()=='18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418','Pinned cut inventory') +x=json.loads(raw);word=p.core['providers']['base']['canonical'];ports=word['ports'] + +def contains(frame,v): + for basis in sorted(frame,reverse=True):v=min(v,v^basis) + return v==0 + +checks=0;support=set() +for product in x['products']: + frame=word['frames'][product['frame']] + for t,num,den in x['tail_columns'][product['tail_column']]: + p.need(all((v&ports[t]).bit_count()%2==0 for v in frame),'Current frame lies in each final target hole') + for s,ops,num,den in x['source_rows'][product['source_row']]['constrained']: + if s>=112 or ops:continue + p.need(contains(frame,ports[s]),'Raw source line lies in current frame') + p.need((ports[s]&ports[t]).bit_count()%2==0,'Source and target ports are orthogonal') + support.add((t,s));checks+=1 +# The full centre mixer must vanish at all forbidden off-diagonal positions. +basis={};equations=0 +for t in range(112): + for s in range(112): + if t==s or (ports[t]&ports[s]).bit_count()%2==0:continue + row={a*8+b:p.r[a].get(t,F(0))*p.r[b].get(s,F(0)) for a in range(8) for b in range(8)} + row={k:v for k,v in row.items() if v};equations+=1 + while row: + pivot=min(row) + if pivot not in basis: + c=row[pivot];basis[pivot]={k:v/c for k,v in row.items()};break + p.e.add(row,basis[pivot],-row[pivot]) +free=[i for i in range(64) if i not in basis];kernel=[] +for f in free: + sol={f:F(1)} + for pivot,row in sorted(basis.items(),reverse=True): + value=-sum(c*sol.get(k,F(0)) for k,c in row.items() if k!=pivot) + if value:sol[pivot]=value + kernel.append(sol) +p.need(len(basis)==63 and len(kernel)==1,'Exact scalar-mixer constraint rank') +p.need(kernel[0]=={9*i:F(1) for i in range(8)},'Only scalar identity centre mixers') +report={'status':'PASS_EXACT_FRAME_SUPPORT_AND_CENTRE_RIGIDITY','inventory_decompressed_sha256':sha256(raw).hexdigest(),'scalar_source_target_checks':checks,'reachable_raw_scalar_pairs':len(support),'forbidden_offdiagonal_equations':equations,'centre_mixer_constraint_rank':len(basis),'centre_mixer_kernel':[{str(k):str(v) for k,v in row.items()} for row in kernel],'scope':'Fixed native source and Y frame paths with added or retuned one-way equal-frame scalar transfers, in the exact free-warp-word model. Physical operator-valued transfers, changed source circuits, and nonmonotone frame paths remain outside this result.'} +report['checker_sha256']=sha256(Path(__file__).read_bytes()).hexdigest() +(HERE/'FRAME-SUPPORT.json').write_text(json.dumps(report,indent=2,sort_keys=True)+'\n') +print(report,flush=True) diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/inventory_new_edges.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/inventory_new_edges.py new file mode 100644 index 0000000000..8c57c12112 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/inventory_new_edges.py @@ -0,0 +1,81 @@ +#!/usr/bin/env python3 +"""List legal equal-frame scalar products at all native schedule cuts.""" +from collections import defaultdict,Counter +from fractions import Fraction as F +import gzip,json +from hashlib import sha256 +from pathlib import Path +import probe_readiness as p +HERE=Path(__file__).resolve().parent + +def main(): + item=p.core['providers']['base'];word=item['canonical'];events=item['programs']['forward'];n=len(word['start']) + sources=list(range(112))+list(range(224,n));allowed={i for i in range(224,n) if word['start'][i]==0} + source_frame={i:word['start'][i] for i in sources};target_frame={i:0 for i in range(112)} + source_groups=defaultdict(set);target_groups=defaultdict(set) + for i,f in source_frame.items():source_groups[f].add(i) + for i,f in target_frame.items():target_groups[f].add(i) + tails=[{i:F(1)} for i in range(112)] + source_pool=[];source_ids={};tail_pool=[];tail_ids={};products={};checks=0 + source_current={} + def source_id(field,state): + row=state[field] + constrained=tuple(sorted((s,ops,c.numerator,c.denominator) for (s,ops),c in row.items() if s not in allowed or ops)) + if not constrained:return None + if constrained not in source_ids: + source_ids[constrained]=len(source_pool) + source_pool.append({'constrained':constrained,'complete':tuple(sorted((s,ops,c.numerator,c.denominator) for (s,ops),c in row.items()))}) + return source_ids[constrained] + def tail_id(target): + row=tuple(sorted((i,c.numerator,c.denominator) for i,c in tails[target].items())) + if row not in tail_ids:tail_ids[row]=len(tail_pool);tail_pool.append(row) + return tail_ids[row] + def consider(field,target,pos,state,frames): + nonlocal checks + checks+=1 + p.need(frames[field]==frames[112+target],'Equal actual frames') + sid=source_current.get(field) + if sid is None:return + tid=tail_id(target);key=(sid,tid) + if key not in products: + products[key]={'source_row':sid,'tail_column':tid,'after_event':pos,'source_field':field,'target_Y_port':target,'frame':frames[field]} + def changed_source(field,pos,state,frames): + old=source_frame[field];new=frames[field] + if old!=new:source_groups[old].remove(field);source_groups[new].add(field);source_frame[field]=new + source_current[field]=source_id(field,state) + for target in target_groups[new]:consider(field,target,pos,state,frames) + def changed_target(target,pos,state,frames): + old=target_frame[target];new=frames[112+target] + if old!=new:target_groups[old].remove(target);target_groups[new].add(target);target_frame[target]=new + for field in source_groups[new]:consider(field,target,pos,state,frames) + def observe(pos,event,state,frames): + if event is None: + for field in sources:changed_source(field,pos,state,frames) + return + tag=event[0] + if tag=='scalar': + op=event[1];t=op[1] + if t[0]=='L' and t[1] in source_frame:changed_source(t[1],pos,state,frames) + if t[0]=='L' and 112<=t[1]<224: + target=t[1]-112 + if op[0]=='add' and op[2][0]=='L' and 112<=op[2][1]<224: + source=op[2][1]-112;p.e.add(tails[source],tails[target],-F(*op[3:5]));changed_target(source,pos,state,frames) + elif op[0]=='scale': + c=F(*op[2:4]);tails[target]={i:v/c for i,v in tails[target].items()};changed_target(target,pos,state,frames) + elif tag=='climb': + field=event[2] + if field in source_frame:changed_source(field,pos,state,frames) + elif 112<=field<224:changed_target(field-112,pos,state,frames) + elif tag=='warp': + field=event[1] + if field[0]=='L' and field[1] in source_frame:changed_source(field[1],pos,state,frames) + identity={i:{(i,()):F(1)} for i in range(n+8)} + p.replay(events,identity,word,False,observe) + p.need(tails==[{i:F(1)} for i in range(112)],'Y scalar endpoint identity') + output={'schema':'native-all-cut-equal-frame-products-v1','source_core_sha256':p.PIN,'provider':'base','initial_I_helpers':sorted(allowed),'source_rows':source_pool,'tail_columns':tail_pool,'products':list(products.values()),'all_considered_pairs':checks,'scope':'New one-way X/helper-to-Y ADDs at exact equal-frame cuts. Existing native chains and Y scalar subword remain fixed. Raw I-helper debt is quotiented but complete representative source rows are retained.'} + raw=(json.dumps(output,separators=(',',':'),sort_keys=True)+'\n').encode() + (HERE/'ALL-CUT-EDGES.json.gz').write_bytes(gzip.compress(raw,mtime=0)) + report={'source_rows':len(source_pool),'tail_columns':len(tail_pool),'distinct_products':len(products),'all_considered_pairs':checks,'payload_decompressed_sha256':sha256(raw).hexdigest(),'payload_compressed_sha256':sha256((HERE/'ALL-CUT-EDGES.json.gz').read_bytes()).hexdigest(),'checker_sha256':sha256(Path(__file__).read_bytes()).hexdigest()} + (HERE/'ALL-CUT-EDGES.json').write_text(json.dumps(report,indent=2,sort_keys=True)+'\n') + print(report,flush=True) +if __name__=='__main__':main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/probe_readiness.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/probe_readiness.py new file mode 100644 index 0000000000..1ce1a9bde3 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/interior-cut/probe_readiness.py @@ -0,0 +1,131 @@ +#!/usr/bin/env python3 +"""Check row readiness inside each pinned clean native word.""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +CORE = LANES / 'new-core-transfer-20261017' +PIN = 'a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa' +A = [0, 7, 20, 27, 36, 46, 57, 111] + +def need(test, label): + if not test: + raise ValueError(label) + +spec = importlib.util.spec_from_file_location('raw_transfer', CORE / 'emit_raw_selected.py') +e = importlib.util.module_from_spec(spec) +spec.loader.exec_module(e) +payload = gzip.decompress((CORE / 'CLEAN-J-PROGRAMS.json.gz').read_bytes()) +need(sha256(payload).hexdigest() == PIN, 'Pinned clean core') +core = json.loads(payload) +r = [{int(p): F(c) for p, c in row.items()} for row in core['R']] +D = {p: {a: sum(row.get(p, 0)*row.get(a, 0) for row in r)/4 for a in A} for p in range(112) if p not in A} +D = {p: {a: c for a,c in row.items() if c} for p,row in D.items()} +B = {a: {p: D[p][a] for p in D if a in D[p]} for a in A} + + +def replay(program, state, word, backward=False, observer=None): + state = deepcopy(state) + n = len(word['start']) + frames = {p: f for p,f in enumerate(word['start'])} + frames.update({n+p:0 for p in range(8)}) + zero = set() + def slot(x): + if x[0] == 'L': return x[1] + if x[0] == 'C': return n+x[1] + need(x[0] == 'Z', 'Slot token') + return ('Z',x[1]) + if observer: observer(-1, None, state, frames) + for pos,event in enumerate(program): + tag = event[0] + if tag == 'scalar': + gate,f = event[1:] + t,op = slot(gate[1]),gate[0] + if op == 'clear': + state[t],frames[t] = {},f + else: + need(frames[t] == f, ('Scalar target frame',pos)) + if op == 'scale': + c=F(*gate[2:4]); state[t]={k:c*v for k,v in state[t].items() if c*v} + else: + s=slot(gate[2]); need(t!=s and frames[s]==f, ('Scalar source frame',pos)) + if op=='copy': state[t]=dict(state[s]) + else: + need(op=='add','Scalar operation'); e.add(state[t],state[s],F(*gate[3:5])) + elif tag=='climb': + t,old,new,rank=event[2:6] + need(frames[t]==old and len(word['frames'][new])-len(word['frames'][old])==rank,('Climb',pos)) + frames[t]=new + elif tag=='warp': + t,op,old,new=slot(event[1]),event[2],event[3],event[4] + need(frames[t]==old,('Warp frame',pos));frames[t]=new + state[t]=e.operator(state[t],('dual_K' if backward else 'K',abs(op)),1 if op>0 else -1) + elif tag=='zero_buffer': + t=('Z',event[2]) + if event[1]=='alloc': + need(t not in zero,'Private allocation');state[t],frames[t]={},1;zero.add(t) + else: + need(t in zero and not state[t],'Private return');zero.remove(t) + else: need(tag in ('phase','adapter','residual_adapter'),'Event tag') + if observer: observer(pos,event,state,frames) + need(not zero,'No live private buffer') + need([frames[p] for p in range(n)]==word['final'],'Final live frames') + need(all(frames[n+p]==0 for p in range(8)),'Final owned frames') + return state + + +def setup(word, backward): + n=len(word['start']);identity={p:{(p,()):F(1)} for p in range(n+8)} + physical=deepcopy(identity) + for p in range(112):physical[p]=e.line(physical[p],p,1) + if backward: + for a in A: + for p,c in B[a].items():e.add(physical[a],physical[112+p],-c) + else: + for p in D: + for a,c in D[p].items():e.add(physical[112+p],physical[a],c) + for a in A:physical[a],physical[112+a]=physical[112+a],physical[a] + for p in range(112):physical[p]=e.line(physical[p],p,-1) + return physical + + +def run(provider, item, direction): + backward=direction=='backward';word=item['canonical'];program=item['programs'][direction] + start=setup(word,backward);final=replay(program,start,word,backward) + watched=A+[112+a for a in A] + periods={p:[] for p in watched};active={} + phases=[];last_climbs={p:None for p in range(112,224)} + exact_rows=[] + def observe(pos,event,state,frames): + if event and event[0]=='climb' and 112<=event[2]<224:last_climbs[event[2]]=pos + for p in watched: + good=state[p]==final[p] + if good and p not in active: + active[p]=[pos,frames[p],sum(frames[112+u]==0 for u in range(112) if u not in A),sum(frames[112+u]==word['final'][112+u] for u in range(112) if u not in A)] + elif not good and p in active: + periods[p].append(active.pop(p)+[pos-1]) + if event and event[0]=='phase': + phases.append({'position':pos,'name':event[1],'selected_X_frames':[frames[a] for a in A],'selected_Y_frames':[frames[112+a] for a in A],'Y_frame_counts':dict(Counter(frames[p] for p in range(112,224))), 'ready_fields':[p for p in watched if state[p]==final[p]]}) + if event and event[0]=='climb' and 112<=event[2]<224: + t=event[2] + exact_rows.append({'position':pos,'target':t,'rank':event[5],'from':event[3],'to':event[4], 'ready_selected_X':[a for a in A if state[a]==final[a]],'ready_selected_Y':[a for a in A if state[112+a]==final[112+a]]}) + actual=replay(program,start,word,backward,observe) + need(actual==final,'Repeat replay') + for p,v in active.items():periods[p].append(v+[len(program)-1]) + result={'phases':phases,'selected_final_value_intervals':periods,'last_Y_climbs':last_climbs,'Y_climb_readiness':exact_rows,'all_input_columns':len(word['start'])+8} + print(provider,direction,'stable',[(p,periods[p][-1][0],periods[p][-1][1:4]) for p in watched],flush=True) + return result + +if __name__=='__main__': + out={'schema':'native-interior-row-readiness-v1','source_payload_sha256':PIN,'providers':{}} + for provider,item in core['providers'].items(): + out['providers'][provider]={direction:run(provider,item,direction) for direction in ('forward','backward')} + out['checker_sha256']=sha256(Path(__file__).read_bytes()).hexdigest() + (HERE/'READINESS.json').write_text(json.dumps(out,indent=2,sort_keys=True)+'\n') diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md new file mode 100644 index 0000000000..d936b5d986 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md @@ -0,0 +1,190 @@ +# A unit criterion for the mixed source partition + +This theorem gives the exact condition under which an input log repairs +the mixed source partition of the raw selected backward word. It also +gives an inverse for the complementary data code. The theorem applies +to ordered operators. It needs no commutation relation and no identity +for BD. It is a content theorem. Native placement and cost are separate +obligations. + +## Modules and the local map + +Let E and U be finite free right modules over a ring with identity. Let +Q be an invertible map on E, and put q=Q^-1. Let + + B:U->E, D:E->U, M:U->E, K=MD:E->E. + +Products denote composition, with the rightmost map applied first. +The original data are (a,u) in E+U. The original source is (b,v) in +E+U. Put beta=qb. Consider the local map + + d=Qa+Mv, + h=beta+Bv, + w=u-v+D(d-beta), + r=v. (1) + +The actual A8 input-minor word has this map. It has dim(E)=8, +dim(U)=104, BD=13I, and a current ordinary minor with MD=I. The +native packet MINOR-INPUT-LOG.md proves that particular instance. +Equation (1) defines the algebraic family in this note. It does not +assert a native implementation for every B, D, and M. + +The complete map (1) is a unit for every M. Its direct inverse is + + b=Q(h-Br), + a=q(d-Mr), + u=w+r-D(d-h+Br), + v=r. + +The question is stronger: does the mixed partition (w,d), by itself, +give a unit map on the source when the original data are fixed? + +## The exact criterion + +The source map to (w,d) is a unit if and only if K=MD is a unit on E. +To prove this, remove the fixed data terms from (w,d). Its linear +source part is + + w=-D beta-v+DMv, d=Mv. + +Make the reversible output change + + f0=-w+Dd, g=d-Mf0. + +This gives + + f0=v+D beta, g=-K beta. + +The reversible input change (beta,v)->(beta,v+D beta), followed by +a change of component order, leaves diag(I,-K). Therefore the source +map is a unit exactly when K is a unit. This factorization proves +necessity over the ring; a test for a nonzero kernel alone would not +prove that statement over a general ring. + +Over a field, a source code for this partition therefore needs a log +of rank at least dim(E). This lower bound applies to the partition +(w,d) in (1). It is not a lower bound for every native controller or +every possible output partition. + +## Source and data codes when K is a unit + +Assume that K has a two-sided inverse H. Define + + e=(I-H)d-HMw, + f=-w+DH(d+Mw), + z=h-e-Bf, + t=r-f. (2) + +Put C=H(Qa+Mu). Direct substitution gives + + e=beta-C, + f=v-u+DC, + z=Bu+(I-BD)C, + t=u-DC. (3) + +Thus, for fixed data, (e,f) has source coefficients q and I, with +no source cross term. The complementary coordinates (z,t) contain +no source value. Their exact inverse is + + Qa=-Mt, + C=z-Bt, + u=t+DC. (4) + +Equation (4) follows from MD=K and HK=KH=I: more directly, +-Mt=-Mu+KC=Qa, and z-Bt=C. Equation (4) needs no further inverse. +If B, D, M, and H are dyadic, all of these coefficients are dyadic. +After (4), recover a=q(Qa), b=Q(e+C), and v=f+u-DC. + +The full change of output coordinates in (2) is also a unit. An +inverse that uses no H is + + d=Mf, + w=-f+D(Mf-e), + h=z+e+Bf, + r=t+f. (5) + +To prove the first two identities, use Mf=d and H(d+Mw)=d-e. +These follow directly from (2). The other two identities are the +definitions of z and t. The order of the factors in (2)--(5) is part +of each formula. + +For the actual current minor, K=I. Then (2) reduces to + + e=-Mw, f=-w+D(d+Mw). + +The source code resides in this mixed (w,d) partition. The selected +output d=Qa+Mv contains the input ordinary-source minor; it is not +the complete selected source code. In particular, e reads ordinary +X. This specifies the meaning of the source-channel sentence in +the frozen MINOR-INPUT-LOG.md proof. + +## Composition through every pair count + +The same result extends the controller in MIXED-CONTROLLER.md. +Each backward stage s has maps B_s,D_s,M_s and a unit K_s=M_sD_s. +Put H_s=K_s^-1. Each forward stage t has the stated content map + + (h,k;d,v)->(h-qB_t k,k;d,v+L_t k), + L_t=I-D_tB_t. + +Keep the ordinary suffix, bridge, and final triangle order from the +companion proof. There is no selected bridge. Recover each w_i +from the final ordinary X triangle. Let + + P_i=L_t(i-1)w_(i-1), P_0=0, + e_i=(I-H_s)d_i-H_sM_s w_i, + F_i=-w_i+D_sH_s(d_i+M_s w_i)-P_i, + C_i=H_s(Qa_i+M_s z_i). + +The same substitutions as in (3) give + + e_i=qb_i-C_i, + F_0=y_0+D_s0 C_0, + F_i=y_i+D_si C_i-D_t(i-1)B_t(i-1)z_i, i>0. + +Define + + Z_i=f_i-e_i-B_s F_i-B_s P_i+qB_t w_i, + T_i=r_i-F_i-P_i-L_t w_i. + +Then + + Z_i=B_s z_i+(I-B_sD_s)C_i-qB_t z_(i+1), + T_i=z_i-D_sC_i+L_t z_(i+1). + +Start with z_m=0 and work backwards. Remove the known next suffix +from these two equations. Apply (4) to the remaining local pair. +This recovers Qa_i and z_i. Then x_i=z_i+z_(i+1). Recover the +source from the displayed e_i and F_i equations. At the first pair, +subtract a_0 from the recovered b_0 to undo the initial full forward +call. This proves an inverse for every positive pair count. + +This general proof does not use B_sD_s=13I. The actual emitted +native words still have their own fixed graph hypotheses. The +extension permits other input logs with unit M_sD_s at the content +level. A proposed log must still have legal access in its current +chart, and its decoder must still pass native placement and cost +checks. + +## Verification and scope + +The companion check_unit_completion.py checks the local map and +its two inverses with ordered formal operators. It uses only +Qq=qQ=I, MD=K, and HK=KH=I. It also checks the exact necessity +factorization. The earlier check_mixed_controller.py checks the +actual K=I controller for one through eight pairs. Its proof supplies +the controller order used above. + +The current native instance has a 32-term signed-half input log and +adds no native child to the raw B word. The complete decoder still +needs access to d in its hole frame, cross-frame output operations, +terminal types, helper ownership, and a full recursive cost. This +note does not resolve those obligations or claim a kappa change. + +The coordinating lane supplied the general K=MD criterion and its +source and data formulas. The oblique-native lane supplied the +explicit unit factorization and the all-pair extension. The +independent-review lane supplied the short output-code inverse for +K=I; equation (5) gives the same inverse for every unit K. The work +used OpenAI Codex under the user's direction. Independent review +is required. No PR, push, or publication commit was made. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/HANDOFF.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/HANDOFF.md new file mode 100644 index 0000000000..17b3e48c25 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/HANDOFF.md @@ -0,0 +1,555 @@ +# Schur selection handoff + +The current task is the nonlinear finite-grid centre interface. The +local redundant tag word and its numerical proof have passed independent +review. The current complete precision bill +is negative. The earlier plane and Schur results remain recorded below. +No PR, commit, or push is authorized. + +## Current finite-grid interface + +`finite-grid/GRID-RESET-PROOF-V2.md` gives a backward construction on declared +dyadic-grid inputs. Tag both data banks by `(1+delta)`, leave arbitrary +helpers unchanged, and run the raw prefix to event 12995. Round every +non-centre field back to its untagged prefix value. At each centre decode +the fine residue to remove its source part. Then run the old positive +suffix. The exact result is the unit backward shear, with all 480 helper +contents restored in their inherited native endpoint frames. + +The local word reuses one owned private field. It adds 2361 field-pass +operations, including all input tags, cut rounds, centre decoders, and +output rounds. The new code has no final division by delta on data. +The exact centre response cone has 132 old native jobs with profile +`{1:124,4:8}` and rank mass 156. These jobs receive twice the leading +accuracy parameter. Every other job receives ordinary accuracy. The +proof gives explicit coarse grids, growth bounds, delta, and error +margins. It distinguishes exact finite-grid restoration from conversion +of a finer approximate caller record. It makes no complete supplier claim. + +The current frozen packet is: + +- Proof V2 SHA256 `40fa4d2cbd2a6cfa3a7ec6facd81e04af727b18d77bed11643b13f19e38428e7`. +- Checker SHA256 `90c7b4fdeac34f6a04c39da323c082e45ce7385e76afd6003b997d7acce683ba`. +- Receipt SHA256 `fd7b11c4d6ea5855b1901445fd219b14dbcc94de511c4ff003bafdd5ef6752eb`. +- Compressed word SHA256 `26247471aaca9c8b80f365c0f012fa93000c8bd10db0e4ff74d0cdace9e85e87`. + +Run `finite-grid/check_redundant_grid.py` with `python3 -I -O -B`. +It passes all 704 logical input columns, 3267 exact scalar decoder +cases, the eight-query source witness, and the complete reverse cone. +The package-review lane accepted V2 without a remaining material local +finding. Its independent receipt is +`../paired-package-review/tagged-grid-review/REVIEW.json`, SHA256 +`495b538abd3358f4b668a06f618850625f4ceb5306ae9a06ca99d3192071fd82`. +Its checker has SHA256 +`924cda79d17d0a6ae14c4a8a5f1e1ebc91afd0eb9b082f347ccae75d050315a9`. +The review checks all 704 columns and 480 helper outputs, every one of +132 native error impulses, 11025 signed decoder cases, exact margins, +2361 field passes, and the relative carrier witness. It also includes +coarse-only error and tiny-child return-format failure controls. +Caller grid conversion, the complete-node endpoint, finite tape costs, +and global kappa remain outside that accepted local claim. + +Independent review found that a fixed parent return conversion must +have a separate absolute fine-grid error bound. It cannot be included +in an arbitrary tiny child's relative error contract. V2 incorporates +that repair and the correct fine-centre margin `2^(G+6)`. It also +excludes coarse caller entry conversion from the local fine-error +budget. That entry conversion remains a complete-node obligation. +The original proof and both correction addenda remain as review history. + +The actual minor `A=[0,7,20,27,36,46,57,111]` has Gram `4I`. Inputs +`y_A=R_A^T v` and `u=h0-v`, with fixed nonzero `h0=e0/8`, keep a +nonzero coarse carrier while leaving eight independent fine queries v. +This also blocks normalization of the carrier as an escape from the +relative two-t resolution. This is not a lower bound for other data +accesses or a new native error contract. The separate frozen addendum +is `finite-grid/CARRIER-RESOLUTION.md`, SHA256 +`1dd7b6bcb4e38b576abb549fe92283c762a20d435733768dceea69adbd0ed754`. + +The temporal lane screened 227 saved pure-helper reset policies and all +255 nonempty centre subsets. Its best four-query union has mass 65; +its best all-eight union has mass 153. Every screened union has at +least `8|S|+13` rank-one jobs. All those policies worsen the retained +moment at doubled width. The finite screen is not an optimum over all +reset sets. This lane independently checked every saved union cost and +the layer-cake and beta `97/65` consequences. The review is +`finite-grid/TAGGED-SUBSET-ARITHMETIC-REVIEW.md`, with receipt SHA256 +`a035475c11318b0bfba6377ee8ffa8e38b1c9b168f4a86763c710de024ac8eb5`. + +The separate earlier small-tag code `delta data` needs final division +by delta. Its 760 mixed-sensitive native jobs have rank mass 1040. +`finite-grid/BACKWARD-GRID-WORD.json.gz` and its receipt preserve that +negative experiment. Do not use its cone for the redundant code. + +The temporal lane has since solved its full unary pure-helper reset +family by three independent 12-site enumerations. It reports the same +minima. That extension has a separate independent review in progress; +this lane's arithmetic receipt only covers the earlier saved policies. + +The coordinator has stopped new work on this branch. The local theorem +and its review are complete. The negative global comparison is frozen +at `../portable-source-codes/digit-encoding-budget/TAGGED-BUDGET.json`, +SHA256 `ab4abaa916c73548d37856ef575534f08433dbc01542381aece2ec1af28c7693`. +That comparison grants the new scalar and decoder access for free and +still rejects every screened partial-centre policy at doubled width. +A useful new escape must change +native error structure, source access, or the code. Repeating the finite +reset screen or applying the old clean-input precision census is not +justified. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. + +## Earlier plane and Schur work + +Independent review found a legal private CLEAR that removes the +centre return. The new exact local singleton word has native rank +1,792, compared with 2,016 for full transforms on its 224 data fields. +It still has no complete supplier saving: the conditional retained +nine-call plane invoice has rank deficit -3,584 over 16 replicas. +The earlier bounded Schur search did not find a selected +set with fewer than 40 ports; no general minimum of 40 is claimed. +No supplier or kappa improvement is claimed. All writes are confined +to this lane. No PR was prepared, and the user has suspended new PRs. + +## Current plane interface and fixed-query cost + +The current packet is `plane-repair/OPEN-CLIQUE-NATIVE.md`. It replaces +the unrestricted no-saving conclusion of the closed-return packet +below. The old construction and lower bound remain valid under their +return-cut assumptions; the frozen files stay unchanged. + +The open word clears one private field after its last response. It +also clears the field once on entry, so all 225 initial data/private +columns are checked. Both direct orientations pass exact native and +symbolic checks. The rank-49 partition costs 1,918, while 112 singleton +queries cost 1,792. The latter has 560 native children, 1,456 affine +maps, 112 COPYs, 112 ADDs and 113 CLEARs. Its uniform real scalar bound +is 1,346. Packed map work and child work are separate obligations. + +The actual selected template has nine calls and eight data fields per +port in each of 16 replicas. A 65-axis plane replacement with one +complete productive residual pass would pay 56,448 productive native +ranks plus 2,016 fresh private query ranks per replica, versus the +full baseline 58,240. This conditional invoice loses 224 per replica. +The new plane global endpoint is not certified by that arithmetic. + +The same arithmetic applies to a proposed unpaid rank r. If a local +involution T commutes with an m-axis full phase and the advance FT has +rank m-r, the private-CLEAR singleton shear costs 2m-r. With nine +fresh queries and eight complete productive residual advances, the +mass per port is 8(m-r)+9r=8m+r. A larger unpaid rank does not repair +that controller. Its query count, carried information, or endpoint +contract must change. + +The open packet pins are: + +- Proof: `161819babdbaa8aa943065153f10a975d1dfa33e3fa2923659e69e84cd7ade56`. +- Checker: `fde5274220f955277f241d5b1e072fb1088926a273e8727ad362a70a85cc4ce8`. +- Receipt: `4e3a71f684b8d629e7c1592bf53e23c181a48135fd34a44240ce327dd10f7150`. +- Word: `ad2aff0ad007fc5790e57f5c2dde3819fbda60a3bdd093617963ad8ac3ba3907`. + +The interface-proof review passed those fixed bytes. Its note is +`interface-proof/plane-clique-review/REVIEW.md`, SHA256 +`bd1963fd2a70534b891a3f864d6ccba3cf0c30d5431223bf9257d6edda68ec7e`. +Its receipt is `CLEAR-SCHEDULE-REVIEW.json`, SHA256 +`42a0a4f405eef12b4e970ba0a6746f19950dc5d7054fcfd619d5bf97989c43af`. +It covers all 225 inputs in both families and orientations, exact +frame access, 229,376 new phase columns, gathers and local counts. +It found the CLEAR escape and the direct backward schedule. Parent +identified the stronger singleton family. + +The separate `plane-repair/PLANE-CONTROLLER.md` proves the scalar and +phase part of the new 65-coordinate endpoint. The selected 19-event +role controller gives T I_8. The nine stage phases multiply to F_65 +times one explicit residual translation. The checker verifies 120,120 +mod-four coefficients for all 56 actual planes. Its proof, checker +and receipt pins are, respectively: + +- `08105ecef6d00d619a6a7fc3544f97a1c2b64ff0dfc84c5b4e7b0ae7d6b8cf9b`. +- `ccb759a897e0a004a68f7cfc387cb7bd48f30ace501bc173ae43ef502e819389`. +- `dbcf4e426b1f0b58e1955bae339b74ec5446c0bf07173399c8161b5c6d84ea05`. + +That packet passed independent proof review. The review note is +`interface-proof/plane-clique-review/CONTROLLER-REVIEW.md`, SHA256 +`b5d888089fcb445c2eaad64fbfc79c48e2f020dc00463b910fa23c7ac28f902e`. +Its receipt is +`5d402fda009a145fa2be0a87fd0b404f5e63332b7ec2c47a9a106c39051e48a2`. +It does not give the full cover compiler, hosting, recursive contract +or finite invoice. Equal residual advances on all eight roles remain +an interface premise of the endpoint factorization. +Its rank bound applies to a common nontrivial T with scalar normalized +role gates. The rank difference of the positive and negative sectors +shows that n productive T endpoints require at least n rank-one T +queries. It permits private CLEAR and query reuse, but excludes mixed +plane operators and payload-dependent code changes. Thus a productive +dirty carrier, a mixed-plane controller or a changed endpoint remains +an open route; temporal reuse alone in that fixed scalar grammar +cannot give a strict native deficit. + +Do not extend a specialization at T=-I across distinct actual plane +operators without a common sector or a proved formal-algebra premise. +At tensor depth one, plane indices 0,3,4,6,8 have the five q+r labels +24,467,483,347,371 with XOR zero. Their common negative eigenspace is +zero, since its Fourier support would have to satisfy all five dot +products equal to one. This control does not prove the same statement +at larger tensor depth. + +The separate `plane-repair/QUERY-SPAN.md` gives a stronger, different +representation theorem. After c one-field payload queries with scalar +free role maps, the operator matrix has scalar response span and scalar +source span of dimension at most c. This follows from the two exact +factorizations `M=A tensor I+UV` with U scalar and `M=A tensor I+WZ` +with Z scalar. No commutation of payload operators is assumed. + +The actual plain-input query `R diag(C_q^-1)` has scalar source rank +112, although it has only eight output fields. Distinct q labels give +separating spatial matrix-entry functionals. The proposed plane query +`R diag(T_p)` also has scalar source rank 112: character sums separate +the 56 plane operators, and a 112-column stacked minor has determinant +8. Constant-character compression proves the same statement at all +positive tensor depths. The common trace-minus-constant functional +also gives the mixed-plane endpoint query bound without a common +negative eigenspace. + +This theorem counts every non-scalar payload operation, including an +address permutation. It is not a native-child lower bound. The actual +compiler's rank-zero maps and the sources' existing non-scalar phase +codes are explicit escapes. At depth one, a line phase is a scalar +combination of identity and one translation, so a native-child +interpretation would be false. Keep this distinction in every use. + +Query-span pins, proof/checker/receipt respectively: + +- `785e27fdc6f2bcd83318afee14103f3e021065d32be2265b8afdec3fea3e1081`. +- `bcc8bb5482c76578014512d51dd5d650d4bf13d6546b29e355ae01bec8a07811`. +- `a06939cba2c937f452027ee4a1f20b31121a70b7fc7393d9ccad091817ee448e`. + +Interface-proof independently accepted both factorization arguments +and the line tensor extension. Source-domain then completed a separate +source and certificate review. It reconstructed R from 10,851 original +scalar events, checked all 28,672 plane Fourier columns and 802,816 +functional contributions, and confirmed the 41 directions, Gram +determinants 12, and selected minor determinant eight. No material +finding remains. The review files in `../source-domain/query-span-review` +have these SHA-256 values: + +- `review_query_span.py`: `f13d88dffbe36b9d6e349786fd368343fd57f46766e839ca52d3cf46f7c82184`. +- `REVIEW.json`: `36820f2267d5f1388d554c12f7f79b91792b964060d2fb639654bbd7cc30c148`. +- `REVIEW.md`: `a79b0d779e80b06db5f97debe555df9917449b05bc5e9e0eaf31ee82160d4064`. + +The frozen proof retains its earlier review-pending sentence. This +receipt supersedes that status without changing the reviewed bytes. +The theorem remains a payload-query count in its stated scalar grammar; +it gives no native-child or complete supplier cost bound. + +`plane-repair/PLANE-INVOLUTION.md` gives an exact endpoint without a +replica: for an ordered matched plane, P swaps q and r, A=X_r P, and +T=C_q C_r A is an involution. All actual labels have weight three +modulo four, so P and T commute with the full phase F. The advance +FT has native rank seven and a fully specified affine adapter. +Every one of the 896 retained positive-stage routes moves the other +plane direction. The checker constructs 504 replacement routes on +65 coordinates, fixing each plane pointwise and covering all 65 +directions in nine local calls. No owner schedule is supplied by that +geometry alone. + +`plane-repair/CLIQUE-NATIVE.md` carries the explicit rank-49 fitting +matrix through a complete local native word. A cyclic schedule makes +every off-diagonal correction legal. Each clique uses one private +zero centre, restored before the next clique. The two orientations +are checked on all arbitrary data input columns. The emitted word is +`plane-repair/CLIQUE-NATIVE-WORD.json`. + +The finite counts are 49 complex COPYs, 453 complex ADDs including +centre erasure, and 821 native children with profile 2:522, 3:224, +4:75. Their rank is 2,016. There are 2,359 conservative affine maps +forward and 2,583 backward. Map implementations, child work, complete +hosting, and the outer supplier are not included in those map counts. + +The lower bound in the note applies to one fixed aggregate query. +If a clique has g orthogonal planes, the query born at their union +must visit a response frame missing each plane. If it is erased at +the union, its native cost is at least 4g, attained by the word. If +it is erased at the full frame, the cost is at least 9+2g. The latter +sums to 665, whereas 217 counts only the initial climbs and omits +448 ranks. A fixed invertible query encoding leaves every relative +transition unchanged. Changed query content, joint query codes, +changed target representations, and different fitting supports are +outside this bound. + +The plane-clique packet is frozen and is under independent review +by the interface-proof lane. Its current pins are: + +- Plane involution proof: + `2a7af353a6e6dd26f31b84c5590f16463200755855e6137e341f0d435825f097`. +- Plane involution receipt: + `f55bd0e7b81a15b6526ca3056ef3bf1bbf57b13137699e71a374f4cf8f55f794`. +- Clique proof: + `429bc00663ffa05985128fee55f98afafc2fa41201e63e1d93e81718295ae8de`. +- Clique emitter: + `cfa46d5f5367d98edd2be9cee74fcec734ae0a9e40ad30d5c07b9e92e2178499`. +- Clique receipt: + `59c68154655db819829ec400f700224ef5524e0fdead98e4f9cec349ba2225d7`. +- Complete native word: + `177c8707df7b2dce6aa794f15b3cbf2033bf6f713fc098008cffc03dee75a798`. + +## Productive spectator transport + +`spectator/PROOF.md` proves the exact identification of two replicas +with two arbitrary slices of one existing payload bit. The map +`A|x,z>=|x+(z+1)v,z+1>` gives the original paired involution. It also +states the common scalar-square variant from the residual-syndrome +lane. It does not change the paired controller's mixed endpoint. + +The local paired word folds to one 704-role core with 5,056 native +events and paid rank 5,522. There are 1,344 added full-field ADDs and +448 affine maps. Each field covers both productive slices, so the +fold does not itself halve the physical work. The parent and child +types must preserve the same physical z. The temporal and interface +lanes own that physical layout and packed-control admission. + +The local proof passed independent review in +`../interface-proof/spectator-native/LOCAL-REVIEW.md`, with receipt +SHA256 `87ee5444573579072e5306b3b3dbb03e8ecc24c03547955e5af7455470955d69`. +The proof pin is +`b42418480d15eef90a40053c080a92f9b127028898d034e44427af51d1300dd5`; +its receipt pin is +`aed86dead5533b5c4827803ed15fa7c98d2be252d0c2f4d0f291e1988cb79e35`. + +The coherent-port terminal product received a separate bounded +independent order review here. Its receipt is +`spectator/TERMINAL-PRODUCT-REVIEW.json`, SHA256 +`70898079acdaa070adebad6eef835056c39ffdf2fecc061d1437fe7c2dbe82a8`. +It does not admit a full layer or an all-size decoder. A later +conjugation addendum correctly requires layer maps to act as the +identity on z, not only to fix its address. + +## Latest route and gauge result + +`PAST-CATALYST-v2.md` is the current proof. The original +`PAST-CATALYST.md` is retained evidence and is superseded: its claim +that every local frame becomes diagonal was too strong. Support within +the past space is enough for the active-rank argument. The checker and +receipt did not use the removed claim. + +The actual q labels span the first nine axes. Closure of a common cover +domain under even one port's eight retained stage routes forces their +images to span all 73 axes. Thus a smaller common cover with these same +routes cannot keep all centres in a proper fixed past space. + +The literal native views cost at least 1,615,856 active rank, including +the idle remainders, against productive active mass 917,504. Borrowed +helpers contribute 468,976 active directions before their two views. +`PAST-GAUGE-FUSION.md` proves that persistence and adjacent fusion of +the prescribed local-nine gauges do not reduce this active count. The +actual owner histories use disjoint active axes. The proof charges all +native work on gauge-only paths. It excludes a new content code, +folding through in-core operations, changed owner paths, and extra +exterior factors in the required gauges. + +Both results passed independent algebra and source review in +`../cover-algebra/PAST-CATALYST-REVIEW.md`. The review rebuilt all routes +and all 14,336 individual owner masks. It did not re-extract the paired +candidate's promoted role list; its arithmetic check is scoped to that +stated list. + +- Corrected proof SHA256: + `566cfb7794202a2462a41da8abef69066c51a06ab7802c01f76b996e58e976e5`. +- Original checker SHA256: + `12bb08ed9c420a8a9aa6a06d2bb1d973b322d409778a91d5ecc1dce44dde1a03`. +- Original receipt SHA256: + `5eefd5390bdf778d9ca1a34b8efc19f295f069138e1ca1f4784af3ad9e0bd320`. +- Fusion proof SHA256: + `a84b77d2ef0d0747713063a7bd08e211b5a75eabbba6ff085a3967676fc12c6f`. +- Fusion checker SHA256: + `fb2a8bb398e8446efdfb0193a4c84848f0a9ffc0ca5cfa38ea18d33e1141a546`. +- Fusion receipt SHA256: + `cfa2cb2920608d190a05e331f18f353b23104389e51df30553d3f56f638a3d37`. +- Independent review note SHA256: + `c94657a67f2eebf5cb3b995615ff21b77fe4bf7ed8f90d09a78224a8f8227b98`. +- Independent review receipt SHA256: + `06da67966668dbd2c49deb21abf6c36f80840c766bd2ebac315379ced854a37f`. + +## Current paired-plane follow-through + +The new `plane-repair/` directory consumes the pinned PR #1825 matching +and PR #1889 scalar-mask audit. It does not repeat their finite searches +or failure census. Its exact checker passes under `python3 -I -O -B`. +Independent review by the cover-algebra lane passed. The receipt is +`../cover-algebra/PLANE-REPAIR-REVIEW.json`, SHA256 +`66dea8e099f61887e44001098b8930071a8d8222f591a1ee6208ca45fdc7ad76`. + +A 24-plane incompatibility witness forces a 48 by 48 scalar identity +submatrix. Every fitting decoder over Q or C therefore has rank at +least 48. The first 26-clique partition gave a rank-52 rational +fitting matrix. The cover-algebra lane then found a rank-49 matrix +by allowing the two ports of a plane to use different clique groups. +The interval 48 to 49 is unresolved. This excludes any +coefficient-only repair of the predecessor's 23 scalar columns, and +also 16 terms of scalar rank at most two. It is not a native-cost bound. + +The symmetric binary certificate has a positive complex interpretation. +Its 16 plane operators give the full nine-coordinate phase followed by +translation 187. Exact local adapters give native profile 1:9, 2:7, +total rank 23, and a conservative 48 monomial maps on one field. It +does not implement the multi-port coupling. A valid one-port physical +plane endpoint was also checked on arbitrary source and target values; +its halving-compatible profile is 2:2, 3:2, 4:2, total rank 18. It gives +no native rank saving over two full nine-coordinate transforms. + +The next mathematical task is an affordable scalar fitting factorization +with at least 48 modes, or a new operator-valued correction contract. +The inherited binary copy charge 126 is not an admitted implementation +of either. `plane-repair/PROOF.md` states the exact equations, scope, +source links, and replay command. No full supplier or recursive invoice +has been produced for this plane interface. + +## Results + +For the actual R and the fixed A and T, any dyadic-unit Schur block +requires at least 27 selected ports. The factor 11 excludes fewer than +24 ports. The new unpaired spectral argument excludes sizes 24, 25, 26, +28, 29, 30, and 31. A size-27 support must have det(-4D)=2^42. Its +existence remains open. The spectral proof is frozen and has passed +independent proof and source review. + +In the split-pair class, the exact minimum is 40. An additional root +(a,b) must be selected with (a,-b), up to overall signs. The actual 96 +other ports form 48 pairs. The first half of each pair is one of twelve +signed D4 root types, each with multiplicity four. For at most eleven +pairs, all 1,130,168 multiplicity vectors fail the dyadic-unit determinant +condition. Exact elimination and a separate determinant polynomial give +the same result. The latter checker also rebuilds R from the pinned word. +The paired bound has passed bounded independent review. That review +reconstructed the actual geometry and checked the determinant polynomial; +it did not repeat the 1,130,168-vector enumeration. The support family +also has a separate independent check. The frozen proof retains its +earlier review-pending sentence; the review receipts below supersede it. + +The pair graph is exactly three disjoint K_(4,4) components. Each choice +of a perfect matching in all three components gives a different support +of size 40. There are 13,824 such supports. Every one has Gram matrix +20I, Schur block -8I, and inverse -I/8. The receipt gives the full pair +list, the graph components, and one explicit selected set. + +The coherent-port lane reports that its one-C0 construction has the same +local operation counts on every support in this family. Its reported +counts remain the responsibility of that lane. No routing optimization +over this family was run here. + +## Decisive files + +- `PAIR-BOUND.md`: proof and replay command. + SHA256 `6ef5d5c787d151c41b0fefc896ea722379fdde79eb8e8eb2cf0470ce8f2fe82c`. +- `PAIR-BOUND.json`: exact source, structure, count, and witness receipt. + SHA256 `77e6d0e69dacc72a8bf110d13bd5708283ebcae8155d1b6666613806ee1be5a0`. +- `check_pair_bound.py`: source reconstruction and polynomial check. + SHA256 `0fa40b727d95c24de974746480f5883a2b787f9af7c540c97107f4ff4e8aba7b`. +- `enumerate_four_block.cpp`: exact elimination check. + SHA256 `6526f8ec97f54b534ead9b01e8b49243449aea6e0458ed968a9ef645408cdae8`. +- `FOUR-BLOCK-CANDIDATES.json`: first enumeration receipt. + SHA256 `2277f67451ed6f805aac41020902c17d2d35b0280ad29e4b4f05401b37063b47`. +- `SPECTRAL-BOUND.md`: unpaired spectral proof and fifteen-root edge lemma. + SHA256 `6dd2afed08d8873a2277ccfef4edd1bc212e831b8495bb659809f76d77802af1`. +- `check_spectral_bound.py`: finite residual cases and rational log bounds. + SHA256 `ecc031e20c309c4e1d04443b60a58fe03d32ce73a5a3b43078e9cb673341c61c`. +- `SPECTRAL-BOUND.json`: exact unpaired exclusion receipt. + SHA256 `d1124af128b6e526461c7587c2a7331dc4d19c9d90433d8d08bf9676c33a8a84`. + +## Independent review receipts + +- `../cover-algebra/PAIR-BOUND-REVIEW.json`: + SHA256 `2fef74db8f780f1690ceffd039c0d603399d5d8ddcce40d0c7e4596adb938111`. + This review checks the source, proof, polynomial, count, and witness. + It does not repeat the large determinant enumeration. +- `../coherent-port/MATCHING-SUPPORTS-REVIEW.json`: + SHA256 `a8ba739b3acbef23dcc3ac3ec342de2ea4630cc3081073a5c64870b21e8de5df`. + This review reconstructs the pair graph, checks all 72 component + matchings, and enumerates the 13,824 distinct support masks. It does + not review the determinant lower bound. +- `../temporal-reuse/SPECTRAL-BOUND-REVIEW.json`: + SHA256 `9639db0bdbc82255ef85273ac15a0aff68d5c659190557bf331d260eb714964f`. + The review note has SHA256 + `9bded2961ce5c0b0124b376e3f832c0ea326b85b6d31851a79801bd827f682bd`. + The checker `../temporal-reuse/review_spectral_bound.py` has SHA256 + `83de0b4694a8ef1ee501130bca9ddedf6e265f6be44b855e61e327646a7529d9`. + It reconstructs the actual matrix by reverse source propagation, + checks the complete residual case split, checks all 16 determinant + rows, and uses a separate 64-term rational logarithm routine. It + proves that the critical size-31 logarithmic margin is above 1/1250. + The frozen spectral proof retains its review-pending sentence; this + review receipt supersedes it. + +## Unpaired spectral result + +For v additional columns, set M=R_V R_V^T and B=44I-M=-4D. Actual +distinct columns have squared norm 4 and pair products 0 or 2 or -2. +The nonorthogonal graph has clique number at most eight. Its edge bound +controls tr(M^2), which gives a rational upper bound for the largest +eigenvalue. A power-series inequality then gives a determinant lower +bound. The upper bound is (44-v/2)^8. + +The new geometric lemma says that any fifteen such roots have at most +93 nonorthogonal pairs. It splits on clique number at most six, seven, +or eight. The seven-clique case uses its one-dimensional orthogonal +complement. The finite case checker includes the h=2, z=2 residual case; +omitting it would give an invalid bound. The final inequalities use +exact rational logarithm intervals with 32 terms. They exclude size 31 +with a small positive margin. No decimal approximation proves the claim. + +The remaining determinant powers for selected sizes below 40 are: + + 27: [42] + 32, 33, 34: [41] + 35, 36: [40] + 37: [39, 40] + 38: [38, 39, 40] + 39: [37, 38, 39, 40]. + +These are necessary conditions, not existence results. The bound applies +to the specified selected-baseline source interface. It does not apply +to an interface that changes those baselines. No native source cost or +supplier gain follows from these exclusions. + +## Other experiments + +These experiments are not used to prove the paired-class bound. + +- `search_block_schur.py` tested prescribed two-dimensional block forms + for -4D. At size 38, the flexible family gave 105 infeasible reports. + At size 39, 70 cases were infeasible and 35 reached the one-second limit. + The time-limited cases remain unresolved. +- `search_hadamard_schur.py` tested 9,216 prescribed size-38 forms + obtained from a four-dimensional Hadamard shear. The solver reported + all infeasible. It used one worker and at most 0.2 seconds per case. +- `search_random.cpp` sampled five million size-39 sets and five million + size-34 sets with seed 1862. It found no unit determinant. The maximum + valuations of det(-4D) were 33 and 37. The size-34 run was repeated to + retain its best selected set; the repeat is not five million new draws. +- `RANDOM-34-DETAIL.json` retains a size-34 set with determinant + 15 times 2^37. `LOCAL-34.json` covers all 459,459 selections obtained + by removing two nonfixed selected ports and adding two unselected + ports. None is a unit. This does not cover larger changes. +- `enumerate_seidel.cpp` checks all 2^21 sign-normalized symmetric + matrices with diagonal 35 and off-diagonal entries 1 or -1. None has + unit determinant. `SEIDEL-35.jsonl` is the receipt. This experiment + has not had a second determinant check or independent agent review. + +The random and local search commands use `R.txt`, which stores the same +actual R. The decisive proof checker verifies R independently of that +text file. The CP-SAT scripts use the existing interpreter at +`work/autonomous-kappa-run/venv/bin/python` with one worker and +`OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1`. + +## Remaining work + +If a smaller support is still needed, use selections that break +split-sign pairing and the remaining sizes listed above. A full source +construction and its global invoice are outside this lane's result. +The 13,824 sharp supports may permit a better port choice without +changing the local Schur inverse; no such gain is proved. The independent +spectral checker can be replayed with the command in its review note. + +No command process remains active in this lane. The last disk check showed +18.57 GiB available. The lane uses about 1.03 MiB apart from transient process +memory. The repository, frozen evidence, upstream, and other lanes were +not changed. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/PLANE-INVOLUTION.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/PLANE-INVOLUTION.json new file mode 100644 index 0000000000..19ae747536 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/PLANE-INVOLUTION.json @@ -0,0 +1,6806 @@ +{ + "actual_fourier_cases": 28672, + "archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "halving_split": [ + 3, + 4 + ], + "matching_sha256": "4fd648f7b5178bff5441bf364d58234b7bc1a43b924bc6da03013c948f1473b1", + "native_advance_rank": 7, + "negative_eigenspace_dimensions": [ + 1, + 6, + 28, + 120, + 496, + 2016 + ], + "new_dimension": 65, + "new_routes_checked": 504, + "phase_sha256": 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} + ] + } + ], + "retained_positive_route_failures": 896, + "retained_route_proof_sha256": "566cfb7794202a2462a41da8abef69066c51a06ab7802c01f76b996e58e976e5", + "scope": "Exact local phase and replacement label geometry; no scalar core, owner schedule, or supplier invoice.", + "spatial_plane_columns": 4, + "status": "PASS_EXACT_PLANE_INVOLUTION_AND_ROUTES", + "trace_one_plane": 2 +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/PLANE-INVOLUTION.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/PLANE-INVOLUTION.md new file mode 100644 index 0000000000..63abd8c169 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/PLANE-INVOLUTION.md @@ -0,0 +1,179 @@ +# A plane phase involution without a replica + +The actual paired planes admit an exact involutive endpoint with two +unpaid directions. It differs from the original complex plane phase +by an affine address map. No extra data field or spectator bit is +needed. This resolves the local phase condition for a possible new +plane core. It does not implement its scalar queries or restore its +borrowed owners. + +Every selected positive-stage route fails to preserve the matched +plane. The note gives explicit replacement routes on 65 coordinates. +They preserve both plane directions and cover all coordinates in nine +local calls. A complete core and owner schedule on that geometry remain +open. No supplier or kappa improvement is claimed. + +## The exact local operator + +Use the actual convention + + C_q=((1+i)I+(1-i)X_q)/2, C_q^2=X_q. + +Let q,r be an ordered orthonormal pair for the binary dot product. +Put E=span(q,r), and let P be the orthogonal map that exchanges q and +r and fixes E perpendicular. Its explicit action is + + P x=x+((q+r) dot x)(q+r). (1) + +Use the same symbol for its address-permutation operator. Let + + C_E=C_q C_r, A=X_r P, T=C_E A. (2) + +Operator products act from right to left. Thus A first exchanges the +two plane coordinates, then translates by r. Since P sends r to q, + + A^2=X_(q+r)=C_E^2. + +The swap P commutes with C_E, and translations commute with C_E. +Consequently A commutes with C_E. The exact formulas are + + T=C_q C_r^-1 P, T^2=I. (3) + +There is no scalar phase in (3). The two plane directions remain +native Fourier directions. Right multiplication by the monomial A +preserves the Fourier rank and the output Lagrangian of C_E. Thus the +new endpoint has the same plane frame as the old one. A fitting mask +derived only from those frames does not change. Complete physical +scalar words still need their ordered phase adapters. + +## Compatibility with the actual full phase + +Let F=C_(e_0)...C_(e_8) be the nine-coordinate phase. An orthogonal +swap of q and r need not commute with F. The needed condition is + + wt(q)=wt(r) modulo 4. (4) + +To prove this, set w=q+r. Orthogonality gives an even intersection of +the supports of q and r. Under (4), wt(w)=2 modulo 4. For any x with +w dot x=1, + + wt(x+w)-wt(x)=wt(w)-2|support(x) intersect support(w)| + +is zero modulo 4. For w dot x=0, P fixes x. Hence the Fourier multiplier +i^wt(x) is invariant under P, so PF=FP. This proof also applies in any +larger canonical address space when q and r lie in it. + +Every actual matched label has weight 3 or 7. Thus every selected pair +satisfies (4). All line phases commute with F, so + + FT=TF (5) + +on every actual plane. + +Choose an orthonormal basis B=(q,r,b_2,...,b_8). Let C_B be its product +of line phases. There is an exact translation delta with + + C_B=F X_delta. + +For coordinate a, set +`delta_a=(sum_(b in B) b_a-1)/2 modulo 2`. The same mod-four expansion +as in the preceding plane-repair proof gives this identity. In the +actual case, delta dot q=delta dot r=1, so P fixes delta. It follows +that + + FT=X_(delta+q) C_(E perpendicular) P. (6) + +The middle factor uses the seven displayed complement directions. +Equation (6) gives a rank-seven physical data advance, with all phases +and address maps explicit. Splitting the seven directions into three +and four gives two halving-compatible native children. The surrounding +address operations and their legal selected-slot implementation still +need a finite invoice. The operator identity does not set their cost +to zero. + +## A scope limit and an even-rank extension + +At tensor depth lambda, take the tensor power of (2). The same monomial +adapter gives T^2=I. On one four-dimensional plane space, trace(T)=2. +Therefore the dimension of the negative eigenspace at depth lambda is + + (4^lambda-2^lambda)/2. (7) + +The one-column negative eigenspace has dimension one. This does not +give a one-quarter volume code at arbitrary tensor depth; the ratio +in (7) tends to one half. + +More generally, let E have an even orthonormal basis grouped into +pairs. Let P exchange each pair, and let b be the sum of one chosen +axis from every pair. Then A=X_b P has square equal to the product +of translations along all axes in E. It commutes with C_E. Therefore +T=C_E A is an involution with the same Fourier frame as C_E. If the +two axes of every pair have equal weights modulo four, P also commutes +with the canonical full phase. + +There is a precise odd-rank limit to this particular construction. +For an orthogonal P on a binary dot-product space, the characteristic +vector omega is fixed. Thus `(I+P)b` always has even parity. An affine +map X_b P cannot square to translation by the sum of an odd number of +orthonormal directions: that sum has odd parity. This statement covers +orthogonal affine address square roots only. The nonorthogonal +controlled map using an extra spectator bit is a counterexample to +any unrestricted version of the statement. + +## The retained routes fail, and exact plane routes exist + +The selected route for port q fixes q and exchanges all eight axes of +q perpendicular in the base nine-space with a fresh eight-space. +Since its partner r belongs to q perpendicular, every positive-stage +route sends r out of the base plane E. Thus none of the 896 positive +port-stage routes preserves its matched plane. The old geometry cannot +be used without a new interface proof. + +Here is one exact replacement geometry. Use 65 coordinates, with the +base nine-space and eight disjoint fresh seven-spaces E_s. For a plane +chart B as above, define rho_s to fix q,r and exchange b_2,...,b_8 +with the seven standard axes of E_s. It fixes every other coordinate. +Let rho_0=I. Each rho_s is an orthogonal involution and commutes with +the plane phase and the adapter A. The nine local spaces are + + E plus span(b_2,...,b_8), E plus E_1, ..., E plus E_8. + +Their complement parts are disjoint and their sum has dimension +`2+9*7=65`. A common orthogonal cover on 65 coordinates can therefore +carry these exact plane-preserving routes at the level of labels. +This is a route construction, not an owner-matching construction. +The changed dimension also changes helper jobs, idle work, cover size, +parent volume, and the recursive exponent calculation. + +The present scalar mask has an independently checked rank-49 fitting +matrix and a rank-48 lower bound. Its queries, responses, and free +corrections are explicit. This local plane involution removes the need +to double that core solely to obtain T^2=I. It does not make any of +those 49 queries, responses, or owner paths free. Their copied-rank +cost must be derived for the new plane frames; the old line-only +functional is not an admitted plane cost. + +## Exact checks and credit + +Run from this directory: + + python3 -I -O -B check_plane_involution.py + +Expected first line: + + PASS_EXACT_PLANE_INVOLUTION_AND_ROUTES + +The checker consumes the pinned matching from [PR #1825](https://github.com/CrocSwap/integer-mult-bounds/pull/1825), +the actual DATA-PHASES member, and the frozen plane charts. It checks +(3) on all four spatial basis columns, (4)--(6) on all 512 characters +for all 56 actual planes, every retained positive-route failure, and +all 504 replacement routes. It also checks the complete dimension-65 +span and rejects a wrong translation in A. All arithmetic is integral +or exact Gaussian arithmetic. The all-depth and even-rank conclusions +follow from the displayed proofs. + +The predecessor supplied the matching. The plane-repair proof supplied +the exact phase lift and charts. The cover-algebra lane supplied the +rank-49 scalar construction; its native implementation remains open. +This work used substantial OpenAI Codex assistance under the user's +direction. It does not alter frozen evidence or the selected frontier. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/QUERY-SPAN.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/QUERY-SPAN.json new file mode 100644 index 0000000000..99a99bfe32 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/QUERY-SPAN.json @@ -0,0 +1,1364 @@ +{ + "archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "input_fields": 112, + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "line_pivot_functionals": [ + { + "centre_row": 0, + "pivot": 1, + "port": 0, + "q": 11 + }, + { + "centre_row": 1, + "pivot": 1, + "port": 1, + "q": 19 + }, + { + "centre_row": 0, + "pivot": 1, + "port": 2, + "q": 35 + }, + { + "centre_row": 1, + "pivot": 1, + 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This is a payload-query count bound under scalar free gates, not a native-child or rank-zero-map lower bound for the full supplier.", + "status": "PASS_EXACT_QUERY_SOURCE_SPANS" +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/QUERY-SPAN.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/QUERY-SPAN.md new file mode 100644 index 0000000000..95088fb511 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/QUERY-SPAN.md @@ -0,0 +1,240 @@ +# Scalar source and response spans of payload queries + +The actual eight-row centre query has 112 independent non-scalar +source directions when its inputs are plain fields. The same statement +holds for the proposed matched-plane version. This is an exact +representation statement. It does not give a native-child lower bound +for the full supplier, which also uses payload address maps and +sources that already have different phase encodings. + +The theorem below also removes the common-negative-eigenspace premise +from the earlier controller query-count bound. Distinct actual plane +operators need not have a common negative sector. A linear functional +on operators is sufficient. + +## The gate grammar + +Let H be a finite-dimensional complex payload space. A state has a +finite number of fields, each with values in H. A scalar role map has +the form `B tensor I_H`, with arbitrary complex B. Such maps can be +singular. They include scalar additions, COPY and private CLEAR. +The initial input embedding and final output projection must also +be scalar role maps. + +A payload query changes one scalar combination of fields by one +operator on H. It has the form + + L=I+u Q v, + +where u is a scalar column, v is a scalar row, and Q is an operator +on H. Applying a payload operator P to one field is the case +`u=e_k`, `v=e_k^T`, `Q=P-I`. The Q operators at different queries can +be arbitrary and need not commute. A block query with r scalar +response directions is counted r times. + +Every non-scalar payload operation must be counted or included in +an explicitly changed input/output contract. In particular an address +permutation is a payload query in this grammar. It is not a free +scalar role map, even when the native compiler gives it Fourier +rank zero. This distinction is essential. + +## Two exact factorizations + +After c queries, the input-to-state operator matrix M has both forms + + M=A tensor I+U V, U scalar with at most c columns, + M=A tensor I+W Z, Z scalar with at most c rows. (1) + +The operator-valued matrices V and W in the two forms need not be +related. Extra private or borrowed fields do not change the claim. + +Initially take A to be the scalar input embedding and take the +other factors to have size zero. A scalar gate B replaces A by BA, +U by BU and W by BW. It leaves the query count unchanged. + +For the first form, a query gives + + LM=M+u Q v M + =A tensor I+[U,u] [V; Q v M]. (2) + +Thus it adds at most one scalar response column. For the second form, + + LM=A tensor I+(LW)Z+u Q (v A tensor I) + =A tensor I+[LW,u Q] [Z; v A]. (3) + +It adds at most one scalar source row. These equations preserve the +operator order. They do not commute Q through an earlier operator. +They also do not assume an invertible intermediate gate. A scalar +final projection or input restriction preserves both forms. + +Let ell be any complex linear functional on operators on H with +`ell(I)=0`, and apply ell entrywise. Equations (1) give + + ell(M)=U ell(V)=ell(W)Z. (4) + +For any finite collection of such functionals, all the resulting +column spaces lie in the same c-dimensional scalar response span, +and all their row spaces lie in the same c-dimensional scalar source +span. Consequently both the horizontal column rank and the vertical +row rank of these matrices are at most c. + +This is a payload-query count theorem. A separate contract is needed +to turn that count into a native rank or primitive-operation cost. + +## The actual line-centre query + +The pinned supplier matrix R has eight rows and 112 columns. It +satisfies `R R^T=56 I_8`. Every column is nonzero. Its 112 actual line +labels q_p are distinct and nonzero. + +Use the exact phase convention + + C_q=a I+b X_q, + a=(1+i)/2, b=(1-i)/2, + C_q^-1=b I+a X_q. (5) + +For a physical input `X_p=C_(q_p) x_p`, the centre Rx is the operator +query + + G=R diag(C_(q_p)^-1) (6) + +on the physical X fields. The same argument applies to the positive +phase version `R diag(C_(q_p))`. + +For each p, let ell_p be the spatial matrix entry +``. It kills I and all the other line translations. +Applied to (6), it gives a matrix whose only nonzero column is p, +equal to `a R[:,p]`. For the positive phase it is `b R[:,p]`. +Choose one nonzero entry from each R column. The 112 selected rows +of the stacked functional matrices form a nonzero diagonal minor. +After the common Gaussian scalar is removed, every diagonal entry +is 1 or -1. Thus the scalar source rank is exactly 112. + +It follows from (4) that a circuit in the stated grammar needs at +least 112 payload queries to form these eight outputs from plain +inputs. Eight output fields do not imply eight scalar source +directions. + +The conclusion holds at every positive tensor depth lambda. Let v +be the constant character, which is fixed by each C_q and its inverse. +Choose Q_q to be either C_q or its inverse. Compress all but one +tensor factor to v. This sends I to I and `Q_q^tensor(lambda)` to +Q_q. Compose ell_p with this compression. The same diagonal minor +remains nonzero. Spectator coordinates can be compressed in the +same way. + +This does not add 112 queries to the selected supplier. Its productive +source advances already provide a non-scalar input encoding before +the eight centres are formed. Such an encoding is outside the plain +input premise of (1). A reusable code can therefore matter by carrying +these directions from earlier work. The theorem requires a proposed +shortcut to state where that information enters its interface. + +## The matched-plane version + +For one actual ordered matched pair q,r, put w=q+r and let +`P_w y=y+(w dot y)w`. The exact plane involution is +`T=C_q C_r^-1 P_w`. In the Fourier basis it fixes each character y +with `w dot y=0`. On the other characters it has the matrix entry + + T_(y+w,y)=i (-1)^(q dot y). (7) + +For its plane index k, define + + ell_k(M)=(-i/256) sum_(w_k dot y=1) + (-1)^(q_k dot y) M_(y+w_k,y). (8) + +It kills I. If another plane has a different w, its contribution +is zero. For the same w, character orthogonality on the affine +hyperplane gives zero unless its q is q_k or q_k+w. Distinct actual +matched planes use neither of those labels. Thus + + ell_k(T_j)=1 if k=j, and 0 otherwise. (9) + +There are 41 distinct swap directions among the 56 actual planes. +The checker does not assume they are all distinct. It checks every +character sum within each repeated-direction group. + +Assign the same ordered plane T to its two matched ports, as in the +new plane core. For `G_plane=R diag(T_p)`, each ell_k isolates the +two R columns of its matched ports. Their two-column Gram determinant +is 12, so they are independent. The checker selects two centre rows +per plane. The resulting 112-column minor is block diagonal in +matching order and has exact determinant 8. Therefore G_plane also +has scalar source rank 112 and obeys the same query-count limit. + +Compression to constant characters gives the same conclusion at all +positive tensor depths. The statement concerns this proposed plane +interface with the actual R; it does not claim that it is the selected +native source interface. + +## A mixed-plane endpoint consequence + +For an endpoint that applies T_p independently to n productive fields, +use one common functional + + ell(M)=trace(M)/dim(H)-, (10) + +where v is the normalized constant character. Every T_p fixes v and +has normalized trace `2^-lambda`. Therefore + + ell(I)=0, ell(T_p)=2^-lambda-1 != 0. (11) + +Applying (10) to `diag(T_p)` gives a nonzero scalar multiple of I_n. +Equation (4) requires at least n queries. Fixed invertible scalar +input and output maps do not change this rank. No common negative +eigenvector is used, so this statement permits distinct plane labels +and arbitrary scalar mixing of their field roles. + +The same limit holds with feedback and with reuse of a previously +computed query. If each counted query is required to be a complete +native rank-two plane transfer, its native mass is at least 2n. +That last inference does not apply to arbitrary smaller native +operations or to rank-zero address maps. + +## Limits relevant to the supplier + +The full native compiler is larger than the gate grammar above. +It permits different payload maps on different fields. Factoring +different productive advances E_(s,p) out of a port-mixing R/K bridge +can make that bridge operator-valued. Such a bridge no longer acts +as B tensor I and cannot be treated as free in (1). + +There is a direct check against an incorrect native-cost inference. +At tensor depth one, (5) forms a line phase from the identity and one +rank-zero translation X_q, using scalar arithmetic. Therefore 112 +payload accesses need not mean 112 native Fourier calls. At larger +depth a direct translation expansion has exponentially many terms; +the present theorem does not price or admit that expansion. + +The result excludes neither changed source encodings nor rank-zero +address algorithms, partial native phase algorithms, productive dirty +carriers, or a changed recursive interface. It identifies the scalar +source and response support which those mechanisms must supply. +It makes no new supplier or kappa claim. + +## Checks and credit + +Run from the workspace root: + + python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/schur-selection/plane-repair/check_query_span.py + +Expected first line: + + PASS_EXACT_QUERY_SOURCE_SPANS + +The checker pins the actual R, actual phase labels and the frozen +plane construction. It checks the line diagonal minor, all repeated +plane-direction character sums, all 56 pair Grams and the exact +plane minor determinant. The all-depth result and the circuit +invariant follow from the displayed proofs. No broad search is used +as evidence for a lower bound. + +The interface-proof lane checked both factorization arguments and +the line tensor-compression argument independently before this note +was frozen. The exact emitted certificate still needs its own frozen +review. The source R comes from the circuit-interface reconstruction; +the plane matching comes from +[PR #1825](https://github.com/CrocSwap/integer-mult-bounds/pull/1825). +Substantial OpenAI Codex assistance was used under the user's direction. +No new publication is authorized. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/SOURCES.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/SOURCES.json new file mode 100644 index 0000000000..bfab222265 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/SOURCES.json @@ -0,0 +1,30 @@ +{ + "predecessor": { + "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/1825", + "head": "d16fb8936795ff101e4d2f63cfdc6a25066ebabf", + "repository": "1337isnot1337/integer-mult-bounds", + "certificate_path": "research/paired-plane-port-matching-seed6c563a/CERTIFICATE.json", + "certificate_sha256": "4fd648f7b5178bff5441bf364d58234b7bc1a43b924bc6da03013c948f1473b1", + "proof_sha256": "c79d7bb1d11dc4db4c3bb85f20ff3257b42fc711636adc7b3108761bde069a1b" + }, + "scalar_mask_audit": { + "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/1889", + "head": "5f05652c7dc7f51555ddb59b716000199a72c0ff", + "repository": "adamgall/integer-mult-bounds", + "proof_path": "research/paired-plane-scalar-mask-obstruction/README.md", + "proof_sha256": "355f6e6b61a858c75143f0ac2c2338af089e2e9390c8caa7ecd4ebc71dd4019c" + }, + "selected_source": { + "archive": "worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz", + "archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "member": "candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json", + "member_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "actual_interface": "../../circuit-interface/INTERFACE.json", + "actual_interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" + }, + "other_source_copies": { + "INHERITED-COMPLEX-GEOMETRY.txt": "c1ff55536594222a8d2a30bc0e0956959774e1be2d5420b7838ad553ee556df2", + "RANK8-RIGIDITY.md": "bccab452803cb0094685c298fe4fba5ceeddf9d6158a6af0b584712391db14c9" + }, + "scope": "Pinned finite scalar interface and exact local complex operators. No current selected-frontier claim or complete supplier admission." +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/check_query_span.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/check_query_span.py new file mode 100644 index 0000000000..f48611449b --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/check_query_span.py @@ -0,0 +1,88 @@ +"""Check exact scalar source spans for the actual line and plane queries.""" + +from hashlib import sha256 +from pathlib import Path +import json +import tarfile + + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[4] +INTERFACE_PIN = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" +PLANE_PIN = "f55bd0e7b81a15b6526ca3056ef3bf1bbf57b13137699e71a374f4cf8f55f794" +ARCHIVE_PIN = "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6" +PHASE_PIN = "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + + +def need(value, message): + if not value: + raise ValueError(message) + + +def dot(x,y): + return (x & y).bit_count() & 1 + + +def main(): + raw = (HERE.parents[1] / "circuit-interface/INTERFACE.json").read_bytes() + need(sha256(raw).hexdigest() == INTERFACE_PIN, "Actual eight centre rows") + interface = json.loads(raw) + rows = [[int(row.get(str(p),0)) for p in range(112)] for row in interface["R"]] + need(len(rows) == 8, "Eight required centre outputs") + need([[sum(rows[i][p]*rows[j][p] for p in range(112)) for j in range(8)] for i in range(8)] + == [[56*int(i == j) for j in range(8)] for i in range(8)], "Actual row Gram") + archive = ROOT / "worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz" + need(sha256(archive.read_bytes()).hexdigest() == ARCHIVE_PIN, "Selected source archive") + with tarfile.open(archive) as source: + phase = source.extractfile("candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json").read() + need(sha256(phase).hexdigest() == PHASE_PIN, "Actual line labels") + labels = [r["q"] for r in sorted(json.loads(phase)["recipes"],key=lambda r:r["port"])] + need(len(labels) == len(set(labels)) == 112 and all(labels), "Distinct nonzero actual line labels") + line_pivots = [] + for p,q in enumerate(labels): + i = next(i for i in range(8) if rows[i][p]) + line_pivots.append({"port":p,"q":q,"centre_row":i,"pivot":rows[i][p]}) + need(all(abs(x["pivot"]) == 1 for x in line_pivots), "Explicit nonzero diagonal stacked minor") + raw_plane = (HERE / "PLANE-INVOLUTION.json").read_bytes() + need(sha256(raw_plane).hexdigest() == PLANE_PIN, "Frozen actual plane operators") + planes = json.loads(raw_plane)["planes"] + plane_pivots = [] + character_checks = 0 + determinant = 1 + for k,plane in enumerate(planes): + q,r = plane["q"],plane["r"] + w = q ^ r + need(w != 0, "A nonzero plane swap direction") + for j,other in enumerate(planes): + if other["q"] ^ other["r"] == w: + numerator = sum((-1) ** dot(q ^ other["q"],y) for y in range(512) if dot(w,y)) + need(numerator == 256*int(k == j), "Exact plane-separating functional") + character_checks += 256 + p,s = plane["ports"] + need([labels[p],labels[s]] == [q,r], "Matching uses actual line labels") + gram = [[sum(rows[i][a]*rows[i][b] for i in range(8)) for b in (p,s)] for a in (p,s)] + need(gram[0][0]*gram[1][1]-gram[0][1]*gram[1][0] == 12, + "Each matched pair has two independent scalar input columns") + i,j,d = next((i,j,rows[i][p]*rows[j][s]-rows[i][s]*rows[j][p]) + for i in range(8) for j in range(i+1,8) + if rows[i][p]*rows[j][s]-rows[i][s]*rows[j][p]) + determinant *= d + plane_pivots.append({"plane":k,"ports":[p,s],"centre_rows":[i,j],"determinant":d}) + need(sum(not dot(w,y) for y in range(512)) == 256, "Plane trace in the Fourier basis") + need(determinant != 0, "Explicit nonsingular 112-column plane stacked minor") + result = {"status":"PASS_EXACT_QUERY_SOURCE_SPANS", "interface_sha256":INTERFACE_PIN, + "archive_sha256":ARCHIVE_PIN,"phase_sha256":PHASE_PIN,"plane_receipt_sha256":PLANE_PIN, + "output_fields":8,"input_fields":112,"line_scalar_input_rank":112, + "line_pivot_functionals":line_pivots,"plane_scalar_input_rank":112, + "plane_pivot_functionals":plane_pivots,"plane_minor_determinant_in_matching_order":determinant, + "plane_character_sum_checks":character_checks, + "plane_endpoint_functional":"normalized trace minus constant-character expectation", + "plane_endpoint_value_at_tensor_depth_lambda":"2^(-lambda)-1", + "scope":"Exact scalar input spans for plain-input operator matrices, plus proof-based all-depth extension. This is a payload-query count bound under scalar free gates, not a native-child or rank-zero-map lower bound for the full supplier."} + (HERE / "QUERY-SPAN.json").write_text(json.dumps(result,indent=2,sort_keys=True)+"\n") + print(result["status"]) + print(json.dumps({k:result[k] for k in ("line_scalar_input_rank","plane_scalar_input_rank","plane_minor_determinant_in_matching_order","plane_character_sum_checks")},sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/sources/PR1825-CERTIFICATE.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/sources/PR1825-CERTIFICATE.json new file mode 100644 index 0000000000..7ca668d7d5 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/sources/PR1825-CERTIFICATE.json @@ -0,0 +1,539 @@ +{ + "schema_version": 1, + "selected_archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "selected_payload_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "port_count": 112, + "label_space_dimension": 9, + "edge_rule": "i != j and parity(q_i dot q_j)=0", + "matching": [ + [ + 0, + 1 + ], + [ + 2, + 3 + ], + [ + 4, + 5 + ], + [ + 78, + 12 + ], + [ + 80, + 6 + ], + [ + 82, + 7 + ], + [ + 83, + 8 + ], + [ + 84, + 9 + ], + [ + 79, + 10 + ], + [ + 81, + 11 + ], + [ + 77, + 13 + ], + [ + 85, + 31 + ], + [ + 36, + 15 + ], + [ + 21, + 16 + ], + [ + 23, + 17 + ], + [ + 33, + 14 + ], + [ + 35, + 22 + ], + [ + 53, + 18 + ], + [ + 55, + 20 + ], + [ + 47, + 25 + ], + [ + 24, + 19 + ], + [ + 91, + 26 + ], + [ + 32, + 28 + ], + [ + 41, + 29 + ], + [ + 39, + 27 + ], + [ + 50, + 30 + ], + [ + 96, + 43 + ], + [ + 56, + 38 + ], + [ + 86, + 37 + ], + [ + 88, + 34 + ], + [ + 89, + 40 + ], + [ + 90, + 42 + ], + [ + 87, + 44 + ], + [ + 45, + 46 + ], + [ + 64, + 54 + ], + [ + 69, + 57 + ], + [ + 102, + 58 + ], + [ + 59, + 49 + ], + [ + 92, + 48 + ], + [ + 62, + 52 + ], + [ + 93, + 51 + ], + [ + 94, + 61 + ], + [ + 95, + 65 + ], + [ + 97, + 60 + ], + [ + 63, + 66 + ], + [ + 111, + 67 + ], + [ + 106, + 68 + ], + [ + 109, + 71 + ], + [ + 98, + 70 + ], + [ + 72, + 75 + ], + [ + 99, + 73 + ], + [ + 101, + 76 + ], + [ + 100, + 74 + ], + [ + 103, + 104 + ], + [ + 105, + 108 + ], + [ + 107, + 110 + ] + ], + "plane_translation_labels": [ + 24, + 96, + 384, + 467, + 483, + 427, + 347, + 187, + 371, + 219, + 437, + 483, + 411, + 272, + 272, + 3, + 243, + 437, + 485, + 258, + 144, + 235, + 12, + 68, + 132, + 18, + 249, + 486, + 231, + 215, + 159, + 63, + 497, + 160, + 12, + 264, + 175, + 12, + 423, + 12, + 399, + 435, + 243, + 483, + 160, + 207, + 95, + 399, + 311, + 48, + 311, + 183, + 215, + 96, + 48, + 160 + ], + "matching_degree": 52, + "plane_matrices_2bit_rows": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 8, + 0, + 0, + 0, + 8, + 6, + 14, + 1, + 0, + 0, + 0, + 0, + 0, + 6, + 8, + 0, + 0, + 0, + 0, + 0, + 8, + 0, + 1, + 8, + 14, + 6, + 8, + 1, + 9, + 9, + 0 + ], + "plane_matrix_rank_histogram": { + "0": 40, + "1": 9, + "2": 7 + }, + "active_query_terms": [ + { + "pair_index": 25, + "ports": [ + 50, + 30 + ], + "M_bits": 8, + "matrix_rank": 1, + "support_pairing_rank": 7 + }, + { + "pair_index": 29, + "ports": [ + 88, + 34 + ], + "M_bits": 8, + "matrix_rank": 1, + "support_pairing_rank": 7 + }, + { + "pair_index": 30, + "ports": [ + 89, + 40 + ], + "M_bits": 6, + "matrix_rank": 2, + "support_pairing_rank": 9 + }, + { + "pair_index": 31, + "ports": [ + 90, + 42 + ], + "M_bits": 14, + "matrix_rank": 2, + "support_pairing_rank": 9 + }, + { + "pair_index": 32, + "ports": [ + 87, + 44 + ], + "M_bits": 1, + "matrix_rank": 1, + "support_pairing_rank": 7 + }, + { + "pair_index": 38, + "ports": [ + 92, + 48 + ], + "M_bits": 6, + "matrix_rank": 2, + "support_pairing_rank": 9 + }, + { + "pair_index": 39, + "ports": [ + 62, + 52 + ], + "M_bits": 8, + "matrix_rank": 1, + "support_pairing_rank": 7 + }, + { + "pair_index": 45, + "ports": [ + 111, + 67 + ], + "M_bits": 8, + "matrix_rank": 1, + "support_pairing_rank": 7 + }, + { + "pair_index": 47, + "ports": [ + 109, + 71 + ], + "M_bits": 1, + "matrix_rank": 1, + "support_pairing_rank": 7 + }, + { + "pair_index": 48, + "ports": [ + 98, + 70 + ], + "M_bits": 8, + "matrix_rank": 1, + "support_pairing_rank": 7 + }, + { + "pair_index": 49, + "ports": [ + 72, + 75 + ], + "M_bits": 14, + "matrix_rank": 2, + "support_pairing_rank": 9 + }, + { + "pair_index": 50, + "ports": [ + 99, + 73 + ], + "M_bits": 6, + "matrix_rank": 2, + "support_pairing_rank": 9 + }, + { + "pair_index": 51, + "ports": [ + 101, + 76 + ], + "M_bits": 8, + "matrix_rank": 1, + "support_pairing_rank": 7 + }, + { + "pair_index": 52, + "ports": [ + 100, + 74 + ], + "M_bits": 1, + "matrix_rank": 1, + "support_pairing_rank": 7 + }, + { + "pair_index": 53, + "ports": [ + 103, + 104 + ], + "M_bits": 9, + "matrix_rank": 2, + "support_pairing_rank": 9 + }, + { + "pair_index": 54, + "ports": [ + 105, + 108 + ], + "M_bits": 9, + "matrix_rank": 2, + "support_pairing_rank": 9 + } + ], + "copy_charge": 126, + "copy_rank_histogram": { + "7": 9, + "9": 7 + }, + "exact_dirty_basis_states_checked": 28672, + "negative_controls_rejected": 4, + "ceiling_screen": { + "a_lo": "6894407/2000000000", + "a_hi": "3447203501/1000000000000", + "kappa_planning_cap_exact": "3447203501/1003447203501", + "kappa_planning_cap_decimal_12": "0.003435361112", + "model": { + "m": 73, + "families": 896, + "stages": 9, + "unpaid": 2, + "centre": 126, + "idle_rank_cap": 51 + } + } +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/sources/PR1825-PROOF.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/sources/PR1825-PROOF.md new file mode 100644 index 0000000000..952fe47dcc --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/schur-selection/plane-repair/sources/PR1825-PROOF.md @@ -0,0 +1,135 @@ +# Exact paired-plane decoder certificate + +## Result + +Let (q_0,\ldots,q_{111}\in\mathbb F_2^9) be the labels at the selected PR1094 +complex ports. Their convention is (UU^T=(J+G)\bmod2), so the selected +pairing matrix is (B_0=UU^T), with (B_0[t,u]=q_t\cdot q_u). Each label has +weight 3 or 7, and distinct labels are joined when (q_i\cdot q_j=0), which +is precisely the odd-Gram edge condition. + +The complete graph is 52-regular. A deterministic minimum-remaining-degree +backtracking rule, breaking ties by port index and then neighbor index, returns +the 56 pairs stored in [CERTIFICATE.json](CERTIFICATE.json). Each pair + +\[ + k=(i,j),\qquad A_k=[q_i\ q_j]\in\mathbb F_2^{9\times2} +\] + +defines one shared plane (E_k=\operatorname{span}(q_i,q_j)) assigned to both +ports. The pair labels are independent and orthogonal, so they form an +orthonormal basis for that plane under the inherited binary form. + +## Global factorization + +For the 56 planes, solve the exact binary linear system + +\[ + \sum_{k=1}^{56} A_k M_k A_k^T=I_9, + \qquad M_k\in\mathbb F_2^{2\times2}. +\] + +The verifier uses highest-index pivots and sets free variables to zero. The +certificate has 40 zero matrices, nine rank-one matrices, and seven rank-two +matrices. For each rank-one matrix choose (M_k=x_ky_k^T). For each +rank-two matrix choose (X_k=I_2,\ Y_k=M_k^T), so in either case +\(M_k=X_kY_k^T\). Concatenating the port columns gives + +\[ + D=U[A_1X_1\;\cdots\;A_{56}X_{56}],\qquad + T=U[A_1Y_1\;\cdots\;A_{56}Y_{56}], +\] + +where zero matrices contribute no columns. Therefore +\(DT^T=U I_9 U^T=B_0\) on all 112 by 112 entries. The verifier separately +checks the 9 by 9 identity and the full port matrix. + +## Copy-rank invoice + +For a scalar outer-product term with supports (R,C\subseteq[112]), the +inherited B14 copy charge is +\(\rho(R,C)=\operatorname{rank}_{\mathbb F_2}B_0[R,C]\). A rank-one plane +matrix contributes its factor supports. A rank-two plane matrix contributes +the union supports of its two columns; since its change of basis is invertible, +both sides have the support of the same plane. Recomputing the restricted +pairing ranks gives: + +| Query type | Count | Pairing rank each | Copy charge | +|---|---:|---:|---:| +| Rank-one plane query | 9 | 7 | 63 | +| Rank-two plane query | 7 | 9 | 63 | +| Total active plane queries | 16 | | **126** | + +This exact copy charge uses the separate-term support-pairing convention from +PR717/PR968. The comparison budget (C\le160) in open PR1808 is a planning +threshold for its stated complex-side screen; the 34-unit difference is not a +certificate that all supplier overhead fits in that screen. + +## Exact dirty-state endpoint + +The inherited operators are + +\[ + C_q=((1+i)I+(1-i)X_q)/2,\qquad C_q^2=X_q. +\] + +For a matched plane (E=\operatorname{span}(q_i,q_j)), put +\(C_E=C_{q_i}C_{q_j}\). The two commuting translations give +\(C_E^2=X_{q_i+q_j}\). `verify.py` applies the four exact Gaussian-dyadic +operators to every one of the 512 computational basis states for each of the +56 planes. It checks the complete state vector with integer Gaussian +numerators and denominator 16. Since these basis states span the local address +space, the checked equality holds for every dirty superposition on that +space, and tensoring identity on spectator registers preserves it. + +The 56 matched planes therefore determine 56 endpoint translation labels +\(q_i+q_j\). Their exact operator identities are checked here, while their +application multiplicity across hosted families is not priced. + +This checks the endpoint operator identity. It does not construct the full +selected route that hosts the plane operations, schedules frame changes, +restores every other live register, or charges their precision and interface +costs. + +## Changed-law screen and scope + +The selected local profile is +\(\{1:2412,2:418,3:432,4:142,5:82,8:8\}\). Replacing the eight rank-8 +centre children by the 16 active paired-plane queries gives +\(\{1:2412,2:418,3:432,4:142,5:82,7:9,9:7\}\), with local mass 5,648. +Under the hypothetical two-unpaid-coordinate law, (m=73), (W=896/9), +nine stages, and centre charge 126, the total per-call mass is +\(71(896/9)+126=64750/9\), leaving (13918/9) idle mass. The pinned exact +ceiling routine, with fractional idle mass assigned optimistically at rank 51, +certifies + +\[ + a_{hi}=3447203501/10^{12}=0.003447203501, + \qquad a_{hi}/(1+a_{hi})=3447203501/1003447203501 + \approx0.003435361112. +\] + +This is only a favorable complex-side relaxation for the proposed profile. It +does not prove that the changed coverage law is realized by a supplier, that +the 34 remaining copy-rank units cover all other expenses, or that the bit-side +supplier and joint assembly improve. No new \(\kappa\), selected record, or +integrated bound is claimed. + +## Controls and reproduction + +The verifier rejects a non-edge partner, omission of an active decoder term, +mutation of a plane matrix, and omission of the endpoint correction. It reads +the 112 labels from the exact selected archive entry pinned in `SOURCES.json`; +no predecessor code, solver, or network access is used. + +From the repository root: + +```sh +python3 -B research/paired-plane-port-matching-seed6c563a/verify.py +python3 scripts/research_package.py --package research/paired-plane-port-matching-seed6c563a --check-only +python3.12 scripts/research_package.py --package research/paired-plane-port-matching-seed6c563a +``` + +Expected verifier output begins `PASS_PAIRED_PLANE_PORT_MATCHING` and reports +56 pairs, 16 active queries, copy charge 126, and 28,672 exact endpoint basis +checks. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/source-domain/query-span-review/REVIEW.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/source-domain/query-span-review/REVIEW.json new file mode 100644 index 0000000000..7dc0853730 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/source-domain/query-span-review/REVIEW.json @@ -0,0 +1,138 @@ +{ + "all_depth": "Proof: compress all but one tensor factor to the fixed constant character.", + "archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "controls": [ + "Exact reversed-orientation moved-character sign differs." + ], + "distinct_plane_directions": 41, + "exact_Fourier_columns": 28672, + "exact_block_minor_determinant": 8, + "frozen_packet_sha256": { + "PLANE-INVOLUTION.json": "f55bd0e7b81a15b6526ca3056ef3bf1bbf57b13137699e71a374f4cf8f55f794", + "QUERY-SPAN.json": "a06939cba2c937f452027ee4a1f20b31121a70b7fc7393d9ccad091817ee448e", + "QUERY-SPAN.md": "785e27fdc6f2bcd83318afee14103f3e021065d32be2265b8afdec3fea3e1081", + "check_query_span.py": "bcc8bb5482c76578014512d51dd5d650d4bf13d6546b29e355ae01bec8a07811" + }, + "grammar": "Every non-scalar payload map is counted, including rank-zero address maps; scalar initial and final contracts are required.", + "line_source_rank": 112, + "nonzero_line_columns": 112, + "not_certified": [ + "Native-child lower bound", + "Native-cost bound", + "Changed source interface", + "Supplier or kappa improvement" + ], + "pair_Gram_determinants": [ + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12 + ], + "plane_source_rank": 112, + "planes": 56, + "repeated_direction_group_sizes": [ + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 2, + 2, + 2, + 2, + 2, + 2, + 2, + 2, + 3, + 3, + 4 + ], + "separating_functional_column_checks": 802816, + "source_member_sha256": { + "phases": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "program": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a", + "word": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219" + }, + "source_reconstruction": "Independent data-only scalar propagation to the original centre boundary; no producer import or execution.", + "source_rows": 8, + "source_scalar_events_replayed": 10851, + "status": "PASS_INDEPENDENT_QUERY_SPAN_SOURCE_AND_CERTIFICATE" +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/source-domain/query-span-review/REVIEW.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/source-domain/query-span-review/REVIEW.md new file mode 100644 index 0000000000..6d1570364c --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/source-domain/query-span-review/REVIEW.md @@ -0,0 +1,81 @@ +# Independent review of the query-span certificate + +The frozen source theorem and its exact certificate pass this review. +No material finding remains. The accepted conclusion is a payload-query +count in the stated scalar gate grammar. It is not a lower bound on +native children or native rank in the supplier. + +The reviewed proof has SHA-256 +`785e27fdc6f2bcd83318afee14103f3e021065d32be2265b8afdec3fea3e1081`. +The reviewed producer and receipt have SHA-256 +`bcc8bb5482c76578014512d51dd5d650d4bf13d6546b29e355ae01bec8a07811` +and `a06939cba2c937f452027ee4a1f20b31121a70b7fc7393d9ccad091817ee448e`. +Those files were not changed or executed by this review. + +## Independent source and finite checks + +The review checker reads the pinned original selected archive. It +propagates the 112 data columns through 10,851 original scalar events +up to the centre boundary. It reconstructs all eight R rows and compares +them with the interface receipt. This check does not import the +producer or the interface reconstruction code. + +The reconstructed matrix has `R R^T=56I`. Each of its 112 columns has +four nonzero entries. The original canonical word and original complex +phase ledger give the same 112 distinct odd labels. Every displayed +line pivot is an actual entry equal to 1 or -1. The line functionals +therefore give the stated diagonal minor of rank 112. + +For each of the 56 matched planes, the checker builds all 512 Fourier +columns directly from `C_q C_r^-1 P_(q+r)`. It verifies the involution, +the fixed constant character, and trace 256. It then applies every one +of the 56 functionals to every plane column on its full 256-character +support. All 802,816 contributions are checked. The full functional +matrix is the identity, including the repeated directions. There are +41 directions, and the 56 pairs partition all 112 actual ports. + +All 56 two-column Gram determinants are 12. The certificate's selected +two-row minors are nonzero, and their product in matching order is +exactly 8. This proves the second source rank is also 112. Reversing +one plane orientation changes the exact moved-character sign; the +checker verifies this control. + +## Proof checks and scope + +Both factorization inductions are valid for singular scalar gates, +private CLEAR, and arbitrary query order. For the source factorization, +`L M = A + (L W) Z + u Q v A` adds the scalar row `v A`. For the response +factorization, it adds the scalar column `u`. These equations do not +move one payload operator past another. Applying a functional that +kills the identity proves the simultaneous row and column span bounds. +Arbitrary borrowed inputs can be included as separate initial scalar +columns. Restricting those inputs is a scalar input map and does not +invalidate the bound. + +The tensor compression also holds. Every line phase and every matched +plane fixes the constant character. Compressing all but one tensor +factor to that character retains each single-factor operator. The +same exact minors therefore work at every positive tensor depth. +For the endpoint theorem, normalized trace minus the constant-character +expectation gives `2^(-lambda)-1` on every plane and zero on the identity. +It does not require a common negative eigenspace. + +The two main scope objections are resolved by explicit hypotheses in +the proof. First, a rank-zero address permutation is a counted payload +query here; it is not a free scalar role map. At depth one, a line phase +is a scalar combination of the identity and a rank-zero translation. +Thus a query lower bound is not a native-child lower bound. Second, a +port-dependent phase already present in a productive input is a changed +input contract. It can supply the 112 source directions before this +grammar starts. The theorem does not charge that encoding a second +time. The accepted result excludes neither mechanism. + +Reproduction: + + python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/source-domain/query-span-review/review_query_span.py + +The run passed with status `PASS_INDEPENDENT_QUERY_SPAN_SOURCE_AND_CERTIFICATE`. +The checker, receipt, and this note are new review artifacts. They do +not certify a native implementation, a complete supplier, or a kappa +improvement. The work used OpenAI Codex assistance under the user's +direction. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/source-domain/query-span-review/review_query_span.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/source-domain/query-span-review/review_query_span.py new file mode 100644 index 0000000000..2a9d3ace60 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/lanes/source-domain/query-span-review/review_query_span.py @@ -0,0 +1,187 @@ +"""Check the source rows and the exact line and plane query certificates.""" + +from collections import Counter +from fractions import Fraction +from hashlib import sha256 +import gzip +import json +from pathlib import Path +import tarfile + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +ROOT = LANES.parents[2] +PACKET = LANES / "schur-selection/plane-repair" +PINS = { + "QUERY-SPAN.md": "785e27fdc6f2bcd83318afee14103f3e021065d32be2265b8afdec3fea3e1081", + "check_query_span.py": "bcc8bb5482c76578014512d51dd5d650d4bf13d6546b29e355ae01bec8a07811", + "QUERY-SPAN.json": "a06939cba2c937f452027ee4a1f20b31121a70b7fc7393d9ccad091817ee448e", + "PLANE-INVOLUTION.json": "f55bd0e7b81a15b6526ca3056ef3bf1bbf57b13137699e71a374f4cf8f55f794", +} +ARCHIVE = "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6" +MEMBERS = { + "word": ("candidate/strict/global/base/providers/gauge44/CANONICAL-WORD.json.gz", + "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219"), + "program": ("candidate/strict/global/base/providers/gauge44/LOCAL-PROGRAMS.json.gz", + "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a"), + "phases": ("candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json", + "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"), +} + + +def need(value, reason): + if not value: + raise ValueError(reason) + + +def dot(a, b): + return (a & b).bit_count() % 2 + + +def add(target, source, coefficient): + for key, value in source.items(): + new = target.get(key, 0) + coefficient * value + if new: + target[key] = new + else: + target.pop(key, None) + + +def main(): + for name, pin in PINS.items(): + need(sha256((PACKET / name).read_bytes()).hexdigest() == pin, "Frozen packet: " + name) + certificate = json.loads((PACKET / "QUERY-SPAN.json").read_bytes()) + planes = json.loads((PACKET / "PLANE-INVOLUTION.json").read_bytes())["planes"] + path = ROOT / "worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz" + need(sha256(path.read_bytes()).hexdigest() == ARCHIVE, "Selected source archive") + source = {} + with tarfile.open(path) as archive: + for key, (name, pin) in MEMBERS.items(): + raw = archive.extractfile(name).read() + need(sha256(raw).hexdigest() == pin, "Selected member: " + key) + source[key] = json.loads(gzip.decompress(raw) if name.endswith(".gz") else raw) + word, program, phases = [source[key] for key in MEMBERS] + rows = [{i: Fraction(1)} if i < 112 else {} for i in range(712)] + count = 0 + for event in program["forward"]: + if event == ["phase", "centers"]: + break + if event[0] != "scalar": + continue + gate = event[1] + t = gate[1][1] + (704 if gate[1][0] == "C" else 0) + if gate[0] == "clear": + rows[t] = {} + elif gate[0] == "scale": + coefficient = Fraction(gate[2], gate[3]) + rows[t] = {i: value * coefficient for i, value in rows[t].items() if value * coefficient} + else: + s = gate[2][1] + (704 if gate[2][0] == "C" else 0) + if gate[0] == "copy": + rows[t] = rows[s].copy() + else: + add(rows[t], rows[s], Fraction(gate[3], gate[4])) + count += 1 + else: + raise ValueError("The original centre boundary is absent") + matrix = [[rows[centre].get(p, 0) for p in range(112)] for centre in word["centers"]] + interface_raw = (LANES / "circuit-interface/INTERFACE.json").read_bytes() + need(sha256(interface_raw).hexdigest() == certificate["interface_sha256"], "Accepted interface pin") + interface = json.loads(interface_raw) + expected = [[Fraction(row.get(str(p), "0")) for p in range(112)] for row in interface["R"]] + need(matrix == expected and len(matrix) == 8, "Independent source reconstruction of R") + gram = [[sum(a * b for a, b in zip(row, other)) for other in matrix] for row in matrix] + need(gram == [[56 * int(i == j) for j in range(8)] for i in range(8)], "Actual row Gram") + labels = [record["q"] for record in phases["recipes"]] + need(labels == word["ports"] == interface["ports"] and len(set(labels)) == 112 + and all(q and q.bit_count() % 2 for q in labels), "Exact distinct odd line labels") + need(all(sum(matrix[i][p] != 0 for i in range(8)) == 4 for p in range(112)), + "Four nonzero source entries in every column") + for p, row in enumerate(certificate["line_pivot_functionals"]): + need(row["port"] == p and row["q"] == labels[p] + and matrix[row["centre_row"]][p] == row["pivot"] + and abs(row["pivot"]) == 1, "Every line diagonal pivot") + need(len(planes) == 56 and sorted(p for plane in planes for p in plane["ports"]) == list(range(112)), + "The 56 planes partition the actual ports") + directions = Counter(plane["q"] ^ plane["r"] for plane in planes) + need(len(directions) == 41, "Repeated plane directions are retained") + # Build each exact Fourier column from C_q C_r^-1 P_(q+r). + columns = [] + trace_counts = [] + for plane in planes: + p, s = plane["ports"] + q, r = plane["q"], plane["r"] + need([q, r] == [labels[p], labels[s]] and dot(q, r) == 0, "Actual ordered orthogonal pair") + w = q ^ r + operator = [] + for y in range(512): + image = y ^ (w if dot(w, y) else 0) + power = (dot(q, image) - dot(r, image)) % 4 + operator.append((image, power)) + need(all(operator[image][0] == y and (power + operator[image][1]) % 4 == 0 + for y, (image, power) in enumerate(operator)), "Exact plane involution") + need(operator[0] == (0, 0), "Constant character is fixed") + trace = sum(1 for y, (image, power) in enumerate(operator) if image == y and power == 0) + need(trace == 256 and all(power == 0 for y, (image, power) in enumerate(operator) if image == y), + "Exact normalized plane trace") + trace_counts.append(trace) + columns.append(operator) + unit = [(1, 0), (0, 1), (-1, 0), (0, -1)] + functional_checks = 0 + for k, plane in enumerate(planes): + q, w = plane["q"], plane["q"] ^ plane["r"] + support = [y for y in range(512) if dot(w, y)] + for j, operator in enumerate(columns): + real = imag = 0 + for y in support: + image, power = operator[y] + if image == y ^ w: + a, b = unit[(power - 1 + 2 * dot(q, y)) % 4] + real += a + imag += b + functional_checks += 1 + need((real, imag) == (256 * int(j == k), 0), "Full plane-separating functional matrix") + determinant = 1 + for k, (plane, pivot) in enumerate(zip(planes, certificate["plane_pivot_functionals"])): + p, s = plane["ports"] + a, b = [matrix[i][p] for i in range(8)], [matrix[i][s] for i in range(8)] + det_gram = sum(x*x for x in a) * sum(y*y for y in b) - sum(x*y for x, y in zip(a, b))**2 + need(det_gram == 12 and pivot["plane"] == k and pivot["ports"] == [p, s], "Actual pair Gram and order") + i, j = pivot["centre_rows"] + det = a[i] * b[j] - b[i] * a[j] + need(det == pivot["determinant"] and det != 0, "Exact certified two-column pivot") + determinant *= det + need(determinant == certificate["plane_minor_determinant_in_matching_order"] == 8, + "Exact 112-column block determinant") + need(certificate["line_scalar_input_rank"] == certificate["plane_scalar_input_rank"] == 112, + "Stated source ranks") + # A reversed plane orientation changes the moved-character sign. + q, r = planes[0]["q"], planes[0]["r"] + w = q ^ r + y = next(y for y in range(512) if dot(w, y)) + image = y ^ w + need((dot(q, image) - dot(r, image)) % 4 != (dot(r, image) - dot(q, image)) % 4, + "Wrong plane orientation control") + result = dict(status="PASS_INDEPENDENT_QUERY_SPAN_SOURCE_AND_CERTIFICATE", + frozen_packet_sha256=PINS, archive_sha256=ARCHIVE, + source_member_sha256={k: pin for k, (_, pin) in MEMBERS.items()}, + source_scalar_events_replayed=count, source_rows=8, nonzero_line_columns=112, + line_source_rank=112, plane_source_rank=112, + planes=56, distinct_plane_directions=len(directions), + repeated_direction_group_sizes=sorted(directions.values()), + exact_Fourier_columns=56*512, separating_functional_column_checks=functional_checks, + pair_Gram_determinants=[12]*56, exact_block_minor_determinant=int(determinant), + source_reconstruction="Independent data-only scalar propagation to the original centre boundary; no producer import or execution.", + all_depth="Proof: compress all but one tensor factor to the fixed constant character.", + grammar="Every non-scalar payload map is counted, including rank-zero address maps; scalar initial and final contracts are required.", + controls=["Exact reversed-orientation moved-character sign differs."], + not_certified=["Native-child lower bound", "Native-cost bound", "Changed source interface", "Supplier or kappa improvement"]) + (HERE / "REVIEW.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n", encoding="utf-8") + print(result["status"]) + print(json.dumps({key: result[key] for key in ("source_scalar_events_replayed", "exact_Fourier_columns", + "separating_functional_column_checks", "exact_block_minor_determinant")})) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/CENTRE-SUPPORT-GEOMETRY-20261018.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/CENTRE-SUPPORT-GEOMETRY-20261018.json new file mode 100644 index 0000000000..b2c06708c8 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/CENTRE-SUPPORT-GEOMETRY-20261018.json @@ -0,0 +1,394 @@ +{ + "annihilators": [ + [ + 7, + 42, + 45 + ], + [ + 25, + 45, + 52 + ], + [ + 45, + 82, + 127 + ], + [ + 45, + 76, + 97 + ], + [ + 45, + 76, + 97 + ], + [ + 7, + 42, + 45 + ], + [ + 25, + 45, + 52 + ], + [ + 45, + 82, + 127 + ] + ], + "binary_support_ranks": [ + 7, + 7, + 7, + 7, + 7, + 7, + 7, + 7 + ], + "common_hyperplane_normal": 45, + "common_intersection_rank": 5, + "conditional_eight_query_rank_lower_bound": 62, + "equal_subspace_classes": [ + [ + 0, + 5 + ], + [ + 1, + 6 + ], + [ + 2, + 7 + ], + [ + 3, + 4 + ] + ], + "incidence_edges": [ + [ + 0, + 1 + ], + [ + 0, + 2 + ], + [ + 0, + 3 + ], + [ + 0, + 4 + ], + [ + 0, + 6 + ], + [ + 0, + 7 + ], + [ + 1, + 2 + ], + [ + 1, + 3 + ], + [ + 1, + 4 + ], + [ + 1, + 5 + ], + [ + 1, + 7 + ], + [ + 2, + 3 + ], + [ + 2, + 4 + ], + [ + 2, + 5 + ], + [ + 2, + 6 + ], + [ + 3, + 5 + ], + [ + 3, + 6 + ], + [ + 3, + 7 + ], + [ + 4, + 5 + ], + [ + 4, + 6 + ], + [ + 4, + 7 + ], + [ + 5, + 6 + ], + [ + 5, + 7 + ], + [ + 6, + 7 + ] + ], + "intersection_ranks": [ + [ + 7, + 6, + 6, + 6, + 6, + 7, + 6, + 6 + ], + [ + 6, + 7, + 6, + 6, + 6, + 6, + 7, + 6 + ], + [ + 6, + 6, + 7, + 6, + 6, + 6, + 6, + 7 + ], + [ + 6, + 6, + 6, + 7, + 7, + 6, + 6, + 6 + ], + [ + 6, + 6, + 6, + 7, + 7, + 6, + 6, + 6 + ], + [ + 7, + 6, + 6, + 6, + 6, + 7, + 6, + 6 + ], + [ + 6, + 7, + 6, + 6, + 6, + 6, + 7, + 6 + ], + [ + 6, + 6, + 7, + 6, + 6, + 6, + 6, + 7 + ] + ], + "maximum_independent_set_size": 2, + "maximum_independent_sets": [ + [ + 3, + 4 + ], + [ + 0, + 5 + ], + [ + 1, + 6 + ], + [ + 2, + 7 + ] + ], + "query_supports": [ + [ + 0, + 2, + 25, + 27, + 70, + 71, + 72, + 76, + 87, + 89, + 90, + 91 + ], + [ + 0, + 13, + 14, + 15, + 27, + 51, + 52, + 53, + 78, + 81, + 92, + 99 + ], + [ + 11, + 15, + 21, + 36, + 41, + 47, + 53, + 63, + 70, + 91, + 106, + 111 + ], + [ + 9, + 13, + 36, + 37, + 43, + 51, + 61, + 72, + 89, + 104, + 110, + 111 + ], + [ + 2, + 16, + 20, + 21, + 25, + 44, + 46, + 47, + 78, + 79, + 94, + 99 + ], + [ + 7, + 9, + 10, + 11, + 57, + 61, + 62, + 63, + 79, + 81, + 92, + 94 + ], + [ + 7, + 16, + 41, + 42, + 43, + 44, + 57, + 76, + 87, + 104, + 105, + 106 + ], + [ + 10, + 14, + 20, + 37, + 42, + 46, + 52, + 62, + 71, + 90, + 105, + 110 + ] + ], + "scope": "Exact source geometry. The rank-62 statement assumes one scalar capture per stated query and one monotone subspace path per unwarped source value, with no extra carrier. No new native word or general query lower bound is claimed.", + "source_decompressed_sha256": { + "centres": "2b9de1454c2025ae4e230bd64de36b4f6c937628c63fc5afede6640dd3c0e1e1", + "directions": "b08cb4146f1aec241e027cd62c942f6eca4ddab3e97f000a9c0017575d36deb5" + }, + "status": "PASS_CENTRE_SUPPORT_GEOMETRY" +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/CENTRE-SUPPORT-GEOMETRY-20261018.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/CENTRE-SUPPORT-GEOMETRY-20261018.md new file mode 100644 index 0000000000..a282ac04ec --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/CENTRE-SUPPORT-GEOMETRY-20261018.md @@ -0,0 +1,94 @@ +# Source geometry of the eight structured centre queries + +All eight structured centre rows have source directions of binary rank +seven. The missing six rank-seven captures in the retained source word +are not forced to have rank eight by their source support alone. +There are only four distinct rank-seven support spaces. Each contains +the supports of two centre rows. + +This note uses the actual port directions from the fresh native packet +and the actual centre rows from the structured response packet. The +checker pins both decompressed payloads. It does not change either input. + +Let `q_p` be the source direction of port `p`. For centre row `K_j`, put + +```text +U_j = span_F2 {q_p : K_jp != 0}. +``` + +Each row has twelve nonzero coefficients. Direct binary elimination gives +the following complete lists of nonzero vectors in the annihilators. +The integers encode binary vectors in the pinned nine-axis chart. + +| Centre rows | Nonzero annihilator vectors | Support rank | +| --- | --- | ---: | +| 0, 5 | 7, 42, 45 | 7 | +| 1, 6 | 25, 45, 52 | 7 | +| 2, 7 | 45, 82, 127 | 7 | +| 3, 4 | 45, 76, 97 | 7 | + +Different spaces in this table intersect in rank six. Their sum is the +common rank-eight hyperplane `45^perp`. The intersection of all four +spaces has rank five. + +Each of the 48 physical ports occurs in exactly two centre rows. The +incidence graph on the eight rows is the complete four-partite graph +with parts `{0,5}`, `{1,6}`, `{2,7}`, and `{3,4}`. Each graph edge has +two physical ports. Thus two centres have a common source port exactly +when their support spaces are different. + +## A limit for a specific direct capture schedule + +Assume all of the following for a proposed source schedule: + +1. Each original source value has one carrier. Its frame subspaces form + an increasing chain. +2. A direct capture of `K_j x` reads the unwarped source values with their + stated scalar coefficients in a common subspace that contains `U_j`. +3. There is one such capture per centre row. No stored partial query, + additional carrier, or operator-valued source code supplies a term. + +A rank-seven capture of row `j` must then use `U_j` itself. If rows `i` +and `j` share a port, that port's increasing chain would have to contain +both `U_i` and `U_j`. They are distinct rank-seven spaces and neither +contains the other. This is impossible in an increasing chain. + +The rank-seven captured rows must therefore form an independent set in +the incidence graph. The largest such set has size two. Its four +possible values are precisely the pairs in the table. All eight query +supports have rank seven, so under the stated assumptions the sum of +the eight capture ranks is at least + +```text +2*7 + 6*8 = 62. +``` + +This is a conditional lower bound, not a construction at rank 62. In +particular, this note does not emit the six rank-eight captures or prove +their scalar cost. The retained source word's two known rank-seven +captures use rows 0 and 5, which attain the largest possible set in this +restricted model. + +A changed source code, another carrier, partial queries, or a path that +does not increase monotonically is outside the proof. A native monomial +frame change can change logical source values. It must not be counted +as an unwarped step under assumption 1 without a separate proof. + +## Exact check + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/root/check_centre_support_geometry_20261018.py +``` + +Expected output is `PASS_CENTRE_SUPPORT_GEOMETRY`. The checker computes +all annihilators by exhaustive enumeration of the 511 nonzero binary +vectors. It checks the 48 source incidences and all 256 vertex subsets. +All operations are exact. The native and physical phase claims remain +in their separate packets. Independent review of this conditional +schedule consequence is recorded separately. + +This AI-assisted work uses the structured centre rows from the +controller-followthrough lane and the actual port chart from the +history-encoding lane. It makes no supplier or kappa claim. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/DYADIC-QUERY-SEPARATION-20261018.json b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/DYADIC-QUERY-SEPARATION-20261018.json new file mode 100644 index 0000000000..7752f31b41 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/DYADIC-QUERY-SEPARATION-20261018.json @@ -0,0 +1,33 @@ +{ + "status": "PASS_DYADIC_QUERY_SEPARATION", + "core_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "proof_sha256": "664f430efd099f35cbc7c2abc8025968c03020707027857d2882daa51a065a1a", + "checker_sha256": "b4ed000b5b600944f614b86ae7a88ac55af8eac3213e6827ed211a2630ccd342", + "selected": [ + 0, + 7, + 20, + 27, + 36, + 46, + 57, + 111 + ], + "ordinary_minor": [ + 21, + 37, + 47, + 76, + 81, + 87, + 92, + 110 + ], + "BD": "13I", + "prime": 13, + "B_rank": 8, + "dyadic_section_stack_rank": 16, + "kernel_perturbed_sections": 64, + "matched_section_stack_rank": 8, + "scope": "Source information rank and exact representation choice; no native child bound or supplier claim." +} diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/DYADIC-QUERY-SEPARATION-20261018.md b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/DYADIC-QUERY-SEPARATION-20261018.md new file mode 100644 index 0000000000..c5e5ae0490 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/DYADIC-QUERY-SEPARATION-20261018.md @@ -0,0 +1,116 @@ +# A dyadic unit log needs two independent centre queries + +The input-log construction has a representation choice with a precise +cost in information. Every dyadic log that makes its mixed source block +a unit needs sixteen independent query fields in the stated terminal +observation class. An exact division by 13 permits a log with eight. +This theorem concerns information rank. It is not a native-child bound. + +## Unit separation over a residue field + +Let B have r rows and n columns, and let D have n rows and r columns. +Let their coefficients lie in a commutative ring R with a homomorphism +to a field k. Assume the following conditions: + +1. BD=cI, and c maps to zero in k. +2. B has row rank r over k. +3. M has r rows and n columns, and MD is a unit over R. + +Then the stack [B;M] has row rank 2r over k. To prove this, suppose +that alpha B+beta M=0 over k. Multiply on the right by D. This gives +beta(MD)=0, so beta=0. Full row rank of B then gives alpha=0. +The proof also shows that n must be at least 2r. + +If R is an integral domain and the map to k is a residue map, a nonzero +2r-minor over k is nonzero over the fraction field of R. Thus the stack +also has rank 2r over that fraction field. This conclusion applies to +every M with the stated unit condition, not only to a sparse minor log. + +## The actual eight-centre construction + +Use R=Z[1/2], k=F_13, r=8, and n=104. The pinned current core has + + BD=13I. + +Its ordinary minor T=[21,37,47,76,81,87,92,110] has D_T orthogonal +over the dyadic ring. Since B=D^T in the canonical chart, B_T is a +dyadic unit too. It follows that B has rank eight modulo 13. + +For every dyadic M with a dyadic inverse for MD, the theorem therefore +gives + + rank [B;M]=16. (1) + +The hypothesis is exactly the mixed-source unit criterion in +`../lanes/oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md`. +That criterion was independently reviewed. It holds in a more general +operator ring; the present residue argument makes a distinct statement +about the dyadic representation. + +The same result applies to a finite routed array with ell scalar +coordinates in each field. Use the Gaussian dyadic ring and reduce +modulo 13 with i mapped to 5. The current routing maps and their +inverses have Gaussian dyadic coefficients. The ordered identities +BD=13I and the inverse-minor identities therefore survive reduction. +If MD has an inverse in that same ring, the stack has rank 16ell. +This argument does not commute Q through B, D, M, or a route. It uses +the complete finite operator matrices and their proved inverses. + +## Consequence for the controller + +The source-access theorem in +`../lanes/controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md` +uses a full-null family. All completed X fields and retired selected +Y fields are zero on that family. The retired ordinary Y field is an +arbitrary v. Its required original outputs include -Mv and DBv. +The full-null substitution is x_U=(I-DB)v, y_U=DBv, Qa=-Mv, +and original b=-QBv+qMv. Its proof does not use MD=I, so it applies +to every M in the present theorem. If the terminal's only further +observation is Nv, it must satisfy + + ker N is contained in ker B intersect ker M. (2) + +Over the underlying field, (2) implies that the row space of [B;M] +is contained in the row space of N. Equation (1) proves that a dyadic +unit log requires at least sixteen complete query fields in this +observation model. The result permits arbitrary postprocessing of N. +It does not restrict a different controller, more observations, a +different output partition, or operations that read ordinary Y directly. + +An exact odd grid changes this limit. Set M=B/13. Then MD=I, while +[B;M] has rank eight. Thus it gives a unit mixed source code and meets +the necessary query-rank lower bound eight for this family. In contrast, +no dyadic unit log can meet that bound. The odd-grid theorem supplies +the arithmetic representation for this choice, under its exact-child, +arbitrary-borrowed-input, and outer-endpoint hypotheses. + +This is a useful enabling result for the matched-log attempt. It cuts +the independent query content from sixteen fields to eight. It does +not make the remaining old-stage B query cheap. Its physical source +access, target scatter, output phases, and recursive cost remain open. + +## Checks and attribution + +Run from the workspace root: + + python3 -I -B work/centre-encoding-campaign-20261014/root/check_dyadic_query_separation_20261018.py + +Expected status: `PASS_DYADIC_QUERY_SEPARATION`. +The checker pins the actual core, verifies both inverse-minor orders, +BD=13I, and the rank-sixteen dyadic example modulo 13. It verifies the +matched log with exact fractions. It also checks 64 dyadic +unit logs obtained by changes in the kernel of D. These finite checks +support the stated application; the argument above proves the universal +claim. Independent proof review is still required. + +The oblique-native lane supplied the input-log unit construction. The +controller-followthrough lane supplied (2) and the rank-sixteen sparse +example. The native-escape lane proposed the matched log. The prior +interface-proof work and the current odd-grid review supplied the exact +division contract. The coordinating lane supplied the residue-field +argument for every dyadic unit log. This work used OpenAI Codex under +the user's direction. No independent human review is claimed. + +No PR, push, or publication commit is authorized. Before any future PR +description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/check_centre_support_geometry_20261018.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/check_centre_support_geometry_20261018.py new file mode 100644 index 0000000000..469eb425db --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/check_centre_support_geometry_20261018.py @@ -0,0 +1,133 @@ +#!/usr/bin/env python3 +"""Check the binary source geometry of the eight structured queries.""" + +from fractions import Fraction +from hashlib import sha256 +from itertools import combinations +import gzip +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent / "lanes" +SOURCES = { + "directions": ( + "history-encoding/independent-skeleton-20261018/fresh-three-child/" + "FRESH-THREE-CHILD-PROGRAMS.json.gz", + "b08cb4146f1aec241e027cd62c942f6eca4ddab3e97f000a9c0017575d36deb5", + ), + "centres": ( + "controller-followthrough-20261017/structured-centres/" + "STRUCTURED-CENTRES-PROGRAM.json.gz", + "2b9de1454c2025ae4e230bd64de36b4f6c937628c63fc5afede6640dd3c0e1e1", + ), +} + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def basis(values): + pivots = {} + for value in values: + while value: + pivot = value.bit_length() - 1 + if pivot not in pivots: + pivots[pivot] = value + break + value ^= pivots[pivot] + return list(pivots.values()) + + +def annihilator(values): + return [v for v in range(1, 512) + if all((v & w).bit_count() % 2 == 0 for w in values)] + + +def main(): + data = {} + for label, (relative, pin) in SOURCES.items(): + raw = gzip.decompress((LANES / relative).read_bytes()) + need(sha256(raw).hexdigest() == pin, label + " source pin") + data[label] = json.loads(raw) + + records = data["directions"]["transfers"] + need([r["port"] for r in records] == list(range(112)), "Port order") + q = [r["q"] for r in records] + need(len(set(q)) == 112 and all(v.bit_count() % 2 == 1 for v in q), + "Distinct anisotropic port lines") + rows = data["centres"]["centre_rows"] + need(len(rows) == 8, "Eight centre rows") + supports = [sorted(int(p) for p, c in row.items() if Fraction(c)) + for row in rows] + need(all(len(s) == 12 for s in supports), "Twelve ports per row") + spaces = [basis(q[p] for p in support) for support in supports] + need([len(s) for s in spaces] == [7] * 8, "Eight rank-seven supports") + duals = [annihilator(s) for s in spaces] + expected = [[7, 42, 45], [25, 45, 52], [45, 82, 127], [45, 76, 97], + [45, 76, 97], [7, 42, 45], [25, 45, 52], [45, 82, 127]] + need(duals == expected, "Actual annihilator planes") + classes = [[i for i, dual in enumerate(duals) if tuple(dual) == value] + for value in dict.fromkeys(map(tuple, duals))] + need(classes == [[0, 5], [1, 6], [2, 7], [3, 4]], "Four classes") + incidence = {} + for i, support in enumerate(supports): + for port in support: + incidence.setdefault(port, []).append(i) + need(len(incidence) == 48 and all(len(v) == 2 for v in incidence.values()), + "Two incident centres per port") + edges = sorted({tuple(v) for v in incidence.values()}) + expected_edges = [pair for pair in combinations(range(8), 2) + if duals[pair[0]] != duals[pair[1]]] + need(edges == expected_edges and len(edges) == 24, + "The incidence graph is complete four-partite") + need(all(sum(tuple(v) == edge for v in incidence.values()) == 2 + for edge in edges), "Two physical ports per graph edge") + intersections = [[14 - len(basis(left + right)) for right in spaces] + for left in spaces] + need(all(intersections[i][j] == (7 if duals[i] == duals[j] else 6) + for i in range(8) for j in range(8)), "Pair intersections") + common_dual = set.intersection(*(set(d) for d in duals)) + need(common_dual == {45}, "Common rank-eight ambient hyperplane") + need(len(basis(sum(spaces, []))) == 8, "All supports span that hyperplane") + need(len(basis(sum(duals, []))) == 4, "Common intersection has rank five") + independent = [] + for mask in range(256): + chosen = [i for i in range(8) if (mask >> i) & 1] + if all(not ((mask >> i) & 1 and (mask >> j) & 1) for i, j in edges): + independent.append(chosen) + maximum = max(map(len, independent)) + need(maximum == 2, "At most two compatible rank-seven query vertices") + maximizers = [s for s in independent if len(s) == maximum] + need(sorted(maximizers) == sorted(classes), "The four maximal compatible pairs") + receipt = { + "status": "PASS_CENTRE_SUPPORT_GEOMETRY", + "source_decompressed_sha256": {k: v[1] for k, v in SOURCES.items()}, + "query_supports": supports, + "binary_support_ranks": list(map(len, spaces)), + "annihilators": duals, + "equal_subspace_classes": classes, + "intersection_ranks": intersections, + "common_hyperplane_normal": 45, + "common_intersection_rank": 5, + "incidence_edges": edges, + "maximum_independent_set_size": maximum, + "maximum_independent_sets": maximizers, + "conditional_eight_query_rank_lower_bound": 62, + "scope": ( + "Exact source geometry. The rank-62 statement assumes one scalar " + "capture per stated query and one monotone subspace path per " + "unwarped source value, with no extra carrier. No new native word " + "or general query lower bound is claimed." + ), + } + target = HERE / "CENTRE-SUPPORT-GEOMETRY-20261018.json" + target.write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/check_dyadic_query_separation_20261018.py b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/check_dyadic_query_separation_20261018.py new file mode 100644 index 0000000000..2f7896f61e --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/frozen/root/check_dyadic_query_separation_20261018.py @@ -0,0 +1,129 @@ +"""Check the actual source matrices for the query separation theorem.""" + +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +CORE = HERE.parent / "lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz" +CORE_PIN = "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa" +A = [0, 7, 20, 27, 36, 46, 57, 111] +T = [21, 37, 47, 76, 81, 87, 92, 110] + + +def need(value, message): + if not value: + raise ValueError(message) + + +def multiply(a, b): + bt = list(zip(*b)) + return [[sum(x * y for x, y in zip(row, col)) for col in bt] for row in a] + + +def transpose(a): + return [list(row) for row in zip(*a)] + + +def identity(n): + return [[F(i == j) for j in range(n)] for i in range(n)] + + +def residue(x, prime): + x = F(x) + need(x.denominator % prime != 0, "The residue map must be defined") + return x.numerator * pow(x.denominator, -1, prime) % prime + + +def rank_mod(a, prime): + rows = [[residue(x, prime) for x in row] for row in a] + rank = 0 + for col in range(len(rows[0])): + pivot = next((i for i in range(rank, len(rows)) if rows[i][col]), None) + if pivot is None: + continue + rows[rank], rows[pivot] = rows[pivot], rows[rank] + scale = pow(rows[rank][col], -1, prime) + rows[rank] = [x * scale % prime for x in rows[rank]] + for i in range(len(rows)): + if i != rank and rows[i][col]: + scale = rows[i][col] + rows[i] = [(x - scale * y) % prime for x, y in zip(rows[i], rows[rank])] + rank += 1 + if rank == len(rows): + break + return rank + + +def main(): + raw = gzip.decompress(CORE.read_bytes()) + need(sha256(raw).hexdigest() == CORE_PIN, "The actual core pin must match") + core = json.loads(raw) + r = [[F(row.get(str(p), 0)) for p in range(112)] for row in core["R"]] + ordinary = [p for p in range(112) if p not in A] + ra = [[row[p] for p in A] for row in r] + ru = [[row[p] for p in ordinary] for row in r] + d = [[x / 4 for x in row] for row in multiply(transpose(ru), ra)] + b = transpose(d) + dt = [d[ordinary.index(p)] for p in T] + need(multiply(dt, transpose(dt)) == identity(8), "D_T D_T^t must be identity") + need(multiply(transpose(dt), dt) == identity(8), "D_T^t D_T must be identity") + need(multiply(b, d) == [[13 * x for x in row] for row in identity(8)], "BD must be 13I") + m = [[F(0) for _ in ordinary] for _ in A] + for j, p in enumerate(T): + for i in range(8): + m[i][ordinary.index(p)] = dt[j][i] + need(multiply(m, d) == identity(8), "The sparse log must be a section") + need(rank_mod(b, 13) == 8, "B must have full row rank at 13") + need(rank_mod(b + m, 13) == 16, "The dyadic stack must have rank sixteen") + + # Each new row is a dyadic kernel row plus the original section. + kernel = [] + for j in range(len(ordinary)): + row = [F(j == k) for k in range(len(ordinary))] + for i in range(8): + for k in range(len(ordinary)): + row[k] -= d[j][i] * m[i][k] + kernel.append(row) + cases = 64 + for case in range(cases): + candidate = [row[:] for row in m] + for i in range(8): + row = kernel[(11 * case + 7 * i) % len(kernel)] + scale = F((case % 5) - 2, 2 ** (case % 4)) + candidate[i] = [x + scale * y for x, y in zip(candidate[i], row)] + need(multiply(candidate, d) == identity(8), "Each perturbed log must remain a section") + need(rank_mod(b + candidate, 13) == 16, "Each perturbed stack must have rank sixteen") + + matched = [[x / 13 for x in row] for row in b] + need(multiply(matched, d) == identity(8), "The matched log must be a rational section") + need(rank_mod(b + matched, 17) == 8, "The matched stack must have rank eight") + need(any(x.denominator % 13 == 0 for row in matched for x in row), "The matched log leaves the dyadic ring") + need(all(13 * x == y for row, source in zip(matched, b) for x, y in zip(row, source)), "The exact row dependence must hold") + bad = [[13 * x for x in row] for row in m] + need(rank_mod(b + bad, 13) == 8, "The nonunit control must defeat the residue rank conclusion") + receipt = { + "status": "PASS_DYADIC_QUERY_SEPARATION", + "core_decompressed_sha256": CORE_PIN, + "proof_sha256": sha256((HERE / "DYADIC-QUERY-SEPARATION-20261018.md").read_bytes()).hexdigest(), + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "selected": A, + "ordinary_minor": T, + "BD": "13I", + "prime": 13, + "B_rank": 8, + "dyadic_section_stack_rank": 16, + "kernel_perturbed_sections": cases, + "matched_section_stack_rank": 8, + "scope": "Source information rank and exact representation choice; no native child bound or supplier claim.", + } + destination = HERE / "DYADIC-QUERY-SEPARATION-20261018.json" + destination.write_text(json.dumps(receipt, indent=2) + "\n", encoding="utf-8") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/notices/LICENSE b/research/actual-query-information-bounds/annexes/source-geometry/notices/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/notices/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/notices/PR2588-NOTICE b/research/actual-query-information-bounds/annexes/source-geometry/notices/PR2588-NOTICE new file mode 100644 index 0000000000..46411b80b2 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/notices/PR2588-NOTICE @@ -0,0 +1,10 @@ +Anticipatory dirty borrowing: PR2226 (Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance) is credited first. Its alias rule, changed-reference K_G handoffs, initial compensation and exact free-operator replay (vendored under new/code/borrow/vendor, see new/code/borrow/NOTICE-PR2226.md) are applied here to the T74 pivot-566+554 words; the native lowering, window-exact owner fill and independent audit of the borrow words are new in this package. Bootstrap carried-cutoff repair: PR1956 (Josie Elliston); Lemma G label/adapter checks and X/Y/Z mutants: PR1964 (thakrarsagar), extended here with borrow warp/zero-buffer controls. + +New research prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. Parent words and build recipe method derive from Jeremy Kothe PR1274 and Rohan Arun PR1218, with lineage credited in README.md. All inherited mathematical qualifications are retained. +Additional pivot555 and567 composition by Rohan Arun with substantial OpenAI Codex assistance. + +T74 exact-fill owner construction by Rohan Arun with substantial OpenAI Codex assistance. + +PR1377 grid refinement credited to Jeremy Kothe. Outer witness refinement by Rohan Arun with OpenAI Codex assistance; construction unchanged. + +Pivot-566 kernel, words, edits, rebuild.py and rebind.py: PR1625 (mdumitrean). Endpoint/outer-witness stacking, fine_cache.py and oracle stage by jeremykothe2 with oh-my-pi assistance. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/notices/PR3133-CREDITS.md b/research/actual-query-information-bounds/annexes/source-geometry/notices/PR3133-CREDITS.md new file mode 100644 index 0000000000..24f00912d4 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/notices/PR3133-CREDITS.md @@ -0,0 +1,19 @@ +# Credits + +- **PR #2908, Jeremy Diviney**: the paired input/output extraction, its compensation rule `C*S`, the exact two-sided certificate (`structure.py`, vendored unchanged) and the closed-adapter admission chain. +- **PR #2917, Mason Hale**: the nine paired extractions and 82-endpoint words under PR2942, the refit/compose producer model that stage 2 follows, the T74 chronology (ORDER/DISPATCH), the allocation checker, moment auditor, extension stage and adapter derivation reused here. +- **PR #2957 / #2948 / #2966, Jeremy Kothe (jeremykothe2)**: the fourteen declared exactness-preserving gate rewrites in five classes (R-retime, A3779-cut-start-read, PM-carrier-lender-entry, B-carrier-retime, A-commuting-swap) and their pure applier (`vendor/declared_rewrites.py`, vendored unchanged); stage 3 composes exactly these rewrites onto this package's stage-2 word (`data/REWRITES-2957.json`, re-addressed with exact preimages). PR2966 composed the same rewrites onto our PR2942 words. +- **PR #2969, Dugongue**: the PR2942 + PR2957 composition at T370 and its cap-level headline nomination, this package's comparator and moment baseline (`allocation/baseline/`). Our stage 3 composes the same fourteen rewrites, here onto the stage-2 word. +- **PR #2918 (research/helper408-rank7-pairing), RossRichardson**: the fixed-cut rank-seven obstruction for helper408; this package's census of fresh rank-7 extractions reproduces it exactly and is consistent with it. +- **PR #2894 / #2833, Jeremy Kothe**: the preload re-synthesis supplier, the frame accounting and inverse-reverse cleanup (`vendor/preload_move.py`), the source materializer and the inherited supplier lineage. +- **PR #2857 / #2848, Yiyang Lu (Lyy-iiis)**: the shared-kernel words, the staged native/overlay tooling and the chronological flow model and realization (edge colouring) used to construct the allocation; PR2843 (Marius-Paul Dumitrean) is that flow model's starting point. +- **PR #2863 / #2839, Dugongue**: the packing lineage and the PR2839 owner engine. +- **Tekalign**: the independent owner/chronology checker (`allocation/vendor/independent_owners.py`) and admission tooling. +- **icekylinx**: the exact free-operator auditor retained as `vendor/audit_local.py` (PR2833). +- **themilkman216**: the observation that a cap-level allocation of these inventories needs a T whose basic counts are integral, which the allocation's degenerate-face step builds on. +- **Gareth Davidson (bitplane), PR #1995 / #2013**: the fixed-word terminal-subspace bounds that frame stage 1's scope; earlier rank-seven helper ends on other words are in `research/complex-rank7-end-pair`, `research/k8-rank7-composition` and the PR1090/PR1104 lineage (credited there). +- **PR #2930 / #2942, Marius-Paul Dumitrean**: the cap allocation of PR2917's words, the four normal-45 extractions under these words, the relaxation tools and the overlay/producer conventions reused here. +- **PR #2979, Marius-Paul Dumitrean (with substantial AI assistance from Anthropic Claude via Claude Code)**: the codimension-2 census on paired-extraction words, the joint end-frame lowering of 22 restored helpers in five groups (stage 1), the five further extractions it makes profitable (stage 2), the exact composition with PR2957's rewrites (stage 3), the producer and local verification for all three stages, the overlay stage `rank7-joint-endframes` with its rebuild guards, the adapter generalization to six width classes, the literal T74 allocation of the changed inventory, its relaxation certificates and recorded gap, and the complete fresh replay. +- **PR #3015, Jeremy Kothe (jeremykothe2)**: the declared literal edit stage (`edits/`, `tools/build_edits.py`) with its independent review (`edits/edits_review.py`), and edit R1 on PR #2979's restore section (carrier 61 for register 63). +- **PR #3042, dcharb78 (with AI assistance)**: the six restore carrier/pivot skips (`R1_E42` at `restore[162:188]`, `26 -> 33` gates skipping `{22, 40, 54, 63}`, and `R2_E7` at `restore[190:203]`, `13 -> 15` gates skipping `{5, 73}`) on PR #2979's words that serve as the direct starting words for `B_586_438` and `B_588_440`. +- **New here (dcharb78, with AI assistance)**: the two coupled `B` + `restore` dying-helper carrier folds (`B_586_438` and `B_588_440`, `6` hunks / `6 -> 5` gates each) and `helper_final` lowerings on entering helpers `586` ($E_{30} \to V_{30,76,82}$) and `588` ($E_{30} \to V_{30,97,127}$) shifting the helper width inventory from `{4:26, 5:2, 6:16, 7:52, 8:99, 9:213}` to `{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}` (`+665` net profit per helper, `+1,330` joint), the literal `T74_optimal_idle39` allocation (`allocation/FILL.json.gz`), the 21-control per-word edit review (`edits/edits_review.py`) and 100-control four-stage replay (`verify.py`), and the re-derived paid profile, cap certificate (`certificates/RELAX-CAP.json`), and complete fresh-native admission and release receipts. PR #2979 (mdumitrean), PR #3015 (jeremykothe2), and PR #3042 (dcharb78) are credited first. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/notices/PR3133-NOTICE b/research/actual-query-information-bounds/annexes/source-geometry/notices/PR3133-NOTICE new file mode 100644 index 0000000000..89c20926ea --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/notices/PR3133-NOTICE @@ -0,0 +1,28 @@ +research/rank7-joint-endframes +Copyright 2026 Marius-Paul Dumitrean. Licensed under the Apache License, Version 2.0. +Prepared with substantial AI assistance (Anthropic Claude, via Claude Code). + +This package retains, byte-identical, Apache-2.0 files from: PR #2942 (Marius-Paul Dumitrean, head +a027b0f6fdb0ab2b42ba10fc31b53960166bf2bf, research/paired-extension-normal45): data/PARENT-base.json.gz and +data/PARENT-extra.json.gz (its data/WORD-*.json.gz), comparators/PR2942-CLAIM.json and tools/wordedit.py; PR #2917 +(Mason Hale, head 224bd5e56041c40078ff6b5fa7393733a215de5c, research/paired-helper-extension): structure.py (Jeremy +Diviney's PR2908 two-sided certificate checker), vendor/audit_local.py (PR2833's independent exact auditor, icekylinx +attribution), vendor/preload_move.py (Jeremy Kothe's PR2894 frame accounting and cleanup), allocation/ORDER.json, +allocation/DISPATCH.json and allocation/vendor/ (independent_owners.py: Tekalign's independent owner checker as vendored +by PR2839/PR2917; PLAN.json.gz, TEMPLATE.json.gz); PR #2957 (Jeremy Kothe, head b74b25f3ccc84c16e1a801d73b2f47e5ea764c78, +research/paired-extension-cap-fill-swaps): vendor/declared_rewrites.py (the pure applier of the fourteen declared +rewrites) and comparators/PR2957-CLAIM.json; PR #2966 (Jeremy Kothe, head e62d3eb9005117d82a9babcfa937ecc53237c490, +research/paired-extension-normal45-rewrites): comparators/PR2966-CLAIM.json; PR #2969 (Dugongue, head +e2ca469b08385d3d5e29a918d66dbefaf889e9f3, research/paired-swap-normal45): allocation/baseline/ (its CLAIM.json and its +allocation ORDER.json and PROFILE.json); and PR #2930 (head 81f3b5d12977eba09e06fbff729167d59faabe90): tools/relax.py, +tools/root.py, tools/relax_exact.py. +data/REWRITES-2957.json is Jeremy Kothe's PR2957 rewrite list, re-addressed to this package's stage-2 word with exact +preimages (every entry keeps a credit field). producer.py follows PR2917's producer.py (Mason Hale) for its paired steps; +verify.py, check_allocation.py, check_cap.py, run_registered.py and reproduce.py adapt our PR2942 versions of PR2917's and +PR2930's; tools/audit_allocation_moment.py is PR2917's exact moment auditor with only its authenticated baseline changed (to +the PR2969 headline); tools/derive_adapters.py generalizes PR2917's adapter derivation (PR2908, Jeremy Diviney); +tools/build_overlay.py follows the overlay conventions of PR2908's and PR2917's builders. construction/allocation/ retains +the flow model of PR2857/PR2843 (Yiyang Lu, Marius-Paul Dumitrean) as adapted for this allocation. All original notices of +the exported predecessor packages remain in force. + +Derived work (Apache-2.0): this package (`research/rank7-restore-carrier-skips`) builds on PR #2979 (Marius-Paul Dumitrean, head be191346, research/rank7-joint-endframes) and PR #3015 (Jeremy Kothe, jeremykothe2, research/rank7-joint-endframes-restore-edit), retained byte-identical except for the files named in README.md, plus two declared restore edit blocks (`R1_E42` and `R2_E7` in `edits/EDITS.json` and `edits/FINAL-WORD-*.json.gz`) and their re-derived certificates and complete fresh-native admission and release receipts by dcharb78, with AI assistance. PR #2979's own evidence is kept under evidence/pr2979/. diff --git a/research/actual-query-information-bounds/annexes/source-geometry/portable/centre-mixing-review.py b/research/actual-query-information-bounds/annexes/source-geometry/portable/centre-mixing-review.py new file mode 100644 index 0000000000..133d49ac56 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/portable/centre-mixing-review.py @@ -0,0 +1,436 @@ +"""Check the centre restriction from the native fields and cut intervals.""" + +from collections import Counter, defaultdict +from fractions import Fraction as Q +from hashlib import sha256 +import gzip +import json +from pathlib import Path + + +import argparse + +ANNEX = Path(__file__).resolve().parents[1] +PARENT = ANNEX.parents[1] +parser = argparse.ArgumentParser(description=__doc__) +parser.add_argument("--out", required=True) +OUT = Path(parser.parse_args().out).resolve() +OUT.mkdir(parents=True, exist_ok=True) +HERE = ANNEX / "frozen" / 'lanes/bridge-review-20261017/centre-mixing-review-20261018' +LANES = HERE.parents[1] +CORE = LANES / "new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz" +CUTS = LANES / "oblique-native-20261017/interior-cut/ALL-CUT-EDGES.json.gz" +CERT = LANES / "coherent-port/centre-mixing-20261018/SUPPORT.json" +PINS = { + "coherent-port/centre-mixing-20261018/MIXING.md": "e8ac0be5c3bd03cf853e9cb5718325d1f401eb1fc68d68869843ac6ded408903", + "coherent-port/centre-mixing-20261018/check_support.py": "82d608f7220d9959925c2990fd717b028a2fce47fcf41ee9f061d0687c32f97c", + "coherent-port/centre-mixing-20261018/SUPPORT.json": "251e656ce50b87f21149915d73b5c07d968d62aff2f47ccf2e1566cc5d6c756a", + "coherent-port/centre-mixing-20261018/check_mixing.py": "fe017063d3b5bad93bf2f884813576e169d59daad1c5aec8051001e0a3476dc7", + "coherent-port/centre-mixing-20261018/MIXING.json": "1a55e02768ad814b1441bfc616244a083ca3776007dcc0a370820059b83bdf11", + "oblique-native-20261017/interior-cut/ALL-CUT-SUPPORT.md": "758f8750a833ba08b44d9fe1df555f747eef62bd53302993bca6cdae7769d431", + "oblique-native-20261017/interior-cut/FRAME-SUPPORT.json": "6d9e1de85b7a2492bcef42514da240d74b81559c738aedac54cf65169a5a3fb5", + "oblique-native-20261017/interior-cut/check_frame_support.py": "3a81e98c83e418408eb7490771867a11f491a6af403820ad722c43a51026b508", + "oblique-native-20261017/interior-cut/inventory_new_edges.py": "6d77e20d6ef1a10951b7abeaa65852fad9161cc3b48e82d538a9748c3c9cc786", + "new-native-recipes-20261017/sources/bw_adapters.py": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce", +} + + +def need(test, label): + if not test: + raise ValueError(label) + + +def read_gzip(path, pin): + raw = gzip.decompress(path.read_bytes()) + need(sha256(raw).hexdigest() == pin, str(path.name) + " input pin") + return json.loads(raw) + + +def add(left, right, value=Q(1)): + for key, coefficient in right.items(): + result = left.get(key, Q(0)) + value * coefficient + if result: + left[key] = result + else: + left.pop(key, None) + + +def lin(columns, value): + answer = 0 + for j, column in enumerate(columns): + if value >> j & 1: + answer ^= column + return answer + + +def inverse(columns): + # Solve nine binary systems. Do not use a 512-value inverse table. + rows = [sum(((columns[j] >> i) & 1) << j for j in range(9)) | (1 << (9+i)) + for i in range(9)] + for j in range(9): + pivot = next((k for k in range(j, 9) if rows[k] >> j & 1), None) + need(pivot is not None, "Invertible binary warp") + rows[pivot], rows[j] = rows[j], rows[pivot] + for k in range(9): + if k != j and rows[k] >> j & 1: + rows[k] ^= rows[j] + return [sum(((rows[i] >> (9+j)) & 1) << i for i in range(9)) for j in range(9)] + + +def space(vectors): + result = {0} + for value in vectors: + result |= {x ^ value for x in result} + need(len(result) == 1 << len(vectors), "Independent frame basis") + return result + + +def row_key(row, allowed): + return tuple(sorted((s, word, c.numerator, c.denominator) + for (s, word), c in row.items() if s not in allowed or word)) + + +def tail_key(row): + return tuple(sorted((t, c.numerator, c.denominator) for t, c in row.items())) + + +def add_interval(out, field, start, end, frame, value): + if start < end and value: + out.append((field, start, end, frame, value)) + + +def replay_sources(item, centre_rows): + word, events = item["canonical"], item["programs"]["forward"] + size = len(word["start"]) + sources = set(range(112)) | set(range(224, size)) + allowed = {p for p in range(224, size) if word["start"][p] == 0} + rows = {p: {(p, ()): Q(1)} for p in range(size+8)} + frames = dict(enumerate(word["start"] + [0]*8)) + keys = {p: row_key(rows[p], allowed) for p in sources} + starts = {p: 0 for p in sources} + intervals, views, counts = [], [], Counter() + spaces = [space(vectors) for vectors in word["frames"]] + canonical_start = events.index(["phase", "A"]) + canonical_end = events.index(["phase", "exit_adapters"]) + need((canonical_start, canonical_end) == (7502, 17249), "Actual canonical interval") + need(all(e[0] in ("scalar", "climb", "warp", "phase") + for e in events[canonical_start:canonical_end]), "No wrapper inside the canonical interval") + maps = {record["op"]: record["G_columns"] for record in word["warps"]} + maps.update({-k: inverse(v) for k, v in list(maps.items())}) + for s in range(112): + need(word["ports"][s] in spaces[frames[s]], "Initial X line") + need(all((v & word["ports"][s]).bit_count() % 2 == 0 + for v in spaces[word["final"][112+s]]), "Final Y hyperplane") + + def slot(value): + return value[1] if value[0] == "L" else size+value[1] if value[0] == "C" else ("Z", value[1]) + + for pos, event in enumerate(events): + tag, changed = event[0], None + if pos == canonical_start: + for field, row in rows.items(): + if isinstance(field, int) and field < 112: + need(row == {(field, ()): Q(1)}, "The exterior prefix preserves each X input") + else: + need(not any(s < 112 for s, _ in row), "The exterior prefix has no other X branch") + counts[tag] += 1 + if tag == "scalar": + gate, frame = event[1:] + op, target = gate[0], slot(gate[1]) + if pos >= canonical_end: + need(not (isinstance(target, int) and 112 <= target < 224), "The exterior suffix makes no Y write") + old_frame = frames.get(target) + if op == "clear": + rows[target], frames[target] = {}, frame + else: + need(frames[target] == frame, "Literal scalar target frame") + if op == "scale": + q = Q(*gate[2:4]) + rows[target] = {k: q*v for k, v in rows[target].items() if q*v} + else: + source = slot(gate[2]) + need(source != target and frames[source] == frame, "Literal scalar source frame") + if op == "copy": + rows[target] = dict(rows[source]) + else: + need(op == "add", "Known scalar operation") + need(not (isinstance(source, int) and 112 <= source < 224) + or isinstance(target, int) and 112 <= target < 224, + "No Y feedback to fixed sources") + add(rows[target], rows[source], Q(*gate[3:5])) + changed = target + elif tag == "climb": + target, old_frame, new, rank = event[2:6] + need(frames[target] == old_frame and spaces[old_frame] < spaces[new], "Nested positive climb") + need(len(word["frames"][new]) - len(word["frames"][old_frame]) == rank, "Exact climb rank") + frames[target], changed = new, target + elif tag == "warp": + target, op, old_frame, new = slot(event[1]), event[2], event[3], event[4] + need(frames[target] == old_frame, "Literal warp input frame") + need({lin(maps[op], v) for v in spaces[old_frame]} == spaces[new], "Actual warp frame image") + updated = {} + for (s, history), coefficient in rows[target].items(): + history = history[1:] if history and history[0] == -op else (op,) + history + add(updated, {(s, history): coefficient}) + rows[target], frames[target], changed = updated, new, target + elif tag == "zero_buffer": + target = ("Z", event[2]) + if event[1] == "alloc": + need(target not in rows, "Private buffer allocation") + rows[target], frames[target] = {}, 1 + else: + need(not rows[target], "Private buffer return") + del rows[target], frames[target] + elif tag in ("adapter", "residual_adapter"): + target = event[2] + x_terms = [(s, history) for s, history in rows[target] if s < 112] + if x_terms: + views.append({"event": pos, "kind": event[:2], "field": target, + "frame": frames[target], "X_terms": len(x_terms)}) + if target >= 224: + need(tag == "adapter" and event[1] == "new_to_old" and frames[target] == 1, + "Every X-dependent helper view change is at FULL") + else: + need(tag == "phase", "Known event kind") + if changed in sources: + new_key = row_key(rows[changed], allowed) + if new_key != keys[changed] or frames[changed] != old_frame: + add_interval(intervals, changed, starts[changed], pos+1, old_frame, keys[changed]) + starts[changed], keys[changed] = pos+1, new_key + if tag == "scalar" and isinstance(changed, int) and changed >= size: + need(not any(s < 112 for s, _ in rows[changed]), "Owned fields have no X input branch") + for field in sources: + add_interval(intervals, field, starts[field], len(events)+1, frames[field], keys[field]) + need([frames[p] for p in range(size)] == word["final"], "All final frames") + for p in range(size): + if not 112 <= p < 224: + need(rows[p] == {(p, ()): Q(1)}, "Every fixed source and helper restores") + else: + target = p-112 + goal = {(p, ()): Q(1), (target, ()): Q(1)} + for row in centre_rows: + add(goal, {(s, ()): value for s, value in row.items()}, -row.get(target, Q(0))/4) + need(rows[p] == goal, "Exact clean-J response on every arbitrary input") + need(not rows[size] and all(rows[size+p] == {(size+p, ()): Q(1)} for p in range(1, 8)), "Owned endpoint") + return intervals, views, dict(counts), [canonical_start, canonical_end] + + +def replay_tails(item): + word, events = item["canonical"], item["programs"]["forward"] + rows = [{t: Q(1)} for t in range(112)] + frames = word["final"][112:224].copy() + ends = [len(events)+1]*112 + intervals = [] + for pos in range(len(events)-1, -1, -1): + event, changed = events[pos], None + if event[0] == "climb" and 112 <= event[2] < 224: + changed = event[2]-112 + old_key, old_frame = tail_key(rows[changed]), frames[changed] + need(old_frame == event[4], "Reverse Y frame") + frames[changed] = event[3] + elif event[0] == "scalar": + gate = event[1] + if gate[1][0] == "L" and 112 <= gate[1][1] < 224: + target = gate[1][1]-112 + if gate[0] == "scale": + changed = target + old_key, old_frame = tail_key(rows[changed]), frames[changed] + rows[target] = {k: Q(*gate[2:4])*v for k, v in rows[target].items()} + elif gate[0] == "add" and gate[2][0] == "L" and 112 <= gate[2][1] < 224: + changed = gate[2][1]-112 + old_key, old_frame = tail_key(rows[changed]), frames[changed] + add(rows[changed], rows[target], Q(*gate[3:5])) + elif event[0] == "warp": + need(not (event[1][0] == "L" and 112 <= event[1][1] < 224), "No Y warp") + if changed is not None: + new_key = tail_key(rows[changed]) + if new_key != old_key or frames[changed] != old_frame: + add_interval(intervals, changed, pos+1, ends[changed], old_frame, old_key) + ends[changed] = pos+1 + for target in range(112): + add_interval(intervals, target, 0, ends[target], frames[target], tail_key(rows[target])) + need(rows == [{t: Q(1)} for t in range(112)] and frames == [0]*112, "Y scalar subword is identity") + return intervals + + +def join_intervals(source, target): + groups = defaultdict(list) + for kind, intervals in enumerate((source, target)): + for index, (_, lo, hi, frame, value) in enumerate(intervals): + groups[frame].append((lo, 1, kind, index, value)) + groups[frame].append((hi, 0, kind, index, value)) + products, overlaps = set(), 0 + for events in groups.values(): + active = [{}, {}] + for _, start, kind, index, value in sorted(events): + if not start: + del active[kind][index] + continue + for other in active[1-kind].values(): + products.add((value, other) if kind == 0 else (other, value)) + overlaps += 1 + active[kind][index] = value + return products, overlaps + + +def determinant_fraction(matrix): + rows = [[Q(x) for x in row] for row in matrix] + det = Q(1) + for j in range(len(rows)): + pivot = next((k for k in range(j, len(rows)) if rows[k][j]), None) + if pivot is None: + return Q(0) + if pivot != j: + rows[pivot], rows[j] = rows[j], rows[pivot] + det = -det + value = rows[j][j] + det *= value + rows[j] = [x/value for x in rows[j]] + for k in range(j+1, len(rows)): + value = rows[k][j] + if value: + rows[k] = [x-value*y for x, y in zip(rows[k], rows[j])] + return det + + +def two_basis_certificate(r, ports): + left = [0, 7, 20, 27, 36, 46, 57, 111] + right = [3, 6, 18, 21, 89, 92, 105, 109] + disconnected = [21, 37, 47, 76, 81, 87, 92, 110] + + def gram(a, b): + return [[sum(r[k][s]*r[k][t] for k in range(8)) for t in b] for s in a] + + def check_basis(fields): + need(gram(fields, fields) == [[4*int(i == j) for j in range(8)] for i in range(8)], + "Actual orthogonal centre basis") + need(all((ports[s] & ports[t]).bit_count() % 2 for s in fields for t in fields), + "All within-basis pairs have binary dot one") + + def components(matrix): + neighbours = {i: set() for i in range(16)} + for i in range(8): + for j in range(8): + if matrix[i][j]: + neighbours[i].add(8+j) + neighbours[8+j].add(i) + groups, tree = [], [] + unseen = set(range(16)) + while unseen: + seed = min(unseen) + group, queue = {seed}, [seed] + unseen.remove(seed) + for node in queue: + for next_node in sorted(neighbours[node] & unseen): + unseen.remove(next_node) + group.add(next_node) + queue.append(next_node) + tree.append([node, next_node]) + groups.append(sorted(group)) + return groups, tree + + for fields in (left, right, disconnected): + check_basis(fields) + numerator = gram(left, right) + need(all(x in (-2, 0, 2) for row in numerator for x in row), "Every overlap is zero or a dyadic unit") + groups, tree = components(numerator) + need(len(groups) == 1 and len(tree) == 15, "Connected two-basis graph") + control_groups, _ = components(gram(left, disconnected)) + need(len(control_groups) == 2 and all(len(group) == 8 for group in control_groups), + "A real disconnected basis pair has two scalar blocks") + return dict(core_decompressed_sha256="a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + left_ports=left, right_ports=right, overlap_denominator=4, + overlap_numerator=numerator, components=groups, spanning_tree=tree, + disconnected_control_ports=disconnected, disconnected_control_components=control_groups, + exact_common_diagonal_algebra="scalar multiples of I8") + + +def main(): + for path, pin in PINS.items(): + need(sha256((LANES/path).read_bytes()).hexdigest() == pin, "Pinned producer file " + path) + core = read_gzip(CORE, "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa") + cuts = read_gzip(CUTS, "18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418") + cert = json.loads(CERT.read_text()) + supplied = set() + for product in cuts["products"]: + source = tuple(sorted((s, tuple(sign*op[1] for op, sign in history), num, den) + for s, history, num, den in cuts["source_rows"][product["source_row"]]["constrained"])) + tail = tuple(tuple(x) for x in cuts["tail_columns"][product["tail_column"]]) + supplied.add((source, tail)) + reports = {} + centre_rows = [{int(k): Q(v) for k, v in row.items()} for row in core["R"]] + for name, item in core["providers"].items(): + sources, views, counts, canonical_cuts = replay_sources(item, centre_rows) + tails = replay_tails(item) + actual, overlaps = join_intervals(sources, tails) + need(actual == supplied, "Independent interval inventory equals the supplied product set") + word = item["canonical"] + spaces = [space(vectors) for vectors in word["frames"]] + maps = {record["op"]: record["G_columns"] for record in word["warps"]} + maps.update({-k: inverse(v) for k, v in list(maps.items())}) + checks, history_lengths = set(), Counter() + for _, _, _, frame, row in sources: + for s, history, _, _ in row: + if s >= 112 or (frame, s, history) in checks: + continue + checks.add((frame, s, history)) + value = word["ports"][s] + for op in reversed(history): + value = lin(maps[op], value) + need(value in spaces[frame], "Actual X term support at every source interval") + history_lengths[len(history)] += 1 + tail_checks = set() + for _, _, _, frame, row in tails: + for t, _, _ in row: + if (frame, t) not in tail_checks: + tail_checks.add((frame, t)) + need(all((x & word["ports"][t]).bit_count() % 2 == 0 for x in spaces[frame]), + "Every reverse tail frame is inside the target hyperplane") + reports[name] = dict(source_intervals=len(sources), target_intervals=len(tails), + interval_overlaps=overlaps, distinct_products=len(actual), + actual_X_term_frame_checks=len(checks), history_lengths=dict(history_lengths), + target_frame_checks=len(tail_checks), event_counts=counts, + canonical_rewiring_cuts=canonical_cuts, + X_dependent_view_changes=views) + print(name, len(actual), "products from", overlaps, "interval overlaps", flush=True) + r = [[int(row.get(str(p), 0)) for p in range(112)] for row in core["R"]] + need([[sum(r[a][p]*r[b][p] for p in range(112)) for b in range(8)] for a in range(8)] + == [[56*int(a == b) for b in range(8)] for a in range(8)], "Actual full centre Gram matrix") + ports = core["providers"]["base"]["canonical"]["ports"] + equations = [] + for t in range(112): + need(sum(r[a][t]**2 for a in range(8)) == 4 and ports[t].bit_count() % 2, "Each port is odd and each R column has norm four") + for s in range(112): + if t != s and (ports[t] & ports[s]).bit_count() % 2: + row = [r[a][t]*r[b][s] for a in range(8) for b in range(8)] + need(sum(row[9*a] for a in range(8)) == 0, "Scalar identity satisfies all constraints") + equations.append((t, s, row)) + need(len(equations) == 6608, "Every forbidden off-diagonal pair") + two_bases = two_basis_certificate(r, ports) + (OUT/"TWO-BASES.json").write_text(json.dumps(two_bases, indent=2, sort_keys=True)+"\n") + by_pair = {(t, s): row for t, s, row in equations} + matrix = [[by_pair[tuple(pair)][j] for j in cert["centre_entry_columns"]] + for pair in cert["independent_pairs"]] + need(len(matrix) == 63 and cert["centre_entry_columns"] == list(range(63)), "Full centre matrix certificate") + det = determinant_fraction(matrix) + need(det == -(1 << 71), "Independent rational determinant") + projection = [Q(a == b)-Q(1, 8) for a in range(8) for b in range(8)] + failures = [(t, s) for t, s, row in equations if sum(x*y for x, y in zip(row, projection))] + need(failures, "Dense rank-seven projection is rejected") + duplicated = [row[:] for row in matrix] + duplicated[-1] = duplicated[0][:] + need(determinant_fraction(duplicated) == 0, "Duplicate certificate row is rejected") + report = dict(status="PASS_INDEPENDENT_NATIVE_CENTRE_REVIEW", producer_pins=PINS, + core_decompressed_sha256="a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + inventory_decompressed_sha256="18c89367243fc7c09411f28a8022884130373ce4886de806f4b011edec030418", + providers=reports, forbidden_pairs=len(equations), determinant=str(det), + two_basis_certificate=two_bases, + exact_kernel="scalar multiples of I8", dense_rank_seven_failures=len(failures), + negative_controls=["dense rank-seven projection", "duplicate certificate row"], + checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest()) + (OUT/"REVIEW.json").write_text(json.dumps(report, indent=2, sort_keys=True)+"\n") + print(report["status"], "determinant", det, flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/portable/centre-support-producer.py b/research/actual-query-information-bounds/annexes/source-geometry/portable/centre-support-producer.py new file mode 100644 index 0000000000..cacfce4c57 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/portable/centre-support-producer.py @@ -0,0 +1,141 @@ +#!/usr/bin/env python3 +"""Check the binary source geometry of the eight structured queries.""" + +from fractions import Fraction +from hashlib import sha256 +from itertools import combinations +import gzip +import json +from pathlib import Path + + +import argparse + +ANNEX = Path(__file__).resolve().parents[1] +PARENT = ANNEX.parents[1] +parser = argparse.ArgumentParser(description=__doc__) +parser.add_argument("--out", required=True) +OUT = Path(parser.parse_args().out).resolve() +OUT.mkdir(parents=True, exist_ok=True) +HERE = ANNEX / "frozen" / 'root' +LANES = HERE.parent / "lanes" +SOURCES = { + "directions": ( + "history-encoding/independent-skeleton-20261018/fresh-three-child/" + "FRESH-THREE-CHILD-PROGRAMS.json.gz", + "b08cb4146f1aec241e027cd62c942f6eca4ddab3e97f000a9c0017575d36deb5", + ), + "centres": ( + "controller-followthrough-20261017/structured-centres/" + "STRUCTURED-CENTRES-PROGRAM.json.gz", + "2b9de1454c2025ae4e230bd64de36b4f6c937628c63fc5afede6640dd3c0e1e1", + ), +} + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def basis(values): + pivots = {} + for value in values: + while value: + pivot = value.bit_length() - 1 + if pivot not in pivots: + pivots[pivot] = value + break + value ^= pivots[pivot] + return list(pivots.values()) + + +def annihilator(values): + return [v for v in range(1, 512) + if all((v & w).bit_count() % 2 == 0 for w in values)] + + +def main(): + data = {} + for label, (relative, pin) in SOURCES.items(): + raw = gzip.decompress((LANES / relative).read_bytes()) + need(sha256(raw).hexdigest() == pin, label + " source pin") + data[label] = json.loads(raw) + + records = data["directions"]["transfers"] + need([r["port"] for r in records] == list(range(112)), "Port order") + q = [r["q"] for r in records] + need(len(set(q)) == 112 and all(v.bit_count() % 2 == 1 for v in q), + "Distinct anisotropic port lines") + rows = data["centres"]["centre_rows"] + need(len(rows) == 8, "Eight centre rows") + supports = [sorted(int(p) for p, c in row.items() if Fraction(c)) + for row in rows] + need(all(len(s) == 12 for s in supports), "Twelve ports per row") + spaces = [basis(q[p] for p in support) for support in supports] + need([len(s) for s in spaces] == [7] * 8, "Eight rank-seven supports") + duals = [annihilator(s) for s in spaces] + expected = [[7, 42, 45], [25, 45, 52], [45, 82, 127], [45, 76, 97], + [45, 76, 97], [7, 42, 45], [25, 45, 52], [45, 82, 127]] + need(duals == expected, "Actual annihilator planes") + classes = [[i for i, dual in enumerate(duals) if tuple(dual) == value] + for value in dict.fromkeys(map(tuple, duals))] + need(classes == [[0, 5], [1, 6], [2, 7], [3, 4]], "Four classes") + incidence = {} + for i, support in enumerate(supports): + for port in support: + incidence.setdefault(port, []).append(i) + need(len(incidence) == 48 and all(len(v) == 2 for v in incidence.values()), + "Two incident centres per port") + edges = sorted({tuple(v) for v in incidence.values()}) + expected_edges = [pair for pair in combinations(range(8), 2) + if duals[pair[0]] != duals[pair[1]]] + need(edges == expected_edges and len(edges) == 24, + "The incidence graph is complete four-partite") + need(all(sum(tuple(v) == edge for v in incidence.values()) == 2 + for edge in edges), "Two physical ports per graph edge") + intersections = [[14 - len(basis(left + right)) for right in spaces] + for left in spaces] + need(all(intersections[i][j] == (7 if duals[i] == duals[j] else 6) + for i in range(8) for j in range(8)), "Pair intersections") + common_dual = set.intersection(*(set(d) for d in duals)) + need(common_dual == {45}, "Common rank-eight ambient hyperplane") + need(len(basis(sum(spaces, []))) == 8, "All supports span that hyperplane") + need(len(basis(sum(duals, []))) == 4, "Common intersection has rank five") + independent = [] + for mask in range(256): + chosen = [i for i in range(8) if (mask >> i) & 1] + if all(not ((mask >> i) & 1 and (mask >> j) & 1) for i, j in edges): + independent.append(chosen) + maximum = max(map(len, independent)) + need(maximum == 2, "At most two compatible rank-seven query vertices") + maximizers = [s for s in independent if len(s) == maximum] + need(sorted(maximizers) == sorted(classes), "The four maximal compatible pairs") + receipt = { + "status": "PASS_CENTRE_SUPPORT_GEOMETRY", + "source_decompressed_sha256": {k: v[1] for k, v in SOURCES.items()}, + "query_supports": supports, + "binary_support_ranks": list(map(len, spaces)), + "annihilators": duals, + "equal_subspace_classes": classes, + "intersection_ranks": intersections, + "common_hyperplane_normal": 45, + "common_intersection_rank": 5, + "incidence_edges": edges, + "maximum_independent_set_size": maximum, + "maximum_independent_sets": maximizers, + "conditional_eight_query_rank_lower_bound": 62, + "scope": ( + "Exact source geometry. The rank-62 statement assumes one scalar " + "capture per stated query and one monotone subspace path per " + "unwarped source value, with no extra carrier. No new native word " + "or general query lower bound is claimed." + ), + } + target = OUT / "CENTRE-SUPPORT-GEOMETRY-20261018.json" + target.write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/portable/centre-support-review.py b/research/actual-query-information-bounds/annexes/source-geometry/portable/centre-support-review.py new file mode 100644 index 0000000000..add48a6b18 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/portable/centre-support-review.py @@ -0,0 +1,127 @@ +#!/usr/bin/env python3 +"""Check the actual support spaces by XOR closure and nullspace equations.""" +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json + +import argparse + +ANNEX = Path(__file__).resolve().parents[1] +PARENT = ANNEX.parents[1] +parser = argparse.ArgumentParser(description=__doc__) +parser.add_argument("--out", required=True) +OUT = Path(parser.parse_args().out).resolve() +OUT.mkdir(parents=True, exist_ok=True) +HERE = ANNEX / "frozen" / 'lanes/independent-review-20261017/centre-support-review-20261018' +CAMPAIGN = HERE.parents[2] +LANES = CAMPAIGN/'lanes' +ROOT = CAMPAIGN/'root' +PINS = { + 'CENTRE-SUPPORT-GEOMETRY-20261018.md': 'a3df65d159899fbaf7110958275615fc406ecbd077d9d620f7f49ccbe4b923f5', + 'CENTRE-SUPPORT-GEOMETRY-20261018.json': 'dafd6c0af3f8aad852a7c80258118487744921c9a61474b1441e3755f8e3b205', + 'check_centre_support_geometry_20261018.py': '99582e42007012d31dcddc14e05da8c5aac75c1f3b546c00ef0fcf0169f081b2', +} +SOURCE_PINS = { + 'history-encoding/independent-skeleton-20261018/fresh-three-child/FRESH-THREE-CHILD-PROGRAMS.json.gz': + 'b08cb4146f1aec241e027cd62c942f6eca4ddab3e97f000a9c0017575d36deb5', + 'controller-followthrough-20261017/structured-centres/STRUCTURED-CENTRES-PROGRAM.json.gz': + '2b9de1454c2025ae4e230bd64de36b4f6c937628c63fc5afede6640dd3c0e1e1', +} + + +def need(test, label): + if not test: + raise ValueError(label) + + +def span(vectors): + values = {0} + for vector in vectors: + values |= {x ^ vector for x in values} + return values + + +def nullspace(equations): + rows = list(dict.fromkeys(equations)) + pivots = [] + for column in range(9): + choice = next((i for i in range(len(pivots), len(rows)) if rows[i] >> column & 1), None) + if choice is None: + continue + slot = len(pivots) + rows[slot], rows[choice] = rows[choice], rows[slot] + for i in range(len(rows)): + if i != slot and rows[i] >> column & 1: + rows[i] ^= rows[slot] + pivots.append(column) + answer = [] + for free in range(9): + if free not in pivots: + value = 1 << free + for row, column in zip(rows, pivots): + if row >> free & 1: + value |= 1 << column + answer.append(value) + need(all(not (row & vector).bit_count() % 2 for row in equations for vector in answer), 'Nullspace equations') + return span(answer) + + +def main(): + for name, pin in PINS.items(): + need(sha256((ROOT/name).read_bytes()).hexdigest() == pin, 'Root source pin '+name) + data = [] + for relative, pin in SOURCE_PINS.items(): + raw = gzip.decompress((LANES/relative).read_bytes()) + need(sha256(raw).hexdigest() == pin, 'Actual source pin '+relative) + data.append(json.loads(raw)) + ports = [record['q'] for record in data[0]['transfers']] + need([record['port'] for record in data[0]['transfers']] == list(range(112)), 'Actual port order') + need(len(set(ports)) == 112 and all(q.bit_count() % 2 for q in ports), 'Distinct odd source lines') + supports = [set(int(p) for p, value in row.items() if F(value)) for row in data[1]['centre_rows']] + need(len(supports) == 8 and all(len(s) == 12 for s in supports), 'Eight twelve-port supports') + spaces = [span(ports[p] for p in support) for support in supports] + duals = [nullspace([ports[p] for p in support]) for support in supports] + need(all(len(s) == 128 for s in spaces) and all(len(d) == 4 for d in duals), 'Primal and dual dimensions') + wanted = [{0, 7, 42, 45}, {0, 25, 45, 52}, {0, 45, 82, 127}, {0, 45, 76, 97}, + {0, 45, 76, 97}, {0, 7, 42, 45}, {0, 25, 45, 52}, {0, 45, 82, 127}] + need(duals == wanted, 'All actual annihilator vectors') + groups = [[0, 5], [1, 6], [2, 7], [3, 4]] + group = {v: k for k, values in enumerate(groups) for v in values} + for i in range(8): + for j in range(8): + same = group[i] == group[j] + need((spaces[i] == spaces[j]) == same, 'Exact equal-space classes') + need(len(spaces[i] & spaces[j]) == (128 if same else 64), 'Exact pair intersection') + if i != j: + need(len(supports[i] & supports[j]) == (0 if same else 2), 'Complete four-partite incidence') + all_ports = set.union(*supports) + need(len(all_ports) == 48 and all(sum(p in s for s in supports) == 2 for p in all_ports), 'All source incidences') + ambient = span(ports[p] for p in all_ports) + need(ambient == {v for v in range(512) if not (v & 45).bit_count() % 2}, 'Exact common hyperplane') + common = set.intersection(*spaces) + need(len(common) == 32, 'Exact common intersection dimension') + independent = [set()] + [{i} for i in range(8)] + [set(g) for g in groups] + for chosen in independent: + need(all(not supports[i] & supports[j] for i in chosen for j in chosen if i != j), 'All compatible subsets') + certificate = json.loads((ROOT/'CENTRE-SUPPORT-GEOMETRY-20261018.json').read_bytes()) + need(certificate['query_supports'] == [sorted(s) for s in supports] + and certificate['annihilators'] == [sorted(d-{0}) for d in duals] + and certificate['equal_subspace_classes'] == groups + and sorted(certificate['maximum_independent_sets']) == sorted(groups) + and certificate['conditional_eight_query_rank_lower_bound'] == 62, 'Certificate binding') + result = {'status': 'PASS_INDEPENDENT_CENTRE_SUPPORT_GEOMETRY', 'source_pins': PINS, + 'source_decompressed_pins': SOURCE_PINS, 'support_dimensions': [7]*8, + 'equal_space_classes': groups, 'pairwise_distinct_space_intersection_dimension': 6, + 'common_space_dimension': 5, 'ambient_dimension': 8, + 'direct_schedule_lower_bound': 62, + 'method': 'Explicit primal XOR closure; independent RREF nullspace equations; exact set intersections; complete multipartite graph proof.', + 'scope': 'One direct capture per row with single unwarped carriers on monotone source-subspace chains. Pair coding violates this carrier premise.', + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest()} + (OUT/'CHECKS.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(result['status']) + + +if __name__ == '__main__': + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/portable/dyadic-producer.py b/research/actual-query-information-bounds/annexes/source-geometry/portable/dyadic-producer.py new file mode 100644 index 0000000000..a63fa4bb00 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/portable/dyadic-producer.py @@ -0,0 +1,137 @@ +"""Check the actual source matrices for the query separation theorem.""" + +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json + + +import argparse + +ANNEX = Path(__file__).resolve().parents[1] +PARENT = ANNEX.parents[1] +parser = argparse.ArgumentParser(description=__doc__) +parser.add_argument("--out", required=True) +OUT = Path(parser.parse_args().out).resolve() +OUT.mkdir(parents=True, exist_ok=True) +HERE = ANNEX / "frozen" / 'root' +CORE = HERE.parent / "lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz" +CORE_PIN = "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa" +A = [0, 7, 20, 27, 36, 46, 57, 111] +T = [21, 37, 47, 76, 81, 87, 92, 110] + + +def need(value, message): + if not value: + raise ValueError(message) + + +def multiply(a, b): + bt = list(zip(*b)) + return [[sum(x * y for x, y in zip(row, col)) for col in bt] for row in a] + + +def transpose(a): + return [list(row) for row in zip(*a)] + + +def identity(n): + return [[F(i == j) for j in range(n)] for i in range(n)] + + +def residue(x, prime): + x = F(x) + need(x.denominator % prime != 0, "The residue map must be defined") + return x.numerator * pow(x.denominator, -1, prime) % prime + + +def rank_mod(a, prime): + rows = [[residue(x, prime) for x in row] for row in a] + rank = 0 + for col in range(len(rows[0])): + pivot = next((i for i in range(rank, len(rows)) if rows[i][col]), None) + if pivot is None: + continue + rows[rank], rows[pivot] = rows[pivot], rows[rank] + scale = pow(rows[rank][col], -1, prime) + rows[rank] = [x * scale % prime for x in rows[rank]] + for i in range(len(rows)): + if i != rank and rows[i][col]: + scale = rows[i][col] + rows[i] = [(x - scale * y) % prime for x, y in zip(rows[i], rows[rank])] + rank += 1 + if rank == len(rows): + break + return rank + + +def main(): + raw = gzip.decompress(CORE.read_bytes()) + need(sha256(raw).hexdigest() == CORE_PIN, "The actual core pin must match") + core = json.loads(raw) + r = [[F(row.get(str(p), 0)) for p in range(112)] for row in core["R"]] + ordinary = [p for p in range(112) if p not in A] + ra = [[row[p] for p in A] for row in r] + ru = [[row[p] for p in ordinary] for row in r] + d = [[x / 4 for x in row] for row in multiply(transpose(ru), ra)] + b = transpose(d) + dt = [d[ordinary.index(p)] for p in T] + need(multiply(dt, transpose(dt)) == identity(8), "D_T D_T^t must be identity") + need(multiply(transpose(dt), dt) == identity(8), "D_T^t D_T must be identity") + need(multiply(b, d) == [[13 * x for x in row] for row in identity(8)], "BD must be 13I") + m = [[F(0) for _ in ordinary] for _ in A] + for j, p in enumerate(T): + for i in range(8): + m[i][ordinary.index(p)] = dt[j][i] + need(multiply(m, d) == identity(8), "The sparse log must be a section") + need(rank_mod(b, 13) == 8, "B must have full row rank at 13") + need(rank_mod(b + m, 13) == 16, "The dyadic stack must have rank sixteen") + + # Each new row is a dyadic kernel row plus the original section. + kernel = [] + for j in range(len(ordinary)): + row = [F(j == k) for k in range(len(ordinary))] + for i in range(8): + for k in range(len(ordinary)): + row[k] -= d[j][i] * m[i][k] + kernel.append(row) + cases = 64 + for case in range(cases): + candidate = [row[:] for row in m] + for i in range(8): + row = kernel[(11 * case + 7 * i) % len(kernel)] + scale = F((case % 5) - 2, 2 ** (case % 4)) + candidate[i] = [x + scale * y for x, y in zip(candidate[i], row)] + need(multiply(candidate, d) == identity(8), "Each perturbed log must remain a section") + need(rank_mod(b + candidate, 13) == 16, "Each perturbed stack must have rank sixteen") + + matched = [[x / 13 for x in row] for row in b] + need(multiply(matched, d) == identity(8), "The matched log must be a rational section") + need(rank_mod(b + matched, 17) == 8, "The matched stack must have rank eight") + need(any(x.denominator % 13 == 0 for row in matched for x in row), "The matched log leaves the dyadic ring") + need(all(13 * x == y for row, source in zip(matched, b) for x, y in zip(row, source)), "The exact row dependence must hold") + bad = [[13 * x for x in row] for row in m] + need(rank_mod(b + bad, 13) == 8, "The nonunit control must defeat the residue rank conclusion") + receipt = { + "status": "PASS_DYADIC_QUERY_SEPARATION", + "core_decompressed_sha256": CORE_PIN, + "proof_sha256": sha256((HERE / "DYADIC-QUERY-SEPARATION-20261018.md").read_bytes()).hexdigest(), + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "selected": A, + "ordinary_minor": T, + "BD": "13I", + "prime": 13, + "B_rank": 8, + "dyadic_section_stack_rank": 16, + "kernel_perturbed_sections": cases, + "matched_section_stack_rank": 8, + "scope": "Source information rank and exact representation choice; no native child bound or supplier claim.", + } + destination = OUT / "DYADIC-QUERY-SEPARATION-20261018.json" + destination.write_text(json.dumps(receipt, indent=2) + "\n", encoding="utf-8") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/portable/dyadic-review.py b/research/actual-query-information-bounds/annexes/source-geometry/portable/dyadic-review.py new file mode 100644 index 0000000000..4bc5e1dee1 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/portable/dyadic-review.py @@ -0,0 +1,308 @@ +"""Review the residue-field query theorem on the actual centre matrices.""" + +from fractions import Fraction as Q +from hashlib import sha256 +import gzip +import json +from pathlib import Path + + +import argparse + +ANNEX = Path(__file__).resolve().parents[1] +PARENT = ANNEX.parents[1] +parser = argparse.ArgumentParser(description=__doc__) +parser.add_argument("--out", required=True) +OUT = Path(parser.parse_args().out).resolve() +OUT.mkdir(parents=True, exist_ok=True) +HERE = ANNEX / "frozen" / 'lanes/bridge-review-20261017/dyadic-query-separation-review-20261018' +CAMPAIGN = HERE.parents[2] +PINS = { + "root/DYADIC-QUERY-SEPARATION-20261018.md": "664f430efd099f35cbc7c2abc8025968c03020707027857d2882daa51a065a1a", + "root/check_dyadic_query_separation_20261018.py": "b4ed000b5b600944f614b86ae7a88ac55af8eac3213e6827ed211a2630ccd342", + "root/DYADIC-QUERY-SEPARATION-20261018.json": "e66d5c311490c06973bf604d207fb5cf7a9cd4800c0cea049623c3b5e2369732", + "lanes/oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md": "1a4d715e089773a9063fba88d5b83ec770bb5eb6ed501bc8f96b290c19b08401", + "lanes/controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md": "50ce523e083f70556cc62694219da94b684cc898f3d5e358767fcc40dd77e4bc", +} +CORE = "lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz" +CORE_RAW_PIN = "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa" +A = [0, 7, 20, 27, 36, 46, 57, 111] +T = [21, 37, 47, 76, 81, 87, 92, 110] +U = [p for p in range(112) if p not in A] +P = 13 + + +def require(ok, label): + if not ok: + raise ValueError(label) + + +def eye(n): + return [[Q(i == j) for j in range(n)] for i in range(n)] + + +def tr(a): + return [list(c) for c in zip(*a)] + + +def mm(a, b): + out = [[Q(0) for _ in b[0]] for _ in a] + for i, row in enumerate(a): + for k, value in enumerate(row): + if value: + for j, right in enumerate(b[k]): + if right: + out[i][j] += value * right + return out + + +def inverse(a): + n = len(a) + rows = [list(row) + unit for row, unit in zip(a, eye(n))] + for j in range(n): + pivot = next((k for k in range(j, n) if rows[k][j]), None) + require(pivot is not None, "Invertible exact minor") + rows[j], rows[pivot] = rows[pivot], rows[j] + value = rows[j][j] + rows[j] = [x / value for x in rows[j]] + for k in range(n): + if k != j: + value = rows[k][j] + rows[k] = [x - value * y for x, y in zip(rows[k], rows[j])] + return [row[n:] for row in rows] + + +def dyadic(a): + return all(x.denominator & (x.denominator - 1) == 0 for row in a for x in row) + + +def mod(a): + out = [] + for row in a: + values = [] + for x in row: + x = Q(x) + require(x.denominator % P != 0, "The coefficient has a defined residue") + values.append(x.numerator * pow(x.denominator, -1, P) % P) + out.append(values) + return out + + +def pivots(a): + # Build a column basis, instead of reducing the source matrix by rows. + basis = {} + chosen = [] + for j, col in enumerate(zip(*a)): + v = list(col) + for pivot, b in sorted(basis.items()): + value = v[pivot] + v = [(x - value * y) % P for x, y in zip(v, b)] + pivot = next((k for k, value in enumerate(v) if value), None) + if pivot is not None: + inv = pow(v[pivot], -1, P) + basis[pivot] = [x * inv % P for x in v] + chosen.append(j) + return chosen + + +def determinant(a): + rows = [list(r) for r in a] + det = Q(1) + for j in range(len(rows)): + pivot = next((k for k in range(j, len(rows)) if rows[k][j]), None) + if pivot is None: + return Q(0) + if pivot != j: + rows[j], rows[pivot] = rows[pivot], rows[j] + det *= -1 + v = rows[j][j] + det *= v + for k in range(j + 1, len(rows)): + c = rows[k][j] / v + for col in range(j + 1, len(rows)): + rows[k][col] -= c * rows[j][col] + return det + + +def actual_matrices(): + for path, pin in PINS.items(): + require(sha256((CAMPAIGN / path).read_bytes()).hexdigest() == pin, path) + raw = gzip.decompress((CAMPAIGN / CORE).read_bytes()) + require(sha256(raw).hexdigest() == CORE_RAW_PIN, "Actual clean-core payload pin") + core = json.loads(raw) + r = [[Q(row.get(str(p), 0)) for p in range(112)] for row in core["R"]] + ra = [[row[p] for p in A] for row in r] + ru = [[row[p] for p in U] for row in r] + rai = inverse(ra) + b = mm(rai, ru) + d = mm(tr(ru), tr(rai)) + require(dyadic(b) and dyadic(d), "Actual graphs are dyadic") + require(mm(b, d) == [[13 * x for x in row] for row in eye(8)], "Actual BD=13I") + dt = [d[U.index(p)] for p in T] + dti = inverse(dt) + bt = [[row[U.index(p)] for p in T] for row in b] + bti = inverse(bt) + require(dyadic(dti) and dyadic(bti), "Actual source and query minors are dyadic units") + require(mm(dt, dti) == mm(dti, dt) == eye(8), "Both ordinary inverse-minor orders") + require(mm(bt, bti) == mm(bti, bt) == eye(8), "Both B inverse-minor orders") + m = [[Q(0) for _ in U] for _ in A] + for i in range(8): + for j, p in enumerate(T): + m[i][U.index(p)] = dti[i][j] + require(mm(m, d) == eye(8), "Sparse starting section") + return b, d, m + + +def log_checks(b, d, m): + require(len(pivots(mod(b))) == 8, "B has full row rank modulo 13") + cols = pivots(mod(b + m)) + require(len(cols) == 16, "Independent source stack modulo 13") + minor = [[row[j] for j in cols] for row in b + m] + det = determinant(minor) + require(det and mod([[det]])[0][0], "Explicit minor lifts to a nonzero rational determinant") + ker = eye(104) + projection = mm(d, m) + ker = [[x - y for x, y in zip(row, sub)] for row, sub in zip(ker, projection)] + require(mm(ker, d) == [[0] * 8 for _ in U], "Exact kernel projector rows") + cases = [] + last = None + for case in range(24): + unit = eye(8) + a, j = case % 8, (case + 1) % 8 + unit[a][a] = Q(2) if case % 2 else Q(1, 2) + unit[a][j] = Q((-1) ** case, 2 ** (case % 3)) + unit_inv = inverse(unit) + require(unit != eye(8) and dyadic(unit_inv) and mm(unit, unit_inv) == mm(unit_inv, unit) == eye(8), "Nonidentity dyadic unit K") + candidate = mm(unit, m) + for row in range(8): + krow = ker[(17 * case + 9 * row + 1) % 104] + coefficient = Q(1 + case % 5, 2 ** (row % 3)) + candidate[row] = [x + coefficient * y for x, y in zip(candidate[row], krow)] + require(mm(candidate, d) == unit, "MD can be a general unit, not only identity") + require(len(pivots(mod(b + candidate))) == 16, "Every general-unit fixture has rank 16") + cases.append({"case": case, "MD_is_identity": False, "stack_rank_mod_13": 16}) + last = candidate + matched = [[x / 13 for x in row] for row in b] + require(mm(matched, d) == eye(8) and all(13 * x == y for row, base in zip(matched, b) for x, y in zip(row, base)), "Matched exact section and row dependence") + require(not dyadic(matched), "Matched section leaves the dyadic ring") + try: + mod(matched) + except ValueError: + pass + else: + raise ValueError("The matched coefficient must not have a mod-13 residue") + require(len(pivots(mod(b + b))) == 8 and mm(b, d) != eye(8), "A rationally invertible MD alone is insufficient") + require(len(pivots([[0], [1]])) == 1, "B=13,D=M=1 defeats the conclusion without full residue rank") + require(len(pivots([[1], [1]])) == 1, "B=D=M=1 defeats the conclusion when c survives reduction") + return last, {"B_rank_mod_13": 8, "stack_rank_mod_13": 16, + "explicit_minor_ports": [U[j] for j in cols], "explicit_minor_determinant": str(det), + "nonidentity_MD_cases": cases, "matched_rank_over_Q": 8, + "controls": ["M=B has MD=13I and rank-eight stack", "Missing B residue rank", "Missing zero residue of c", "Matched coefficients have no residue at 13"]} + + +def mm_mod(a, b): + columns = list(zip(*b)) + return [[sum(x * y for x, y in zip(row, col)) % P for col in columns] for row in a] + + +def route(index): + # This is the residue of L(b) U(i*a), a Gaussian-dyadic unit. + a, b = (index % 7) + 1, (index % 5) + 1 + ia = 5 * a % P + forward = [[1, ia], [b, (1 + b * ia) % P]] + back = [[(1 + b * ia) % P, -ia % P], [-b % P, 1]] + require(mm_mod(forward, back) == mm_mod(back, forward) == [[1, 0], [0, 1]], "Gaussian unit route and its inverse") + return forward, back + + +def lift(a, target_routes, source_routes): + out = [[0] * (2 * len(a[0])) for _ in range(2 * len(a))] + for i, row in enumerate(a): + left = target_routes[i][1] + for j, x in enumerate(row): + block = mm_mod(left, source_routes[j][0]) + for s in range(2): + for t in range(2): + out[2 * i + s][2 * j + t] = x * block[s][t] % P + return out + + +def routed_check(b, d, m): + require((5 * 5 + 1) % P == 0 and 2 * 7 % P == 1, "Gaussian dyadic residue i->5, 1/2->7") + eroutes = [route(3 * j + 1) for j in range(8)] + uroutes = [route(5 * j + 2) for j in range(104)] + require(mm_mod(eroutes[0][0], uroutes[0][0]) != mm_mod(uroutes[0][0], eroutes[0][0]), "The fixture uses noncommuting routes") + br = lift(mod(b), eroutes, uroutes) + dr = lift(mod(d), uroutes, eroutes) + mr = lift(mod(m), eroutes, uroutes) + require(mm_mod(br, dr) == [[0] * 16 for _ in range(16)], "Routed BD reduces to zero with the exact order") + require(len(pivots(mm_mod(mr, dr))) == 16, "Routed MD is a unit") + require(len(pivots(br)) == 16 and len(pivots(br + mr)) == 32, "Routed two-coordinate stack has rank 32") + return {"coordinates_per_field": 2, "query_rank_mod_13": 32, "noncommuting_routes": True, + "scope": "An actual-B Gaussian-unit conjugation fixture; the general finite-operator version follows from the residue proof, not a new native route replay."} + + +def full_null_check(): + zero, v, beta = {}, {(): 1}, {("beta",): 1} + + def add(a, b, coefficient=1): + out = dict(a) + for word, value in b.items(): + out[word] = out.get(word, 0) + coefficient * value + if not out[word]: + del out[word] + return out + + def apply(op, a): + out = {} + for word, value in a.items(): + term = (op,) + word + if len(term) >= 2 and term[:2] in [("Q", "q"), ("q", "Q")]: + term = term[2:] + out[term] = out.get(term, 0) + value + return {word: value for word, value in out.items() if value} + + bv, mv = apply("B", v), apply("M", v) + dbv = apply("D", bv) + original_u = add(v, dbv, -1) + qa = add(zero, mv, -1) + a = apply("q", qa) + original_b = add(apply("Q", bv), apply("q", mv), -1) + original_b = {word: -value for word, value in original_b.items()} + incoming_v = add(dbv, original_u) + incoming_b = add(original_b, a) + d = add(qa, apply("M", incoming_v)) + h = add(apply("q", incoming_b), apply("B", incoming_v)) + w = add(add(original_u, incoming_v, -1), apply("D", add(d, apply("q", incoming_b), -1))) + require(incoming_v == v and d == h == w == zero, "Full-null family without any MD or BD relation") + require(add(add(zero, incoming_v, -1), v) == zero, "The next ordinary bridge cancels for every pair count") + bad_b = add(zero, apply("Q", bv), -1) + require(add(apply("q", add(bad_b, a)), bv) != zero, "The original-b qMv term is necessary") + source_w = add(add(zero, apply("D", beta), -1), add(apply("D", mv), v, -1)) + source_d = mv + f0 = add(add(zero, source_w, -1), apply("D", source_d)) + g = add(source_d, apply("M", f0), -1) + require(f0 == add(v, apply("D", beta)) and g == add(zero, apply("M", apply("D", beta)), -1), "General MD unit-criterion factorization") + return {"operator_relations": ["Qq=I", "qQ=I"], "uses_MD_identity": False, + "uses_BD_identity_for_null_family": False, "unit_factorization": "diag(I,-MD)", + "wrong_original_b_control": True, "all_pair_counts": "The future inputs and all visible outputs are zero; the only nonzero next-bank bridge is -v+v."} + + +def main(): + b, d, m = actual_matrices() + candidate, actual = log_checks(b, d, m) + routed = routed_check(b, d, candidate) + full_null = full_null_check() + out = {"status": "PASS_INDEPENDENT_DYADIC_QUERY_SEPARATION", "source_pins": PINS, + "core_decompressed_sha256": CORE_RAW_PIN, "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "actual_source": actual, "routed_operator_fixture": routed, "formal_full_null": full_null, + "universal_proof": "Residue row relation times D forces beta=0 because MD is a unit; full residue rank of B forces alpha=0. A nonzero residue minor lifts to the fraction field.", + "scope": "Fixed linear observations on the full underlying field space, with arbitrary postprocessing. No native-child, bit-packing, arbitrary nonlinear-encoding or complete supplier lower bound."} + (OUT / "REVIEW.json").write_text(json.dumps(out, sort_keys=True, indent=2) + "\n") + print(out["status"]) + print(json.dumps({"rank": 16, "matched_rank": 8, "MD_nonidentity_cases": 24, "routed_rank": 32, + "null_family_uses_MD_identity": False}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/portable/query-span-producer.py b/research/actual-query-information-bounds/annexes/source-geometry/portable/query-span-producer.py new file mode 100644 index 0000000000..717420c19d --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/portable/query-span-producer.py @@ -0,0 +1,94 @@ +"""Check exact scalar source spans for the actual line and plane queries.""" + +from hashlib import sha256 +from pathlib import Path +import json + + +import argparse + +ANNEX = Path(__file__).resolve().parents[1] +PARENT = ANNEX.parents[1] +parser = argparse.ArgumentParser(description=__doc__) +parser.add_argument("--out", required=True) +OUT = Path(parser.parse_args().out).resolve() +OUT.mkdir(parents=True, exist_ok=True) +HERE = ANNEX / "frozen" / 'lanes/schur-selection/plane-repair' +ROOT = HERE.parents[4] +INTERFACE_PIN = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" +PLANE_PIN = "f55bd0e7b81a15b6526ca3056ef3bf1bbf57b13137699e71a374f4cf8f55f794" +ARCHIVE_PIN = "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6" +PHASE_PIN = "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + + +def need(value, message): + if not value: + raise ValueError(message) + + +def dot(x,y): + return (x & y).bit_count() & 1 + + +def main(): + raw = (PARENT / "payload/lanes/circuit-interface/INTERFACE.json").read_bytes() + need(sha256(raw).hexdigest() == INTERFACE_PIN, "Actual eight centre rows") + interface = json.loads(raw) + rows = [[int(row.get(str(p),0)) for p in range(112)] for row in interface["R"]] + need(len(rows) == 8, "Eight required centre outputs") + need([[sum(rows[i][p]*rows[j][p] for p in range(112)) for j in range(8)] for i in range(8)] + == [[56*int(i == j) for j in range(8)] for i in range(8)], "Actual row Gram") + archive_record = json.loads((ANNEX / "ARCHIVE-CHECK.json").read_bytes()) + need(archive_record["archive_sha256"] == ARCHIVE_PIN, "Historical archive binding") + phase = (PARENT / "payload/upstream/DATA-PHASES.json").read_bytes() + need(sha256(phase).hexdigest() == PHASE_PIN, "Actual line labels") + labels = [r["q"] for r in sorted(json.loads(phase)["recipes"],key=lambda r:r["port"])] + need(len(labels) == len(set(labels)) == 112 and all(labels), "Distinct nonzero actual line labels") + line_pivots = [] + for p,q in enumerate(labels): + i = next(i for i in range(8) if rows[i][p]) + line_pivots.append({"port":p,"q":q,"centre_row":i,"pivot":rows[i][p]}) + need(all(abs(x["pivot"]) == 1 for x in line_pivots), "Explicit nonzero diagonal stacked minor") + raw_plane = (HERE / "PLANE-INVOLUTION.json").read_bytes() + need(sha256(raw_plane).hexdigest() == PLANE_PIN, "Frozen actual plane operators") + planes = json.loads(raw_plane)["planes"] + plane_pivots = [] + character_checks = 0 + determinant = 1 + for k,plane in enumerate(planes): + q,r = plane["q"],plane["r"] + w = q ^ r + need(w != 0, "A nonzero plane swap direction") + for j,other in enumerate(planes): + if other["q"] ^ other["r"] == w: + numerator = sum((-1) ** dot(q ^ other["q"],y) for y in range(512) if dot(w,y)) + need(numerator == 256*int(k == j), "Exact plane-separating functional") + character_checks += 256 + p,s = plane["ports"] + need([labels[p],labels[s]] == [q,r], "Matching uses actual line labels") + gram = [[sum(rows[i][a]*rows[i][b] for i in range(8)) for b in (p,s)] for a in (p,s)] + need(gram[0][0]*gram[1][1]-gram[0][1]*gram[1][0] == 12, + "Each matched pair has two independent scalar input columns") + i,j,d = next((i,j,rows[i][p]*rows[j][s]-rows[i][s]*rows[j][p]) + for i in range(8) for j in range(i+1,8) + if rows[i][p]*rows[j][s]-rows[i][s]*rows[j][p]) + determinant *= d + plane_pivots.append({"plane":k,"ports":[p,s],"centre_rows":[i,j],"determinant":d}) + need(sum(not dot(w,y) for y in range(512)) == 256, "Plane trace in the Fourier basis") + need(determinant != 0, "Explicit nonsingular 112-column plane stacked minor") + result = {"status":"PASS_EXACT_QUERY_SOURCE_SPANS", "interface_sha256":INTERFACE_PIN, + "archive_sha256":ARCHIVE_PIN,"phase_sha256":PHASE_PIN,"plane_receipt_sha256":PLANE_PIN, + "output_fields":8,"input_fields":112,"line_scalar_input_rank":112, + "line_pivot_functionals":line_pivots,"plane_scalar_input_rank":112, + "plane_pivot_functionals":plane_pivots,"plane_minor_determinant_in_matching_order":determinant, + "plane_character_sum_checks":character_checks, + "plane_endpoint_functional":"normalized trace minus constant-character expectation", + "plane_endpoint_value_at_tensor_depth_lambda":"2^(-lambda)-1", + "scope":"Exact scalar input spans for plain-input operator matrices, plus proof-based all-depth extension. This is a payload-query count bound under scalar free gates, not a native-child or rank-zero-map lower bound for the full supplier."} + (OUT / "QUERY-SPAN.json").write_text(json.dumps(result,indent=2,sort_keys=True)+"\n") + print(result["status"]) + print(json.dumps({k:result[k] for k in ("line_scalar_input_rank","plane_scalar_input_rank","plane_minor_determinant_in_matching_order","plane_character_sum_checks")},sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/portable/query-span-review.py b/research/actual-query-information-bounds/annexes/source-geometry/portable/query-span-review.py new file mode 100644 index 0000000000..df1898069d --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/portable/query-span-review.py @@ -0,0 +1,193 @@ +"""Check the source rows and the exact line and plane query certificates.""" + +from collections import Counter +from fractions import Fraction +from hashlib import sha256 +import gzip +import json +from pathlib import Path + + +import argparse + +ANNEX = Path(__file__).resolve().parents[1] +PARENT = ANNEX.parents[1] +parser = argparse.ArgumentParser(description=__doc__) +parser.add_argument("--out", required=True) +OUT = Path(parser.parse_args().out).resolve() +OUT.mkdir(parents=True, exist_ok=True) +HERE = ANNEX / "frozen" / 'lanes/source-domain/query-span-review' +LANES = HERE.parents[1] +ROOT = LANES.parents[2] +PACKET = LANES / "schur-selection/plane-repair" +PINS = { + "QUERY-SPAN.md": "785e27fdc6f2bcd83318afee14103f3e021065d32be2265b8afdec3fea3e1081", + "check_query_span.py": "bcc8bb5482c76578014512d51dd5d650d4bf13d6546b29e355ae01bec8a07811", + "QUERY-SPAN.json": "a06939cba2c937f452027ee4a1f20b31121a70b7fc7393d9ccad091817ee448e", + "PLANE-INVOLUTION.json": "f55bd0e7b81a15b6526ca3056ef3bf1bbf57b13137699e71a374f4cf8f55f794", +} +ARCHIVE = "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6" +MEMBERS = { + "word": ("candidate/strict/global/base/providers/gauge44/CANONICAL-WORD.json.gz", + "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219"), + "program": ("candidate/strict/global/base/providers/gauge44/LOCAL-PROGRAMS.json.gz", + "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a"), + "phases": ("candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json", + "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"), +} + + +def need(value, reason): + if not value: + raise ValueError(reason) + + +def dot(a, b): + return (a & b).bit_count() % 2 + + +def add(target, source, coefficient): + for key, value in source.items(): + new = target.get(key, 0) + coefficient * value + if new: + target[key] = new + else: + target.pop(key, None) + + +def main(): + for name, pin in PINS.items(): + need(sha256((PACKET / name).read_bytes()).hexdigest() == pin, "Frozen packet: " + name) + certificate = json.loads((PACKET / "QUERY-SPAN.json").read_bytes()) + planes = json.loads((PACKET / "PLANE-INVOLUTION.json").read_bytes())["planes"] + archive_record = json.loads((ANNEX / "ARCHIVE-CHECK.json").read_bytes()) + need(archive_record["archive_sha256"] == ARCHIVE, "Historical archive binding") + source = {} + for key, (name, pin) in MEMBERS.items(): + raw = (PARENT / "payload/upstream" / Path(name).name).read_bytes() + need(sha256(raw).hexdigest() == pin, "Selected member: " + key) + source[key] = json.loads(gzip.decompress(raw) if name.endswith(".gz") else raw) + word, program, phases = [source[key] for key in MEMBERS] + rows = [{i: Fraction(1)} if i < 112 else {} for i in range(712)] + count = 0 + for event in program["forward"]: + if event == ["phase", "centers"]: + break + if event[0] != "scalar": + continue + gate = event[1] + t = gate[1][1] + (704 if gate[1][0] == "C" else 0) + if gate[0] == "clear": + rows[t] = {} + elif gate[0] == "scale": + coefficient = Fraction(gate[2], gate[3]) + rows[t] = {i: value * coefficient for i, value in rows[t].items() if value * coefficient} + else: + s = gate[2][1] + (704 if gate[2][0] == "C" else 0) + if gate[0] == "copy": + rows[t] = rows[s].copy() + else: + add(rows[t], rows[s], Fraction(gate[3], gate[4])) + count += 1 + else: + raise ValueError("The original centre boundary is absent") + matrix = [[rows[centre].get(p, 0) for p in range(112)] for centre in word["centers"]] + interface_raw = (PARENT / "payload/lanes/circuit-interface/INTERFACE.json").read_bytes() + need(sha256(interface_raw).hexdigest() == certificate["interface_sha256"], "Accepted interface pin") + interface = json.loads(interface_raw) + expected = [[Fraction(row.get(str(p), "0")) for p in range(112)] for row in interface["R"]] + need(matrix == expected and len(matrix) == 8, "Independent source reconstruction of R") + gram = [[sum(a * b for a, b in zip(row, other)) for other in matrix] for row in matrix] + need(gram == [[56 * int(i == j) for j in range(8)] for i in range(8)], "Actual row Gram") + labels = [record["q"] for record in phases["recipes"]] + need(labels == word["ports"] == interface["ports"] and len(set(labels)) == 112 + and all(q and q.bit_count() % 2 for q in labels), "Exact distinct odd line labels") + need(all(sum(matrix[i][p] != 0 for i in range(8)) == 4 for p in range(112)), + "Four nonzero source entries in every column") + for p, row in enumerate(certificate["line_pivot_functionals"]): + need(row["port"] == p and row["q"] == labels[p] + and matrix[row["centre_row"]][p] == row["pivot"] + and abs(row["pivot"]) == 1, "Every line diagonal pivot") + need(len(planes) == 56 and sorted(p for plane in planes for p in plane["ports"]) == list(range(112)), + "The 56 planes partition the actual ports") + directions = Counter(plane["q"] ^ plane["r"] for plane in planes) + need(len(directions) == 41, "Repeated plane directions are retained") + # Build each exact Fourier column from C_q C_r^-1 P_(q+r). + columns = [] + trace_counts = [] + for plane in planes: + p, s = plane["ports"] + q, r = plane["q"], plane["r"] + need([q, r] == [labels[p], labels[s]] and dot(q, r) == 0, "Actual ordered orthogonal pair") + w = q ^ r + operator = [] + for y in range(512): + image = y ^ (w if dot(w, y) else 0) + power = (dot(q, image) - dot(r, image)) % 4 + operator.append((image, power)) + need(all(operator[image][0] == y and (power + operator[image][1]) % 4 == 0 + for y, (image, power) in enumerate(operator)), "Exact plane involution") + need(operator[0] == (0, 0), "Constant character is fixed") + trace = sum(1 for y, (image, power) in enumerate(operator) if image == y and power == 0) + need(trace == 256 and all(power == 0 for y, (image, power) in enumerate(operator) if image == y), + "Exact normalized plane trace") + trace_counts.append(trace) + columns.append(operator) + unit = [(1, 0), (0, 1), (-1, 0), (0, -1)] + functional_checks = 0 + for k, plane in enumerate(planes): + q, w = plane["q"], plane["q"] ^ plane["r"] + support = [y for y in range(512) if dot(w, y)] + for j, operator in enumerate(columns): + real = imag = 0 + for y in support: + image, power = operator[y] + if image == y ^ w: + a, b = unit[(power - 1 + 2 * dot(q, y)) % 4] + real += a + imag += b + functional_checks += 1 + need((real, imag) == (256 * int(j == k), 0), "Full plane-separating functional matrix") + determinant = 1 + for k, (plane, pivot) in enumerate(zip(planes, certificate["plane_pivot_functionals"])): + p, s = plane["ports"] + a, b = [matrix[i][p] for i in range(8)], [matrix[i][s] for i in range(8)] + det_gram = sum(x*x for x in a) * sum(y*y for y in b) - sum(x*y for x, y in zip(a, b))**2 + need(det_gram == 12 and pivot["plane"] == k and pivot["ports"] == [p, s], "Actual pair Gram and order") + i, j = pivot["centre_rows"] + det = a[i] * b[j] - b[i] * a[j] + need(det == pivot["determinant"] and det != 0, "Exact certified two-column pivot") + determinant *= det + need(determinant == certificate["plane_minor_determinant_in_matching_order"] == 8, + "Exact 112-column block determinant") + need(certificate["line_scalar_input_rank"] == certificate["plane_scalar_input_rank"] == 112, + "Stated source ranks") + # A reversed plane orientation changes the moved-character sign. + q, r = planes[0]["q"], planes[0]["r"] + w = q ^ r + y = next(y for y in range(512) if dot(w, y)) + image = y ^ w + need((dot(q, image) - dot(r, image)) % 4 != (dot(r, image) - dot(q, image)) % 4, + "Wrong plane orientation control") + result = dict(status="PASS_INDEPENDENT_QUERY_SPAN_SOURCE_AND_CERTIFICATE", + frozen_packet_sha256=PINS, archive_sha256=ARCHIVE, + source_member_sha256={k: pin for k, (_, pin) in MEMBERS.items()}, + source_scalar_events_replayed=count, source_rows=8, nonzero_line_columns=112, + line_source_rank=112, plane_source_rank=112, + planes=56, distinct_plane_directions=len(directions), + repeated_direction_group_sizes=sorted(directions.values()), + exact_Fourier_columns=56*512, separating_functional_column_checks=functional_checks, + pair_Gram_determinants=[12]*56, exact_block_minor_determinant=int(determinant), + source_reconstruction="Independent data-only scalar propagation to the original centre boundary; no producer import or execution.", + all_depth="Proof: compress all but one tensor factor to the fixed constant character.", + grammar="Every non-scalar payload map is counted, including rank-zero address maps; scalar initial and final contracts are required.", + controls=["Exact reversed-orientation moved-character sign differs."], + not_certified=["Native-child lower bound", "Native-cost bound", "Changed source interface", "Supplier or kappa improvement"]) + (OUT / "REVIEW.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n", encoding="utf-8") + print(result["status"]) + print(json.dumps({key: result[key] for key in ("source_scalar_events_replayed", "exact_Fourier_columns", + "separating_functional_column_checks", "exact_block_minor_determinant")})) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/annexes/source-geometry/replay.py b/research/actual-query-information-bounds/annexes/source-geometry/replay.py new file mode 100644 index 0000000000..858fb38149 --- /dev/null +++ b/research/actual-query-information-bounds/annexes/source-geometry/replay.py @@ -0,0 +1,116 @@ +"""Replay the seven exact source-geometry checks with one process at a time.""" + +import argparse +import hashlib +import json +import os +from pathlib import Path +import shutil +import subprocess +import sys +import time + + +HERE = Path(__file__).resolve().parent +PARENT = HERE.parents[1] + + +def require(test, reason): + if not test: + raise ValueError(reason) + + +def digest(path): + return hashlib.sha256(path.read_bytes()).hexdigest() + + +def check_files(root, records): + for relative, record in records.items(): + path = root / relative + require(path.is_file(), "Missing file: " + str(path)) + require(path.stat().st_size == record["bytes"], "File size: " + str(path)) + require(digest(path) == record["sha256"], "File hash: " + str(path)) + + +def compare(actual, expected, location="$"): + require(type(actual) is type(expected), "JSON type: " + location) + if isinstance(actual, dict): + require(actual.keys() == expected.keys(), "JSON keys: " + location) + for key in actual: + compare(actual[key], expected[key], location + "/" + key) + elif isinstance(actual, list): + require(len(actual) == len(expected), "JSON length: " + location) + for index, (left, right) in enumerate(zip(actual, expected)): + compare(left, right, location + "/" + str(index)) + else: + require(actual == expected, "JSON value: " + location) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--out", type=Path, required=True) + arguments = parser.parse_args() + out = arguments.out.resolve() + require(not out.is_relative_to(PARENT), "The output must be outside the package") + require(not out.exists(), "Use a new output directory") + require(shutil.disk_usage(HERE).free >= 3 * 1024**3, "At least 3 GiB must be free") + manifest = json.loads((HERE / "ANNEX-MANIFEST.json").read_bytes()) + parent = json.loads((HERE / "PARENT-SNAPSHOT.json").read_bytes()) + portability = json.loads((HERE / "PORTABILITY.json").read_bytes()) + check_files(HERE, manifest["files"]) + check_files(PARENT, parent["files"]) + actual_paths = {str(p.relative_to(HERE)) for p in HERE.rglob("*") if p.is_file()} + require(actual_paths == set(manifest["files"]) | {"ANNEX-MANIFEST.json"}, + "The annex manifest must list every file") + out.mkdir(parents=True) + env = dict(os.environ) + env.update({key: "1" for key in ["OPENBLAS_NUM_THREADS", "OMP_NUM_THREADS", + "MKL_NUM_THREADS", "NUMEXPR_NUM_THREADS"]}) + env["PYTHONDONTWRITEBYTECODE"] = "1" + flags = ["-I", "-B"] + (["-O"] if sys.flags.optimize else []) + results = [] + started = time.monotonic() + for job in portability["checks"]: + script = HERE / job["portable_script"] + destination = out / job["name"] + command = [sys.executable, *flags, str(script), "--out", str(destination)] + begin = time.monotonic() + run = subprocess.run(command, text=True, capture_output=True, env=env, + cwd=out, check=False) + (out / (job["name"] + ".stdout.txt")).write_text(run.stdout) + (out / (job["name"] + ".stderr.txt")).write_text(run.stderr) + require(run.returncode == 0, job["name"] + " failed: " + run.stderr) + require(any(line.startswith(job["expected_status"]) for line in run.stdout.splitlines()), + "Expected PASS status: " + job["name"]) + receipts = [] + for relative in job["receipts"]: + expected = json.loads((HERE / relative).read_bytes()) + actual_path = destination / Path(relative).name + actual = json.loads(actual_path.read_bytes()) + metadata = [] + if "checker_sha256" in expected: + expected["checker_sha256"] = digest(script) + metadata.append("checker_sha256") + compare(actual, expected, relative) + receipts.append({"frozen_receipt": relative, "output": str(actual_path.relative_to(out)), + "sha256": digest(actual_path), "typed_json_equal": True, + "declared_metadata_updates": metadata}) + seconds = time.monotonic() - begin + results.append({"name": job["name"], "status": job["expected_status"], + "seconds": seconds, "receipts": receipts}) + print(job["expected_status"], flush=True) + check_files(HERE, manifest["files"]) + check_files(PARENT, parent["files"]) + result = {"status": "PASS_SOURCE_GEOMETRY_ANNEX", "checks": results, + "seconds": time.monotonic() - started, "optimized": bool(sys.flags.optimize), + "python": sys.version, "interpreter": sys.executable, + "annex_manifest_sha256": digest(HERE / "ANNEX-MANIFEST.json"), + "parent_files_unchanged": len(parent["files"]), + "annex_files_unchanged": len(manifest["files"]), + "execution": "Seven serial standard-library checks; no external tools, Git, network, or solver."} + (out / "REPLAY.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(result["status"], flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/COLD-REPLAY-CHECKS.json b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/COLD-REPLAY-CHECKS.json new file mode 100644 index 0000000000..0a6b6bebc4 --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/COLD-REPLAY-CHECKS.json @@ -0,0 +1,156 @@ +{ + "cold_package": "/private/tmp/source-geometry-independent-20261022-xfycu8mc/actual-query-information-bounds", + "command": [ + "/opt/homebrew/opt/python@3.14/bin/python3.14", + "-I", + "-O", + "-B", + "/private/tmp/source-geometry-independent-20261022-xfycu8mc/actual-query-information-bounds/annexes/source-geometry/replay.py", + "--out", + "/private/tmp/source-geometry-independent-20261022-xfycu8mc/cold-replay" + ], + "cwd": "/private/tmp/source-geometry-independent-20261022-xfycu8mc/unrelated-working-directory", + "environment_overrides": { + "MKL_NUM_THREADS": "1", + "NUMEXPR_NUM_THREADS": "1", + "OMP_NUM_THREADS": "1", + "OPENBLAS_NUM_THREADS": "1", + "PATH": "/no-external-tools", + "VECLIB_MAXIMUM_THREADS": "1" + }, + "exit_code": 0, + "free_bytes_after": 8758206464, + "free_bytes_before": 8792248320, + "package_files": 229, + "relocated_and_original_packages_equal": true, + "replay": { + "annex_files_unchanged": 99, + "annex_manifest_sha256": "cc7279ee48a7751a57f59a98f991ba879cf6e63144fcb7885ed1e4b69b432663", + "checks": [ + { + "name": "centre-support-producer", + "receipts": [ + { + "declared_metadata_updates": [], + "frozen_receipt": "frozen/root/CENTRE-SUPPORT-GEOMETRY-20261018.json", + "output": "centre-support-producer/CENTRE-SUPPORT-GEOMETRY-20261018.json", + "sha256": "dafd6c0af3f8aad852a7c80258118487744921c9a61474b1441e3755f8e3b205", + "typed_json_equal": true + } + ], + "seconds": 0.166397916036658, + "status": "PASS_CENTRE_SUPPORT_GEOMETRY" + }, + { + "name": "centre-support-review", + "receipts": [ + { + "declared_metadata_updates": [ + "checker_sha256" + ], + "frozen_receipt": "frozen/lanes/independent-review-20261017/centre-support-review-20261018/CHECKS.json", + "output": "centre-support-review/CHECKS.json", + "sha256": "61690f10c5d08981c68eaf148a7b54f81ac4e00b33fb8ebac0bc8c275368be10", + "typed_json_equal": true + } + ], + "seconds": 0.16556150000542402, + "status": "PASS_INDEPENDENT_CENTRE_SUPPORT_GEOMETRY" + }, + { + "name": "dyadic-producer", + "receipts": [ + { + "declared_metadata_updates": [ + "checker_sha256" + ], + "frozen_receipt": "frozen/root/DYADIC-QUERY-SEPARATION-20261018.json", + "output": "dyadic-producer/DYADIC-QUERY-SEPARATION-20261018.json", + "sha256": "f32f611e5d583beb5ccc2a809f37692e2fc35ed40706cb96845051c9a71befb9", + "typed_json_equal": true + } + ], + "seconds": 1.0329124580021016, + "status": "PASS_DYADIC_QUERY_SEPARATION" + }, + 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"receipts_matched": 8, + "thread_settings_one": true + }, + "material_findings_remaining": [], + "not_rerun": [ + "Historical mixing inventory emitters and modular rank checker", + "Native recipe generator", + "Plane routes", + "Odd-grid implementation", + "Parent and chronological-cache mathematics", + "Complete supplier" + ], + "package_or_prior_review_edits": false, + "preservation_and_dependencies": { + "complete_portability_diff_and_main_functions_manually_reviewed": true, + "equal_non_main_function_ASTs": 47, + "exact_original_source_files": 72, + "exact_unique_regular_archive_members": 3, + "local_README_and_NOTICE_links": 36, + "old_package_files_unchanged": 129, + "original_archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "parent_runtime_inputs": 4, + "portable_checkers": 7, + "prior_review_files_unchanged": 94 + }, + "proof_review": { + "complete_proofs_and_prior_independent_reviews_read": true, + "dependent_unit_criterion_and_full_null_arguments_read": true, + "finite_checks_used_as_universal_proof": false, + "inherited_limit": "The old mixing support producer uses forward operator order. Its consumed X histories have lengths only zero or one. The independent replay uses reverse order and checks this length limit.", + "new_mathematical_claims": false, + "query_span_prior_independent_review_gate": "Satisfied by the source-domain review, matching source/certificate pins, and retained schur-selection handoff.", + "two_basis_and_peer_extension_proofs_read": true + }, + "publication_base": "b58ad9ef4d4e861b0eaa5dba41742bdc072dca51", + "publication_gates_remaining": [ + "Replace COMMIT with the exact publication commit.", + "Verify all GitHub file and PR targets at publication.", + "Inspect the GitHub-rendered Markdown and contributor mentions.", + "Read the published body and rendered HTML back." + ], + "review_date": "2026-10-22", + "reviewed_annex": "research/actual-query-information-bounds/annexes/source-geometry", + "reviewer_role": "Separate OpenAI Codex agent; not an independent human reviewer.", + "schema": "source-geometry-independent-publication-review-v1", + "selected_conditional_kappa": "60403/20000000", + "status": "PASS_INDEPENDENT_SOURCE_GEOMETRY_PUBLICATION_REVIEW" +} diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/REVIEW.md b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/REVIEW.md new file mode 100644 index 0000000000..d574bf5fd8 --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/REVIEW.md @@ -0,0 +1,164 @@ +# Independent review of the source-geometry annex + +Accepted on 2026-10-22. No material finding remains in the four stated +theorem families, source closure, portable replay, or final description. +This is a fresh review by a separate OpenAI Codex agent. It is not human +review or proof-assistant verification. The four results have different +models. Their bounds must not be added as one cost invoice. + +The accepted annex is `actual-query-information-bounds/annexes/source-geometry`. +Its `ANNEX-MANIFEST.json` SHA256 is +`cc7279ee48a7751a57f59a98f991ba879cf6e63144fcb7885ed1e4b69b432663`. +The accepted supplemental description SHA256 is +`6a77b8b0d00506b09f2a11262c39ca9f576be968a5c261bc3f0a4c6cbb783d15`. +The description standard at +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md` +was read before this check. This review made no Git or PR action and +changed no package or prior review file. + +The review read the complete proofs, their prior independent reviews, +the source dependencies that support the adopted claims, all seven +portable checkers, and the complete portability diff. The source pins are +in [REVIEWED-SOURCE-PINS.json](REVIEWED-SOURCE-PINS.json). The proof checks +and their limits follow. + +1. **Binary support geometry and direct capture.** Each of the eight row + supports has rank seven. They form four equal-space pairs. Distinct + spaces intersect in dimension six; all eight intersect in dimension + five and span dimension eight. The shared-port graph is + `K_(2,2,2,2)`. In the stated direct-capture model, a rank-seven capture + must equal its row support. A shared unwarped carrier on an increasing + subspace chain cannot visit two distinct rank-seven support spaces. + Thus the rank-seven rows form an independent set of size at most two, + and the capture-rank sum is at least `2*7+6*8=62`. The proof needs one + carrier per source and one complete direct common-frame capture per + row. Partial queries, extra carriers, and operator-valued codes are + outside this class. Pair coding does not satisfy the one-carrier + premise. The result is not a construction at 62 or a native-cost bound. + The producer's binary elimination and the reviewer's XOR spans and + nullspaces agree in the cold replay. + +2. **Dyadic fixed-observation separation.** The residue argument is valid + for every log `M` with a two-sided unit `MD`, not only `MD=I`. From + `alpha B+beta M=0`, multiplication by `D` and reduction modulo 13 force + `beta=0`, then `alpha=0`. The actual `B` has a dyadic unit minor, so + `rank[B;M]=16`. The full-null family works for general `M`; its ordered + cancellation uses `Qq=qQ=I`. The mixed-source unit criterion reduces + to `diag(I,-MD)`. With fixed linear `N` as the only further observation + of retired ordinary Y, `ker N` must lie in `ker B` intersect `ker M`. + Nonlinear postprocessing cannot distinguish equal observations. This + bounds total observation rank, not concurrent scratch or native + children. The rank-eight alternative `M=B/13` is outside the dyadics. + The stronger coefficient-ring statement uses an integral domain, an + invertible minor of `B`, and fraction-field rank eight. Under `MD=I`, + that rank-eight log is uniquely `B/13`. The finite routed extension + needs the stated ordered identities and Gaussian-dyadic two-sided + inverses after flattening. Its two-coordinate test is only a fixture. + Cold checks include 24 logs with nonidentity unit `MD`, a determinant + `1/8`, the full-null correction, and a noncommuting route fixture of + rank 32. No cheap query, scatter, decoder, or odd-grid implementation + follows from these checks. + +3. **Constant scalar centre mixing.** The physical-support proof applies + to the fixed source/Y-tail one-way insertion class. The separate + canonical-interval extension covers cuts 7502 through 17249 with a + fixed exterior, fixed wrappers, and the stated support and endpoint + conditions. The basis-state support test justifies 6,608 forbidden + off-diagonal equations on all 64 entries of `A`. A 63-row minor has + determinant `-2^71`. Since `I8` satisfies the equations, their kernel + is exactly `A=cI8`; the diagonal response is the same `c` at every + port. A nonzero response therefore cannot factor through seven + constant scalar centre channels. This conclusion does not cover new + native paths, new query/scatter spaces, arbitrary wrapper edits, or + operator-valued centre entries. The second proof uses two actual + orthogonal bases and a connected overlap graph. Its ring extension + needs units on the nonzero overlap entries. The independent checker + rebuilt both complete interval inventories and all 4,276 products, + checked physical views, and recomputed the determinant and overlap + graph. It uses reverse operator order. The old producer's forward + loop is valid for this packet because all consumed X histories have + length zero or one. That limit is checked. It must not be assumed for + longer histories. A dense rank-seven projection fails 2,534 equations; + a repeated determinant row gives zero; another actual basis pair has + two overlap components. + +4. **Payload-query source and response spans.** Both ordered + factorizations remain valid for arbitrary noncommuting payload maps: + scalar gates are `B tensor I`, queries are `I+uQv` with scalar `u,v`, + and the initial and final interfaces are scalar. Scalar COPY and + CLEAR need not be invertible. An `r`-direction block counts `r` times. + Every non-scalar payload map counts, including rank-zero address maps. + The simultaneous scalar source and response spans have dimension at + most the counted query total. Separating functionals give source rank + 112 for the actual line query and the proposed matched-plane query. + Tensor compression proves the same result at every positive depth. + The mixed-plane endpoint on `n` fields has a separate `n`-query lower + bound without a common negative eigenvector. These are not native + invoices. Prior port-dependent input encoding changes the premise. + The prior source-domain review is present and its pins agree. The + frozen proof's old pending-review note is superseded by the retained + handoff and review. Cold replay reconstructed `R` from 10,851 scalar + events and checked 28,672 Fourier columns, 802,816 functional + contributions, all 56 pair Gram determinants, and the exact block + minor determinant 8. Reversing one plane changes the expected sign. + +The source and dependency audit passed. All 72 source and notice files +are byte-equal to their originals. All 129 older package files and all 94 +prior review files are unchanged. The full historical query-span archive +has 6,095,634 bytes and SHA256 +`f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6`. +Its three consumed members are unique regular files and match the parent +members exactly. The portable replay needs those members, not the full +archive. Four parent runtime inputs are pinned. All 47 non-main function +ASTs in the seven portable checkers equal their originals. The complete +diff changes only input/output handling and two archive reads. The main +functions and driver were also read; AST equality alone was not used to +approve them. All 36 local README and notice links resolve. These checks +are recorded in +[SOURCE-AND-DEPENDENCY-CHECKS.json](SOURCE-AND-DEPENDENCY-CHECKS.json), with +the repeatable source audit in [check_annex_sources.py](check_annex_sources.py). + +The independent cold run copied the full parent package to a new temporary +directory. It ran from a separate empty working directory with +`PATH=/no-external-tools`, one-process thread settings, and Python 3.14.7 +under `-I -O -B`. All seven checks passed in 5.114940 seconds. All eight +receipts match in value and type. Four are byte-equal; the other four +change only `checker_sha256` to the actual portable checker hash. All 229 +relocated package files remained equal to the original files. Free disk +space exceeded 3 GiB before and after the run. See +[COLD-REPLAY-CHECKS.json](COLD-REPLAY-CHECKS.json), +[TYPED-RECEIPT-CHECKS.json](TYPED-RECEIPT-CHECKS.json), and +[cold.stdout.txt](cold.stdout.txt). + +From a checkout with the full parent package at its published path, use a +new output directory: + +```sh +python3 -I -O -B research/actual-query-information-bounds/annexes/source-geometry/replay.py --out /tmp/source-geometry-replay +``` + +Expected final output: + +```text +PASS_SOURCE_GEOMETRY_ANNEX +``` + +The normal and optimized producer runs are retained in the annex. This +fresh review independently ran the optimized cold check. It did not rerun +the old mixing emitters or modular checker, the native recipe generator, +plane routes, an odd-grid implementation, the parent/cache mathematics, +or a complete supplier. The counterexamples and fixtures above are not +claims that every input-mutation class was rejected. + +The final description states the four models, the cost limits, the +executed checks, the known history-order limit, omitted checks, source +credit, and substantial AI assistance. The historical source base is +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. The publication base is +`b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`, with selected conditional +kappa `60403/20000000`. Transfer of these historical results to that +selected construction is unproved. No complete kappa improvement follows. +The description's local template targets and credit evidence are recorded +in [PR-DESCRIPTION-CHECK.json](PR-DESCRIPTION-CHECK.json). The publication +coordinator must replace `COMMIT`, verify GitHub objects, inspect rendered +Markdown, and read back the published body and HTML. 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"centre-mixing-review", + "metadata_fields": [] + }, + { + "all_typed_fields_match_after_declared_metadata": true, + "byte_equal": true, + "fresh": "cold-replay/query-span-producer/QUERY-SPAN.json", + "fresh_sha256": "a06939cba2c937f452027ee4a1f20b31121a70b7fc7393d9ccad091817ee448e", + "frozen": "frozen/lanes/schur-selection/plane-repair/QUERY-SPAN.json", + "job": "query-span-producer", + "metadata_fields": [] + }, + { + "all_typed_fields_match_after_declared_metadata": true, + "byte_equal": true, + "fresh": "cold-replay/query-span-review/REVIEW.json", + "fresh_sha256": "36820f2267d5f1388d554c12f7f79b91792b964060d2fb639654bbd7cc30c148", + "frozen": "frozen/lanes/source-domain/query-span-review/REVIEW.json", + "job": "query-span-review", + "metadata_fields": [] + } + ], + "scope": "Four separate exact source/interface results. No sum of the bounds, native-cost result, new supplier, or kappa improvement is claimed.", + "status": "PASS_INDEPENDENT_SOURCE_GEOMETRY_TYPED_RECEIPTS" +} diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/check_annex_sources.py b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/check_annex_sources.py new file mode 100644 index 0000000000..a1b4e789b3 --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/check_annex_sources.py @@ -0,0 +1,134 @@ +"""Check the source-geometry annex against its source files and old package.""" + +import argparse +import ast +from collections import Counter +import difflib +from hashlib import sha256 +import json +from pathlib import Path +import re +import tarfile + + +def require(test, reason): + if not test: + raise ValueError(reason) + + +def digest(path): + return sha256(path.read_bytes()).hexdigest() + + +def read_json(path): + return json.loads(path.read_text()) + + +def check_records(root, records): + for name, record in records.items(): + path = root / name + require(path.stat().st_size == record['bytes'], 'File size: ' + name) + require(digest(path) == record['sha256'], 'File hash: ' + name) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--repo', type=Path, required=True) + parser.add_argument('--package', type=Path, required=True) + parser.add_argument('--manifest-sha256', required=True) + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + repo, package = args.repo.resolve(), args.package.resolve() + annex = package / 'annexes/source-geometry' + review = Path(__file__).resolve().parent + baseline = read_json(review / 'HISTORICAL-PINS.json') + check_records(package, baseline['package_files']) + check_records(review.parent, baseline['prior_review_files']) + old_paths = {str(p.relative_to(package)) for p in package.rglob('*') + if p.is_file() and not p.is_relative_to(annex)} + require(old_paths == set(baseline['package_files']), 'Complete old package inventory') + parent = read_json(annex / 'PARENT-SNAPSHOT.json') + require(parent['files'] == baseline['package_files'], 'Independent parent snapshot match') + manifest = read_json(annex / 'ANNEX-MANIFEST.json') + require(digest(annex / 'ANNEX-MANIFEST.json') == args.manifest_sha256, 'Annex freeze') + check_records(annex, manifest['files']) + paths = {str(p.relative_to(annex)) for p in annex.rglob('*') if p.is_file()} + require(paths == set(manifest['files']) | {'ANNEX-MANIFEST.json'}, 'Complete annex inventory') + require(not any(p.is_symlink() for p in annex.rglob('*')), 'No annex symlinks') + + sources = read_json(annex / 'SOURCES.json') + for name, record in sources['files'].items(): + require((annex / name).read_bytes() == (repo / record['original_path']).read_bytes(), + 'Exact original source: ' + name) + check_records(annex, sources['files']) + check_records(package, sources['parent_runtime_dependencies']) + prior_sources = read_json(review / 'REVIEWED-SOURCE-PINS.json') + campaign = repo / 'work/centre-encoding-campaign-20261014' + check_records(campaign, prior_sources['campaign_relative_sources']) + + archive_check = read_json(annex / 'ARCHIVE-CHECK.json') + archive_path = repo / archive_check['archive_original_path'] + require(archive_path.stat().st_size == archive_check['archive_bytes'], 'Full archive size') + require(digest(archive_path) == archive_check['archive_sha256'], 'Full archive hash') + with tarfile.open(archive_path) as archive: + for item in archive_check['unique_regular_members']: + matches = [m for m in archive.getmembers() if m.name == item['archive_member']] + require(len(matches) == 1 and matches[0].isfile(), 'Unique regular member') + data = archive.extractfile(matches[0]).read() + require(data == (package / item['parent_path']).read_bytes(), 'Exact parent archive member') + require(len(data) == item['bytes'] and sha256(data).hexdigest() == item['sha256'], + 'Archive member pin') + + portability = read_json(annex / 'PORTABILITY.json') + reviewed_portability = read_json(review / 'PORTABILITY-REVIEWED-PINS.json') + require(digest(annex / 'PORTABILITY.patch') == reviewed_portability['patch_sha256'], + 'The complete patch was manually reviewed') + ast_checks, patch = [], [] + for job in portability['checks']: + old, new = annex / job['frozen_script'], annex / job['portable_script'] + require(digest(old) == job['original_sha256'] and digest(new) == job['portable_sha256'], + 'Portable source pins: ' + job['name']) + require(digest(new) == reviewed_portability['portable_scripts'][job['portable_script']], + 'The portable main function was manually reviewed: ' + job['name']) + functions = [] + for path in (old, new): + functions.append({node.name: ast.dump(node, include_attributes=False) + for node in ast.parse(path.read_text()).body + if isinstance(node, ast.FunctionDef) and node.name != 'main'}) + require(functions[0] == functions[1], 'All non-main function ASTs: ' + job['name']) + require(len(functions[0]) == job['function_count'], 'Function count: ' + job['name']) + patch.extend(difflib.unified_diff(old.read_text().splitlines(True), + new.read_text().splitlines(True), + fromfile=job['frozen_script'], tofile=job['portable_script'])) + ast_checks.append({'name': job['name'], 'function_names': sorted(functions[0]), + 'original_sha256': digest(old), 'portable_sha256': digest(new)}) + require(''.join(patch) == (annex / 'PORTABILITY.patch').read_text(), 'Complete portability diff') + links = [] + for doc in ('README.md', 'NOTICE.md'): + for target in re.findall(r'\]\(([^)]+)\)', (annex / doc).read_text()): + if '://' not in target: + require((annex / target.split('#')[0]).is_file(), 'Local document link: ' + target) + links.append({'document': doc, 'target': target}) + result = { + 'status': 'PASS_INDEPENDENT_SOURCE_GEOMETRY_CLOSURE', + 'annex_manifest_sha256': args.manifest_sha256, + 'annex_listed_files': len(manifest['files']), + 'annex_total_files': len(paths), + 'annex_bytes': sum((annex / path).stat().st_size for path in paths), + 'old_package_files_unchanged': len(baseline['package_files']), + 'prior_review_files_unchanged': len(baseline['prior_review_files']), + 'exact_original_source_files': len(sources['files']), + 'original_source_roles': dict(Counter(x['role'] for x in sources['files'].values())), + 'parent_runtime_inputs': sources['parent_runtime_dependencies'], + 'complete_archive_check': archive_check, + 'portable_checker_function_checks': ast_checks, + 'all_main_changes_reviewed_as_io_only': True, + 'local_document_links': links, + 'no_git_network_or_external_program_used': True, + } + args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + '\n') + print(result['status']) + + +if __name__ == '__main__': + main() diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/REPLAY.json b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/REPLAY.json new file mode 100644 index 0000000000..dbf0ccad1c --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/REPLAY.json @@ -0,0 +1,126 @@ +{ + "annex_files_unchanged": 99, + "annex_manifest_sha256": "cc7279ee48a7751a57f59a98f991ba879cf6e63144fcb7885ed1e4b69b432663", + "checks": [ + { + "name": "centre-support-producer", + "receipts": [ + { + "declared_metadata_updates": [], + "frozen_receipt": "frozen/root/CENTRE-SUPPORT-GEOMETRY-20261018.json", + "output": "centre-support-producer/CENTRE-SUPPORT-GEOMETRY-20261018.json", + "sha256": "dafd6c0af3f8aad852a7c80258118487744921c9a61474b1441e3755f8e3b205", + "typed_json_equal": true + } + ], + "seconds": 0.166397916036658, + "status": "PASS_CENTRE_SUPPORT_GEOMETRY" + }, + { + "name": "centre-support-review", + "receipts": [ + { + "declared_metadata_updates": [ + "checker_sha256" + ], + "frozen_receipt": "frozen/lanes/independent-review-20261017/centre-support-review-20261018/CHECKS.json", + "output": "centre-support-review/CHECKS.json", + "sha256": "61690f10c5d08981c68eaf148a7b54f81ac4e00b33fb8ebac0bc8c275368be10", + "typed_json_equal": true + } + ], + "seconds": 0.16556150000542402, + "status": "PASS_INDEPENDENT_CENTRE_SUPPORT_GEOMETRY" + }, + { + "name": "dyadic-producer", + "receipts": [ + { + "declared_metadata_updates": [ + "checker_sha256" + ], + "frozen_receipt": "frozen/root/DYADIC-QUERY-SEPARATION-20261018.json", + "output": "dyadic-producer/DYADIC-QUERY-SEPARATION-20261018.json", + "sha256": "f32f611e5d583beb5ccc2a809f37692e2fc35ed40706cb96845051c9a71befb9", + "typed_json_equal": true + } + ], + "seconds": 1.0329124580021016, + "status": "PASS_DYADIC_QUERY_SEPARATION" + }, + { + "name": "dyadic-review", + "receipts": [ + { + "declared_metadata_updates": [ + "checker_sha256" + ], + "frozen_receipt": "frozen/lanes/bridge-review-20261017/dyadic-query-separation-review-20261018/REVIEW.json", + "output": "dyadic-review/REVIEW.json", + "sha256": "c1c3006be5100ef6a5f74402e7c5edd6409d817124dd192c2854615c0b74bf66", + "typed_json_equal": true + } + ], + "seconds": 0.4280027089989744, + "status": "PASS_INDEPENDENT_DYADIC_QUERY_SEPARATION" + }, + { + "name": "centre-mixing-review", + "receipts": [ + { + "declared_metadata_updates": [ + "checker_sha256" + ], + "frozen_receipt": "frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/REVIEW.json", + "output": "centre-mixing-review/REVIEW.json", + "sha256": "1eb05efb021de47c5414f14509e2d756cb27266f608f2722b9805c303ad0ee60", + "typed_json_equal": true + }, + { + "declared_metadata_updates": [], + "frozen_receipt": "frozen/lanes/bridge-review-20261017/centre-mixing-review-20261018/TWO-BASES.json", + "output": "centre-mixing-review/TWO-BASES.json", + "sha256": 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a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/centre-support-producer/CENTRE-SUPPORT-GEOMETRY-20261018.json b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/centre-support-producer/CENTRE-SUPPORT-GEOMETRY-20261018.json new file mode 100644 index 0000000000..b2c06708c8 --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/centre-support-producer/CENTRE-SUPPORT-GEOMETRY-20261018.json @@ -0,0 +1,394 @@ +{ + "annihilators": [ + [ + 7, + 42, + 45 + ], + [ + 25, + 45, + 52 + ], + [ + 45, + 82, + 127 + ], + [ + 45, + 76, + 97 + ], + [ + 45, + 76, + 97 + ], + [ + 7, + 42, + 45 + ], + [ + 25, + 45, + 52 + ], + [ + 45, + 82, + 127 + ] + ], + "binary_support_ranks": [ + 7, + 7, + 7, + 7, + 7, + 7, + 7, + 7 + ], + "common_hyperplane_normal": 45, + "common_intersection_rank": 5, + "conditional_eight_query_rank_lower_bound": 62, + 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"maximum_independent_set_size": 2, + "maximum_independent_sets": [ + [ + 3, + 4 + ], + [ + 0, + 5 + ], + [ + 1, + 6 + ], + [ + 2, + 7 + ] + ], + "query_supports": [ + [ + 0, + 2, + 25, + 27, + 70, + 71, + 72, + 76, + 87, + 89, + 90, + 91 + ], + [ + 0, + 13, + 14, + 15, + 27, + 51, + 52, + 53, + 78, + 81, + 92, + 99 + ], + [ + 11, + 15, + 21, + 36, + 41, + 47, + 53, + 63, + 70, + 91, + 106, + 111 + ], + [ + 9, + 13, + 36, + 37, + 43, + 51, + 61, + 72, + 89, + 104, + 110, + 111 + ], + [ + 2, + 16, + 20, + 21, + 25, + 44, + 46, + 47, + 78, + 79, + 94, + 99 + ], + [ + 7, + 9, + 10, + 11, + 57, + 61, + 62, + 63, + 79, + 81, + 92, + 94 + ], + [ + 7, + 16, + 41, + 42, + 43, + 44, + 57, + 76, + 87, + 104, + 105, + 106 + ], + [ + 10, + 14, + 20, + 37, + 42, + 46, + 52, + 62, + 71, + 90, + 105, + 110 + ] + ], + "scope": "Exact source geometry. The rank-62 statement assumes one scalar capture per stated query and one monotone subspace path per unwarped source value, with no extra carrier. No new native word or general query lower bound is claimed.", + "source_decompressed_sha256": { + "centres": "2b9de1454c2025ae4e230bd64de36b4f6c937628c63fc5afede6640dd3c0e1e1", + "directions": "b08cb4146f1aec241e027cd62c942f6eca4ddab3e97f000a9c0017575d36deb5" + }, + "status": "PASS_CENTRE_SUPPORT_GEOMETRY" +} diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/centre-support-review.stderr.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/centre-support-review.stderr.txt new file mode 100644 index 0000000000..e69de29bb2 diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/centre-support-review.stdout.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/centre-support-review.stdout.txt new file mode 100644 index 0000000000..25e89d3c17 --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/centre-support-review.stdout.txt @@ -0,0 +1 @@ +PASS_INDEPENDENT_CENTRE_SUPPORT_GEOMETRY diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/centre-support-review/CHECKS.json b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/centre-support-review/CHECKS.json new file mode 100644 index 0000000000..409eddca6b --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/centre-support-review/CHECKS.json @@ -0,0 +1,47 @@ +{ + "ambient_dimension": 8, + "checker_sha256": "e2785466e186ad51ddc3c9f2335f4f441206531e7b2dbf61e5cb080ba23c8c46", + "common_space_dimension": 5, + "direct_schedule_lower_bound": 62, + "equal_space_classes": [ + [ + 0, + 5 + ], + [ + 1, + 6 + ], + [ + 2, + 7 + ], + [ + 3, + 4 + ] + ], + "method": "Explicit primal XOR closure; independent RREF nullspace equations; exact set intersections; complete multipartite graph proof.", + "pairwise_distinct_space_intersection_dimension": 6, + "scope": "One direct capture per row with single unwarped carriers on monotone source-subspace chains. Pair coding violates this carrier premise.", + "source_decompressed_pins": { + "controller-followthrough-20261017/structured-centres/STRUCTURED-CENTRES-PROGRAM.json.gz": "2b9de1454c2025ae4e230bd64de36b4f6c937628c63fc5afede6640dd3c0e1e1", + "history-encoding/independent-skeleton-20261018/fresh-three-child/FRESH-THREE-CHILD-PROGRAMS.json.gz": "b08cb4146f1aec241e027cd62c942f6eca4ddab3e97f000a9c0017575d36deb5" + }, + "source_pins": { + "CENTRE-SUPPORT-GEOMETRY-20261018.json": "dafd6c0af3f8aad852a7c80258118487744921c9a61474b1441e3755f8e3b205", + "CENTRE-SUPPORT-GEOMETRY-20261018.md": "a3df65d159899fbaf7110958275615fc406ecbd077d9d620f7f49ccbe4b923f5", + "check_centre_support_geometry_20261018.py": "99582e42007012d31dcddc14e05da8c5aac75c1f3b546c00ef0fcf0169f081b2" + }, + "status": "PASS_INDEPENDENT_CENTRE_SUPPORT_GEOMETRY", + "support_dimensions": [ + 7, + 7, + 7, + 7, + 7, + 7, + 7, + 7 + ] +} diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-producer.stderr.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-producer.stderr.txt new file mode 100644 index 0000000000..e69de29bb2 diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-producer.stdout.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-producer.stdout.txt new file mode 100644 index 0000000000..d8220d9bf7 --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-producer.stdout.txt @@ -0,0 +1 @@ +PASS_DYADIC_QUERY_SEPARATION diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-producer/DYADIC-QUERY-SEPARATION-20261018.json b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-producer/DYADIC-QUERY-SEPARATION-20261018.json new file mode 100644 index 0000000000..fb7259adcd --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-producer/DYADIC-QUERY-SEPARATION-20261018.json @@ -0,0 +1,33 @@ +{ + "status": "PASS_DYADIC_QUERY_SEPARATION", + "core_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "proof_sha256": "664f430efd099f35cbc7c2abc8025968c03020707027857d2882daa51a065a1a", + "checker_sha256": "f949b92e3672c1b854f584c46c3ec36664db38c5cd0dfa80767c2d41996d4130", + "selected": [ + 0, + 7, + 20, + 27, + 36, + 46, + 57, + 111 + ], + "ordinary_minor": [ + 21, + 37, + 47, + 76, + 81, + 87, + 92, + 110 + ], + "BD": "13I", + "prime": 13, + "B_rank": 8, + "dyadic_section_stack_rank": 16, + "kernel_perturbed_sections": 64, + "matched_section_stack_rank": 8, + "scope": "Source information rank and exact representation choice; no native child bound or supplier claim." +} diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-review.stderr.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-review.stderr.txt new file mode 100644 index 0000000000..e69de29bb2 diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-review.stdout.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-review.stdout.txt new file mode 100644 index 0000000000..e86d4513df --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-review.stdout.txt @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_DYADIC_QUERY_SEPARATION +{"MD_nonidentity_cases": 24, "matched_rank": 8, "null_family_uses_MD_identity": false, "rank": 16, "routed_rank": 32} diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-review/REVIEW.json b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-review/REVIEW.json new file mode 100644 index 0000000000..e1822bc13c --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/dyadic-review/REVIEW.json @@ -0,0 +1,183 @@ +{ + "actual_source": { + "B_rank_mod_13": 8, + "controls": [ + "M=B has MD=13I and rank-eight stack", + "Missing B residue rank", + "Missing zero residue of c", + "Matched coefficients have no residue at 13" + ], + "explicit_minor_determinant": "1/8", + "explicit_minor_ports": [ + 1, + 2, + 3, + 4, + 5, + 6, + 8, + 12, + 21, + 37, + 47, + 76, + 81, + 87, + 92, + 110 + ], + "matched_rank_over_Q": 8, + "nonidentity_MD_cases": [ + { + "MD_is_identity": false, + "case": 0, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 1, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 2, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 3, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 4, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 5, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 6, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 7, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 8, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 9, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 10, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 11, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 12, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 13, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 14, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 15, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 16, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 17, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 18, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 19, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 20, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 21, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 22, + "stack_rank_mod_13": 16 + }, + { + "MD_is_identity": false, + "case": 23, + "stack_rank_mod_13": 16 + } + ], + "stack_rank_mod_13": 16 + }, + "checker_sha256": "bdc237dd266102fa99170aab0d309c3f03894924875f5a8a79d198d6fbd02548", + "core_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "formal_full_null": { + "all_pair_counts": "The future inputs and all visible outputs are zero; the only nonzero next-bank bridge is -v+v.", + "operator_relations": [ + "Qq=I", + "qQ=I" + ], + "unit_factorization": "diag(I,-MD)", + "uses_BD_identity_for_null_family": false, + "uses_MD_identity": false, + "wrong_original_b_control": true + }, + "routed_operator_fixture": { + "coordinates_per_field": 2, + "noncommuting_routes": true, + "query_rank_mod_13": 32, + "scope": "An actual-B Gaussian-unit conjugation fixture; the general finite-operator version follows from the residue proof, not a new native route replay." + }, + "scope": "Fixed linear observations on the full underlying field space, with arbitrary postprocessing. No native-child, bit-packing, arbitrary nonlinear-encoding or complete supplier lower bound.", + "source_pins": { + "lanes/controller-followthrough-20261017/MINOR-LOG-SOURCE-ACCESS.md": "50ce523e083f70556cc62694219da94b684cc898f3d5e358767fcc40dd77e4bc", + "lanes/oblique-native-20261017/minor-input-log/UNIT-COMPLETION.md": "1a4d715e089773a9063fba88d5b83ec770bb5eb6ed501bc8f96b290c19b08401", + "root/DYADIC-QUERY-SEPARATION-20261018.json": "e66d5c311490c06973bf604d207fb5cf7a9cd4800c0cea049623c3b5e2369732", + "root/DYADIC-QUERY-SEPARATION-20261018.md": "664f430efd099f35cbc7c2abc8025968c03020707027857d2882daa51a065a1a", + "root/check_dyadic_query_separation_20261018.py": "b4ed000b5b600944f614b86ae7a88ac55af8eac3213e6827ed211a2630ccd342" + }, + "status": "PASS_INDEPENDENT_DYADIC_QUERY_SEPARATION", + "universal_proof": "Residue row relation times D forces beta=0 because MD is a unit; full residue rank of B forces alpha=0. A nonzero residue minor lifts to the fraction field." +} diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-producer.stderr.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-producer.stderr.txt new file mode 100644 index 0000000000..e69de29bb2 diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-producer.stdout.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-producer.stdout.txt new file mode 100644 index 0000000000..1e57068879 --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-producer.stdout.txt @@ -0,0 +1,2 @@ +PASS_EXACT_QUERY_SOURCE_SPANS +{"line_scalar_input_rank": 112, "plane_character_sum_checks": 24576, 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This is a payload-query count bound under scalar free gates, not a native-child or rank-zero-map lower bound for the full supplier.", + "status": "PASS_EXACT_QUERY_SOURCE_SPANS" +} diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-review.stderr.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-review.stderr.txt new file mode 100644 index 0000000000..e69de29bb2 diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-review.stdout.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-review.stdout.txt new file mode 100644 index 0000000000..64a99244dc --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-review.stdout.txt @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_QUERY_SPAN_SOURCE_AND_CERTIFICATE +{"source_scalar_events_replayed": 10851, "exact_Fourier_columns": 28672, "separating_functional_column_checks": 802816, "exact_block_minor_determinant": 8} diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-review/REVIEW.json b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-review/REVIEW.json new file mode 100644 index 0000000000..7dc0853730 --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold-replay/query-span-review/REVIEW.json @@ -0,0 +1,138 @@ +{ + "all_depth": "Proof: compress all but one tensor factor to the fixed constant character.", + "archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "controls": [ + "Exact reversed-orientation moved-character sign differs." + ], + "distinct_plane_directions": 41, + "exact_Fourier_columns": 28672, + "exact_block_minor_determinant": 8, + "frozen_packet_sha256": { + "PLANE-INVOLUTION.json": "f55bd0e7b81a15b6526ca3056ef3bf1bbf57b13137699e71a374f4cf8f55f794", + "QUERY-SPAN.json": "a06939cba2c937f452027ee4a1f20b31121a70b7fc7393d9ccad091817ee448e", + "QUERY-SPAN.md": "785e27fdc6f2bcd83318afee14103f3e021065d32be2265b8afdec3fea3e1081", + "check_query_span.py": "bcc8bb5482c76578014512d51dd5d650d4bf13d6546b29e355ae01bec8a07811" + }, + "grammar": "Every non-scalar payload map is counted, including rank-zero address maps; scalar initial and final contracts are required.", + "line_source_rank": 112, + "nonzero_line_columns": 112, + "not_certified": [ + "Native-child lower bound", + "Native-cost bound", + "Changed source interface", + "Supplier or kappa improvement" + ], + "pair_Gram_determinants": [ + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12 + ], + "plane_source_rank": 112, + "planes": 56, + "repeated_direction_group_sizes": [ + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 2, + 2, + 2, + 2, + 2, + 2, + 2, + 2, + 3, + 3, + 4 + ], + "separating_functional_column_checks": 802816, + "source_member_sha256": { + "phases": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "program": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a", + "word": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219" + }, + "source_reconstruction": "Independent data-only scalar propagation to the original centre boundary; no producer import or execution.", + "source_rows": 8, + "source_scalar_events_replayed": 10851, + "status": "PASS_INDEPENDENT_QUERY_SPAN_SOURCE_AND_CERTIFICATE" +} diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold.stderr.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold.stderr.txt new file mode 100644 index 0000000000..e69de29bb2 diff --git a/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold.stdout.txt b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold.stdout.txt new file mode 100644 index 0000000000..ed8fef414d --- /dev/null +++ b/research/publication-reviews/actual-query-information-bounds/source-geometry-review/cold.stdout.txt @@ -0,0 +1,8 @@ +PASS_CENTRE_SUPPORT_GEOMETRY +PASS_INDEPENDENT_CENTRE_SUPPORT_GEOMETRY +PASS_DYADIC_QUERY_SEPARATION +PASS_INDEPENDENT_DYADIC_QUERY_SEPARATION +PASS_INDEPENDENT_NATIVE_CENTRE_REVIEW +PASS_EXACT_QUERY_SOURCE_SPANS +PASS_INDEPENDENT_QUERY_SPAN_SOURCE_AND_CERTIFICATE +PASS_SOURCE_GEOMETRY_ANNEX

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Each requested subspace of dimension `k` needs at least `9k` +native rank in the model below. The bound includes shared rank-one +prefixes. It follows from five source tests, each of which is injective +on the candidate query space. + +The same test also gives bounds for the displayed rank-three and +rank-four query spaces. This note does not give a bound for a network +that joins different merge spaces or uses an unlisted intermediate +frame. + +## Model and source premise + +Use the pinned backward clean-J word and its exact snapshot rows. Put +`X=JY` and set every helper and private input to zero. Then all completed +X rows and all restored helper rows are zero. This is a valid input +family for any proposed algorithm that works on arbitrary inputs. + +The independently checked snapshot support law states that a snapshot +at canonical frame `U` uses only source ports whose labels lie in +`U` perpendicular. This law holds at all listed snapshot times. The +full snapshot table has 712 input columns. Its earlier quotient does +not discard the 78 helpers that have non-FULL final frames. + +Fix an actual merge frame `V` of dimension `d`. Permit all times of all +retained observations at actual positive-rank frames contained in V. +Permit every monotone native edge `U -> W` between these frames, with +cost `(dim W - dim U)` per carried field. Equal-frame scalar operations +can split, add, and cancel fields. Thus one paid field can serve several +output queries. After the requested query fields reach V, no new +observation enters. Their completion to FULL9 has cost at least +`(9-d)k` for `k` independent queries. + +This model grants more access than a chronological native word. An +obstruction in this model needs no claim that all granted edges have +the indicated phase-correct recipe. It does not permit a change to +the retained core or a change to the source-port meaning of a frame. + +## Union-cut lemma + +For a nonzero character `alpha` on V, let `E_alpha` be the source ports +whose label restricts to alpha. Let `Omega_alpha` be the nodes U at +which alpha does not vanish. For a set A of nonzero characters, put + +\[ + E_A=\bigcup_{\alpha\in A}E_\alpha, + \qquad + \Omega_A=\bigcap_{\alpha\in A}\Omega_\alpha. +\] + +Test inputs Y supported on `E_A`. Every free observation at a node in +`Omega_A` is zero by the support law. The set `Omega_A` is upward +closed. Hence the required query values on these inputs must enter +it through native edges. If the query space has coefficient matrix +S in the eight R rows, this cut has demand + +\[ + r_A=\operatorname{rank}((SR)_{E_A}). +\] + +Assign nonnegative rational weights to these cuts. If the sum of the +weights of the cuts entered by every edge `U -> W` is at most +`dim W - dim U`, then the weighted sum of demands is a lower bound +for native rank before completion. This proof permits arbitrary +sharing and cancellation. For payload dimension N, demands and edge +capacities both multiply by N, so the bound in field units is unchanged. + +A useful stronger case occurs when restriction to `E_A` is injective +on the entire displayed query space. Then it is injective on every +subspace of that space. The same cut has demand k for every requested +subspace of dimension k. If all positive-weight cuts have this property +and their weights sum to w, the total bound is + +\[ + (w+9-d)k. \tag{1} +\] + +## Finite cut construction + +The checker starts with all singleton and pair character sets, plus +the final-V cut. It merges equal inside-node sets. For each resulting +node set I, it uses every character whose singleton cut contains I. +The intersection of those singleton cuts is still I. This change can +increase the tested source set without changing any edge charge. + +A floating-point simplex calculation selects candidate weights. The +checker then reconstructs rational weights and checks every edge +charge exactly. It computes all source restriction ranks over the +rationals. The certificate does not depend on the correctness or +optimality of the floating-point solve. + +## Rank-five result + +The merge frames are + +```text +630, 631, 632, 633, 635, 637, +734, 735, 736, 737, 739, 741. +``` + +Each displayed query space has dimension five. In each case the +certificate has five positive cuts, each with weight one and full +restriction rank five. Thus `w=5` and `d=5` in (1), which gives `9k` +for every requested subspace. In particular, all five queries cost +at least 45 native rank. The target for a strict improvement was less +than 40. + +The first six cases use 288 distinct closed cuts. The last six use +328. Only five cuts per case are needed in the accepted certificate. +The checker stores the exact source ports, node sets, query bases, +weights, and every inclusion edge. + +## Other displayed spaces + +The separate full-rank-cut checker applies the same argument to the +74 displayed maximal-overlap query spaces from the bounded screen. +It gives the following per-query bounds on every subspace of each +displayed space: + +| Merge cases | Number | Bound per query | +|---|---:|---:| +| Rank-three cases | 24 | 9 | +| Rank-four cases with frame ID at most 414 | 14 | 8 | +| Rank-four cases with frame ID from 592 to 629 | 24 | 9 | +| Rank-five cases | 12 | 9 | + +These certificates prove bounds for the displayed exact coefficient +spaces. The initial classification of their full observation overlap +was modular. It is not promoted here to an exact classification of +all query spaces at all merge frames. The independent rank-five +review checks the full 712-column overlap separately. + +## Validation and scope + +Run from the repository root: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/history-encoding/check_rank5_union_cuts.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/history-encoding/check_low_birth_full_rank_cuts.py +``` + +The receipts are `RANK5-UNION-CUTS.json` and +`LOW-BIRTH-SUBSPACE-CUTS.json`. They pin their producers and source +receipts. The snapshot payload has decompressed SHA256 +`3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c`. +The separate source-row review is +`circuit-interface/snapshot-audit/SNAPSHOT-ROWS-REVIEW.json`. +The separate support review is +`cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json`. + +No improved native word, complete supplier cost, universal bound of +64, or optimum over all snapshot networks is claimed. The remaining +models include networks that cross between merge spaces, larger +merge frames, synthetic intermediate frames, and changed core or +query interfaces. + +The root research agent proposed pair-union source tests. The +history-encoding lane implemented the exact cut certificates and +the selective-subspace consequence. The cover-algebra lane is the +independent reviewer of the rank-five certificate. diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-CUT-THEOREM-REVIEW.json b/research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-CUT-THEOREM-REVIEW.json new file mode 100644 index 0000000000..8be3e3c1c7 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-CUT-THEOREM-REVIEW.json @@ -0,0 +1,14 @@ +{ + "checks": [ + "finite causal cut induction", + "kernel quotient rank identity", + "weighted edge charging", + "whole-array capacity qualification", + "source-support specialization", + "two-cut chain example" + ], + "review_sha256": "c66bf73004bbe81441d26a4c69a551d4f439af37dc75d1a4365b0a5bf174ae57", + "scope": "Mathematical proof review only; no original-word replay or numerical cut search.", + "source_proof_sha256": "cc26bd7b4d82bece7bd4b409350313539b953a26e88115d1efecb97bf538ead1", + "status": "PASS_INDEPENDENT_MATHEMATICAL_PROOF_REVIEW" +} diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-CUT-THEOREM-REVIEW.md b/research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-CUT-THEOREM-REVIEW.md new file mode 100644 index 0000000000..fd46dfe3d0 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-CUT-THEOREM-REVIEW.md @@ -0,0 +1,38 @@ +# Independent proof review of movable snapshot cuts + +The reviewed source is +`../cover-algebra/MOVABLE-SNAPSHOT-CUTS.md`, SHA256 +`cc26bd7b4d82bece7bd4b409350313539b953a26e88115d1efecb97bf538ead1`. + +The theorem is correct in its stated finite linear observation model. +For a node set Omega, restrict inputs to the kernel of every free +observation inside Omega. Induction in circuit order shows that every +inside value lies in the span of values that entered Omega. A value +that leaves and returns is still charged on re-entry. No upward-closure +assumption is needed. Thus incoming rank bounds the output rank on +this input kernel. + +The identity + +```text +rank(Q restricted to kernel A) = rank([A;Q]) - rank(A) +``` + +follows from the quotient of row spaces. Nonnegative cut weights can +then be summed when their entering-edge charge does not exceed the +edge cost. This permits arbitrary shared values, cancellation, and +edge multiplicity. The block statement is valid when each field has +the stated fixed payload dimension and all actual observations are +included. It does not grant a new native-frame map. + +The actual source-port test is also valid. On `X=JY` with all helpers +and private inputs zero, the accepted support law makes every inside +observation vanish. Shrinking the node set preserves this property +and its source rank. Enlarging the node set need not preserve the +edge charge, so the distinction from a maximal source cut is real. +The two-cut chain example gives the stated bound of two. + +No material proof finding remains. This is a proof review. It does +not replay the original snapshot rows or establish a new numerical +bound. 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738, + 741, + 990, + 991, + 997 + ], + "ports": [ + 2, + 9, + 10, + 11, + 13, + 14, + 15, + 16, + 25, + 41, + 42, + 43, + 44, + 51, + 52, + 53, + 61, + 62, + 63, + 70, + 71, + 72, + 78, + 79, + 89, + 90, + 91, + 94, + 99, + 104, + 105, + 106 + ] + } + ], + "total_bound": 64, + "trials_completed": 2 + } + ], + "producer_sha256": "8a6091ba612cce398f67661b3e0a8e137adc3f748aef7f7b1c663e46deaa7da1", + "scope": "Two fixed actual rank-eight merge spaces, eight full-rank source tests each, at most 24 integer-flow placement trials. Every stored cut and edge charge is exact. A failed search is not an optimum or a native construction.", + "seed_sha256": "208972f6015ee978875bc25d34cedf69e79fa4414e2e2b9dfee5fe86ba4542be", + "snapshot_decompressed_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", + "status": "EXACT_FEASIBLE_MOVABLE_CUTS_BOUNDED_SEARCH" +} diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-RANK8-CUTS.md b/research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-RANK8-CUTS.md new file mode 100644 index 0000000000..91e86d9337 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/MOVABLE-RANK8-CUTS.md @@ -0,0 +1,95 @@ +# Movable source cuts at two rank-eight merge frames + +The two actual merge frames 983 and 991 cannot give a saving in the +snapshot model below. To form a k-dimensional subspace of the eight +centre queries through either merge frame costs at least `8k` added +native rank. In particular, all eight queries cost at least 64. + +This result permits shared intermediate fields and arbitrary scalar +cancellation. It does not require eight separate cache paths. It does +not give a bound for a network that uses different merge spaces. + +## Source and model + +Use the pinned clean backward word and the snapshot rows in +`BACKWARD-SNAPSHOT-INTERVALS.json.gz`. Its decompressed SHA256 is +`3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c`. +The independently reviewed support law states that, on the input +family `X=JY`, with all helper and private inputs zero, an observation +at frame U uses only source ports q with `q perpendicular to U`. +The completed X and FULL helper baselines vanish on this family. + +The model grants every actual snapshot at every time. All used frames +must be actual canonical subframes of one chosen frame V. Frame zero +is also allowed. A field can move from U to W when `U subset W`, at +cost `dim(W)-dim(U)`. The transition preserves its logical content. +Scalar gates can share, add, or cancel fields in a common frame. +After the queries reach V, they move to FULL. These are relaxations +of the real chronological and native-phase requirements. + +The two chosen frames are + +```text +983: [256,129,64,33,17,9,5,3] +991: [260,128,64,32,16,12,2,1] +``` + +There are 122 and 124 actual contained frames, respectively, when +frame zero is included. Their Hasse graphs have 238 and 246 edges. + +## Cut argument + +For a source-port set S, let `Omega_S` contain the frames at which +every source port in S is excluded by the support law. All free +observations in these frames vanish when Y is supported on S. + +Choose any upward-closed set `Omega subset Omega_S` that contains V. +If `R restricted to S` has rank eight, its restriction is injective +on every k-dimensional centre-query subspace. Thus at least k +independent whole-array fields must enter Omega. This argument also +holds for arbitrary tensor size: the input, output, and field ranks +all acquire the same array-dimension factor. + +The certificate gives seven such cuts for each V. Each has weight +one and a source restriction of exact rank eight. For every actual +inclusion `U subset W`, the number of cuts entered is at most +`dim(W)-dim(U)`. Sum the seven cut demands and charge each entering +field to its native transition. The internal cost is at least `7k`. +Completion from the rank-eight frame to FULL costs at least k. +The total is therefore at least `8k`. + +Upward closure is not needed for the general rank-cut lemma. It is +used here to make the finite search and the edge check simple. The +general statement is in `../cover-algebra/MOVABLE-SNAPSHOT-CUTS.md`. + +## Exact certificate and search + +`MOVABLE-FULL-RANK-CUTS.json` gives all source sets, all seven inside +node sets, and all Hasse edges. The checker also checks every direct +inclusion edge. The two certificates use five and four distinct +source sets. Repeated uses of one source test have different cut +placements. + +`probe_movable_full_rank_cuts.py` selects cut placements with integer +max-flow. It allows at most 24 trials on eight fixed source tests per +merge. Both certificates were found in the second trial. The proof +uses only the displayed cuts, exact source ranks, and exact edge +charges. It uses no float optimization or optimality claim. + +Run: + +```text +python3 -I -O -B probe_movable_full_rank_cuts.py +``` + +The final printed line for each merge reports `unit cuts 7`. +The source tests come from the frozen rank-five cut seed file and +two known orthogonal source minors. No source observation is added +to the clean word. + +This closes strict savings through the two rank-eight convergence +frames above the weaker rank-six cases 982 and 990. Those rank-six +cases have bound `8k`; cases 774 and 782 have bound `9k`. The present +result does not change those bounds and does not prove a global +64-rank obstruction. It emits no new native word and gives no change +to the complete supplier calculation. diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/QUERY-SUPPORT-DISTANCE.json b/research/actual-query-information-bounds/payload/lanes/history-encoding/QUERY-SUPPORT-DISTANCE.json new file mode 100644 index 0000000000..8e06ed6017 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/QUERY-SUPPORT-DISTANCE.json @@ -0,0 +1,478 @@ +{ + "all_255_coefficient_support_bounds": { + "1": 56, + "10": 76, + "100": 78, + "101": 80, + "102": 53, + "103": 73, + "104": 78, + "105": 53, + "106": 80, + "107": 73, + "108": 80, + "109": 73, + "11": 78, + "110": 73, + "111": 75, + "112": 78, + "113": 80, + "114": 80, + "115": 73, + "116": 80, + "117": 73, + "118": 73, + "119": 75, + "12": 76, + "120": 80, + "121": 73, + "122": 73, + "123": 75, + "124": 73, + "125": 75, + "126": 75, + "127": 77, + "128": 56, + "129": 76, + "13": 78, + "130": 76, + 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"controls": { + "duplicate_sign_pattern_rejected": true, + "excessive_quartet_bound_rejected": true + }, + "frame_allowed_port_histogram": { + "0": { + "112": 1 + }, + "1": { + "48": 7, + "52": 112, + "56": 1 + }, + "2": { + "20": 168 + }, + "3": { + "8": 152, + "10": 16 + }, + "4": { + "0": 14, + "6": 51, + "8": 8 + }, + "5": { + "4": 16, + "6": 5, + "8": 6 + }, + "6": { + "2": 16, + "4": 152 + }, + "7": { + "2": 152 + }, + "8": { + "0": 14, + "1": 112 + }, + "9": { + "0": 1 + } + }, + "lower_bounds_by_nonzero_coefficient_count": { + "1": 56, + "2": 76, + "3": 78, + "4": 53, + "5": 73, + "6": 75, + "7": 77, + "8": 70 + }, + "minimum_source_port_support": 53, + "nonzero_per_quartet_lower_bounds": [ + 0, + 8, + 4, + 6, + 5 + ], + "not_claimed": [ + "A native rank lower bound of 64 for shared networks", + "A constructive cache network", + "A full supplier improvement" + ], + "quartets": { + "102": [ + 29, + 30, + 59, + 60, + 73, + 74, + 83, + 84 + ], + "105": [ + 22, + 23, + 33, + 34, + 49, + 50, + 108, + 109 + ], + "15": [ + 0, + 7, + 27, + 57, + 76, + 81, + 87, + 92 + ], + "150": [ + 1, + 6, + 28, + 58, + 75, + 82, + 86, + 93 + ], + "153": [ + 24, + 32, + 35, + 45, + 48, + 85, + 98, + 107 + ], + "165": [ + 18, + 19, + 39, + 40, + 54, + 55, + 101, + 102 + ], + "170": [ + 4, + 5, + 64, + 65, + 68, + 69, + 96, + 97 + ], + "195": [ + 2, + 9, + 25, + 61, + 72, + 79, + 89, + 94 + ], + "204": [ + 13, + 16, + 43, + 44, + 51, + 78, + 99, + 104 + ], + "240": [ + 20, + 21, + 36, + 37, + 46, + 47, + 110, + 111 + ], + "51": [ + 10, + 11, + 62, + 63, + 70, + 71, + 90, + 91 + ], + "60": [ + 14, + 15, + 41, + 42, + 52, + 53, + 105, + 106 + ], + "85": [ + 12, + 17, + 31, + 38, + 56, + 77, + 100, + 103 + ], + "90": [ + 3, + 8, + 26, + 66, + 67, + 80, + 88, + 95 + ] + }, + "sources": { + "independent_support_review_sha256": "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7", + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "snapshot_decompressed_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c" + }, + "status": "PASS_EXACT_QUERY_SUPPORT_MINIMUM_53" +} diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/QUERY-SUPPORT-DISTANCE.md b/research/actual-query-information-bounds/payload/lanes/history-encoding/QUERY-SUPPORT-DISTANCE.md new file mode 100644 index 0000000000..0fe13aff41 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/QUERY-SUPPORT-DISTANCE.md @@ -0,0 +1,129 @@ +# Exact support distance of the eight source queries + +Every nonzero scalar combination of the eight rows of the actual +query matrix `R` uses at least 53 of the 112 source ports. This bound +is exact. Each of the 112 old-root coefficient directions attains it. + +This gives a restriction on shared snapshot proposals. On the valid +input family `X=JY`, with all helper and private inputs zero, each +snapshot in an actual frame of rank at least two uses at most 20 +source ports. Thus a nonzero query cannot be a combination of only +two such snapshot fields. More generally, a `k`-dimensional query +space needs at least `k+2` such fields in one common span. A full +eight-query span therefore needs at least ten fields. This is a +field-count bound, not a native-cost bound for a general shared +network. + +## The quartet structure + +The pinned matrix has 14 groups of eight columns. Each group has one +four-coordinate support. Within that support, the columns give all +16 sign vectors modulo multiplication by minus one. The certificate +checks this fact directly from `INTERFACE.json`; it does not assume +an E8 classification. + +Let `a` be a nonzero complex row of length eight. Fix one quartet, +and let `t` be the number of nonzero entries of `a` on it. The eight +column evaluations are the signed sums on that quartet, modulo sign. +Their number of nonzero values is at least + +```text +t: 0 1 2 3 4 +nonzero values: 0 8 4 6 5 +``` + +Here is a short proof of this table. First project the nonzero +complex coefficients onto a real line that gives no zero coefficient. +A complex zero sum is still a zero sum after this projection. Change +the signs of the coefficients so that all projected coefficients are +positive. The sign patterns in one quartet are closed under this +change. + +Subsets of positive coefficients with a fixed sum form an antichain: +one cannot be a proper subset of another. A permutation gives a +maximal chain of subsets, and an antichain meets it at most once. +Counting the permutations through each subset gives + +\[ +\sum_{S\text{ in the antichain}} + \binom{t}{|S|}^{-1}\leq1. +\] + +Thus there are at most `binomial(t,floor(t/2))` zero sign patterns. +The zero patterns occur in opposite pairs. For `t=1,2,3,4`, their +counts are therefore at most `0,2,2,6`. Each zero coefficient on the +quartet doubles the number of full sign patterns. Division by two +then identifies opposite full patterns. This gives the displayed +table. + +For each of the 255 possible nonempty coefficient supports, add the +14 quartet bounds. The exact minima at each support size are + +| Nonzero coefficients in `a` | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | +| --- | --- | --- | --- | --- | --- | --- | --- | --- | +| Lower bound for support of `aR` | 56 | 76 | 78 | 53 | 73 | 75 | 77 | 70 | + +The smallest bound is 53. The checker also evaluates `aR` exactly +when `a` is any actual column of `R`. Each of these 112 choices has +support 53. The lower bound and its attainment prove the claimed +minimum. The table gives lower bounds at each coefficient support +size; no separate attainment claim is made for its other entries. + +## Consequence for a shared span + +The independent snapshot support theorem says that a snapshot at +frame `U`, on the input family above, uses only ports perpendicular +to `U`. The certificate checks all actual frame bases. Every frame +of rank at least two permits at most 20 ports. The maximum counts +at ranks two through eight are `20,10,8,8,4,2,1`. + +Let `w_1,...,w_m` be independent reduced snapshot rows of this type. +Suppose their span contains a `k`-dimensional subspace of the query +row space. Each query has a unique coefficient row in this basis. +The resulting length-`m` linear code has minimum nonzero Hamming +weight at least three: a combination of at most two birth rows has +support at most 40, while a nonzero query has support at least 53. +Delete any two code coordinates. The deletion is injective, so + +\[ +k\leq m-2. +\] + +If the original birth rows are dependent, first keep a basis from +them. The same bound applies and hence also bounds their original +count. This excludes a four-birth-field, three-query merge of this +type, even if the query basis is changed. It also gives the bound of +ten fields for all eight queries. + +The same support count holds for nonzero operator coefficients on +the query rows. Apply a linear functional to the coefficient +operators that does not kill all of them. Every zero port operator +remains zero, and the scalar support bound applies. For payload +fields of dimension `d`, the coefficient code then has dimension +`kd` and block distance at least three. Deleting two field blocks +gives `kd <= (m-2)d`. This extension still requires each birth field +to have source-port support at most 20. It does not allow new source +reads to enter without counting their fields. + +## Verification and scope + +Run: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/history-encoding/check_query_support_distance.py +``` + +The result is `PASS_EXACT_QUERY_SUPPORT_MINIMUM_53`, saved in +`QUERY-SUPPORT-DISTANCE.json`. The checker reads the pinned query +matrix and frame table. It checks all quartet sign patterns, all 255 +coefficient supports, all 112 attaining directions, and all actual +frame support counts. A duplicate sign-pattern control and an +excessive quartet-bound control both fail. + +This proof inherits the independent exact snapshot support review. +It does not repeat the 712-input core replay. It does not prove a +64-rank lower bound, or an optimal field count for a network with +several merge levels. A new observation at a later frame can add +information; shared paid edges can also change the cost. A positive +circuit still needs time order, phases, arbitrary-state cleanup, +private lifetimes, and complete native and scalar costs. diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/RANK5-UNION-CUTS.json b/research/actual-query-information-bounds/payload/lanes/history-encoding/RANK5-UNION-CUTS.json new file mode 100644 index 0000000000..78d0392080 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/RANK5-UNION-CUTS.json @@ -0,0 +1,165393 @@ +{ + "base_cut_receipt_sha256": "8f95ed88bd5b0777d5accf5458858e569e8260f88b857eb5815be01c8a0bd816", + "merges": [ + { + "completion_bound": 20, + "cuts": [ + { + "characters": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 22, + 23, + 24, + 25, + 26, + 27, + 28, + 29, + 30, + 31 + ], + "demand": 5, + "inside_frames": [ + 630 + ], + "node_mask": 1048576, + "source_ports": [ + 47, + 110, + 46, + 111, + 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111, + "frame": 986, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 129, + 64, + 33, + 16, + 8, + 4, + 2 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 987, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 262, + 135, + 70, + 33, + 18, + 12 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 988, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 320, + 134, + 32, + 18, + 12, + 1 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 989, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 263, + 131, + 67, + 33, + 18, + 12 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 990, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 260, + 128, + 64, + 32, + 16, + 12, + 2, + 1 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 991, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 257, + 128, + 64, + 33, + 17, + 9, + 5, + 3 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 992, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 259, + 192, + 33, + 18, + 8, + 4 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 993, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 257, + 128, + 64, + 33, + 16, + 8, + 4, + 2 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 994, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 258, + 128, + 64, + 32, + 18, + 8, + 4, + 1 + ], + "determinant": "32", + "excluded_count": 111, + "frame": 995, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 263, + 134, + 70, + 33, + 18, + 12 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 996, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 262, + 192, + 32, + 18, + 12, + 1 + ], + "determinant": "32", + "excluded_count": 110, + "frame": 997, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 64, + 33, + 17, + 8, + 4, + 3 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 998, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 64, + 32, + 18, + 10, + 6, + 1 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 999, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 65, + 32, + 16, + 9, + 4, + 3 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 1000, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 66, + 34, + 16, + 8, + 6, + 1 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 1001, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 65, + 32, + 17, + 8, + 5, + 2 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 1002, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + }, + { + "basis": [ + 256, + 128, + 72, + 40, + 24, + 4, + 2, + 1 + ], + "determinant": "32", + "excluded_count": 112, + "frame": 1003, + "minor_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 12 + ] + } + ], + "frames_by_rank": { + "1": 120, + "2": 168, + "3": 168, + "4": 73, + "5": 27, + "6": 168, + "7": 152, + "8": 126 + }, + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "interval_count": 16687, + "normal_lines": [ + 42, + 7, + 25, + 52, + 82, + 127, + 97, + 76 + ], + "normal_lines_are_absent": true, + "scope": "Single positive-birth cone, with all cone snapshots and all completed X/helper baselines. Merged incomparable cones and other protocols remain open.", + "snapshot_payload_sha256": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", + "source_pins": { + "R": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "core": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877", + "word": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219" + }, + "status": "PASS_EXACT_SNAPSHOT_CONE_OBSTRUCTION", + "support_law": "At frame U, every nonzero reduced Y coefficient has q_p perpendicular to U.", + "test_input": "X=JY; all 480 helpers and all 8 private inputs are zero", + "wrong_frame_control": { + "original_frame": 2, + "rejected": true, + "row": 3382, + "source_port": 35, + "wrong_line": 50 + } +} diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md b/research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md new file mode 100644 index 0000000000..09ba0af502 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-CONE-OBSTRUCTION.md @@ -0,0 +1,129 @@ +# An exact obstruction for one monotone snapshot cone + +The backward clean-J word has no nonzero centre query in a single positive +snapshot cone. This result covers all 1,002 positive proper frames in the +actual word. It permits every recorded snapshot in that cone, without a +time constraint. Thus time order is not the obstruction in this model. + +This result does not cover a network that merges captures from different +cones. It also does not cover new internal cuts inside a native child, new +changes to the core, or transitions between incomparable frames. + +## Source and exact check + +`BACKWARD-SNAPSHOT-INTERVALS.json.gz` records the complete rational scalar +rows on 712 input coordinates. Its uncompressed SHA256 is +`3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c`. +The producer is `emit_snapshot_intervals.py`. It checks every scalar frame +access and every native frame transition. It also checks the final map + +\[ + (x,y,h,c)\longmapsto(x-Jy,y,h,0),\qquad + J=I-R^TR/4. +\] + +There are 12,271 distinct rows, 16,687 availability intervals, and 1,004 +native frames. An interval `[a,b,j,f,r]` states that row `r` of wire `j` +is available after each event from `a` through `b`, inclusive, with frame +index `f`. The recorded boundary range is 8,106 through 24,913. + +The scalar content uses the canonical frame coordinates. Before event +17,606, these are the literal native frames after the entry adapters. +After that event, a non-FULL field needs its specified inverse exit +monomial to expose that canonical view. This theorem grants those views. +It makes no claim that they are free in a constructive word. A zero +formal row is zero in both views, which is all that this proof needs. + +Run the exact certificate with: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/history-encoding/check_snapshot_cone_obstruction.py +``` + +The result is `PASS_EXACT_SNAPSHOT_CONE_OBSTRUCTION`. The checker uses +rational arithmetic. It checks 16,023 distinct frame/row pairs and 98,056 +nonzero reduced coefficients. For each of the 1,002 positive proper +frames, it emits an eight-column minor with a nonzero exact determinant. +The receipt is `SNAPSHOT-CONE-OBSTRUCTION.json`. + +The two controls reject a wrong frame for a nonzero source coefficient +and a repeated column in a query minor. No sampled rank or numerical +tolerance is used in this certificate. + +## Support identity + +Write the old port labels as \(q_p\in\mathbb F_2^9\), for +\(0\leq p<112\). Use the following valid family of inputs: + +\[ + x=Jy,\qquad h=0,\qquad c=0. +\] + +Here all 480 helper inputs are zero. This includes the 78 helpers whose +final frame is not FULL. This choice is an input for an impossibility +proof. It is not a clean-helper assumption for a proposed construction. +On this family, all completed X fields and all final helper fields vanish. + +For each actual snapshot in a frame \(U\), its remaining source row has +the form + +\[ + \sum_{p:q_p\perp U} a_p y_p. \tag{1} +\] + +The checker proves (1) directly from every exact row. It substitutes +\(x=Jy\), deletes the zero helper and private inputs, and checks the +support of each remaining coefficient. This includes data snapshots, +not only helper snapshots. + +Fix an actual positive proper frame \(U\), and set + +\[ + E_U=\{p:q_p\not\perp U\}. +\] + +The exact minor certificate proves + +\[ + \operatorname{rank} R_{E_U}=8. \tag{2} +\] + +The eight normal lines \(42,7,25,52,82,127,97,76\) do not contradict (2). +Row \(k\) of \(R\) is supported exactly on the ports perpendicular to +normal \(n_k\). But none of these normal lines is an actual rank-one +frame. The actual rank-one frames consist of the 112 old port lines and +eight even lines. Their absence and the normal support identity are both +checked exactly. + +## Cone theorem + +For an actual positive proper frame \(U\), its snapshot cone consists of +all recorded frames \(V\) such that \(U\subseteq V\). Grant every +snapshot in that cone, without a time constraint. Also grant every final +X and helper field, with arbitrary linear operations on those granted +fields. + +No nonzero scalar combination of the eight completed centre queries +\(F_9 R y\) can be formed from these observations. + +To prove the statement, restrict \(y\) to the coordinates in \(E_U\). +If \(V\supseteq U\), then \(q_p\perp V\) implies +\(q_p\perp U\). Thus (1) makes every snapshot in the cone zero. +The final X and helper fields are also zero. Every linear operation on +these observations is zero, with every native phase and address map. +But (2) allows \(Ry\) to take any value in eight dimensions. Since +\(F_9\) is invertible, the required nonzero query cannot be zero on all +these inputs. This is a contradiction. + +In particular, a cache that starts at zero, first captures content in a +positive actual frame, and then follows only increasing native frames +cannot produce a centre query. The same conclusion holds for any number +of caches restricted to that one cone. Allowing all cone snapshots is +stronger than any one chronological path. A cache that starts empty in +an unrecorded smaller frame must still make its first nonzero capture +in an actual frame; the theorem then applies from that frame onward. + +The theorem does not rule out a cache with earlier nonzero captures from +an incomparable frame. That is the precise remaining escape for a +merged snapshot network. It gives no lower bound for such a network, +for a different core, or for the complete supplier. diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.json b/research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.json new file mode 100644 index 0000000000..e2b2f9aa0d --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.json @@ -0,0 +1,65 @@ +{ + "candidate_proof_sha256": "f550ecd52133f7fb856538abf6ed7ef9241577bf309f7268cd4610b8c12735df", + "candidate_receipt_sha256": "2c001f0336c1f930a41eace304e957eb5da354edc56c4c9b0449bf253d65fb25", + "checked_frames": 1004, + "checked_native_edges": 2880, + "checker_sha256": "e52355cbedf49346d2e27271fa999e68d66ae9b3d00980477d8750b66b0fc919", + "controls": { + "one_unit_native_undercharge_rejected": true, + "reversed_shell_failures": 6293 + }, + "exact_gram_ranks": [ + 0, + 1, + 1, + 2, + 8, + 6, + 8, + 8, + 8 + ], + "flag": [ + 243, + 249, + 311, + 132, + 131, + 489, + 442, + 405, + 178 + ], + "native_rank_lower_bound": 42, + "not_checked": [ + "A positive cache circuit", + "Native phase recipes for new edges", + "Changed address codes", + "Global supplier cost" + ], + "proof_checks": [ + "Pivot-set inclusion for arbitrary nested frames", + "Whole-array dimension in each cut inequality", + "No separate-tree assumption in the cut sum" + ], + "scope": "Same-content monotone frame DAGs with scalar sharing. No 64 bound or construction is proved.", + "separation_checks": 23279, + "shell_sizes": [ + 0, + 1, + 1, + 2, + 8, + 7, + 11, + 22, + 60 + ], + "sources": { + "core": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877", + "interface": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "snapshot": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", + "support_review": "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7" + }, + "status": "PASS_INDEPENDENT_SHARED_SNAPSHOT_FLAG_BOUND_42" +} diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.md b/research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.md new file mode 100644 index 0000000000..85bc0213f8 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/SNAPSHOT-FLAG-CUT-REVIEW.md @@ -0,0 +1,65 @@ +# Independent review of the shared snapshot cut bound + +The proof in `../cover-algebra/SNAPSHOT-FLAG-CUT.md` passes review. It +proves a lower bound of 42 native rank units in the stated scalar +network model. It does not prove 64, and it gives no circuit below 64. + +The proof uses one ordered binary basis. For any subspace, the set of +leading positions is the set of leading positions of its nonzero +vectors. Thus inclusion of subspaces gives inclusion of these sets. +An increasing frame edge enters exactly as many pivot cuts as its +dimension increase. This fact holds for any nested frames, not only +the retained edges checked in the receipt. + +The shell for position `i` has zero dual coordinates above `i` and +dual coordinate one at `i`. A vector with leading position `i` has +zero coordinates below `i`. Their dot product is one. The reviewed +snapshot support law therefore excludes every shell input from all +free observations inside its cut. On the valid input family +`X=JY`, with all helper and private inputs zero, the final free +baselines also vanish. + +The required output on that shell has rank `rank(R_shell)`. If each +payload field has dimension `d`, its output rank is +`d*rank(R_shell)`, while one entering field carries at most `d` +dimensions. This gives the cut inequality for full payload arrays. +It permits scalar fanout, reuse, and cancellation. It does not sum +separate output-tree costs. Summing the nine cuts charges each +monotone edge only its dimension increase. + +## Independent calculation + +`review_snapshot_flag_cut.py` imports no producer or reviewed checker. +It reads the pinned interface, snapshot source, and clean backward +word. It builds all 512 flag coordinates by direct enumeration. It +derives each pivot set by enumerating the frame span. It obtains the +shell ranks from exact rational elimination of the eight-dimensional +Gram matrices. These methods differ from the producer's echelon +calculation. + +The check covers all 1004 frames, 23279 shell separation cases, and +2880 distinct retained native edges. It gives the exact shell ranks +`[0,1,1,2,8,6,8,8,8]`. Reversing the shell order causes 6293 separation +failures. Reducing a positive edge charge by one also fails. + +Run: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/history-encoding/review_snapshot_flag_cut.py +``` + +The result is `PASS_INDEPENDENT_SHARED_SNAPSHOT_FLAG_BOUND_42` in +`SNAPSHOT-FLAG-CUT-REVIEW.json`. The receipt pins both reviewed proof +and candidate receipt. It also pins the independent exact snapshot +support review. That premise is inherited; this small check does not +repeat the full 712-input core replay. + +## Scope + +The bound applies to increasing frame transitions that preserve the +logical field content, with scalar mixing at each frame. It grants +all recorded times and arbitrary cache storage. It does not cover a +change of logical address code, a changed core, or new cross-parent +child access. A positive construction still needs literal phases, +time order, arbitrary-state cleanup, private lifetimes, and a full +supplier invoice. No such construction is part of this review. diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/check_query_support_distance.py b/research/actual-query-information-bounds/payload/lanes/history-encoding/check_query_support_distance.py new file mode 100644 index 0000000000..bb69302e5c --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/check_query_support_distance.py @@ -0,0 +1,114 @@ +"""Check the source data for the exact query support bound.""" + +from collections import Counter, defaultdict +from fractions import Fraction +from hashlib import sha256 +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +INTERFACE_PIN = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" +SNAPSHOT_PIN = "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c" +SUPPORT_PIN = "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7" +NONZERO_PER_QUARTET = [0, 8, 4, 6, 5] + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def quartet_data(columns): + groups = defaultdict(list) + for p, column in enumerate(columns): + support = sum((value != 0) << i for i, value in enumerate(column)) + require(support.bit_count() == 4, "A root has the wrong support size") + require(all(value in (-1, 0, 1) for value in column), "A root coefficient differs") + groups[support].append(p) + require(len(groups) == 14, "The quartet count differs") + for support, ports in groups.items(): + indices = [i for i in range(8) if support >> i & 1] + patterns = {tuple(columns[p][i] * columns[p][indices[0]] for i in indices) + for p in ports} + require(len(ports) == len(patterns) == 8, + "A quartet does not contain all sign patterns up to sign") + return groups + + +def main(): + interface_raw = (HERE.parent / "circuit-interface/INTERFACE.json").read_bytes() + snapshot_raw = gzip.decompress((HERE / "BACKWARD-SNAPSHOT-INTERVALS.json.gz").read_bytes()) + support_raw = (HERE.parent / "cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json").read_bytes() + require(sha256(interface_raw).hexdigest() == INTERFACE_PIN, "The interface pin differs") + require(sha256(snapshot_raw).hexdigest() == SNAPSHOT_PIN, "The snapshot pin differs") + require(sha256(support_raw).hexdigest() == SUPPORT_PIN, "The support review pin differs") + source = json.loads(interface_raw) + snapshots = json.loads(snapshot_raw) + R = [[Fraction(row.get(str(p), "0")) for p in range(112)] for row in source["R"]] + require(all(value.denominator == 1 for row in R for value in row), "A root coefficient is not integral") + R = [[int(value) for value in row] for row in R] + columns = list(zip(*R)) + groups = quartet_data(columns) + lower_by_size = {} + exact_support_bounds = {} + for support in range(1, 256): + bound = sum(NONZERO_PER_QUARTET[(support & block).bit_count()] for block in groups) + size = support.bit_count() + lower_by_size[size] = min(bound, lower_by_size.get(size, bound)) + exact_support_bounds[str(support)] = bound + require(lower_by_size == {1: 56, 2: 76, 3: 78, 4: 53, 5: 73, 6: 75, 7: 77, 8: 70}, + "A coefficient support bound differs") + attained = [sum(sum(a * b for a, b in zip(query, column)) != 0 for column in columns) + for query in columns] + require(set(attained) == {53}, "An old-root query does not attain 53") + frame_histogram = defaultdict(Counter) + for basis in snapshots["frames"]: + allowed = sum(all((label & vector).bit_count() % 2 == 0 for vector in basis) + for label in source["ports"]) + frame_histogram[len(basis)][allowed] += 1 + require(all(count <= 20 for rank, values in frame_histogram.items() + if rank >= 2 for count in values), "A high-rank frame permits more than 20 ports") + broken = list(columns) + first_group = next(iter(groups.values())) + broken[first_group[1]] = broken[first_group[0]] + try: + quartet_data(broken) + except ValueError: + duplicate_rejected = True + else: + duplicate_rejected = False + require(duplicate_rejected, "The duplicate-sign control passed") + wrong_table = [0, 8, 4, 6, 6] + query = columns[0] + query_support = sum((value != 0) << i for i, value in enumerate(query)) + false_bound = sum(wrong_table[(query_support & block).bit_count()] for block in groups) + require(false_bound > attained[0], "The excessive quartet bound control passed") + result = { + "status": "PASS_EXACT_QUERY_SUPPORT_MINIMUM_53", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "sources": {"interface_sha256": INTERFACE_PIN, + "snapshot_decompressed_sha256": SNAPSHOT_PIN, + "independent_support_review_sha256": SUPPORT_PIN}, + "quartets": {str(block): ports for block, ports in sorted(groups.items())}, + "nonzero_per_quartet_lower_bounds": NONZERO_PER_QUARTET, + "lower_bounds_by_nonzero_coefficient_count": lower_by_size, + "all_255_coefficient_support_bounds": exact_support_bounds, + "minimum_source_port_support": 53, + "attaining_old_root_directions": len(attained), + "frame_allowed_port_histogram": {rank: dict(sorted(values.items())) + for rank, values in sorted(frame_histogram.items())}, + "controls": {"duplicate_sign_pattern_rejected": duplicate_rejected, + "excessive_quartet_bound_rejected": True}, + "consequence": "A k-dimensional query space needs at least k+2 rank-at-least-two birth fields in one common span.", + "not_claimed": ["A native rank lower bound of 64 for shared networks", + "A constructive cache network", "A full supplier improvement"], + } + (HERE / "QUERY-SUPPORT-DISTANCE.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(json.dumps({key: value for key, value in result.items() + if key not in ("quartets", "all_255_coefficient_support_bounds")}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/check_snapshot_cone_obstruction.py b/research/actual-query-information-bounds/payload/lanes/history-encoding/check_snapshot_cone_obstruction.py new file mode 100644 index 0000000000..4d1bd22e62 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/check_snapshot_cone_obstruction.py @@ -0,0 +1,160 @@ +"""Check exact support and query minors for the backward snapshot cones.""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import gzip +import json + +HERE = Path(__file__).resolve().parent +SNAPSHOT_PIN = "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c" +INTERFACE_PIN = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" +NORMALS = [42, 7, 25, 52, 82, 127, 97, 76] + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def add(row, other, scale): + for j, a in other.items(): + value = row.get(j, Q(0)) + scale * a + if value: + row[j] = value + else: + row.pop(j, None) + + +def dot(a, b): + return (a & b).bit_count() & 1 + + +def determinant(matrix): + a = [[Q(x) for x in row] for row in matrix] + result = Q(1) + for j in range(len(a)): + pivot = next((i for i in range(j, len(a)) if a[i][j]), None) + if pivot is None: + return Q(0) + if pivot != j: + a[j], a[pivot] = a[pivot], a[j] + result = -result + value = a[j][j] + result *= value + for i in range(j + 1, len(a)): + scale = a[i][j] / value + for k in range(j + 1, len(a)): + a[i][k] -= scale * a[j][k] + return result + + +def independent_columns(R, candidates): + pivots = {} + selected = [] + for p in candidates: + row = {k: r[p] for k, r in enumerate(R) if r.get(p)} + for k, basis in sorted(pivots.items()): + if row.get(k): + add(row, basis, -row[k]) + if row: + k = min(row) + a = row[k] + pivots[k] = {j: b / a for j, b in row.items()} + selected.append(p) + if len(selected) == 8: + return selected + return selected + + +def main(): + raw = gzip.decompress((HERE / "BACKWARD-SNAPSHOT-INTERVALS.json.gz").read_bytes()) + require(sha256(raw).hexdigest() == SNAPSHOT_PIN, "snapshot source pin") + data = json.loads(raw) + raw_interface = (HERE.parent / "circuit-interface/INTERFACE.json").read_bytes() + require(sha256(raw_interface).hexdigest() == INTERFACE_PIN, "interface source pin") + interface = json.loads(raw_interface) + ports = interface["ports"] + require(data["R"] == interface["R"], "query source agreement") + R = [{int(j): Q(a) for j, a in row.items()} for row in data["R"]] + J = [{j: Q(1)} for j in range(112)] + for j in range(112): + for r in R: + add(J[j], r, -r.get(j, Q(0)) / 4) + + def restrict(row): + out = {j - 112: Q(a) for key, a in row.items() + if 112 <= (j := int(key)) < 224} + for key, a in row.items(): + j = int(key) + if j < 112: + add(out, J[j], Q(a)) + return out + + reduced = [restrict(row) for row in data["rows"]] + pairs = sorted({(f, r) for lo, hi, j, f, r in data["intervals"]}) + coefficients = 0 + first_nonzero = None + for f, r in pairs: + U = data["frames"][f] + for p, a in reduced[r].items(): + require(not any(dot(ports[p], u) for u in U), "snapshot support law") + coefficients += 1 + if U and first_nonzero is None: + first_nonzero = (f, r, p) + final = [restrict(row) for row in data["final_rows"]] + require(all(not final[j] for j in list(range(112)) + list(range(224, 712))), + "completed X and all helper/private baselines vanish") + + minors = [] + for f, U in enumerate(data["frames"]): + if not 0 < len(U) < 9: + continue + excluded = [p for p, q in enumerate(ports) if any(dot(q, u) for u in U)] + chosen = independent_columns(R, excluded) + require(len(chosen) == 8, "excluded query rank") + matrix = [[r.get(p, Q(0)) for p in chosen] for r in R] + det = determinant(matrix) + require(det != 0, "exact query minor") + minors.append({"frame": f, "basis": U, "excluded_count": len(excluded), + "minor_ports": chosen, "determinant": str(det)}) + + lines = {U[0] for U in data["frames"] if len(U) == 1} + require(lines.isdisjoint(NORMALS), "normal lines absent from actual frame list") + for k, n in enumerate(NORMALS): + require({p for p, q in enumerate(ports) if not dot(q, n)} == set(R[k]), + "normal query support") + f, r, p = first_nonzero + require(dot(ports[p], ports[p]) == 1, "wrong-frame control is nonzero") + bad_matrix = [[row.get(j, Q(0)) for j in minors[0]["minor_ports"]] for row in R] + for row in bad_matrix: + row[-1] = row[0] + require(determinant(bad_matrix) == 0, "duplicate-minor-column control") + report = { + "status": "PASS_EXACT_SNAPSHOT_CONE_OBSTRUCTION", + "snapshot_payload_sha256": SNAPSHOT_PIN, + "interface_sha256": INTERFACE_PIN, + "source_pins": data["pins"], + "test_input": "X=JY; all 480 helpers and all 8 private inputs are zero", + "support_law": "At frame U, every nonzero reduced Y coefficient has q_p perpendicular to U.", + "distinct_frame_row_pairs": len(pairs), + "exact_nonzero_support_coefficients": coefficients, + "interval_count": len(data["intervals"]), + "actual_positive_proper_frames": len(minors), + "frames_by_rank": dict(sorted(Counter(len(m["basis"]) for m in minors).items())), + "excluded_query_minors": minors, + "normal_lines": NORMALS, + "normal_lines_are_absent": True, + "wrong_frame_control": {"row": r, "original_frame": f, "source_port": p, + "wrong_line": ports[p], "rejected": True}, + "duplicate_minor_column_rejected": True, + "scope": "Single positive-birth cone, with all cone snapshots and all completed X/helper baselines. Merged incomparable cones and other protocols remain open.", + } + path = HERE / "SNAPSHOT-CONE-OBSTRUCTION.json" + path.write_text(json.dumps(report, sort_keys=True, indent=2) + "\n") + print(json.dumps({k: report[k] for k in ("status", "distinct_frame_row_pairs", + "exact_nonzero_support_coefficients", "actual_positive_proper_frames")}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/payload/lanes/history-encoding/review_snapshot_flag_cut.py b/research/actual-query-information-bounds/payload/lanes/history-encoding/review_snapshot_flag_cut.py new file mode 100644 index 0000000000..a2671bb307 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/history-encoding/review_snapshot_flag_cut.py @@ -0,0 +1,161 @@ +"""Check the shared snapshot cut certificate from its source data.""" + +from fractions import Fraction +from hashlib import sha256 +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent +PINS = { + "interface": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "snapshot": "3dd1d7388c7d3bca104a21e642b5fcafe175d83a2f1dfce1a3ee3e86b864276c", + "core": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877", + "support_review": "d3a7dc571b2ac2e55945918b0bccd66d99d0d08b6b7af8326e53999578e61fe7", +} + + +def check(value, message): + if not value: + raise ValueError(message) + + +def read(path, key, compressed=False): + raw = path.read_bytes() + if compressed: + raw = gzip.decompress(raw) + check(sha256(raw).hexdigest() == PINS[key], "Source pin differs: " + key) + return json.loads(raw) + + +def span(basis): + values = {0} + for vector in basis: + values |= {value ^ vector for value in tuple(values)} + return values + + +def gram_rank(columns): + matrix = [[Fraction(sum(col[i] * col[j] for col in columns)) + for j in range(8)] for i in range(8)] + # A Gram matrix is positive semidefinite. A zero diagonal has a zero row. + rank = 0 + for pivot in range(8): + value = matrix[pivot][pivot] + if not value: + check(all(not a for a in matrix[pivot]), "Invalid Gram pivot") + continue + check(value > 0, "A Gram pivot is negative") + rank += 1 + column = [matrix[i][pivot] for i in range(8)] + for i in range(8): + for j in range(8): + matrix[i][j] -= column[i] * column[j] / value + return rank + + +def main(): + receipt_path = LANES / "cover-algebra/SNAPSHOT-FLAG-CUT.json" + proof_path = LANES / "cover-algebra/SNAPSHOT-FLAG-CUT.md" + candidate = json.loads(receipt_path.read_bytes()) + interface = read(LANES / "circuit-interface/INTERFACE.json", "interface") + snapshots = read(HERE / "BACKWARD-SNAPSHOT-INTERVALS.json.gz", "snapshot", True) + core = read(LANES / "circuit-interface/CENTRE-FREE-PROGRAMS.json.gz", "core", True) + support = read(LANES / "cover-algebra/SNAPSHOT-SUPPORT-REVIEW.json", "support_review") + check(support["status"] == "PASS_EXACT_SNAPSHOT_SUPPORT_AND_SINGLE_CONE_EXCLUSION", + "The independent support premise did not pass") + flag = candidate["flag_basis"] + coordinate = {} + for bits in range(512): + value = 0 + for i, vector in enumerate(flag): + if bits >> i & 1: + value ^= vector + check(value not in coordinate, "The flag is dependent") + coordinate[value] = bits + check(len(coordinate) == 512, "The flag is incomplete") + labels = interface["ports"] + R = [[Fraction(row.get(str(p), "0")) for p in range(112)] + for row in interface["R"]] + check(all(value.denominator == 1 for row in R for value in row), + "The pinned query has a noninteger coefficient") + R = [[int(value) for value in row] for row in R] + columns = list(zip(*R)) + shells = [[] for _ in range(9)] + low_shells = [[] for _ in range(9)] + for p, label in enumerate(labels): + dual = [((label & vector).bit_count() & 1) for vector in flag] + nonzero = [i for i, bit in enumerate(dual) if bit] + check(nonzero, "A port has zero dual coordinates") + shells[max(nonzero)].append(p) + low_shells[min(nonzero)].append(p) + ranks = [gram_rank([columns[p] for p in shell]) for shell in shells] + check(shells == candidate["shells"], "The shell partition differs") + check(ranks == candidate["exact_shell_ranks"], "A shell rank differs") + check(sum(ranks) == 42, "The lower bound differs") + + frame_spans = [span(basis) for basis in snapshots["frames"]] + pivots = [] + separation_count = 0 + wrong_order_failures = 0 + for basis, values in zip(snapshots["frames"], frame_spans): + check(len(values) == 1 << len(basis), "A frame basis is dependent") + lead = {(coordinate[value] & -coordinate[value]).bit_length() - 1 + for value in values if value} + check(len(lead) == len(basis), "The pivot count differs") + pivots.append(lead) + for i in lead: + witness = next(value for value in values if value and + (coordinate[value] & -coordinate[value]).bit_length() - 1 == i) + for p in shells[i]: + separation_count += 1 + check((labels[p] & witness).bit_count() & 1, + "A shell coordinate is not excluded by its pivot witness") + for p in low_shells[i]: + wrong_order_failures += not any((labels[p] & value).bit_count() & 1 + for value in basis) + check(wrong_order_failures > 0, "The reversed-shell control did not fail") + edges = set() + for event in core["backward"]: + if event[0] != "climb": + continue + _, _, wire, before, after, rank = event + check(frame_spans[before] <= frame_spans[after], "An edge is not monotone") + check(pivots[before] <= pivots[after], "A pivot cut can be left") + charge = len(pivots[after] - pivots[before]) + check(charge == rank, "The native edge charge differs") + edges.add((before, after, rank)) + check(len(edges) == 2880, "The retained edge count differs") + positive_edge = next(edge for edge in edges if edge[2]) + check(len(pivots[positive_edge[1]] - pivots[positive_edge[0]]) > positive_edge[2] - 1, + "The undercharged-edge control did not fail") + output = { + "status": "PASS_INDEPENDENT_SHARED_SNAPSHOT_FLAG_BOUND_42", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "sources": PINS, + "candidate_receipt_sha256": sha256(receipt_path.read_bytes()).hexdigest(), + "candidate_proof_sha256": sha256(proof_path.read_bytes()).hexdigest(), + "flag": flag, + "shell_sizes": [len(shell) for shell in shells], + "exact_gram_ranks": ranks, + "native_rank_lower_bound": sum(ranks), + "checked_frames": len(pivots), + "checked_native_edges": len(edges), + "separation_checks": separation_count, + "controls": {"reversed_shell_failures": wrong_order_failures, + "one_unit_native_undercharge_rejected": True}, + "scope": "Same-content monotone frame DAGs with scalar sharing. No 64 bound or construction is proved.", + "proof_checks": ["Pivot-set inclusion for arbitrary nested frames", + "Whole-array dimension in each cut inequality", + "No separate-tree assumption in the cut sum"], + "not_checked": ["A positive cache circuit", "Native phase recipes for new edges", + "Changed address codes", "Global supplier cost"], + } + (HERE / "SNAPSHOT-FLAG-CUT-REVIEW.json").write_text(json.dumps(output, indent=2, sort_keys=True) + "\n") + print(json.dumps(output, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/payload/lanes/interface-proof/NATIVE-LIFT-REVIEW.json b/research/actual-query-information-bounds/payload/lanes/interface-proof/NATIVE-LIFT-REVIEW.json new file mode 100644 index 0000000000..92703ca6d9 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/interface-proof/NATIVE-LIFT-REVIEW.json @@ -0,0 +1,68 @@ +{ + "all_tensor_powers": "Base operators are exactly equal, so their tensor powers are equal for every positive integer. The common frame conjugation proof gives the full array map.", + "archive_sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754", + "base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "changed_payload_sha256": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877", + "checked_endpoint_adapters": 224, + "checked_residual_recipes": 36, + "checked_unique_persistent_edges": 2880, + "exact_operator_method": "Pauli conjugation and exact Gaussian dyadic zero state; no compiler import", + "finite_local_invoice": { + "backward": { + "events": 25155, + "paid_profile": { + "1": 2412, + "2": 418, + "3": 432, + "4": 142, + "5": 82 + }, + "paid_rank_sum": 5522, + "persistent_native_events": 5056, + "prefix_macros": { + "add": 580, + "clear": 16 + }, + "prefix_real_component_primitive_bound": 5532, + "real_component_primitive_bound": 202138, + "scalar_macros": 20089 + }, + "forward": { + "events": 25155, + "paid_profile": { + "1": 2412, + "2": 418, + "3": 432, + "4": 142, + "5": 82 + }, + "paid_rank_sum": 5522, + "persistent_native_events": 5056, + "prefix_macros": { + "add": 580, + "clear": 16 + }, + "prefix_real_component_primitive_bound": 5532, + "real_component_primitive_bound": 202138, + "scalar_macros": 20089 + } + }, + "max_rss_bytes": 113623040, + "member_sha256": { + "CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219", + "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731", + "LOCAL-PROGRAMS.json.gz": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a", + "RESIDUAL-ADAPTERS.json": "383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c" + }, + "negative_controls": [ + "wrong global phase with the same Pauli action, on basis inputs 0 and 1" + ], + "not_claimed": [ + "global chart or owner admission", + "recursive supplier admission", + "new kappa", + "fresh all-size compiler proof" + ], + "seconds": 26.28553620799994, + "status": "PASS_INDEPENDENT_NATIVE_FRAME_LIFT_AND_FINITE_LOCAL_BILL" +} diff --git a/research/actual-query-information-bounds/payload/lanes/interface-proof/PROOF.md b/research/actual-query-information-bounds/payload/lanes/interface-proof/PROOF.md new file mode 100644 index 0000000000..c7fe33cedb --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/interface-proof/PROOF.md @@ -0,0 +1,244 @@ +# A centre-free local native primitive + +This note proves the native meaning of the two emitted centre-free words. +It also proves a cut-removal rule for a class of linear circuits. It does not +admit a new recursive supplier or change the complete kappa calculation. + +The experiment uses commit `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. +The selected word is in the [pinned replay archive](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/community-frontier1042-audit/selected-replay.tar.gz). +Its SHA-256 is `22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754`. +This is an experiment source pin, not a claim about the present repository head. + +`NATIVE-LIFT-REVIEW.json` records the independent native check. +`FACTORIZATION.json` records the cut calculation. +`FRESH-FORWARD-TRANSPOSE.json` and `FRESH-BACKWARD-TRANSPOSE.json` record fresh +replays of all 712 input columns. `PHASE-SOURCE-PINS.json` identifies the +phase compiler and the source proofs. The new verification scripts use explicit checks which +remain active with Python optimization enabled. + +## 1. The scalar contract + +There are 112 source registers x, 112 target registers y, 480 persistent +helper registers h, and eight named private centre registers c. The private +registers need not start at zero. Let R be the actual 8-by-112 source matrix +at the centre cut. Define + + P = R^T R / 4, J = I_112 - P. + +Exact arithmetic gives + + R R^T = 56 I_8, + P^2 = 14 P, + J^2 + 12 J - 13 I_112 = 0. + +The new forward and backward scalar maps are, respectively, + + (x, y, h, c) -> (x, y + J x, h, 0), + (x, y, h, c) -> (x - J^T y, y, h, 0). + +The transpose replay derives R from the original forward word. It then +checks every column of each new 712-by-712 map against these formulas. +This includes every arbitrary helper input and every private input. +The private output rows and input columns are zero. The check also rejects +the omission of the first private CLEAR and of a dirty-correction ADD. + +The producer uses `assert` for its checks. Its own PASS message under `-O` +is therefore not proof. The separate transpose replay uses explicit +`require` calls. The fresh receipts in this directory were made with +`python3 -I -O -B`. + +## 2. Why the dirty correction works + +The insertion site is after the entry adapters and before A. At this site +the target registers and all 404 helper terms used by H have frame zero. +A does not read or change any target register. At the end of A the eight +centre values are + + z = R x + H h_site. + +The matrix H obtained at this insertion site agrees with the H obtained by +pulling the centre values back to the initial scalar inputs. The distinction +was checked. It must not be assumed for another word. + +Let D be the 112-by-8 scatter matrix in the literal centre cut. D has 176 +nonzero entries. It is not R^T/4. The suffix after the centre cut sends an +injection D z into the target bank to an injection K z at the final output, +where + + K = R^T/4. + +This response has no source, helper, or private output component. K has 448 +nonzero entries. `verify_factorization.py` derives this response by carrying +the eight independent columns of D through the actual suffix. + +If the complete centre phase is omitted, the target output loses +K(Rx+Hh_site). Before A, add D H h_site to the target bank. This addition +does not change A or its centre values. The retained suffix sends it to +K H h_site, which cancels the lost helper response. Thus only K R x is lost, +and the target coupling becomes I-KR=J. + +The implementation forms each row of H in a cleared private register, +adds its D column to the targets, and clears the private register again. +It uses 404+176=580 ADD macros and 16 CLEAR macros. Only one centre value +is live at a time. No source is read by this prefix. The backward prefix +first forms each row of D^T y, then adds the negative corresponding H^T +column to the helpers. Its persistent scalar map is the inverse transpose +of the forward prefix. The complete backward endpoint was also checked +directly, without relying on this transpose argument alone. + +## 3. Common-frame lift for every tensor size + +Let V be a complex vector space and let F_f be the invertible native operator +for frame f. A physical register in frame f stores F_f s, where s is its +logical value. A frame transition from a to b acts by F_b F_a^-1. +In logical coordinates this transition is the identity. + +For two registers in the same frame f, a scalar ADD with coefficient q acts as + + F_f s_target + q F_f s_source = F_f(s_target + q s_source). + +The same statement holds for SCALE, COPY, and CLEAR. CLEAR makes the logical +value zero for any physical input. An induction over the literal events +therefore proves that a legal framed scalar circuit has native map + + diag(F_out) (M tensor I_V) diag(F_in^-1), + +with its stated entry and exit adapters. This statement requires equality +of complete frame operators, including their global phases. Equality of +binary frame spaces or of Clifford tableaux alone is not sufficient. + +For the actual word, take V=(C^512)^(tensor lambda), with any retained +spectator factor. Replace each base operator F_f by F_f^(tensor lambda) +and the identity on spectators. Every exact base operator equality remains +an equality under this replacement. Scalar coefficients remain q; they are +not raised to the power lambda. The induction thus proves the map for +every positive integer lambda and every spectator array. + +`verify_native_lift.py` checks the 2,880 distinct retained frame transitions, +all 224 source/target endpoint adapters, and all 36 used residual recipes. +It reconstructs the canonical circuits from their definition. It does not +import the emitter or the Clifford compiler. Its two equality checks are +the images of all Pauli generators and the exact Gaussian-dyadic image of +the zero basis state. These determine a Clifford operator: the Pauli images +determine it up to scalar, and the nonzero state fixes that scalar. +The phase control changes this scalar while leaving all Pauli images fixed; +the checker rejects it on two input basis states. + +The two new programs have exactly the same 5,056 persistent native events +as the old programs. Every new scalar access is in frame zero. The complete +frame replay checks the entry frame of every climb, both operands of every +scalar gate, the original 704 persistent end frames, and cleared private +outputs. No new native identity or unpriced frame transition is assumed. + +## 4. Physical endpoints and borrowed helpers + +Write C_p for the selected source-line operator C_(q_p), and F for the full +nine-axis operator. In this paragraph each operator denotes its lambda-th +tensor power, with identity on spectators. Let X_p and Y_p be physical +source and target inputs. The entry convention is x_p=C_p^-1 X_p and +y_p=Y_p. The source exit is F and the target exit is F C_p^-1. +The new forward physical outputs are + + X'_p = F C_p^-1 X_p, + Y'_p = F C_p^-1 [Y_p + sum_j J[p,j] C_j^-1 X_j]. + +The new backward physical outputs are + + X'_p = F [C_p^-1 X_p - sum_j J[j,p] Y_j], + Y'_p = F C_p^-1 Y_p. + +Thus a canonical scalar source is unchanged by the forward shear, but its +physical source array still receives the original native source transform. +The different target endpoints also remain present. In particular a scalar +J^-1 on raw physical targets is not a free inverse for this native map. + +For a wrapped helper with start frame E and end frame U, the retained recipe +is + + F_U F_E^-1 = L F_w R. + +The entry wrapper is R^-1 and the exit wrapper is L^-1. Since the scalar +endpoint returns the helper coordinate itself, its physical endpoint is +L^-1 F_U F_E^-1 R^-1=F_w on arbitrary input. An ordinary cold helper has the +corresponding full-frame transform. The changed word preserves these +operators; it does not claim that every physical helper is returned unchanged. +No zero initialization is used for a persistent helper. Private centre and +coefficient streams use their stated CLEAR operations. + +## 5. Finite local cost and its limits + +Both orientations have this exact emitted inventory: + +| Item | Count | +|---|---:| +| Events | 25,155 | +| Scalar macros | 20,089 | +| Real-component primitive upper bound | 202,138 | +| Dirty-prefix ADD / CLEAR | 580 / 16 | +| Dirty-prefix real-component primitive bound | 5,532 | +| Persistent native events | 5,056 | +| Paid profile | 1:2412, 2:418, 3:432, 4:142, 5:82 | +| Sum of paid ranks | 5,522 | +| Removed centre children | Eight children of rank eight | + +For q=a/2^b in reduced form, the retained ADD bound is +3+(bitlength(|a|)-1)+popcount(|a|)+b. CLEAR and COPY each cost one per real +component. A signed binary SCALE has the retained shift/sign cost. The +table sums these actual coefficients and both real components. It is an +upper bound on scalar primitives, not a measured runtime. + +The old real-component bounds were 198,766 forward and 198,814 backward. +The net increases are 3,372 and 3,324. The centre private lifetime needs one +live array, as before; the retained Horner compiler also uses its coefficient +stream. Storage and hosting must still be bound to any changed controller. +This table does not price the finite global group, its routers, exterior +helpers, changed data assembly, or the complete recursive moment. The old +profile cannot simply lose 64 rank units while retaining its old data claim: +the coupling has changed from I to J. + +## 6. General cut-removal rule + +The argument applies to any linear framed circuit with these properties: + +1. At an allowed site, the future centre values have the form Rx+Hh. The + source x used here is unchanged between the circuit input and this site. +2. Before the centre cut, A neither reads nor changes the target bank. +3. The cut adds D(Rx+Hh) to the targets. Its suffix sends D z to K z only in + the final target bank, for every z, and has no other output response. +4. The site permits formation of Hh and scatter by D in one common frame. +5. The original persistent scalar contract is a shear with coupling M, + with its stated source and helper restoration. + +Then removing the cut and inserting the dirty prefix gives coupling M-KR, +with the same source and helper contract. The prefix costs nnz(H)+nnz(D) +ADD and 2k CLEAR macros for k centre coordinates and has one live centre +array. All removed centre paths disappear. This rule does not assume that +K=D, that H is the initial-input helper map, or that x is cheaply available +in the preload frame. These are separate, testable conditions. + +This theorem changes the available local interface from an identity shear +to a known low-rank perturbation. It is useful when another construction can +use that perturbation or compose it away. It does not itself supply that +construction. `COEFFICIENTS.md` gives a coefficient implementation and exact +limits on tuning the perturbation by helper-only preloads. + +## Open next questions + +The main obligation is a physical controller that uses these endpoint +operators, restores arbitrary borrowed state, and has a better complete +recursive invoice. Same-chart polynomial identities do not by themselves +meet that obligation. A source-dependent cache may also permit a different +centre coefficient; its legal reads and complete native cost must be paid. + +The phase check does not prove the inherited all-size stream compiler, +common-label and mutable-source realization, precision, fixed-tape, analytic +transfer, or bit-supplier hypotheses. It proves the local operator change +within those retained interfaces. + +Research and verification: OpenAI Codex under the user's direction, with +substantial AI assistance. This is independent agent review, not independent +human review. The selected supplier and compiler retain their original +Jeremy Kothe / Rohan Arun / icekylinx lineage and notices. The circuit-interface +lane supplied the emitted words; the bounds-review lane supplied the exact +transpose replay. The prior centre-sharing lane supplied the native source +map and arbitrary-private-input evidence. No frozen source was changed. diff --git a/research/actual-query-information-bounds/payload/lanes/residual-syndrome/PROOF.md b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/PROOF.md new file mode 100644 index 0000000000..d15b3ae22b --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/PROOF.md @@ -0,0 +1,336 @@ +# The full controller residual does not compress into fewer whole arrays + +This note uses the selected nine-stage controller at commit +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. It uses the centre-free local +interface in `../circuit-interface/INTERFACE.json`. That interface has +`J = I - R*R/4` and `R R* = 56 I_8`. A star denotes the adjoint. + +The source controller is the member +`t16/global/base/split-centres/GLOBAL-TEMPLATE.json.gz` of +`research/community-frontier1042-audit/selected-replay.tar.gz`. +`RESIDUAL.json` gives the byte pins and the exact checks. + +The algebra below assumes that the native words have the stated abstract +routed interface. Three separate sources supply the required application +facts. The local native lift is checked in +`../interface-proof/NATIVE-LIFT-REVIEW.json`. The actual global endpoint +normal form is stated in `../encoded-controller/CONTROLLER.md`. The bound +on the common routed centre image is proved in `../cover-algebra/PROOF.md`. +This note does not re-prove those results. The scalar interface receipt +alone does not prove the native global normal form. + +## Result + +Let `G` be the finite orthogonal cover group. Use its full regular action. +Each port has a function on `G`. Put + +\[ +H=\mathbb C^{112}\otimes\mathbb C^G, +\qquad R_s=(R\otimes I_G)D_s, +\qquad R_s R_s^*=56 I_{8|G|}, +\] + +where `D_s` is the actual port-dependent route at stage `s`. In particular, +`D_0=I`. Let `C_0` be the old controller before its final signed swap. Let +`C` be the same controller with all nine centre blocks omitted by the new +local interface. Define + +\[ +d=\dim\bigcap_{s=0}^8\operatorname{im}R_s^*. +\] + +Then + +\[ +\operatorname{rank}(C-C_0)=72|G|-d. +\tag{1} +\] + +If only a proper set `S` of the nine stages uses the new interface, then + +\[ +\operatorname{rank}(C-C_0)=8|S||G|. +\tag{2} +\] + +The separate routed-projection theorem in `../cover-algebra/PROOF.md` gives +`d <= (8/183)|G|`. Therefore the full nine-stage residual has rank greater +than `71|G|`. Across all 16 independent replicas, its rank is at least + +\[ +\left(1152-\frac{128}{183}\right)|G|>1151|G|. +\tag{3} +\] + +Thus a final linear correction that passes all residual information through +complete cover arrays still needs 72 arrays per replica, or 1,152 arrays +for the selected 16 replicas. A joint linear encoder across replicas does +not reduce either whole-array count. + +These counts concern the dimension of one complete residual encoding. +They are not a lower bound on the number of work arrays that must be live +at one time. A circuit can reuse a smaller workspace if it reads the data +again. The counts do not bound native child rank, phase changes, storage +through time, or a circuit that uses the data arrays directly. In particular, +they are not a proof that the old 64 centre rank units per call are optimal. + +## The actual bank controller + +Order the eight bank roles as + +\[ +(X_0,Y_0,X_1,Y_1,X_2,Y_2,X_3,Y_3). +\] + +The old local steps have the form `Y_i += X_i` or `X_i -= Y_i`. +The bridge from pair `j` to pair `i`, with coefficient `a`, is + +\[ +X_i\gets X_i+aX_j,\qquad Y_j\gets Y_j-aY_i. +\] + +The two updates commute. Every local step and every bridge preserves + +\[ +\Omega=\operatorname{diag}_{i=0}^3 +\begin{pmatrix}0&I_H\\-I_H&0\end{pmatrix}. +\] + +The source row for local stage `s`, pulled back through the old prefix, +is the following row `v_s` on the eight bank roles: + +| Stage | Source row | +| --- | --- | +| 0 | `(1, 0, 0, 0, 0, 0, 0, 0)` | +| 1 | `(1, 1, 0, 0, 0, 0, 0, 0)` | +| 2 | `(0, -1, 1, 0, 0, 0, 0, 0)` | +| 3 | `(0, -1, 1, 1, 0, 0, 0, 0)` | +| 4 | `(0, 1, 0, -1, 1, 0, 0, 0)` | +| 5 | `(0, 1, 0, -1, 1, 1, 0, 0)` | +| 6 | `(0, -1, 0, 1, 0, -1, 1, 0)` | +| 7 | `(0, -1, 0, 1, 0, -1, 1, 1)` | +| 8 | `(0, 1, 0, -1, 0, 1, 0, -1)` | + +These rows have rank eight. Their only relation, up to a scalar, has +coefficient vector + +\[ +c=(1,-1,-1,1,1,-1,-1,1,1). +\tag{4} +\] + +Every coefficient is nonzero. Every proper subset of the rows is +independent. The executable check derives the rows from the pinned recipe +and checks all nine subsets of eight rows. + +## An exact factorization of the residual + +Put + +\[ +V_s=R_s(v_s\otimes I_H),\qquad +V=\begin{pmatrix}V_0\\\vdots\\V_8\end{pmatrix}. +\] + +At an old forward step, the omitted centre term is +`-R_s*R_s/4` in the update to `Y`. At an old backward step it is +`+R_s*R_s/4` in the update to `X`. Both signs give the same interaction +factor after the old prefix is removed: + +\[ +B_s=I+\frac14\Omega V_s^*V_s. +\] + +Thus + +\[ +C_0^{-1}C=B_8B_7\cdots B_0. +\tag{5} +\] + +This identity includes the actual bridge positions. No routed operators +are commuted. In particular, it does not assume that two `J_s` commute. + +Define the strict lower block matrix `L` by + +\[ +L_{ij}=\begin{cases} +V_i\Omega V_j^*,&i>j,\\ +0,&i\le j. +\end{cases} +\] + +Then + +\[ +C_0^{-1}C-I=\Omega V^*(4I-L)^{-1}V. +\tag{6} +\] + +To prove (6), let `x_i=B_i x_{i-1}` and `z_i=V_i x_{i-1}`. Directly, + +\[ +z_i=V_i x_{-1}+\frac14\sum_{jj}c_i c_j(v_i\Omega v_j^*)=4. +\tag{9} +\] + +Here `Omega` in (9) is the eight by eight bank matrix. Since +`R_s*R_s w=56w` on the common image, (7) gives + +\[ +\langle z(w),4z(w')\rangle=\frac9{14}\langle w,w'\rangle, +\] + +and (9) gives + +\[ +\langle z(w),Lz(w')\rangle=4\langle w,w'\rangle. +\] + +Consequently + +\[ +\langle z(w),(4I-L)z(w')\rangle +=-\frac{47}{14}\langle w,w'\rangle. +\tag{10} +\] + +This form on `N` is nonsingular. Suppose `u` lies in `im V` and +`(4I-L)^-1 u` lies in `N`. Put `n=(4I-L)^-1 u`. The relation +`im V=N-perp` implies that `(4I-L)n` is orthogonal to `N`. +Equation (10) then forces `n=0`, and hence `u=0`. +Thus `V*(4I-L)^-1` is injective on `im V`. This proves (1) from +(6) and (8). + +For a proper stage subset, `V*` is injective on its whole domain. The +middle factor remains invertible. This proves (2). + +## Final correction and borrowed state + +Both old and new controllers are invertible. The required final corrector +is `C_0 C^-1`. Its difference from the identity has the same rank as +`C-C_0`. The boundary native frame maps and the final signed permutation +are also invertible, so they preserve this rank. Tensoring with the signal +space multiplies both the rank and one full array's capacity by the same +factor. + +A linear correction that has the form `x -> x+A(Bx)` through `k` complete +cover arrays has residual rank at most `k|G|`. This remains true if those +arrays start with arbitrary borrowed values and the circuit restores them: +linearity forces the borrowed-input contribution to cancel, and the data +contribution still factors through the declared residual channel. + +This statement does not apply to a procedure that reads the data again +after the encoded residual is formed, or that corrects parts of the data +during the original computation. Such a procedure has additional channels +that must be included in its rank factorization. + +## Cost consequence and remaining escape + +The old schedule makes nine separate centre cohorts of eight full +arrays per replica. A plan that runs all centre-free local words and then +stores a smaller complete-array residual does not save centre information. +The same conclusion holds across all 16 selected replicas. + +The result leaves a different route open: carry all required residual +information in a representation with cheaper native phase changes. It +also leaves source-dependent state during the original calls, new bank +controllers, partial-cover processing, and changed recursive children +open. The rank of a map does not price those mechanisms. + +For comparison, putting both final bank types in the common full frame, +undoing the abstract controller by scalar cover operations, and correcting +the remaining boundary frames is algebraically possible. It needs one +rank-one native correction for each of the 896 data families per replica. +The complete centre-free non-centre invoice, divided by 16 replicas, has +rank mass `72*896`. Adding 896 per replica gives `73*896`, which consumes +the entire rank deficit at exponent zero. This is not a supplier +improvement. A useful boundary method must avoid part of that 896-unit +charge and must price all access and restoration steps. This normalization +does not assign cross-replica hosting costs to individual replicas. + +## Reproduction and validation limits + +Run from the workspace root: + +```sh +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/residual-syndrome/verify_residual.py --repo worktrees/k5-centre-sharing --interface work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json --out work/centre-encoding-campaign-20261014/lanes/residual-syndrome/RESIDUAL.json +``` + +Expected first line: + +```text +PASS_SELECTED_CONTROLLER_RESIDUAL_FACTORIZATION +``` + +The checker binds the literal controller and interface bytes. It derives +the bank rows, verifies their unique relation, checks all maximal proper +subsets, and checks the coefficient in (10). A separate direct matrix +product checks (6) on two exact rational examples. One example has a common +centre image and one does not. A missing bridge and an incorrect triangular +sign are rejected. The examples test the general algebra; they are not +substitutes for the proof over the full cover group. + +The normalized numerical rank bound uses the separate routed-projection +theorem. This file does not re-prove that theorem. No new native corrector, +recursive cost certificate, whole-invocation owner assignment, cold supplier +admission, or multiplication exponent is claimed. The finite algebra passed +the separate review in `review/REVIEW.md`. That review also reproduced the +source-bound receipt and ran independent exact matrix examples. It did not +re-prove the three application dependencies listed at the start of this +note. `review/REVIEW-EDITS.json` records the scope and wording edits made +after that review. + +This work used substantial AI assistance. It builds on the selected native +supplier, the campaign's independently checked centre-free local interface, +and the campaign's routed-projection theorem. Apache-2.0. diff --git a/research/actual-query-information-bounds/payload/lanes/residual-syndrome/RESIDUAL.json b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/RESIDUAL.json new file mode 100644 index 0000000000..f401b30e29 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/RESIDUAL.json @@ -0,0 +1,134 @@ +{ + "archive": "research/community-frontier1042-audit/selected-replay.tar.gz", + "archive_sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754", + "bank_relation": [ + 1, + -1, + -1, + 1, + 1, + -1, + -1, + 1, + 1 + ], + "bank_relation_area": "4", + "bank_source_rank": 8, + "bank_sources": [ + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + -1, + 1, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + -1, + 1, + 1, + 0, + 0, + 0, + 0 + ], + [ + 0, + 1, + 0, + -1, + 1, + 0, + 0, + 0 + ], + [ + 0, + 1, + 0, + -1, + 1, + 1, + 0, + 0 + ], + [ + 0, + -1, + 0, + 1, + 0, + -1, + 1, + 0 + ], + [ + 0, + -1, + 0, + 1, + 0, + -1, + 1, + 1 + ], + [ + 0, + 1, + 0, + -1, + 0, + 1, + 0, + -1 + ] + ], + "base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "controller_member": "t16/global/base/split-centres/GLOBAL-TEMPLATE.json.gz", + "controller_member_sha256": "a179dad87651aba340a5a8ddbcd86a8e757cad87b8a1f8bad48106fbecd38518", + "distinct_centre_space_toy": { + "residual_rank": 9, + "syndrome_rank": 9, + "wrong_triangular_sign_rejected": true + }, + "independent_eight_row_subsets": 9, + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "missing_bridge_rejected": true, + "proved_in_note": { + "conditional_two_stage_bound": "rank / |G| >= 13168/183 > 71", + "full_residual_rank": "72 |G| - dim(intersection_s im(R_s^*))", + "proper_subset_residual_rank": "8 |S| |G| for every proper set S of omitted stages", + "relation_compression": "-47/14 times the ambient common-image inner product" + }, + "relation_compression": "-47/14", + "same_centre_space_toy": { + "residual_rank": 8, + "syndrome_rank": 8, + "wrong_triangular_sign_rejected": true + }, + "scope": "Exact controller algebra and finite rational checks. The group rank bound uses the separate routed-projection theorem. No native correction, child-cost lower bound, supplier admission, or kappa claim.", + "status": "PASS_SELECTED_CONTROLLER_RESIDUAL_FACTORIZATION" +} diff --git a/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/ACCEPTED-AMENDMENTS.json b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/ACCEPTED-AMENDMENTS.json new file mode 100644 index 0000000000..fcc3baa9d2 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/ACCEPTED-AMENDMENTS.json @@ -0,0 +1,19 @@ +{ + "accepted_proof_sha256": "442ef8966bbc093c57354e06c2d45b351a1f7c18a9750b2551296c7de6ced68d", + "additional_edits_accepted": [ + "The mass per replica is a normalization of the complete 16-replica invoice.", + "The completed finite algebra review and its limits are stated accurately." + ], + "algebra_rerun": false, + "algebra_rerun_reason": "The inspected changes only clarify prose and scope. The reviewed executable files and receipts have the same hashes.", + "before_proof_sha256": "12cceca361a33aa121cc88d6a3a2ab8c7b8a6b740bae78793d4cfe4502c78f23", + "mathematical_formulas_changed": false, + "remaining_review_findings": [], + "resolved_findings": [ + "The local native lift, global endpoint normal form, and routed-projection bound are separate application dependencies.", + "The centre cohorts are described as separate, not independent." + ], + "reviewed_checker_and_receipts_unchanged": true, + "scope": "Accepts the amended exposition. It does not add a native global normal-form review, native cost proof, supplier admission, or kappa claim.", + "status": "ACCEPTED_PROSE_AMENDMENTS" +} diff --git a/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/INDEPENDENT-RECEIPT.json b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/INDEPENDENT-RECEIPT.json new file mode 100644 index 0000000000..cbcb8aac3c --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/INDEPENDENT-RECEIPT.json @@ -0,0 +1,307 @@ +{ + "area": "4", + "bank_relation": [ + 1, + -1, + -1, + 1, + 1, + -1, + -1, + 1, + 1 + ], + "bank_rows": [ + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + -1, + 1, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + -1, + 1, + 1, + 0, + 0, + 0, + 0 + ], + [ + 0, + 1, + 0, + -1, + 1, + 0, + 0, + 0 + ], + [ + 0, + 1, + 0, + -1, + 1, + 1, + 0, + 0 + ], + [ + 0, + -1, + 0, + 1, + 0, + -1, + 1, + 0 + ], + [ + 0, + -1, + 0, + 1, + 0, + -1, + 1, + 1 + ], + [ + 0, + 1, + 0, + -1, + 0, + 1, + 0, + -1 + ] + ], + "compression": "-47/14", + "conditional_whole_array_bounds": { + "all_replicas": 1152, + "per_replica": 72 + }, + "controller_member_sha256": "a179dad87651aba340a5a8ddbcd86a8e757cad87b8a1f8bad48106fbecd38518", + "data_families_per_replica": 896, + "dependencies_not_reproved": [ + "Native global normal form", + "Routed-projection dimension bound" + ], + "exact_examples": { + "none_shared": { + "rank": 18, + "stages": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8 + ], + "syndrome_nullity": 0 + }, + "one_shared": { + "rank": 17, + "stages": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8 + ], + "syndrome_nullity": 1 + }, + "two_shared": { + "rank": 16, + "stages": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8 + ], + "syndrome_nullity": 2 + } + }, + "independent_data_replicas": 16, + "maximal_proper_minors": [ + 1, + 1, + -1, + -1, + 1, + 1, + -1, + -1, + 1 + ], + "maximal_proper_residual_examples": [ + { + "rank": 16, + "stages": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8 + ], + "syndrome_nullity": 0 + }, + { + "rank": 16, + "stages": [ + 0, + 2, + 3, + 4, + 5, + 6, + 7, + 8 + ], + "syndrome_nullity": 0 + }, + { + "rank": 16, + "stages": [ + 0, + 1, + 3, + 4, + 5, + 6, + 7, + 8 + ], + "syndrome_nullity": 0 + }, + { + "rank": 16, + "stages": [ + 0, + 1, + 2, + 4, + 5, + 6, + 7, + 8 + ], + "syndrome_nullity": 0 + }, + { + "rank": 16, + "stages": [ + 0, + 1, + 2, + 3, + 5, + 6, + 7, + 8 + ], + "syndrome_nullity": 0 + }, + { + "rank": 16, + "stages": [ + 0, + 1, + 2, + 3, + 4, + 6, + 7, + 8 + ], + "syndrome_nullity": 0 + }, + { + "rank": 16, + "stages": [ + 0, + 1, + 2, + 3, + 4, + 5, + 7, + 8 + ], + "syndrome_nullity": 0 + }, + { + "rank": 16, + "stages": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 8 + ], + "syndrome_nullity": 0 + }, + { + "rank": 16, + "stages": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7 + ], + "syndrome_nullity": 0 + } + ], + "scope": "Exact algebra review. No claim about concurrent workspace, native rank cost, or supplier admission.", + "source_base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "status": "PASS_INDEPENDENT_RESIDUAL_ALGEBRA_REVIEW" +} diff --git a/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/REVIEW-EDITS.json b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/REVIEW-EDITS.json new file mode 100644 index 0000000000..ee7cfaf942 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/REVIEW-EDITS.json @@ -0,0 +1,14 @@ +{ + "after_sha256": "442ef8966bbc093c57354e06c2d45b351a1f7c18a9750b2551296c7de6ced68d", + "before_sha256": "12cceca361a33aa121cc88d6a3a2ab8c7b8a6b740bae78793d4cfe4502c78f23", + "checker_or_receipt_changed": false, + "edits": [ + "Name local native lift, global endpoint normal form, and routed-projection bound as separate dependencies.", + "Replace independent centre cohorts with separate centre cohorts.", + "State that mass per replica is a normalization of the full 16-replica invoice.", + "Link the completed finite algebra review and its limits." + ], + "independent_review": "review/REVIEW.md", + "mathematical_formulas_changed": false, + "status": "REVIEW_WORDING_AND_SCOPE_EDITS_APPLIED" +} diff --git a/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/REVIEW-STATUS.json b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/REVIEW-STATUS.json new file mode 100644 index 0000000000..b42a13ac26 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/REVIEW-STATUS.json @@ -0,0 +1,27 @@ +{ + "not_claimed": [ + "native cost lower bound", + "concurrent workspace lower bound", + "new supplier admission", + "kappa improvement" + ], + "not_reproved": [ + "native global normal form", + "routed-projection dimension bound" + ], + "required_wording_changes": [ + "State the local native lift, global normal form, and routed-projection bound as separate dependencies.", + "Replace independent centre cohorts with separate centre cohorts." + ], + "sha256": { + "PROOF.md": "12cceca361a33aa121cc88d6a3a2ab8c7b8a6b740bae78793d4cfe4502c78f23", + "RESIDUAL.json": "e819f407bd7269a0505b1ceca70150825e8e2673321293fadccc20860887a8d2", + "review/INDEPENDENT-RECEIPT.json": "5657cd2219337f897d7f018f8d81f470878f66dd8662897ac501665fa8bfb810", + "review/REPRODUCED-RESIDUAL.json": "e819f407bd7269a0505b1ceca70150825e8e2673321293fadccc20860887a8d2", + "review/REVIEW.md": "c624527db82c498836568cfe316dcee92e6a320676954bd3109dbae105f12068", + "review/independent_residual.py": "8071d3a27df0eb08d8694e75c30c0aa557fed51e5dfe5e0b5e31c122c38699cc", + "verify_residual.py": "847a21d79fcaa1e19793f43348478e6966344d3067b22795f3b2becd68074a97" + }, + "source_receipt_reproduced_exactly": true, + "status": "PASS_FINITE_ALGEBRA_WITH_DECLARED_DEPENDENCIES" +} diff --git a/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/REVIEW.md b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/REVIEW.md new file mode 100644 index 0000000000..fffc307e7b --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/REVIEW.md @@ -0,0 +1,115 @@ +# Independent review of the controller residual theorem + +The finite algebra in `../PROOF.md` passes this review. No error was found in +the factorization, kernel description, kernel form, or residual rank formula. +The source bytes at review time are recorded in `REVIEW-STATUS.json`. + +The review does not prove the native global normal form or the bound from the +routed-projection theorem. These are separate dependencies. In particular, +the scalar interface receipt alone does not establish the native global +normal form. The final note must state that distinction. + +## Algebra checked + +For a forward local step, the removed term adds `-R_s^* R_s/4` to the Y +update. For a backward step, it adds `R_s^* R_s/4` to the X update. The old +step commutes with this error shear. Each old prefix P is symplectic, so +`P^-1 Omega = Omega P^*`. Conjugation by that prefix therefore gives the +same factor `I + Omega V_s^* V_s/4` for both orientations. The order is +`B_8 ... B_0`. No two routed matrices must commute. + +The stacked triangular recurrence gives the stated inverse `4I-L`, with a +minus sign. Its inverse exists without an assumption on the ranks of the +routed matrices. The kernel argument then uses the separate assumption +`R_s R_s^*=56I`. + +The nine bank source rows have a unique relation c. Direct reconstruction +from the source recipe gives + + c = (1,-1,-1,1,1,-1,-1,1,1). + +Every maximal proper minor is 1 or -1. Thus every proper subset is +independent. The relation of the bank rows implies that any vector in +`ker(V^*)` has `R_s^* z_s = c_s w` for one common vector w. Injectivity of +each `R_s^*` gives `z_s = c_s R_s w/56`. This proves the claimed bijection +with the common routed centre image. + +The direct bank calculation gives area 4. Under the above identification, +the identity contribution is `9/14` and the lower triangular contribution +is 4. The compressed form is therefore `-47/14` times the inner product +on the common image. This is not the scalar of the compression in an +orthonormal basis of `ker(V^*)`; the note correctly specifies the common +image inner product. Its nonsingularity suffices. + +To finish the rank proof, let `n=(4I-L)^-1 u` lie in `ker(V^*)`, with +`u in im(V)`. Then `(4I-L)n` is orthogonal to `ker(V^*)`. The nonsingular +compressed form forces n to be zero. This proves that the decoder loses no +further rank. For a proper stage subset, `V^*` is injective, so no kernel +compression argument is needed. + +## Separate exact execution + +`independent_residual.py` does not import `verify_residual.py`. It builds +elementary matrices from the pinned archive recipe and uses exact SymPy +matrix products. It checks the following facts: + +* Every source step is symplectic and the old terminal endpoint is the + identity. +* The nine source rows, their unique relation, all nine maximal proper + minors, area 4, and the form `-47/14` agree with the proof. +* The 16 replicas have disjoint data namespaces, each with 896 families. +* Three exact models with two centre directions have common-image + dimensions 0, 1, and 2. Their residual ranks are 18, 17, and 16. +* In another model, all nine maximal proper stage subsets have residual + rank 16. The full matrix products agree with the triangular formula. +* An incorrect triangular sign fails in every exact model. + +The models include noncommuting centre projections. They test the general +algebra; they do not enumerate the full orthogonal cover group. The proof, +not these small examples, establishes the result for the actual full cover. + +The source checker was also rerun with Python isolation and optimization. +It passed, and its new receipt equals the supplied `RESIDUAL.json`. + +## Whole arrays and limits + +Given the separate bound `d <= 8|G|/183`, the rank is at least +`13168|G|/183 > 71|G|`. Across 16 independent replicas it is at least +`210688|G|/183 > 1151|G|`. The ceilings are therefore 72 and 1152 complete +cover arrays. The full 72-array syndrome per replica gives the matching +information capacity. A joint encoder across the 16 replicas does not +change the second ceiling. + +This counts the dimension of a declared residual channel. It does not +count peak workspace, native child rank, or temporal reads. Borrowed state +does not evade a stated linear channel factorization if it is restored. +A circuit that later reads the original data has additional channels and +is outside that argument. The proof states these exclusions correctly. + +Two wording changes are requested before publication: + +1. Name the local native lift, the global endpoint normal form, and the + routed-projection bound as separate dependencies. +2. Replace `nine independent centre cohorts` with `nine separate centre + cohorts`. The theorem permits the dependence measured by d. + +No code or proof file under review was changed. No native corrector, +supplier admission, full recursive price, or kappa improvement was checked. + +## Commands + +From the workspace root: + +```sh +work/autonomous-kappa-run/venv/bin/python -I -O -B work/centre-encoding-campaign-20261014/lanes/residual-syndrome/review/independent_residual.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/residual-syndrome/verify_residual.py --repo worktrees/k5-centre-sharing --interface work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json --out work/centre-encoding-campaign-20261014/lanes/residual-syndrome/review/REPRODUCED-RESIDUAL.json +``` + +Expected status lines: + +```text +PASS_INDEPENDENT_RESIDUAL_ALGEBRA_REVIEW +PASS_SELECTED_CONTROLLER_RESIDUAL_FACTORIZATION +``` + +This review and its code used AI assistance. diff --git a/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/independent_residual.py b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/independent_residual.py new file mode 100644 index 0000000000..ea4e199283 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/review/independent_residual.py @@ -0,0 +1,154 @@ +"""Audit the residual formula with source matrices and separate exact examples.""" + +from hashlib import sha256 +from pathlib import Path +import gzip +import json + +import sympy as s + + +BASE = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f" +ARCHIVE = "research/community-frontier1042-audit/selected-replay.tar.gz" +MEMBER = "t16/global/base/split-centres/GLOBAL-TEMPLATE.json.gz" +HERE = Path(__file__).resolve().parent + + +def require(value, label): + if not value: + raise RuntimeError(label) + + +def elementary(event, coupling=None): + a = s.eye(8) + if event["kind"] == "local": + i = 2 * event["pair"] + if event["reverse"]: + a[i, i + 1] = -1 + else: + a[i + 1, i] = 1 + if coupling is not None: + return s.eye(8 * coupling.rows) + s.kronecker_product(a - s.eye(8), coupling) + elif event["kind"] == "bridge": + i, j, q = event["dst"], event["src"], event["coefficient"] + a[2 * i, 2 * j] = q + a[2 * j + 1, 2 * i + 1] = -q + elif event["kind"] == "terminal": + a = s.diag(*[s.Matrix([[0, 1], [-1, 0]]) for _ in range(event["pairs"])]) + return a + + +def exact_case(recipe, bank_rows, centre_rows, removed): + dim = centre_rows[0].cols + width = centre_rows[0].rows + require(all(r * r.T == 56 * s.eye(width) for r in centre_rows), "Row Gram") + actual = s.eye(8 * dim) + ideal = s.eye(8 * dim) + for event in recipe: + if event["kind"] == "terminal": + continue + if event["kind"] == "local": + stage = event["stage"] + r = centre_rows[stage] + k = s.eye(dim) - r.T * r / 4 if stage in removed else s.eye(dim) + native = elementary(event, k) + else: + native = s.kronecker_product(elementary(event), s.eye(dim)) + actual = native * actual + ideal = s.kronecker_product(elementary(event), s.eye(dim)) * ideal + residual = ideal.inv() * actual - s.eye(8 * dim) + if not removed: + require(residual.is_zero_matrix, "Empty subset") + return {"stages": [], "rank": 0} + v = s.Matrix.vstack(*[s.kronecker_product(bank_rows[i, :], centre_rows[i]) for i in sorted(removed)]) + omega = s.kronecker_product(s.diag(*[s.Matrix([[0, 1], [-1, 0]])] * 4), s.eye(dim)) + gram = v * omega * v.T + blocks = len(removed) + lower = s.zeros(blocks * width) + for i in range(blocks): + for j in range(i): + lower[i * width:(i + 1) * width, j * width:(j + 1) * width] = gram[i * width:(i + 1) * width, j * width:(j + 1) * width] + middle = 4 * s.eye(v.rows) - lower + require(residual == omega * v.T * middle.inv() * v, "Interaction factorization") + require(residual.rank() == v.rank(), "No decoder cancellation") + require(residual != omega * v.T * (4 * s.eye(v.rows) + lower).inv() * v, + "Wrong triangular sign was not detected") + null = v.T.nullspace() + if null: + basis = s.Matrix.hstack(*null) + compressed = basis.T * middle * basis + require(compressed.det() != 0, "Kernel compression") + return {"stages": sorted(removed), "rank": residual.rank(), "syndrome_nullity": len(null)} + + +def main(): + member = (HERE.parents[2] / "upstream/GLOBAL-TEMPLATE.json.gz").read_bytes() + require(sha256(member).hexdigest() == "a179dad87651aba340a5a8ddbcd86a8e757cad87b8a1f8bad48106fbecd38518", "Controller pin") + template = json.loads(gzip.decompress(member)) + recipe = template["recipe"] + omega = s.diag(*[s.Matrix([[0, 1], [-1, 0]])] * 4) + prefix = s.eye(8) + rows = [] + for event in recipe: + if event["kind"] == "local": + source = 2 * event["pair"] + int(event["reverse"]) + rows.append(s.eye(8)[source, :] * prefix) + step = elementary(event) + require(step * omega * step.T == omega, "Source step is not symplectic") + prefix = step * prefix + require(prefix == s.eye(8), "Old endpoint") + v = s.Matrix.vstack(*rows) + relation = v.T.nullspace() + require(len(relation) == 1, "Bank relation dimension") + c = relation[0] / relation[0][0] + require(list(c) == [1, -1, -1, 1, 1, -1, -1, 1, 1], "Bank relation") + minors = [v[[i for i in range(9) if i != j], :].det() for j in range(9)] + require(all(value != 0 for value in minors), "A maximal proper subset is dependent") + gram = v * omega * v.T + area = sum(c[i] * c[j] * gram[i, j] for i in range(9) for j in range(i)) + compression = s.Rational(4, 56) * (c.T * c)[0] - area + require(area == 4 and compression == -s.Rational(47, 14), "Kernel form") + data_sets = [] + for replica in range(16): + calls = [call for call in template["calls"] if call["replica"] == replica] + require([call["stage"] for call in calls] == list(range(9)), "Replica stages") + families = {owner[0] for call in calls for owner in call["owners"] if owner[0] < 14336} + require(families == set(range(896 * replica, 896 * (replica + 1))), "Replica data namespace") + data_sets.append(families) + require(len(set.union(*data_sets)) == sum(map(len, data_sets)), "Replica data overlap") + r = s.Matrix([[6, 4, 2, 0, 0, 0], [0, 0, 0, 6, 4, 2]]) + one = s.Matrix([[6, 4, 2, 0, 0, 0], [0, 0, 0, 2, 6, 4]]) + zero = s.Matrix([[2, 6, 4, 0, 0, 0], [0, 0, 0, 2, 6, 4]]) + examples = {} + for name, alternate, shared in (("two_shared", r, 2), ("one_shared", one, 1), ("none_shared", zero, 0)): + centres = [r, alternate, r, alternate, r, r, alternate, r, alternate] + result = exact_case(recipe, v, centres, set(range(9))) + require(result["syndrome_nullity"] == shared and result["rank"] == 18 - shared, "Common-image rank") + examples[name] = result + centres = [r, zero, r, one, zero, r, one, zero, r] + proper = [exact_case(recipe, v, centres, set(range(9)) - {missing}) for missing in range(9)] + require(all(item["rank"] == 16 for item in proper), "Maximal proper residual rank") + per_replica = 72 - s.Rational(8, 183) + require(s.ceiling(per_replica) == 72 and s.ceiling(16 * per_replica) == 1152, "Whole-array count") + report = { + "status": "PASS_INDEPENDENT_RESIDUAL_ALGEBRA_REVIEW", + "source_base": BASE, + "controller_member_sha256": sha256(member).hexdigest(), + "bank_rows": [list(map(int, row)) for row in v.tolist()], + "bank_relation": list(map(int, c)), + "maximal_proper_minors": list(map(int, minors)), + "area": str(area), "compression": str(compression), + "independent_data_replicas": len(data_sets), + "data_families_per_replica": 896, + "exact_examples": examples, + "maximal_proper_residual_examples": proper, + "conditional_whole_array_bounds": {"per_replica": 72, "all_replicas": 1152}, + "dependencies_not_reproved": ["Native global normal form", "Routed-projection dimension bound"], + "scope": "Exact algebra review. No claim about concurrent workspace, native rank cost, or supplier admission.", + } + (HERE / "INDEPENDENT-RECEIPT.json").write_text(json.dumps(report, indent=2, sort_keys=True) + "\n") + print(report["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/payload/lanes/residual-syndrome/verify_residual.py b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/verify_residual.py new file mode 100644 index 0000000000..43df62972d --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/residual-syndrome/verify_residual.py @@ -0,0 +1,218 @@ +"""Check the controller source and the residual factorization.""" + +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json + + +BASE = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f" +ARCHIVE = "research/community-frontier1042-audit/selected-replay.tar.gz" +ARCHIVE_HASH = "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754" +MEMBER = "t16/global/base/split-centres/GLOBAL-TEMPLATE.json.gz" +MEMBER_HASH = "a179dad87651aba340a5a8ddbcd86a8e757cad87b8a1f8bad48106fbecd38518" +INTERFACE_HASH = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def eye(n): + return [[Q(i == j) for j in range(n)] for i in range(n)] + + +def transpose(a): + return list(map(list, zip(*a))) + + +def multiply(a, b): + bt = transpose(b) + return [[sum(x*y for x, y in zip(row, col)) for col in bt] for row in a] + + +def subtract(a, b): + return [[x-y for x, y in zip(row, col)] for row, col in zip(a, b)] + + +def rank(a): + b = [list(map(Q, row)) for row in a] + r = 0 + for j in range(len(b[0])): + k = next((i for i in range(r, len(b)) if b[i][j]), None) + if k is None: + continue + b[r], b[k] = b[k], b[r] + d = b[r][j] + b[r] = [x/d for x in b[r]] + for i in range(r+1, len(b)): + d = b[i][j] + if d: + b[i] = [x-d*y for x, y in zip(b[i], b[r])] + r += 1 + if r == len(b): + break + return r + + +def inverse(a): + n = len(a) + b = [list(map(Q, row))+e for row, e in zip(a, eye(n))] + for j in range(n): + k = next(i for i in range(j, n) if b[i][j]) + b[j], b[k] = b[k], b[j] + d = b[j][j] + b[j] = [x/d for x in b[j]] + for i in range(n): + if i != j: + d = b[i][j] + if d: + b[i] = [x-d*y for x, y in zip(b[i], b[j])] + return [row[n:] for row in b] + + +def omega(n): + out = [[Q(0) for _ in range(8*n)] for _ in range(8*n)] + for pair in range(4): + for j in range(n): + x, y = (2*pair)*n+j, (2*pair+1)*n+j + out[x][y], out[y][x] = Q(1), Q(-1) + return out + + +def controller(recipe, kernels, include_terminal=False): + n = len(kernels[0]) + c = eye(8*n) + for event in recipe: + kind = event['kind'] + if kind == 'local': + pair, stage = event['pair'], event['stage'] + source = 2*pair+int(event['reverse']) + target = 2*pair+int(not event['reverse']) + sign = -1 if event['reverse'] else 1 + old = [row.copy() for row in c[source*n:(source+1)*n]] + delta = multiply(kernels[stage], old) + for j, row in enumerate(delta): + t = target*n+j + c[t] = [a+sign*b for a, b in zip(c[t], row)] + elif kind == 'bridge': + i, j, q = event['dst'], event['src'], event['coefficient'] + for bank_t, bank_s, factor in ((2*i, 2*j, q), (2*j+1, 2*i+1, -q)): + for p in range(n): + t, s = bank_t*n+p, bank_s*n+p + c[t] = [a+factor*b for a, b in zip(c[t], c[s])] + elif kind == 'terminal' and include_terminal: + for pair in range(event['pairs']): + for p in range(n): + x, y = 2*pair*n+p, (2*pair+1)*n+p + c[x], c[y] = c[y], [-q for q in c[x]] + return c + + +def bank_sources(recipe): + c = eye(8) + rows = [] + for event in recipe: + if event['kind'] == 'local': + i = event['pair'] + source = 2*i+int(event['reverse']) + target = 2*i+int(not event['reverse']) + sign = -1 if event['reverse'] else 1 + rows.append(c[source].copy()) + c[target] = [a+sign*b for a, b in zip(c[target], c[source])] + elif event['kind'] == 'bridge': + i, j, q = event['dst'], event['src'], event['coefficient'] + c[2*i] = [a+q*b for a, b in zip(c[2*i], c[2*j])] + c[2*j+1] = [a-q*b for a, b in zip(c[2*j+1], c[2*i+1])] + return rows, c + + +def toy_check(recipe, sources, distinct): + # These exact rows have norm squared 56. They are not cover data. + rows = [[Q(6), Q(4), Q(2)] for _ in range(9)] + if distinct: + rows[1] = [Q(2), Q(6), Q(4)] + require(all(sum(x*x for x in row) == 56 for row in rows), 'Toy row norm') + kernels = [subtract(eye(3), [[x*y/4 for y in row] for x in row]) for row in rows] + actual = controller(recipe, kernels) + ideal = controller(recipe, [eye(3)]*9) + residual = subtract(multiply(inverse(ideal), actual), eye(24)) + v = [[b*x for b in source for x in row] for source, row in zip(sources, rows)] + om = omega(3) + g = multiply(multiply(v, om), transpose(v)) + b = [[4*Q(i == j)-(g[i][j] if i > j else 0) for j in range(9)] for i in range(9)] + predicted = multiply(multiply(multiply(om, transpose(v)), inverse(b)), v) + require(residual == predicted, 'The residual factorization failed') + expected = 9 if distinct else 8 + require(rank(v) == rank(residual) == expected, 'The residual rank is wrong') + wrong = [[4*Q(i == j)+(g[i][j] if i > j else 0) for j in range(9)] for i in range(9)] + rejected = residual != multiply(multiply(multiply(om, transpose(v)), inverse(wrong)), v) + require(rejected, 'The wrong-sign control did not fail') + return {'syndrome_rank': rank(v), 'residual_rank': rank(residual), + 'wrong_triangular_sign_rejected': rejected} + + +def run(repo, interface): + member = (repo / 'GLOBAL-TEMPLATE.json.gz').read_bytes() + require(sha256(member).hexdigest() == MEMBER_HASH, 'The controller pin changed') + recipe = json.loads(gzip.decompress(member))['recipe'] + source = interface.read_bytes() + require(sha256(source).hexdigest() == INTERFACE_HASH, 'The interface pin changed') + data = json.loads(source) + r = [[Q(row.get(str(p), '0')) for p in range(112)] for row in data['R']] + require(multiply(r, transpose(r)) == [[56*Q(i == j) for j in range(8)] for i in range(8)], + 'The centre matrix Gram identity failed') + require([event['stage'] for event in recipe if event['kind'] == 'local'] == list(range(9)), + 'The selected stages changed') + sources, ideal = bank_sources(recipe) + require(controller(recipe, [eye(1)]*9, True) == eye(8), 'The ideal controller is not identity') + require(ideal == [[-x for x in row] for row in omega(1)], 'The ideal preterminal map changed') + relation = [Q(x) for x in (1, -1, -1, 1, 1, -1, -1, 1, 1)] + require(all(sum(relation[i]*sources[i][j] for i in range(9)) == 0 for j in range(8)), + 'The stated bank relation failed') + require(all(rank(sources[:i]+sources[i+1:]) == 8 for i in range(9)), + 'A proper subset of the bank rows is dependent') + bank_g = multiply(multiply(sources, omega(1)), transpose(sources)) + area = sum(relation[i]*relation[j]*bank_g[i][j] for i in range(9) for j in range(i)) + require(area == 4, 'The bank relation area changed') + compression = sum(x*x for x in relation)*Q(4, 56)-area + require(compression == Q(-47, 14), 'The relation compression changed') + first_bridge = next(i for i, event in enumerate(recipe) if event['kind'] == 'bridge') + omitted = recipe[:first_bridge]+recipe[first_bridge+1:] + require(controller(omitted, [eye(1)]*9, True) != eye(8), 'The missing-bridge control did not fail') + return { + 'status': 'PASS_SELECTED_CONTROLLER_RESIDUAL_FACTORIZATION', + 'base': BASE, 'archive': ARCHIVE, 'archive_sha256': ARCHIVE_HASH, + 'controller_member': MEMBER, 'controller_member_sha256': MEMBER_HASH, + 'interface_sha256': INTERFACE_HASH, + 'bank_sources': [[int(x) for x in row] for row in sources], + 'bank_relation': [int(x) for x in relation], + 'bank_source_rank': 8, 'independent_eight_row_subsets': 9, + 'bank_relation_area': str(area), 'relation_compression': str(compression), + 'same_centre_space_toy': toy_check(recipe, sources, False), + 'distinct_centre_space_toy': toy_check(recipe, sources, True), + 'missing_bridge_rejected': True, + 'proved_in_note': { + 'full_residual_rank': '72 |G| - dim(intersection_s im(R_s^*))', + 'proper_subset_residual_rank': '8 |S| |G| for every proper set S of omitted stages', + 'conditional_two_stage_bound': 'rank / |G| >= 13168/183 > 71', + 'relation_compression': '-47/14 times the ambient common-image inner product', + }, + 'scope': 'Exact controller algebra and finite rational checks. The group rank bound uses the separate routed-projection theorem. No native correction, child-cost lower bound, supplier admission, or kappa claim.', + } + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--source-dir', type=Path, required=True) + parser.add_argument('--interface', type=Path, required=True) + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + result = run(args.source_dir, args.interface) + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(result['status']) + print('proper_subsets=independent residual_rank=72|G|-common_image_dimension') + print('native_supplier_or_kappa_claim=false') diff --git a/research/actual-query-information-bounds/payload/lanes/source-domain/COVER-REVIEW.json b/research/actual-query-information-bounds/payload/lanes/source-domain/COVER-REVIEW.json new file mode 100644 index 0000000000..396aa5c0f4 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/source-domain/COVER-REVIEW.json @@ -0,0 +1,39 @@ +{ + "allowed_codimension_per_replica": "896/73", + "code_projector_graph_component_sizes": [ + 112 + ], + "common_range_upper_bound_per_cover_element": "8/183", + "difference_trace_fourth": "4758/343", + "difference_trace_square": "104/7", + "fixed_stock_moment_if_one_coded_bank_per_replica": "52704/52487", + "full_73d_routes_checked": 896, + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "nonidentity_group_product_buckets": 5824, + "not_reviewed": [ + "optional sixth moment", + "native phase implementation", + "new supplier", + "new kappa" + ], + "phase_source_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "rank_bound_excess": "48608/13359", + "rank_lower_bound_per_cover_element": "2912/183", + "review_findings": [ + "Corrected a contradictory index condition in the proof case split; the moment value was unchanged." + ], + "reviewed_files_sha256": { + "PROOF.md": "1d72716fc0dc0e2f9071d0940cec54348da1d12d629eda9432baebccb4a65df4", + "verify_algebra.py": "cb23fdc8a14a6f3ff1e73cdba4e1497a9a95f5ca6d765ecb02fdaa3087782949" + }, + "single_coded_bank_in_all_16_replicas_is_not_excluded_at_zero": "843264/854027", + "source_base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "source_matrix_rederived": true, + "status": "PASS_INDEPENDENT_73D_COVER_TRACE_REVIEW", + "trace_PQ": "4/7", + "trace_PQPQ": "27/343", + "trivial_representation_control": { + "rank_difference": 0, + "trace_PQ": "8" + } +} diff --git a/research/actual-query-information-bounds/payload/lanes/source-domain/COVER-REVIEW.md b/research/actual-query-information-bounds/payload/lanes/source-domain/COVER-REVIEW.md new file mode 100644 index 0000000000..a32c8ab10d --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/source-domain/COVER-REVIEW.md @@ -0,0 +1,97 @@ +# Independent review of the cover trace bound + +The bound `rank(J_s-J_0)/|G| >= 2912/183` passes this review. The review +uses the actual 73-dimensional route matrices and the frozen scalar word. +It does not use a phase evaluation of the cover group. The exact receipt is +`COVER-REVIEW.json`; the separate replay of the author's checker is +`COVER-REPLAY.json`. + +The checked source is commit +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. The receipt binds the archive, +the scalar matrix, the route recipes, and the reviewed proof and checker by +SHA-256. The optional sixth moment in the cover-algebra note was not reviewed. + +## Trace and matrix order + +The route at port `q` has local block `q q^T`. Distinct ports therefore have +distinct routes. For an off-diagonal nonzero entry of `A=R^T R`, the two +ports are orthogonal. The local block of their ordered product is +`B_q B_p^T`. Its kernel is `span(p)` and its image is `q`-perp. Thus an +ordered edge product determines both endpoints, for any choice of the +orthonormal complement bases. + +The independent checker reads those bases from the pinned data-phase +recipes. It builds all 896 full 73-dimensional routes, checks their squares +and dot products, and verifies the stage transports. It then groups all +nonzero ordered edges by their full 73-dimensional product. There are 5,824 +distinct nonidentity products and one identity group with the 112 diagonal +pairs. A separate order control distinguishes `rho_0 rho_1` from +`rho_1 rho_0` and checks the product on all 73 basis vectors. + +On the full regular representation, the trace of a nonidentity group element +is zero and the trace of the identity is `|G|`. Thus the identity-coefficient +functional is the ordinary trace divided by `|G|`. This remains true for the +actual group `O(73,2)`. The 17-dimensional block calculation embeds +injectively into that group: each matrix is the identity on the other 56 +coordinates. Restriction of the full regular representation to the generated +subgroup gives a direct sum of regular representations. No 17-dimensional +complex payload representation is substituted for the full cover. + +The checker sums the identity coefficients from the actual collision groups. +It obtains + +\[ +\tau(PQ)=4/7,\qquad \tau((PQ)^2)=27/343. +\] + +The trace equation in the proof is +`rho_b rho_c = rho_a rho_d`. The nonidentity case is +`b=a, c=d, b!=c`. The draft had a contradictory final inequality in this +case. The author corrected it during review. The calculation already used +the correct condition. + +## Rank and the cost comparison + +For `M=P-Q`, the projection identities give + +\[ +\tau(M^2)=104/7,\qquad \tau(M^4)=4758/343. +\] + +Cauchy--Schwarz on the nonzero eigenvalues gives + +\[ +\frac{\operatorname{rank}M}{|G|} +\geq\frac{(104/7)^2}{4758/343}=2912/183. +\] + +The polynomial bound for `PQP` also gives the stated common-range bound +`8/183`. Both calculations were repeated with rational arithmetic. + +Deleting every centre child leaves rank mass `72W` at ambient rank 73. +For a uniform restriction repeated in every replica, the available average +codimension is less than `896/73`. The excess of the proved rank bound is +`48608/13359`. The resulting optimistic moment is `52704/52487 > 1` at +exponent zero. These figures normalize the complete 16-replica invoice; +they do not assign an isolated hosting bill to each replica. + +## Scope controls + +* On constant cover functions every route acts as the identity. Then `Q=P` + and the rank difference is zero. The normalized trace is 8, not `4/7`. + The theorem needs the full regular cover, or a stated sum of regular orbits. +* Applying one codimension loss to the complete 16-replica stock gives the + optimistic moment `843264/854027 < 1`. The rank bound alone does not reject + that different multiplicity. +* A code with extra state, a changed child invoice, a new controller, or a + changed recursive contract is outside this fixed-stock application. +* This review does not verify a new native circuit, supplier, or kappa value. + +Reproduce the independent check from the workspace root: + +```sh +python3 -I -B work/centre-encoding-campaign-20261014/lanes/source-domain/review_cover.py --repo worktrees/k5-centre-sharing --campaign work/centre-encoding-campaign-20261014 --out work/centre-encoding-campaign-20261014/lanes/source-domain/COVER-REVIEW.json +``` + +The result is `PASS_INDEPENDENT_73D_COVER_TRACE_REVIEW`. +This review used OpenAI Codex assistance. No PR or commit was prepared. diff --git a/research/actual-query-information-bounds/payload/lanes/source-domain/review_cover.py b/research/actual-query-information-bounds/payload/lanes/source-domain/review_cover.py new file mode 100644 index 0000000000..7853ba306c --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/source-domain/review_cover.py @@ -0,0 +1,182 @@ +"""Independently check the cover trace and its fixed-stock application.""" + +from collections import defaultdict +from fractions import Fraction as Q +from hashlib import sha256 +from importlib.util import module_from_spec, spec_from_file_location +from pathlib import Path +import argparse +import gzip +import json + + +PHASES = "t16/global/base/work/complex-nine-native/DATA-PHASES.json" +PHASES_SHA = "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" +INTERFACE_SHA = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def parity(a, b): + return (a & b).bit_count() % 2 + + +def apply(columns, x): + answer = 0 + for i, col in enumerate(columns): + if (x >> i) & 1: + answer ^= col + return answer + + +def product(left, right): + return tuple(apply(left, col) for col in right) + + +def swap_route(q, basis, stage): + first = 9 + 8 * (stage - 1) + columns = [1 << i for i in range(73)] + for i in range(9): + columns[i] = q if (q >> i) & 1 else 0 + for j, b in enumerate(basis): + if (b >> i) & 1: + columns[i] ^= 1 << (first + j) + columns[first:first + 8] = basis + return tuple(columns) + + +def run(repo, campaign): + own_source = Path(__file__).with_name("verify_domain.py") + spec = spec_from_file_location("domain_source", own_source) + source = module_from_spec(spec) + spec.loader.exec_module(source) + interface_file = campaign / "lanes/circuit-interface/INTERFACE.json" + interface_raw = interface_file.read_bytes() + require(sha256(interface_raw).hexdigest() == INTERFACE_SHA, "The interface changed") + interface = json.loads(interface_raw) + phase_raw = (repo / "DATA-PHASES.json").read_bytes() + require(sha256(phase_raw).hexdigest() == PHASES_SHA, "The data phases changed") + phases = json.loads(phase_raw) + word = json.loads(gzip.decompress(source.pin(source.WORD, (repo / "CANONICAL-WORD.json.gz").read_bytes()))) + programs = json.loads(gzip.decompress(source.pin(source.PROGRAMS, (repo / "LOCAL-PROGRAMS.json.gz").read_bytes()))) + r = source.clean_centre_map(word, programs["forward"]) + require(r == [[Q(interface["R"][i].get(str(j), "0")) for j in range(112)] + for i in range(8)], "The interface matrix differs from the frozen word") + ports = word["ports"] + require([x["q"] for x in phases["recipes"]] == ports, "The phase port order changed") + a = [[sum(r[k][i] * r[k][j] for k in range(8)) for j in range(112)] for i in range(112)] + identity = tuple(1 << i for i in range(73)) + routes = [] + full_dimension_checks = 0 + for q, recipe in zip(ports, phases["recipes"]): + basis = recipe["idle_children"][0]["orthogonal_axes"][:8] + require(len(basis) == 8 and all(x < 512 and not parity(q, x) for x in basis), + "The pinned local complement is invalid") + require(all(parity(x, y) == (i == j) for i, x in enumerate(basis) + for j, y in enumerate(basis)), "The pinned complement is not orthonormal") + route1 = swap_route(q, basis, 1) + routes.append(route1) + for stage in range(1, 9): + route = swap_route(q, basis, stage) + require(product(route, route) == identity, "A full route is not an involution") + require(all(parity(x, y) == (i == j) for i, x in enumerate(route) + for j, y in enumerate(route)), "A full route is not orthogonal") + transport = list(identity) + for j in range(8): + left, right = 9 + j, 9 + 8 * (stage - 1) + j + transport[left], transport[right] = transport[right], transport[left] + require(product(product(tuple(transport), route1), tuple(transport)) == route, + "The 73-dimensional stage embedding changed") + full_dimension_checks += 1 + + buckets = defaultdict(list) + for b in range(112): + for c in range(112): + if a[b][c]: + buckets[product(routes[b], routes[c])].append((b, c)) + require(len(buckets) == 5825, "The full group labels have different collisions") + require(buckets[identity] == [(i, i) for i in range(112)], "The identity bucket changed") + require(all(len(items) == 1 for g, items in buckets.items() if g != identity), + "Different ordered edges have the same group element") + + # Sum the trace coefficients from the actual group product equality. + # This does not use the two-case closed formula in the reviewed verifier. + fourth_integer = Q(0) + for items in buckets.values(): + for b, c in items: + for aa, d in items: + fourth_integer += a[aa][b] * a[b][c] * a[c][d] * a[d][aa] + first = sum(a[i][i] ** 2 for i in range(112)) / 56 ** 2 + second = fourth_integer / 56 ** 4 + require((first, second) == (Q(4, 7), Q(27, 343)), "The independent trace differs") + tau_m2 = 16 - 2 * first + tau_m4 = 16 - 4 * first + 2 * second + rank_bound = tau_m2 ** 2 / tau_m4 + shift = Q(13, 196) + common_bound = (second - 2 * shift * first + 8 * shift ** 2) / (1 - shift) ** 2 + require((rank_bound, common_bound) == (Q(2912, 183), Q(8, 183)), "The rank bound changed") + + g01, g10 = product(routes[0], routes[1]), product(routes[1], routes[0]) + require(g01 != g10, "The ordering control does not distinguish multiplication") + require(all(apply(g01, 1 << i) == apply(routes[0], apply(routes[1], 1 << i)) + for i in range(73)), "The matrix product order is wrong") + require(all(g01[i] == 1 << i for i in range(17, 73)), "The 17D support is not fixed") + require(all(g[i] == 1 << i for g in buckets for i in range(17, 73)), + "A group product escapes the 17D block") + + seen = {0} + todo = [0] + while todo: + i = todo.pop() + for j in range(112): + if i != j and a[i][j] and j not in seen: + seen.add(j) + todo.append(j) + require(len(seen) == 112, "The nullspace code graph is not connected") + + margin = Q(896, 73) + repeated_moment = Q(72 * 896) / (73 * (896 - rank_bound)) + single_global_moment = Q(72 * 14336) / (73 * (14336 - rank_bound)) + require(rank_bound > margin and repeated_moment > 1, "The repeated code was not rejected") + require(single_global_moment < 1, "The multiplicity control is not effective") + # On constant cover functions every group element acts as identity. + # In that representation Q=P, so their difference has rank zero. + trivial_trace_pq = sum(a[i][j] ** 2 for i in range(112) for j in range(112)) / 56 ** 2 + require(trivial_trace_pq == 8 != first, "The quotient control does not change the trace") + + reviewed = {name: sha256((campaign / "lanes/cover-algebra" / name).read_bytes()).hexdigest() + for name in ("PROOF.md", "verify_algebra.py")} + return { + "status": "PASS_INDEPENDENT_73D_COVER_TRACE_REVIEW", + "reviewed_files_sha256": reviewed, "interface_sha256": INTERFACE_SHA, + "source_base": source.BASE, "phase_source_sha256": PHASES_SHA, + "source_matrix_rederived": True, "full_73d_routes_checked": full_dimension_checks, + "nonidentity_group_product_buckets": len(buckets) - 1, + "trace_PQ": str(first), "trace_PQPQ": str(second), + "difference_trace_square": str(tau_m2), "difference_trace_fourth": str(tau_m4), + "rank_lower_bound_per_cover_element": str(rank_bound), + "common_range_upper_bound_per_cover_element": str(common_bound), + "allowed_codimension_per_replica": str(margin), + "rank_bound_excess": str(rank_bound - margin), + "fixed_stock_moment_if_one_coded_bank_per_replica": str(repeated_moment), + "single_coded_bank_in_all_16_replicas_is_not_excluded_at_zero": str(single_global_moment), + "trivial_representation_control": {"trace_PQ": str(trivial_trace_pq), "rank_difference": 0}, + "code_projector_graph_component_sizes": [len(seen)], + "review_findings": ["Corrected a contradictory index condition in the proof case split; the moment value was unchanged."], + "not_reviewed": ["optional sixth moment", "native phase implementation", "new supplier", "new kappa"], + } + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--source-dir", required=True, type=Path) + parser.add_argument("--campaign", required=True, type=Path) + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + result = run(args.source_dir, args.campaign) + args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(result["status"]) + print("routes73=896 trace_PQ=4/7 trace_PQPQ=27/343 rank>=2912/183>896/73") diff --git a/research/actual-query-information-bounds/payload/lanes/source-domain/verify_domain.py b/research/actual-query-information-bounds/payload/lanes/source-domain/verify_domain.py new file mode 100644 index 0000000000..edb9da41a9 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/source-domain/verify_domain.py @@ -0,0 +1,193 @@ +"""Check the fixed-stock cost of a code that removes centre responses.""" + +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import io +import json +import subprocess +import tarfile + + +BASE = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f" +ARCHIVE = "research/community-frontier1042-audit/selected-replay.tar.gz" +PLAN = "research/complex-t16-rare-pattern-exchanges/data/PLAN.json" +WORD = "slots/local/CANONICAL-WORD.json.gz" +PROGRAMS = "slots/local/LOCAL-PROGRAMS.json.gz" +TEMPLATE = "t16/global/hosted/GLOBAL-TEMPLATE.json.gz" +PINS = { + ARCHIVE: "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754", + PLAN: "7bd786ba8e66408f02aa9ef446eaf20c1bfe981ea2e4dd1e5a929f0aa7767bc0", + WORD: "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219", + PROGRAMS: "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a", + TEMPLATE: "73f47a1e60b1e4ea66dbca9a497c411c8e6adc7984e276a437a10a9a7a13b47a", + "notes/three-stage-cover-complex.tex": "1c5b638aa9b75365b8addec9c8eeee6bc5e499722901079b94c65fce033fde8a", + "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54", + "notes/batched-complex-rows.tex": "64c70926a8705874f1c9b42a2f703e42cad4e90f927f544458cfdf729540236c", + "research/punctured112-global/proof/GLOBAL-RESTRICTION.md": "90f67d1b4385d604318a03878cbb57ab136f8709850f7b1493774e4953892612", + "research/static44-selective/proof/PR510-MUTABLE-SOURCE-CARRYOVER.md": "b2b597491874d6e4ad3ead49bf9a15515745de578bc8c200ab60cf6ec9bac1f2", +} + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def pin(name, data): + require(sha256(data).hexdigest() == PINS[name], "Source pin: " + name) + return data + + +def source(repo, name): + return pin(name, subprocess.check_output(["git", "show", BASE + ":" + name], cwd=repo)) + + +def clean_centre_map(word, events): + v = word["v"] + n = 2 * v + word["R"] + rows = [{p: Q(1)} if p < v else {} for p in range(n + 8)] + + def reg(item): + return item[1] + (n if item[0] == "C" else 0) + + for event in events: + if event == ["phase", "centers"]: + break + if event[0] != "scalar": + continue + gate = event[1] + target = reg(gate[1]) + if gate[0] == "clear": + rows[target] = {} + elif gate[0] == "copy": + rows[target] = rows[reg(gate[2])].copy() + elif gate[0] == "scale": + rows[target] = {p: x * Q(gate[2], gate[3]) for p, x in rows[target].items()} + else: + require(gate[0] == "add", "Unexpected scalar gate") + for p, x in list(rows[reg(gate[2])].items()): + value = rows[target].get(p, Q(0)) + x * Q(gate[3], gate[4]) + if value: + rows[target][p] = value + else: + rows[target].pop(p, None) + else: + raise ValueError("The centre boundary is absent") + return [[rows[c].get(p, Q(0)) for p in range(v)] for c in word["centers"]] + + +def run(repo): + for name in PINS: + if name not in (ARCHIVE, WORD, PROGRAMS, TEMPLATE, PLAN): + source(repo, name) + plan = json.loads(source(repo, PLAN)) + with tarfile.open(fileobj=io.BytesIO(source(repo, ARCHIVE)), mode="r:gz") as stream: + raw = {name: pin(name, stream.extractfile(name).read()) + for name in (WORD, PROGRAMS, TEMPLATE)} + word, programs, template = [json.loads(gzip.decompress(raw[name])) + for name in (WORD, PROGRAMS, TEMPLATE)] + matrix = clean_centre_map(word, programs["forward"]) + r, v = len(matrix), word["v"] + gram = [[sum(matrix[i][p] * matrix[j][p] for p in range(v)) + for j in range(r)] for i in range(r)] + require(gram == [[Q(56 * (i == j)) for j in range(8)] for i in range(8)], + "The centre map does not have the required rank") + norms = [sum(matrix[i][p] ** 2 for i in range(r)) for p in range(v)] + require(norms == [Q(4)] * v, "Unequal column norms") + + # A coordinate permutation copies physical data in different logical coordinates. + q0, q1 = word["ports"][:2] + require((q0, q1) == (11, 19), "The entrance witness uses different ports") + + def swap_coordinates(x): + return x ^ (24 if bool(x & 8) != bool(x & 16) else 0) + + require(swap_coordinates(q0) == q1, "The coordinate map does not send q0 to q1") + logical_address = 8 + wanted_support = sorted([logical_address, logical_address ^ q1]) + routed_support = sorted(swap_coordinates(x) for x in + [logical_address, logical_address ^ q0]) + require(wanted_support == [8, 27] and routed_support == [3, 16], + "The physical-copy control does not change the logical payload") + + # These vectors show that no single input port is forced to zero by R x = 0. + for p in range(v): + witness = [Q(1) if q == p else + -sum(matrix[i][q] * matrix[i][p] for i in range(r)) / 52 + for q in range(v)] + require(all(sum(row[q] * witness[q] for q in range(v)) == 0 for row in matrix), + "A nullspace coordinate witness fails") + require(witness[p] == 1, "A nullspace witness loses its chosen port") + + replicas, m, live = plan["T"], plan["M"], plan["live"] + require((replicas, m, live, plan["K"], plan["L"]) == (16, 73, 14336, 4, 9), + "The stock or controller changed") + calls = {(c["replica"], c["stage"]): c for c in template["calls"]} + for replica in range(replicas): + events = [e for e in template["execution_schedule"] if e.get("replica") == replica] + require([(e["kind"], e.get("stage")) for e in events[:2]] == + [("local_cover_sweep", 0), ("local_cover_sweep", 1)], + "A bridge precedes the second call") + for stage, orientation in ((0, "forward"), (1, "backward")): + c = calls[replica, stage] + require(c["pair"] == 0 and c["orientation"] == orientation, + "The first two calls do not use the same data pair") + require([owner[0] for owner in c["owners"][:2 * v]] == + list(range(replica * 8 * v, replica * 8 * v + 2 * v)), + "The first pair uses unexpected data owners") + require(len(calls) == 9 * replicas, "Incomplete call stock") + + mass = sum(int(rank) * count for rank, count in plan["profile"].items()) + require(m * live - mass == plan["deficit"] == 5120, "The selected rank bill changed") + stripped_mass = mass - len(calls) * 64 + require(stripped_mass == (m - 1) * live, "The all-centre removal bill changed") + per_replica = Q(live, replicas) + codimension = 2 * r + useful = per_replica - codimension + actual_moment = Q(stripped_mass, replicas) / (m * useful) + apparent_moment = Q(stripped_mass, m * live) + one_bank_moment = Q(stripped_mass, replicas) / (m * (per_replica - r)) + require(actual_moment == Q(4032, 4015) > 1, "The two-call code was not rejected") + require(apparent_moment < 1 and one_bank_moment < 1, + "The controls do not distinguish the lost independent data") + additional_saving = m * codimension - per_replica + require(additional_saving == 272, "Incorrect additional rank requirement") + return { + "status": "PASS_FIXED_STOCK_CENTRE_NULLSPACE_CODE_OBSTRUCTION", + "base": BASE, "source_pins": PINS, + "source_map_shape": [r, v], "gram_diagonal": 56, + "column_norm_squared": 4, "nullspace_coordinate_witnesses": v, + "physical_copy_control": { + "input_port": q0, "image_port": q1, "orthogonal_map": "swap coordinates 3 and 4", + "logical_input_address": logical_address, "required_support": wanted_support, + "rank_zero_routed_copy_support": routed_support, + "correct_adapter_rank_from_preimage_frame_formula": 2, + }, + "first_two_calls": {"replicas": replicas, "stages": [0, 1], "pair": 0, + "orientations": ["forward", "backward"], "intervening_bridges": 0}, + "stock_per_replica": str(per_replica), "global_live_stock": live, + "ambient_rank": m, "old_global_rank_mass": mass, + "optimistic_global_rank_mass_without_centres": stripped_mass, + "necessary_codimension_below_per_replica": str(per_replica / m), + "nullspace_protocol_codimension_at_least_per_replica": codimension, + "optimistic_moment_after_code_at_b_zero": str(actual_moment), + "incorrect_full_stock_moment_control": str(apparent_moment), + "insufficient_one_bank_constraint_control": str(one_bank_moment), + "further_rank_saving_needed_strictly_more_than_per_replica": str(additional_saving), + "scope": "Ordinary-shear nullspace codes with the same nine-stage children and stock; no bound on a redesigned coded recursion.", + "not_checked": ["native code preparation", "new hosting", "new supplier", "complete cold replay", "new kappa"], + } + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--repo", required=True, type=Path) + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + result = run(args.repo) + args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(result["status"]) + print("replicas=16 rank=16 per_replica_stock=896 moment_at_b_zero=4032/4015") diff --git a/research/actual-query-information-bounds/payload/lanes/temporal-reuse/QUERY-FIFTH-MOMENT.json b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/QUERY-FIFTH-MOMENT.json new file mode 100644 index 0000000000..27964e4990 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/QUERY-FIFTH-MOMENT.json @@ -0,0 +1,118 @@ +{ + "status": "PASS_ACTUAL_QUERY_FIFTH_MOMENT", + "fourth_checker_sha256": "e7ff30dfdc23dd929599c05aa037a082060906021d5e9a40e9f586e680d0449e", + "fourth_receipt_sha256": "df32110bbd285e3036bdb2082e3307b24edc7515953cab7a1b3b6b684adc1e66", + "new_word": [ + 1, + 2, + 1, + 2, + 0 + ], + "supported_triples": 194400, + "matched_group_terms": 4320, + "identity_matches": 96, + "match_equality_patterns": { + "(False, True, False)": 4224, + "(True, True, True)": 96 + }, + "integer_trace_numerator": 2260992, + "trace_denominator": 254803968, + "new_word_trace_per_cover": "23/2592", + "fixed_source_bounds": [ + { + "charts": 1, + "fifth_moment_per_cover": "8", + "weighted_quadratic_rank_per_cover": "8", + "whole_fields": 8, + "eight_field_cohorts": 1 + }, + { + "charts": 2, + "fifth_moment_per_cover": "3283/108", + "weighted_quadratic_rank_per_cover": "2120/133", + "whole_fields": 16, + "eight_field_cohorts": 2 + }, + { + "charts": 3, + "fifth_moment_per_cover": "32023/432", + "weighted_quadratic_rank_per_cover": "3464/147", + "whole_fields": 24, + "eight_field_cohorts": 3 + }, + { + "charts": 4, + "fifth_moment_per_cover": "15901/108", + "weighted_quadratic_rank_per_cover": "5000/163", + "whole_fields": 31, + "eight_field_cohorts": 4 + }, + { + "charts": 5, + "fifth_moment_per_cover": "55925/216", + "weighted_quadratic_rank_per_cover": "6728/181", + "whole_fields": 38, + "eight_field_cohorts": 5 + }, + { + "charts": 6, + "fifth_moment_per_cover": "22657/54", + "weighted_quadratic_rank_per_cover": "8648/201", + "whole_fields": 44, + "eight_field_cohorts": 6 + }, + { + "charts": 7, + "fifth_moment_per_cover": "276857/432", + "weighted_quadratic_rank_per_cover": "10760/223", + "whole_fields": 49, + "eight_field_cohorts": 7 + }, + { + "charts": 8, + "fifth_moment_per_cover": "50531/54", + "weighted_quadratic_rank_per_cover": "13064/247", + "whole_fields": 53, + "eight_field_cohorts": 7 + }, + { + "charts": 9, + "fifth_moment_per_cover": "47467/36", + "weighted_quadratic_rank_per_cover": "15560/273", + "whole_fields": 57, + "eight_field_cohorts": 8 + } + ], + "finite_free_moment_comparison": [ + "72", + "120", + "244", + "1649/3", + "47467/36" + ], + "nine_chart_optimizing_weight": "9-lambda", + "nine_chart_optimizing_polynomial": "19 lambda - 6 lambda^2", + "moment_relaxation_attainment": { + "nodes": [ + "0", + "(19-2 sqrt(22))/12", + "(19+2 sqrt(22))/12", + "9" + ], + "nonzero_mass": "15560/273", + "mass_at_9": "8/7833", + "interior_mass": "1934592/33943", + "interior_mean": "1157/916", + "recurrence": "x^3-(73/6)x^2+(1459/48)x-273/16", + "ambient_total_mass": 96 + }, + "scope": "The full fixed-source logical regular-cover module. No freeness assumption.", + "not_claimed": [ + "Equality of higher moments", + "A cache construction", + "A native-child bound", + "A result for changing source histories", + "A supplier or kappa improvement" + ] +} diff --git a/research/actual-query-information-bounds/payload/lanes/temporal-reuse/QUERY-FOURTH-MOMENT.json b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/QUERY-FOURTH-MOMENT.json new file mode 100644 index 0000000000..2a02ebce33 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/QUERY-FOURTH-MOMENT.json @@ -0,0 +1,517 @@ +{ + "status": "PASS_ACTUAL_QUERY_FOURTH_MOMENT", + "source_binding": { + "regular_cover": "The actual orthogonal cover group", + "ordinary_ports": [ + 1, + 2, + 3, + 4, + 5, + 6, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 22, + 23, + 24, + 25, + 26, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 38, + 39, + 40, + 41, + 42, + 43, + 44, + 45, + 48, + 49, + 50, + 51, + 52, + 53, + 54, + 55, + 56, + 58, + 59, + 60, + 61, + 62, + 63, + 64, + 65, + 66, + 67, + 68, + 69, + 70, + 71, + 72, + 73, + 74, + 75, + 77, + 78, + 79, + 80, + 82, + 83, + 84, + 85, + 86, + 88, + 89, + 90, + 91, + 93, + 94, + 95, + 96, + 97, + 98, + 99, + 100, + 101, + 102, + 103, + 104, + 105, + 106, + 107, + 108, + 109 + ], + "archive_sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754", + "phase_member_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "canonical_word_sha256": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219", + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "source_matrix_review_sha256": "9639db0bdbc82255ef85273ac15a0aff68d5c659190557bf331d260eb714964f", + "full_payload_alignment_checks": 864, + "route_order_control": { + "port": 1, + "input_axis": 512, + "rho1_rho2_image": 21, + "rho2_rho1_image": 131072 + }, + "relative_pairs": [ + [ + 0, + 1, + 96 + ], + [ + 0, + 2, + 96 + ], + [ + 0, + 3, + 96 + ], + [ + 0, + 4, + 96 + ], + [ + 0, + 5, + 96 + ], + [ + 0, + 6, + 96 + ], + [ + 0, + 7, + 96 + ], + [ + 0, + 8, + 96 + ], + [ + 1, + 2, + 96 + ], + [ + 1, + 3, + 96 + ], + [ + 1, + 4, + 96 + ], + [ + 1, + 5, + 96 + ], + [ + 1, + 6, + 96 + ], + [ + 1, + 7, + 96 + ], + [ + 1, + 8, + 96 + ], + [ + 2, + 3, + 96 + ], + [ + 2, + 4, + 96 + ], + [ + 2, + 5, + 96 + ], + [ + 2, + 6, + 96 + ], + [ + 2, + 7, + 96 + ], + [ + 2, + 8, + 96 + ], + [ + 3, + 4, + 96 + ], + [ + 3, + 5, + 96 + ], + [ + 3, + 6, + 96 + ], + [ + 3, + 7, + 96 + ], + [ + 3, + 8, + 96 + ], + [ + 4, + 5, + 96 + ], + [ + 4, + 6, + 96 + ], + [ + 4, + 7, + 96 + ], + [ + 4, + 8, + 96 + ], + [ + 5, + 6, + 96 + ], + [ + 5, + 7, + 96 + ], + [ + 5, + 8, + 96 + ], + [ + 6, + 7, + 96 + ], + [ + 6, + 8, + 96 + ], + [ + 7, + 8, + 96 + ] + ], + "positive_stage_conjugacy_checks": 672, + "fresh_block_port_checks": 9216 + }, + "route_product": "B_s B_t* uses rho_s(p) rho_t(p); vectors meet t first.", + "pair_cases": [ + { + "stages": [ + 0, + 1 + ], + "nonidentity_terms": 4224, + "collision_multiplicities": { + "1": 4224 + }, + "integer_frobenius_square": 565248, + "alternating_trace_per_cover": "23/216" + }, + { + "stages": [ + 0, + 2 + ], + "nonidentity_terms": 4224, + "collision_multiplicities": { + "1": 4224 + }, + "integer_frobenius_square": 565248, + "alternating_trace_per_cover": "23/216" + }, + { + "stages": [ + 1, + 0 + ], + "nonidentity_terms": 4224, + "collision_multiplicities": { + "1": 4224 + }, + "integer_frobenius_square": 565248, + "alternating_trace_per_cover": "23/216" + }, + { + "stages": [ + 1, + 2 + ], + "nonidentity_terms": 4224, + "collision_multiplicities": { + "1": 4224 + }, + "integer_frobenius_square": 565248, + "alternating_trace_per_cover": "23/216" + }, + { + "stages": [ + 1, + 3 + ], + "nonidentity_terms": 4224, + "collision_multiplicities": { + "1": 4224 + }, + "integer_frobenius_square": 565248, + "alternating_trace_per_cover": "23/216" + } + ], + "mixed_three_cases": [ + { + "word": [ + 0, + 1, + 0, + 2 + ], + "common_group_support": 1, + "integer_coefficient_inner_product": 294912, + "trace_per_cover": "1/18" + }, + { + "word": [ + 1, + 0, + 1, + 2 + ], + "common_group_support": 1, + "integer_coefficient_inner_product": 294912, + "trace_per_cover": "1/18" + }, + { + "word": [ + 1, + 2, + 1, + 3 + ], + "common_group_support": 1, + "integer_coefficient_inner_product": 294912, + "trace_per_cover": "1/18" + } + ], + "distinct_stage_trace": "96/12^k for 1 <= k <= 9", + "singleton_rule": "A positive stage occurring once can be deleted at trace factor 1/12.", + "fixed_source_bounds": [ + { + "charts": 1, + "moments_per_cover": [ + "8", + "8", + "8", + "8" + ], + "quadratic_rank_per_cover": "8", + "whole_fields": 8, + "eight_field_cohorts": 1 + }, + { + "charts": 2, + "moments_per_cover": [ + "16", + "52/3", + "20", + "2615/108" + ], + "quadratic_rank_per_cover": "2304/145", + "whole_fields": 16, + "eight_field_cohorts": 2 + }, + { + "charts": 3, + "moments_per_cover": [ + "24", + "28", + "109/3", + "1823/36" + ], + "quadratic_rank_per_cover": "117/5", + "whole_fields": 24, + "eight_field_cohorts": 3 + }, + { + "charts": 4, + "moments_per_cover": [ + "32", + "40", + "172/3", + "1609/18" + ], + "quadratic_rank_per_cover": "1792/59", + "whole_fields": 31, + "eight_field_cohorts": 4 + }, + { + "charts": 5, + "moments_per_cover": [ + "40", + "160/3", + "250/3", + "7705/54" + ], + "quadratic_rank_per_cover": "1800/49", + "whole_fields": 37, + "eight_field_cohorts": 5 + }, + { + "charts": 6, + "moments_per_cover": [ + "48", + "68", + "344/3", + "7663/36" + ], + "quadratic_rank_per_cover": "9216/217", + "whole_fields": 43, + "eight_field_cohorts": 6 + }, + { + "charts": 7, + "moments_per_cover": [ + "56", + "84", + "455/3", + "10885/36" + ], + "quadratic_rank_per_cover": "238/5", + "whole_fields": 48, + "eight_field_cohorts": 6 + }, + { + "charts": 8, + "moments_per_cover": [ + "64", + "304/3", + "584/3", + "11171/27" + ], + "quadratic_rank_per_cover": "13824/265", + "whole_fields": 53, + "eight_field_cohorts": 7 + }, + { + "charts": 9, + "moments_per_cover": [ + "72", + "120", + "244", + "1649/3" + ], + "quadratic_rank_per_cover": "4104/73", + "whole_fields": 57, + "eight_field_cohorts": 8 + } + ], + "nine_chart_optimizing_polynomial": "13 lambda - 4 lambda^2", + "scope": "Simultaneous linear queries of one arbitrary fixed source in the full logical regular-cover module, with any payload multiplicity.", + "not_claimed": [ + "A native-child lower bound", + "A bound on changing controller sources", + "A supplier or kappa improvement" + ] +} diff --git a/research/actual-query-information-bounds/payload/lanes/temporal-reuse/QUERY-MOMENTS.md b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/QUERY-MOMENTS.md new file mode 100644 index 0000000000..b6aaaa0879 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/QUERY-MOMENTS.md @@ -0,0 +1,303 @@ +# Fourth and fifth moments of the actual routed queries + +For the nine actual charts, the simultaneous query space of one fixed +source has dimension at least + + (4104/73) N + +from the first four moments. A separate fifth-moment calculation gives + + (15560/273) N = (57-1/273) N. + +Here N is the dimension of one complete field in the full logical +regular-cover module. Thus a linear cache for all nine queries needs +at least 57 complete fields. If storage uses complete eight-field +cohorts, it needs at least eight cohorts, or 64 fields. + +This result concerns all nine queries of the same arbitrary source. +The actual controller reads changing sources. This theorem does not +replace those reads by one simultaneous-query obligation. It is not a +native-child bound, an implementation invoice, or a supplier gain. + +## Actual query module and source binding + +Use the fixed sets + + A = [0,7,20,27,36,46,57,111], + T = [21,37,47,76,81,87,92,110], + U = complement(A union T). + +There are 96 ordinary ports in U. Let r_p be column p of the actual +8 by 112 centre matrix R. Then + + sum_(p in U) r_p r_p^T = 48 I8, + r_p^T r_p = 4. + +The centre matrix is bound to the supplier word by the separate +reverse-propagation review in SPECTRAL-BOUND-REVIEW.json. The new +checker reads the actual port bases directly from the pinned +DATA-PHASES archive member. It does not import the root experiment or +the controller's route function. + +Write the nine-dimensional base space as L. For each port p, its +orthonormal basis is (q_p,b_p1,...,b_p8). For s=1,...,8, let E_s be +the new eight-dimensional coordinate block at stage s. In this +paragraph only, E_s denotes a coordinate block, not a query projection. +The route rho_(s,p) exchanges b_pi with the corresponding axis of E_s. +It fixes q_p and all other exterior blocks. Set rho_(0,p)=I. + +The checker verifies the following source facts: + +- The 96 bases are the actual bases in DATA-PHASES. +- All nine routes are orthogonal involutions on 73 axes. +- All 36 pairs of stages have 96 distinct relative port routes. +- A common permutation of exterior blocks conjugates any positive + stage to any other positive stage. +- Every one of the 96 port labels has its expected fresh-block + action. The full test covers all 9,216 ordered port pairs. +- All 864 ordinary-port stage alignments agree as exact phase forms. + This check uses every linear and quadratic coefficient. It is not a + constant-payload sample. + +Let G be the selected finite cover group. It contains these routes. +For a field f on G, define the right pullback + + [P_g f](d) = f(d g). + +Then P_g P_h=P_(g h). On binary address vectors, the matrix g h acts +by h first, then g. In particular, B_s B_t* below uses rho_(s,p) +rho_(t,p), with vector route t first. The checker includes an order +control: on the first E_1 axis, rho_(1,p)rho_(2,p) and its reverse +have different images. + +Take a payload space W and the full module C[G] tensor W. Its field +dimension is N=|G| dim(W). The logical owner routes act as P_g tensor I. +An honest payload representation V_g gives the same result: the action +P_g tensor V_g is unitarily equivalent to copies of the regular action. +For example, the change of coordinates [Uf](d)=V_d f(d) removes V_g. +Thus the normalized trace of a group element is zero unless g=I. +At g=I it is N. + +These are the logical query operators after the accepted physical +chart maps have been removed. The exact phase alignment check binds +that chart identification on arbitrary payloads. A left unitary mode +gauge also cancels from the projections below. A fixed common unitary +source gauge conjugates all projections and leaves every moment +unchanged. The theorem does not cover different extra source gauges +at different stages without a new check. + +A constant-payload subspace alone would not prove the complete-field +width bound: an unrestricted encoder could use other payload slots. +The bound here uses the full module just defined. Physical storage +outside that module or additional source reads are outside its scope. + +## Projections and the singleton rule + +Let D_s be block diagonal in the 96 ports, with block P_(rho_(s,p)). +Define + + B_s = R_U D_s, + P_s = B_s* B_s / 48. + +Since B_s B_s*=48I, each P_s is an orthogonal projection of rank 8N. +We use P_s for projections in the rest of this note. Its (p,q) block is + + (r_p^T r_q) P_(rho_(s,p) rho_(s,q)) / 48. + +Expand a cyclic trace of a word in these projections. A port index is +attached to each edge of the cycle. If a positive stage v occurs once, +its unique group factor is rho_(v,p)rho_(v,q). Every other stage fixes +the fresh coordinate block E_v pointwise. If the complete group product +is I, this unique factor must fix E_v pointwise. + +This forces p=q. In fact, rho_(v,q) sends an E_v basis axis to b_qi. +For rho_(v,p) to return all eight axes unchanged requires b_qi=b_pi +for all i. Their one-dimensional orthogonal complements are then the +same port line, so q_p=q_q and the actual ports are equal. The checker +verifies this condition on all actual ordered port pairs. + +With p=q, that group factor becomes I and its scalar factor is +r_p^T r_p/48=1/12. The remaining port sum is exactly the shorter word. +Therefore: + + A positive stage which occurs once in a cyclic word can be removed + at the exact trace factor 1/12. + +This rule uses the fresh-block action. It does not assume free groups +or free projections. If all k stages in a word are distinct, at most +one is stage zero. Repeated use of the rule gives + + tr(P_(s1)...P_(sk))/N = 96/12^k, 1 <= k <= 9. + +In particular, the distinct triple is 1/18 and the distinct fourth +moment is 1/216. A mixed word P_s P_t P_s P_u with three distinct +stages has a positive singleton among t and u. Its trace is therefore +(1/12) tr(P_s P_t)/N = 1/18, after cyclic idempotence. + +## The alternating pair + +Put A_p=r_p r_p^T and g_p=rho_(s,p)rho_(t,p). The unscaled product +(B_s B_t*)(B_t B_s*) has group coefficients + + sum_(p,q) (r_p^T r_q) r_p r_q^T [g_p g_q^-1]. + +For p=q, the identity coefficient is 192I8. For distinct p,q with +nonzero root product, the checker verifies that all 4,224 group words +are nonidentity and distinct. This is checked for the two stage types +(0,1) and (1,2). Common exterior-block permutations cover every other +type. Reversal does not change the alternating trace. + +The squared Frobenius norm of each nonidentity coefficient is +2^2*4*4=64. The regular trace of the square is therefore + + [8*192^2 + 4224*64] / 48^4 = 23/216. + +As a separate check, the coefficient supports for the three mixed-stage +types (0,1,0,2), (1,0,1,2), and (1,2,1,3) meet only at I. Their +Frobenius inner product is 8*192^2, which again gives 1/18. + +## Fourth moment and rank + +Set S=sum_(s=0)^8 P_s. Classify the fourth-order words by repeated +stage labels. Cyclic idempotence reduces adjacent equal labels. The +only unreduced two-label word is the alternating pair. The singleton +rule handles all three-label and four-label cases. + +For k distinct charts, the fourth moment per field dimension is + + 8k + 4k(k-1) + (23/216)k(k-1) + + k(k-1)(k-2)/3 + k(k-1)(k-2)(k-3)/216. + +At k=9 the first four moments are + + tr(S)/N = 72, + tr(S^2)/N = 120, + tr(S^3)/N = 244, + tr(S^4)/N = 1649/3. + +Use f(x)=13x-4x^2. On the nonzero eigenvalues, Cauchy's inequality gives + + rank(S) >= [tr f(S)]^2 / tr(f(S)^2) + = 456^2 N / (11096/3) + = (4104/73) N. + +No positivity of f is needed. It vanishes at zero. This f is the +optimal linear combination of x and x^2 for this Cauchy bound, as can +be checked by inversion of the two by two moment matrix. + +The range of S is the sum of all query row spaces. If all queries +factor through a linear cache of r complete fields, its dimension is +at most rN. Thus r>=57. Arbitrary borrowed inputs do not evade this +factorization bound: set those independent inputs to zero. Extra +source-dependent outputs or later source reads change the hypothesis. + +## Bounded fifth-order extension + +After cyclic idempotence and the positive-singleton rule, only one new +fifth-order type remains: P_a P_b P_a P_b P_0 with distinct positive +a,b. All such types are conjugate to (1,2,1,2,0). + +The separate checker expands + + (B_1 B_2*)(B_2 B_1*) (B_1 B_2*)(B_2 B_0*)(B_0 B_1*) + +and takes its regular trace. The first two factors have the 4,225-term +coefficient table already checked above. The last three factors have +terms + + (r_r^T r_s)(r_s^T r_t) r_r r_t^T + [g_r rho_(2,s) rho_(1,t)]. + +Each ordinary port has 45 nonzero root products, including itself. +Thus there are 96*45^2=194,400 supported triples to check. Exactly +4,320 group terms match the required inverse coefficient support; +96 of these are identity terms. Exact integer coefficient contraction +gives numerator 2,260,992 and denominator 48^5. Hence this type has +trace 23/2592 per N. This finite aggregation is not a freeness claim. +All triples with s=t already match by the identity +g_r rho_(2,s)rho_(1,s)=g_r g_s^-1. There are 4,320 such supported +triples. The exact count therefore also proves that no other supported +triple matches. + +The checker reduces all fifth-order words to the accepted cases. It +gives + + tr(S^5)/N = 47467/36. + +Since 0<=S<=9I, apply weighted Cauchy with weight 9-x and +f(x)=19x-6x^2. Write r=rank(S)/N. Then + + sum_(lambda != 0) (9-lambda) = (9r-72)N. + +The first five moments give the remaining weighted sums. Optimization +over linear combinations of x and x^2 gives + + r >= 15560/273 = 57-1/273. + +For a direct check, the weighted trace of f is 5,016N and the weighted +trace of f^2 is 57,057N. Thus 9r-72 >= 5016^2/57057 = 40128/91, +which is the same bound. + +This improves the real-valued rank bound. It does not raise the +complete-field or eight-field-cohort counts. + +## Limit of the first-five-moment relaxation + +The last bound is sharp in the continuous positive-measure moment +problem with spectrum in [0,9]. Consider nodes + + 0, a=(19-2 sqrt(22))/12, b=(19+2 sqrt(22))/12, 9. + +Give the nonzero nodes total mass r=15560/273 and node 9 mass 8/7833. +Choose the masses at a and b to match total mass and first moment 72. +Their weighted mean is strictly between 1 and 2. Since 0= 27. +Size 27 is open. Its determinant must equal 2^42 in the normalization +used below. This review does not prove that such a set exists. + +This is a bound for the stated source interface. It is not a general +bound on centre information, native cost, or the supplier. The existing +split-pair result has a narrower selection class. Its exhaustive search +was not repeated here. + +## Source binding and separate replay + +The review reads the archive from the Git object at +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. It checks archive SHA256 +`22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754`. +It checks both compressed and decoded hashes of the canonical word and +local scalar programs. It does not import the producer or its loader. + +The review propagates the eight centre output forms backward through +the 12,550-event source prefix. Their coefficients on all 112 source +inputs reproduce the pinned R. This is a different propagation path +from the producer's full forward matrix replay. The review then checks +RR^T = 56I, both fixed minor Grams 4I, and their disjointness. It checks +all 6,216 unordered root pairs. Their products are 0 in 3,304 cases, +2 in 1,960 cases, and -2 in 952 cases. Every root has squared norm 4. + +Write V for the extra selected columns, v = |S|-16, and M = VV^T. +Then D = I-R_U K_U = -11I+M/4 and B = -4D = 44I-M. In the range +checked here, B is positive definite. A dyadic-unit D therefore needs +det(B) to be a positive power of two. For v < 8, the determinant lemma +gives a factor 11^(8-v) in det(D), with a dyadic second factor. That +factor cannot cancel 11. This proves the earlier exclusion below 24. + +The selected-baseline condition was also checked against +`../cover-algebra/SELECTED-BLOCK-NECESSITY.md`, SHA256 +`2f9bf455a73dfbd176d1a634df9f2a662178e72ad8dfec4cdf1f7a4ee712198d`. +If F has the specified selected rows and (JF)_U is the ordinary U +selector, put C=FE^-1. Then C has lower selected block [0,I]. Its U +block is a unit and J_UU C_UU=I. Thus J_UU is a unit. The ordered block +identity makes this equivalent to a unit D. This condition does not +apply when the selected baselines or the target interface may change. + +## The fifteen-root lemma + +The graph argument is valid for any fifteen distinct real roots in +dimension eight with these norms and pair products. It does not need +the particular list of 112 columns. + +An unbalanced signed triangle can be switched so that x has product 2 +with y and z, while y has product -2 with z. The norm identity gives +x=y+z. A fourth common neighbor cannot exist: its product with x would +be a sum of two values in {2,-2}, and that sum cannot be 2 or -2. +Thus every clique of size at least four can be switched to the positive +Gram matrix 2I+2J. This matrix has full rank, so the clique size is at +most eight. + +The weighted graph bound in the proof is valid. Moving all weight from +one of two nonadjacent support vertices to the other does not decrease +the objective when the larger neighbor sum is chosen. The support +decreases at each step. The final support is a clique. Cauchy's +inequality on that clique gives the stated weighted bound. + +For clique number at most six, the resulting integer edge bound is 93. +For clique number eight, the inverse Gram matrix is (I-J/9)/2. The +outside-root equation 9h-s^2=18 has exactly the five listed solutions. +Its maximum h is six, so the total edge count is at most 91. + +For clique number seven, the inverse Gram matrix is (I-J/8)/2. The +projection and residual formulas follow by direct multiplication. A +root of clique degree six has six products of the same sign and a +residual of length one. After sign choice, its projection is +(sum C)/4-C_i, where i is its omitted clique index. Two high roots +with the same i either coincide or, with six clique roots, give an +eight-clique. Thus the high roots have distinct omitted indices. + +For each remaining root, the review checks all 2,187 possible product +patterns epsilon in {-1,0,1}^7. Exactly 281 have h <= 5 and nonnegative +residual square. The seven possible (h,|s|,a^2) classes and maximum +numbers of possible high neighbors are: + +| h | abs(s) | a^2 | Possible omitted indices for an edge | +|---|-----|-----|--------------------------------------| +| 0 | 0 | 4 | 7 | +| 1 | 1 | 9/4 | 6 | +| 2 | 0 | 0 | 2 | +| 2 | 2 | 1 | 7 | +| 3 | 3 | 1/4 | 4 | +| 4 | 4 | 0 | 3 | +| 5 | 5 | 1/4 | 2 | + +For each omitted index, both residual signs are checked through the +integer expression 2 = s-4 epsilon_i +/- 2a. The allowed values +are -4, 0, and 4. The check permits a separate high-root sign choice +at every index. It therefore covers a superset of the actual compatible +configurations. All 2,248 resulting degree checks satisfy +h+d_H <= max(7,t+2). + +The h=2, |s|=2 class prevents replacement of this bound by a constant +seven. The proof uses the correct t+2 term. For t from zero through +seven, the total edge bounds are 89, 90, 91, 87, 85, 85, 89, and 93. +All clique cases are covered. Averaging over fifteen-element subsets +gives E <= floor(31v(v-1)/70) for every v >= 15. + +## Exact determinant intervals + +The three eigenvalue caps are valid. The first comes from the absolute +row sums of V^T V. The second follows from the weighted graph bound +and the absolute coordinates of a unit vector. For the third, Cauchy's +inequality on the other seven eigenvalues gives +8 lambda^2-2s lambda+s^2-7q <= 0. The stated positive root is its +upper endpoint. Replacing q by a larger bound increases this endpoint. + +The review checks the upward square-root rounding and the selected +rational cap L for every v from 8 through 23. Each cap is below 44. +The extreme-point determinant lower bound follows from concavity on +the eigenvalue box with fixed sum. The second-moment bound is also +valid: the positive-coefficient series +[-log(1-x)-x]/x^2 is increasing for 0 <= x < 1. Its value at L/44 +therefore bounds each summand. The subtracted factor is positive, so +an upper bound on q gives a valid lower determinant bound. + +The independent interval routine uses direct rational powers and 64 +terms, rather than the producer's 32-term recurrence. It also reproduces +every saved 32-term rational margin exactly. All 16 size rows, all +moment bounds, and every remaining exponent agree with the receipt. + +For size 31, q <= 984 and L=29815/1024. The 64-term calculation proves + + lower_bound(log det B) - 41 log 2 > 1/1250 > 0. + +This is an exact rational comparison. The upper bound is below 2^42. +Thus size 31 is excluded without a floating-point estimate. The full +excluded intervals are 2^42 < det(B) < 2^43 at sizes 24 through 26, +and 2^41 < det(B) < 2^42 at sizes 28 through 31. + +## Replay and pins + +Run from the workspace root: + +```sh +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/temporal-reuse/review_spectral_bound.py +``` + +The command was run and printed +`PASS_INDEPENDENT_UNPAIRED_SPECTRAL_BOUND`. It uses explicit checks that +remain active under `-O`. It writes `SPECTRAL-BOUND-REVIEW.json`. + +| File | SHA256 | +|------|--------| +| Producer proof | 6dd2afed08d8873a2277ccfef4edd1bc212e831b8495bb659809f76d77802af1 | +| Producer checker | ecc031e20c309c4e1d04443b60a58fe03d32ce73a5a3b43078e9cb673341c61c | +| Producer receipt | d1124af128b6e526461c7587c2a7331dc4d19c9d90433d8d08bf9676c33a8a84 | +| Independent checker | 83de0b4694a8ef1ee501130bca9ddedf6e265f6be44b855e61e327646a7529d9 | +| Independent receipt | 9639db0bdbc82255ef85273ac15a0aff68d5c659190557bf331d260eb714964f | + +No producer file was changed. No native word, ownership schedule, +recursive invoice, or complete kappa calculation was checked by this +review. OpenAI Codex assisted with this independent proof review and +verification code. diff --git a/research/actual-query-information-bounds/payload/lanes/temporal-reuse/check_query_fifth_moment.py b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/check_query_fifth_moment.py new file mode 100644 index 0000000000..866451ebe8 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/check_query_fifth_moment.py @@ -0,0 +1,169 @@ +"""Check the remaining fifth-order route word and its exact rank bound.""" + +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from itertools import product +from pathlib import Path +import importlib.util +import json + + +HERE = Path(__file__).resolve().parent +FOURTH_CHECKER_PIN = "e7ff30dfdc23dd929599c05aa037a082060906021d5e9a40e9f586e680d0449e" +FOURTH_RECEIPT_PIN = "df32110bbd285e3036bdb2082e3307b24edc7515953cab7a1b3b6b684adc1e66" + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def trace_word(word): + w = list(word) + while len(w) > 1: + remove = next((i for i in range(len(w)) if w[i] == w[(i+1) % len(w)]), None) + if remove is None: + break + w.pop(remove) + if len(w) == 1: + return Q(8) + if len(w) == 2: + return Q(2, 3) + counts = Counter(w) + if len(w) == 4 and len(counts) == 2: + return Q(23, 216) + unique = next((i for i, s in enumerate(w) if s and counts[s] == 1), None) + if unique is not None: + w.pop(unique) + return trace_word(w)/12 + need(len(w) == 5 and counts[0] == 1 and sorted(counts.values()) == [1, 2, 2], + "An unsupported fifth-order word remains") + return Q(23, 2592) + + +def composition_sum(moments, total, factors): + if factors == 0: + return Q(total == 0) + return sum((moments[i]*composition_sum(moments, total-i, factors-1) + for i in range(total+1)), Q(0)) + + +def free_moment_comparison(): + """Check only the finite noncrossing moment recurrence.""" + alpha = Q(1, 12) + bernoulli = [Q(1)]+[alpha]*5 + cumulants = [Q(0)] + for n in range(1, 6): + cumulants.append(alpha-sum((cumulants[k]*composition_sum(bernoulli, n-k, k) + for k in range(1, n)), Q(0))) + moments = [Q(1)] + for n in range(1, 6): + moments.append(sum((9*cumulants[k]*composition_sum(moments, n-k, k) + for k in range(1, n+1)), Q(0))) + expected = [Q(72), Q(120), Q(244), Q(1649, 3), Q(47467, 36)] + need([96*x for x in moments[1:]] == expected, "The finite free-moment comparison differs") + return list(map(str, expected)) + + +def main(): + path = HERE/"check_query_fourth_moment.py" + need(sha256(path.read_bytes()).hexdigest() == FOURTH_CHECKER_PIN, "Fourth checker changed") + raw = (HERE/"QUERY-FOURTH-MOMENT.json").read_bytes() + need(sha256(raw).hexdigest() == FOURTH_RECEIPT_PIN, "Fourth receipt changed") + spec = importlib.util.spec_from_file_location("independent_fourth", path) + fourth = importlib.util.module_from_spec(spec) + spec.loader.exec_module(fourth) + roots, bases, dots, _ = fourth.source() + terms, _ = fourth.covariance(1, 2, roots, bases, dots) + r1 = [fourth.route(b, 1) for b in bases] + r2 = [fourth.route(b, 2) for b in bases] + relative = [fourth.compose(a, b) for a, b in zip(r1, r2)] + neighbors = [[j for j in range(96) if dots[i][j]] for i in range(96)] + need(all(len(x) == 45 for x in neighbors), "The supported degree differs") + total = triples = matches = identity_matches = 0 + match_patterns = Counter() + for r in range(96): + for s in neighbors[r]: + left = fourth.compose(relative[r], r2[s]) + for t in neighbors[s]: + triples += 1 + key = fourth.compose(left, r1[t]) + if key not in terms: + continue + matches += 1 + match_patterns[str((r == s, s == t, r == t))] += 1 + coefficient = terms[key] + if coefficient is None: + identity_matches += 1 + value = 192*dots[r][t] + else: + p, q, scalar = coefficient + value = scalar*dots[r][p]*dots[q][t] + total += dots[r][s]*dots[s][t]*value + need((triples, matches, identity_matches, total) == (194400, 4320, 96, 2260992), + "The fifth-order coefficient aggregation differs") + fifth = Q(total, 48**5) + need(fifth == Q(23, 2592), "The new cyclic trace differs") + rows = [] + for k in range(1, 10): + moments = [Q(x) for x in json.loads(raw)["fixed_source_bounds"][k-1]["moments_per_cover"]] + moments.append(sum((trace_word(w) for w in product(range(k), repeat=5)), Q(0))) + m1, m2, m3, m4, m5 = moments + v1, v2 = k*m1-m2, k*m2-m3 + h11, h12, h22 = k*m2-m3, k*m3-m4, k*m4-m5 + determinant = h11*h22-h12*h12 + if determinant: + rank = (m1+(v1*v1*h22-2*v1*v2*h12+v2*v2*h11)/determinant)/k + else: + rank = Q(8) + fields = (rank.numerator+rank.denominator-1)//rank.denominator + rows.append({"charts": k, "fifth_moment_per_cover": str(m5), + "weighted_quadratic_rank_per_cover": str(rank), + "whole_fields": fields, "eight_field_cohorts": (fields+7)//8}) + need(rows[-1]["fifth_moment_per_cover"] == "47467/36", "The nine-chart fifth moment differs") + rank = Q(rows[-1]["weighted_quadratic_rank_per_cover"]) + need(rank == Q(15560, 273) == 57-Q(1, 273), "The fifth-moment rank bound differs") + + # A positive four-atom measure attains the moment relaxation. + moment = [rank, Q(72), Q(120), Q(244), Q(1649, 3), Q(47467, 36)] + for i in range(3): + need(moment[i+3]-Q(73, 6)*moment[i+2]+Q(1459, 48)*moment[i+1] + -Q(273, 16)*moment[i] == 0, "The extremal cubic recurrence fails") + mass9 = (moment[2]-Q(19, 6)*moment[1]+Q(91, 48)*moment[0])/Q(2611, 48) + need(mass9 == Q(8, 7833), "The top atom mass differs") + interior_mass = rank-mass9 + interior_mean = (moment[1]-9*mass9)/interior_mass + need(1 < interior_mean < 2 and 0 < mass9 < rank < 96, + "The extremal measure is not positive") + # Its interior nodes are (19 +/- 2 sqrt(22))/12, one in (0,1), one in (2,3). + need(7*7 < 4*22 < 19*19 and 5*5 < 4*22 < 17*17, + "The interior node intervals differ") + result = {"status": "PASS_ACTUAL_QUERY_FIFTH_MOMENT", + "fourth_checker_sha256": FOURTH_CHECKER_PIN, + "fourth_receipt_sha256": FOURTH_RECEIPT_PIN, + "new_word": [1, 2, 1, 2, 0], "supported_triples": triples, + "matched_group_terms": matches, "identity_matches": identity_matches, + "match_equality_patterns": dict(sorted(match_patterns.items())), + "integer_trace_numerator": total, "trace_denominator": 48**5, + "new_word_trace_per_cover": str(fifth), "fixed_source_bounds": rows, + "finite_free_moment_comparison": free_moment_comparison(), + "nine_chart_optimizing_weight": "9-lambda", + "nine_chart_optimizing_polynomial": "19 lambda - 6 lambda^2", + "moment_relaxation_attainment": { + "nodes": ["0", "(19-2 sqrt(22))/12", "(19+2 sqrt(22))/12", "9"], + "nonzero_mass": str(rank), "mass_at_9": str(mass9), + "interior_mass": str(interior_mass), "interior_mean": str(interior_mean), + "recurrence": "x^3-(73/6)x^2+(1459/48)x-273/16", + "ambient_total_mass": 96}, + "scope": "The full fixed-source logical regular-cover module. No freeness assumption.", + "not_claimed": ["Equality of higher moments", "A cache construction", "A native-child bound", + "A result for changing source histories", "A supplier or kappa improvement"]} + (HERE/"QUERY-FIFTH-MOMENT.json").write_text(json.dumps(result, indent=2)+"\n") + print(json.dumps({"status": result["status"], "m5": "47467/36", + "rank_per_cover": "15560/273", "whole_fields": 57, + "moment_relaxation_is_sharp": True})) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/payload/lanes/temporal-reuse/check_query_fourth_moment.py b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/check_query_fourth_moment.py new file mode 100644 index 0000000000..83ef5edc04 --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/check_query_fourth_moment.py @@ -0,0 +1,285 @@ +"""Check exact routed query moments from the actual port bases.""" + +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from itertools import product +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent +BASE = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f" +ARCHIVE = "research/community-frontier1042-audit/selected-replay.tar.gz" +ARCHIVE_PIN = "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754" +PHASE_MEMBER = "t16/global/base/work/complex-nine-native/DATA-PHASES.json" +PHASE_PIN = "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" +WORD_MEMBER = "slots/local/CANONICAL-WORD.json.gz" +WORD_PIN = "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219" +INTERFACE_PIN = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" +R_REVIEW_PIN = "9639db0bdbc82255ef85273ac15a0aff68d5c659190557bf331d260eb714964f" +A = [0, 7, 20, 27, 36, 46, 57, 111] +T = [21, 37, 47, 76, 81, 87, 92, 110] +DIM = 33 + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def checked(raw, pin): + need(sha256(raw).hexdigest() == pin, "Source pin differs") + return raw + + +def apply(columns, vector): + result = 0 + while vector: + bit = vector & -vector + result ^= columns[bit.bit_length()-1] + vector ^= bit + return result + + +def compose(left, right): + """Return the product left*right. Vectors meet right first.""" + return tuple(apply(left, x) for x in right) + + +def transpose(columns): + return tuple(sum(((x >> i) & 1) << j for j, x in enumerate(columns)) + for i in range(len(columns))) + + +def route(basis, stage, dimension=DIM): + columns = [1 << i for i in range(dimension)] + if not stage: + return tuple(columns) + start = 9+8*(stage-1) + q = basis[0] + for i in range(9): + columns[i] = q*((q >> i) & 1) + for j, b in enumerate(basis[1:]): + columns[i] ^= ((b >> i) & 1) << (start+j) + for j, b in enumerate(basis[1:]): + columns[start+j] = b + return tuple(columns) + + +def phase_form(axes): + linear, quadratic = [0]*73, [0]*73 + for axis in axes: + for i in range(73): + if (axis >> i) & 1: + linear[i] = (linear[i]+1) % 4 + quadratic[i] ^= axis & ~((1 << (i+1))-1) + return linear, quadratic + + +def alignment_translation(left_axes, right_axes): + left, lq = phase_form(left_axes) + right, rq = phase_form(right_axes) + need(lq == rq and all((x-y) % 2 == 0 for x, y in zip(left, right)), + "The frame alignment has a nontranslation phase defect") + return sum(1 << i for i, (x, y) in enumerate(zip(left, right)) if (x-y) % 4 == 2) + + +def source(): + checked((HERE/"SPECTRAL-BOUND-REVIEW.json").read_bytes(), R_REVIEW_PIN) + interface = json.loads(checked((LANES/"circuit-interface/INTERFACE.json").read_bytes(), INTERFACE_PIN)) + upstream = LANES.parent / "upstream" + phases = json.loads(checked((upstream / "DATA-PHASES.json").read_bytes(), PHASE_PIN)) + word = json.loads(gzip.decompress(checked((upstream / "CANONICAL-WORD.json.gz").read_bytes(), WORD_PIN))) + need(interface["ports"] == word["ports"] == [x["q"] for x in phases["recipes"]], + "Port orders differ") + U = sorted(set(range(112))-set(A)-set(T)) + roots = [tuple(int(row.get(str(p), 0)) for row in interface["R"]) for p in U] + bases = [] + for p in U: + entry = phases["recipes"][p] + axes = entry["idle_children"][0]["orthogonal_axes"] + need(axes[8:] == [1 << i for i in range(9, 17)], "The source complement axes differ") + basis = (entry["q"], *axes[:8]) + need(all((x & y).bit_count() % 2 == (i == j) + for i, x in enumerate(basis) for j, y in enumerate(basis)), + "A source basis is not orthogonal") + bases.append(basis) + dots = [[sum(x*y for x, y in zip(a, b)) for b in roots] for a in roots] + need([dots[p][p] for p in range(96)] == [4]*96, "A root norm differs") + need(all(sum(r[i]*r[j] for r in roots) == 48*(i == j) + for i in range(8) for j in range(8)), "The ordinary Gram differs") + full = [[route(basis, s, 73) for basis in bases] for s in range(9)] + identity = tuple(1 << i for i in range(73)) + for s in range(9): + for p in range(96): + need(transpose(full[s][p]) == full[s][p] and + compose(full[s][p], full[s][p]) == identity, "A route is not an orthogonal involution") + alignment_checks = 0 + for p, actual_port in enumerate(U): + q = bases[p][0] + for s in range(9): + image = full[s][p] + exterior = [1 << i for i in range(9, 9+8*s)] + before = [q] if s == 0 else image[:9+8*(s-1)] + after = image[:9+8*s] + pre = apply(image, alignment_translation(before, [q]+exterior)) + post = apply(image, alignment_translation(after, [1 << i for i in range(9)]+exterior)) + need(phases["recipes"][actual_port]["stage_alignment"][s] == + {"entry_X": pre, "entry_Y": pre, "exit_X": post, "exit_Y": post}, + "A full-payload native alignment differs") + alignment_checks += 1 + pairs = [] + for s in range(9): + for t in range(s+1, 9): + relative = [compose(full[s][p], full[t][p]) for p in range(96)] + need(len(set(relative)) == 96, "Relative port routes collide") + pairs.append([s, t, len(set(relative))]) + # All positive-stage permutations are common coordinate permutations. + conjugacy_checks = 0 + for t in range(2, 9): + swap = list(identity) + for j in range(8): + swap[9+j], swap[9+8*(t-1)+j] = swap[9+8*(t-1)+j], swap[9+j] + for p in range(96): + need(compose(swap, compose(full[1][p], swap)) == full[t][p], + "Positive-stage conjugacy fails") + conjugacy_checks += 1 + fresh_checks = 0 + for p in range(96): + for q in range(96): + fixes = all(apply(full[1][p], bases[q][j+1]) == 1 << (9+j) for j in range(8)) + need(fixes == (p == q), "Fresh-block port test fails") + fresh_checks += 1 + ordered = apply(compose(full[1][0], full[2][0]), 1 << 9) + reversed_order = apply(compose(full[2][0], full[1][0]), 1 << 9) + need(ordered == bases[0][1] and reversed_order == 1 << 17 and ordered != reversed_order, + "The route-order control does not distinguish the two products") + return roots, bases, dots, {"regular_cover": "The actual orthogonal cover group", + "ordinary_ports": U, "archive_sha256": ARCHIVE_PIN, + "phase_member_sha256": PHASE_PIN, "canonical_word_sha256": WORD_PIN, + "interface_sha256": INTERFACE_PIN, "source_matrix_review_sha256": R_REVIEW_PIN, + "full_payload_alignment_checks": alignment_checks, + "route_order_control": {"port": U[0], "input_axis": 512, + "rho1_rho2_image": ordered, + "rho2_rho1_image": reversed_order}, + "relative_pairs": pairs, "positive_stage_conjugacy_checks": conjugacy_checks, + "fresh_block_port_checks": fresh_checks} + + +def covariance(s, t, roots, bases, dots): + """Store coefficients of (B_s B_t*)(B_t B_s*) without scale factors.""" + identity = tuple(1 << i for i in range(DIM)) + relative = [compose(route(b, s), route(b, t)) for b in bases] + terms = {identity: None} + support = 0 + for p in range(96): + for q in range(96): + if p == q or not dots[p][q]: + continue + key = compose(relative[p], transpose(relative[q])) + need(key not in terms, "A supported ordered pair has a group collision") + terms[key] = (p, q, dots[p][q]) + support += 1 + identity_matrix = [[sum(4*r[i]*r[j] for r in roots) for j in range(8)] for i in range(8)] + need(identity_matrix == [[192*(i == j) for j in range(8)] for i in range(8)], + "Identity coefficient differs") + square = sum(x*x for row in identity_matrix for x in row) + square += sum(dots[p][q]**2*dots[p][p]*dots[q][q] + for entry in terms.values() if entry is not None for p, q, _ in [entry]) + need(support == 4224 and square == 565248, "Fourth pair count differs") + return terms, {"stages": [s, t], "nonidentity_terms": support, + "collision_multiplicities": {"1": support}, + "integer_frobenius_square": square, + "alternating_trace_per_cover": str(Q(square, 48**4))} + + +def inner_coeff(left, right, dots): + total = 0 + common = left.keys() & right.keys() + for key in common: + a, b = left[key], right[key] + if a is None or b is None: + need(a is None and b is None, "Only one coefficient is the identity term") + total += 8*192**2 + else: + p, q, x = a + r, s, y = b + total += x*y*dots[p][r]*dots[q][s] + return len(common), total + + +def trace_word(word): + """Reduce fourth-order words by idempotence and the singleton lemma.""" + w = list(word) + while len(w) > 1: + remove = next((i for i in range(len(w)) if w[i] == w[(i+1) % len(w)]), None) + if remove is None: + break + w.pop(remove) + if len(w) == 1: + return Q(8) + if len(w) == 2: + return Q(2, 3) + counts = Counter(w) + if len(w) == 4 and len(counts) == 2: + need(w[0] == w[2] and w[1] == w[3], "An unreduced pair word is not alternating") + return Q(23, 216) + unique = next((i for i, s in enumerate(w) if s and counts[s] == 1), None) + need(unique is not None, "An unsupported trace type remains") + w.pop(unique) + return trace_word(w)/12 + + +def moments(): + rows = [] + for k in range(1, 10): + mm = [sum((trace_word(w) for w in product(range(k), repeat=j)), Q(0)) + for j in range(1, 5)] + m1, m2, m3, m4 = mm + det = m2*m4-m3*m3 + if det: + rank = (m1*m1*m4-2*m1*m2*m3+m2**3)/det + else: + rank = m1*m1/m2 + fields = (rank.numerator+rank.denominator-1)//rank.denominator + rows.append({"charts": k, "moments_per_cover": list(map(str, mm)), + "quadratic_rank_per_cover": str(rank), + "whole_fields": fields, "eight_field_cohorts": (fields+7)//8}) + need(rows[-1]["moments_per_cover"] == ["72", "120", "244", "1649/3"], "Nine-chart moments differ") + need(rows[-1]["quadratic_rank_per_cover"] == "4104/73", "The quadratic bound differs") + return rows + + +def main(): + roots, bases, dots, binding = source() + cache, pairs = {}, [] + for s, t in ((0, 1), (0, 2), (1, 0), (1, 2), (1, 3)): + cache[s, t], row = covariance(s, t, roots, bases, dots) + pairs.append(row) + mixed = [] + for s, t, u in ((0, 1, 2), (1, 0, 2), (1, 2, 3)): + count, total = inner_coeff(cache[s, t], cache[s, u], dots) + need(count == 1 and total == 294912, "Mixed-three support or trace differs") + mixed.append({"word": [s, t, s, u], "common_group_support": count, + "integer_coefficient_inner_product": total, + "trace_per_cover": str(Q(total, 48**4))}) + result = {"status": "PASS_ACTUAL_QUERY_FOURTH_MOMENT", "source_binding": binding, + "route_product": "B_s B_t* uses rho_s(p) rho_t(p); vectors meet t first.", + "pair_cases": pairs, "mixed_three_cases": mixed, + "distinct_stage_trace": "96/12^k for 1 <= k <= 9", + "singleton_rule": "A positive stage occurring once can be deleted at trace factor 1/12.", + "fixed_source_bounds": moments(), + "nine_chart_optimizing_polynomial": "13 lambda - 4 lambda^2", + "scope": "Simultaneous linear queries of one arbitrary fixed source in the full logical regular-cover module, with any payload multiplicity.", + "not_claimed": ["A native-child lower bound", "A bound on changing controller sources", + "A supplier or kappa improvement"]} + (HERE/"QUERY-FOURTH-MOMENT.json").write_text(json.dumps(result, indent=2)+"\n") + print(json.dumps({"status": result["status"], "nine_chart_moments": ["72", "120", "244", "1649/3"], + "rank_per_cover": "4104/73", "whole_fields": 57, "eight_field_cohorts": 8})) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/payload/lanes/temporal-reuse/check_source_matrix.py b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/check_source_matrix.py new file mode 100644 index 0000000000..0805dc9e5a --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/check_source_matrix.py @@ -0,0 +1,106 @@ +"""Rebuild the source matrix with the reviewed reverse propagation.""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import gzip +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent + +ARCHIVE_PIN = "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754" + +INTERFACE_PIN = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" + +MEMBERS = { + "slots/local/CANONICAL-WORD.json.gz": ( + "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219", + "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c"), + "slots/local/LOCAL-PROGRAMS.json.gz": ( + "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a", + "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3"), +} + +A = [0, 7, 20, 27, 36, 46, 57, 111] + +T = [21, 37, 47, 76, 81, 87, 92, 110] + +def need(ok, message): + if not ok: + raise ValueError(message) + +def pinned(path, expected): + raw = path.read_bytes() + need(sha256(raw).hexdigest() == expected, "Changed input: " + str(path)) + return raw + +def source_matrix(): + inputs = {} + for name, (compressed_pin, payload_pin) in MEMBERS.items(): + compressed = (LANES.parent / "upstream" / name.rsplit("/", 1)[-1]).read_bytes() + need(sha256(compressed).hexdigest() == compressed_pin, "Member pin differs") + payload = gzip.decompress(compressed) + need(sha256(payload).hexdigest() == payload_pin, "Payload pin differs") + inputs[name.rsplit("/", 1)[-1]] = json.loads(payload) + word = inputs["CANONICAL-WORD.json.gz"] + events = inputs["LOCAL-PROGRAMS.json.gz"]["forward"] + cut = events.index(["phase", "centers"]) + gradient = [{} for _ in range(712)] + for k, center in enumerate(word["centers"]): + gradient[center][k] = Q(1) + + def register(token): + need(token[0] in ("L", "C"), "Unknown field namespace") + value = token[1] + 704 * (token[0] == "C") + need(0 <= value < 712, "Invalid field") + return value + + for event in reversed(events[:cut]): + if event[0] != "scalar": + continue + op = event[1] + target = register(op[1]) + if op[0] == "clear": + gradient[target] = {} + elif op[0] == "scale": + scale = Q(op[2], op[3]) + gradient[target] = {k: x * scale for k, x in gradient[target].items()} + else: + need(op[0] in ("add", "copy"), "Unknown scalar operation") + source = register(op[2]) + need(source != target, "Unexpected aliased scalar operation") + scale = Q(1) if op[0] == "copy" else Q(op[3], op[4]) + for k, x in gradient[target].items(): + gradient[source][k] = gradient[source].get(k, 0) + scale*x + if op[0] == "copy": + gradient[target] = {} + R = [[gradient[p].get(k, Q(0)) for p in range(112)] for k in range(8)] + interface = json.loads(pinned(LANES / "circuit-interface/INTERFACE.json", INTERFACE_PIN)) + need(R == [[Q(row.get(str(p), 0)) for p in range(112)] for row in interface["R"]], + "Reverse source reconstruction differs from R") + need(all(x.denominator == 1 for row in R for x in row), "R is not integral") + R = [[int(x) for x in row] for row in R] + gram = lambda ports: [[sum(R[i][p]*R[j][p] for p in ports) + for j in range(8)] for i in range(8)] + need(gram(range(112)) == [[56*(i == j) for j in range(8)] for i in range(8)], + "Full source Gram differs") + need(not set(A) & set(T), "Fixed minors overlap") + for ports in (A, T): + need(gram(ports) == [[4*(i == j) for j in range(8)] for i in range(8)], + "A fixed minor differs") + columns = list(zip(*R)) + need(all(sum(x*x for x in col) == 4 for col in columns), "A root norm differs") + dots = Counter(sum(x*y for x, y in zip(columns[i], columns[j])) + for i in range(112) for j in range(i)) + need(dots == {0: 3304, 2: 1960, -2: 952}, "Root products differ") + return {"archive_sha256": ARCHIVE_PIN, "members": MEMBERS, + "reverse_output_forms": 8, "source_columns": 112, "source_cut": cut, + "pair_products": dict(sorted(dots.items())), "full_gram": "56 I8", + "fixed_minor_grams": "4 I8"} + +if __name__ == "__main__": + result = source_matrix() + result["status"] = "PASS_REVERSE_SOURCE_MATRIX_BINDING" + (HERE / "SOURCE-MATRIX-BINDING.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(result["status"]) diff --git a/research/actual-query-information-bounds/payload/lanes/temporal-reuse/review_spectral_bound.py b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/review_spectral_bound.py new file mode 100644 index 0000000000..09f40f654c --- /dev/null +++ b/research/actual-query-information-bounds/payload/lanes/temporal-reuse/review_spectral_bound.py @@ -0,0 +1,281 @@ +"""Review the unpaired spectral bound without producer imports.""" + +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from io import BytesIO +from itertools import product +from math import comb, isqrt +from pathlib import Path +import gzip +import json +import subprocess +import tarfile + + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[3] +LANES = HERE.parent +PRODUCER = LANES / "schur-selection" +BASE = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f" +ARCHIVE = "research/community-frontier1042-audit/selected-replay.tar.gz" +ARCHIVE_PIN = "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754" +PINS = { + "SPECTRAL-BOUND.md": "6dd2afed08d8873a2277ccfef4edd1bc212e831b8495bb659809f76d77802af1", + "check_spectral_bound.py": "ecc031e20c309c4e1d04443b60a58fe03d32ce73a5a3b43078e9cb673341c61c", + "SPECTRAL-BOUND.json": "d1124af128b6e526461c7587c2a7331dc4d19c9d90433d8d08bf9676c33a8a84", + "PAIR-BOUND.json": "77e6d0e69dacc72a8bf110d13bd5708283ebcae8155d1b6666613806ee1be5a0", +} +INTERFACE_PIN = "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" +MEMBERS = { + "slots/local/CANONICAL-WORD.json.gz": ( + "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219", + "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c"), + "slots/local/LOCAL-PROGRAMS.json.gz": ( + "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a", + "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3"), +} +A = [0, 7, 20, 27, 36, 46, 57, 111] +T = [21, 37, 47, 76, 81, 87, 92, 110] + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def pinned(path, expected): + raw = path.read_bytes() + need(sha256(raw).hexdigest() == expected, "Changed input: " + str(path)) + return raw + + +def source_matrix(): + raw = subprocess.check_output(["git", "show", BASE + ":" + ARCHIVE], + cwd=ROOT / "worktrees/k5-centre-sharing") + need(sha256(raw).hexdigest() == ARCHIVE_PIN, "Archive pin differs") + inputs = {} + with tarfile.open(fileobj=BytesIO(raw), mode="r:gz") as archive: + for name, (compressed_pin, payload_pin) in MEMBERS.items(): + matches = [x for x in archive.getmembers() if x.name == name] + need(len(matches) == 1 and matches[0].isfile(), "Invalid archive member") + compressed = archive.extractfile(matches[0]).read() + need(sha256(compressed).hexdigest() == compressed_pin, "Member pin differs") + payload = gzip.decompress(compressed) + need(sha256(payload).hexdigest() == payload_pin, "Payload pin differs") + inputs[name.rsplit("/", 1)[-1]] = json.loads(payload) + word = inputs["CANONICAL-WORD.json.gz"] + events = inputs["LOCAL-PROGRAMS.json.gz"]["forward"] + cut = events.index(["phase", "centers"]) + gradient = [{} for _ in range(712)] + for k, center in enumerate(word["centers"]): + gradient[center][k] = Q(1) + + def register(token): + need(token[0] in ("L", "C"), "Unknown field namespace") + value = token[1] + 704 * (token[0] == "C") + need(0 <= value < 712, "Invalid field") + return value + + for event in reversed(events[:cut]): + if event[0] != "scalar": + continue + op = event[1] + target = register(op[1]) + if op[0] == "clear": + gradient[target] = {} + elif op[0] == "scale": + scale = Q(op[2], op[3]) + gradient[target] = {k: x * scale for k, x in gradient[target].items()} + else: + need(op[0] in ("add", "copy"), "Unknown scalar operation") + source = register(op[2]) + need(source != target, "Unexpected aliased scalar operation") + scale = Q(1) if op[0] == "copy" else Q(op[3], op[4]) + for k, x in gradient[target].items(): + gradient[source][k] = gradient[source].get(k, 0) + scale*x + if op[0] == "copy": + gradient[target] = {} + R = [[gradient[p].get(k, Q(0)) for p in range(112)] for k in range(8)] + interface = json.loads(pinned(LANES / "circuit-interface/INTERFACE.json", INTERFACE_PIN)) + need(R == [[Q(row.get(str(p), 0)) for p in range(112)] for row in interface["R"]], + "Reverse source reconstruction differs from R") + need(all(x.denominator == 1 for row in R for x in row), "R is not integral") + R = [[int(x) for x in row] for row in R] + gram = lambda ports: [[sum(R[i][p]*R[j][p] for p in ports) + for j in range(8)] for i in range(8)] + need(gram(range(112)) == [[56*(i == j) for j in range(8)] for i in range(8)], + "Full source Gram differs") + need(not set(A) & set(T), "Fixed minors overlap") + for ports in (A, T): + need(gram(ports) == [[4*(i == j) for j in range(8)] for i in range(8)], + "A fixed minor differs") + columns = list(zip(*R)) + need(all(sum(x*x for x in col) == 4 for col in columns), "A root norm differs") + dots = Counter(sum(x*y for x, y in zip(columns[i], columns[j])) + for i in range(112) for j in range(i)) + need(dots == {0: 3304, 2: 1960, -2: 952}, "Root products differ") + return {"archive_sha256": ARCHIVE_PIN, "members": MEMBERS, + "reverse_output_forms": 8, "source_columns": 112, "source_cut": cut, + "pair_products": dict(sorted(dots.items())), "full_gram": "56 I8", + "fixed_minor_grams": "4 I8"} + + +def graph_cases(producer): + for n in (7, 8): + G = [[Q(2*(i == j)+2) for j in range(n)] for i in range(n)] + H = [[(Q(i == j)-Q(1, n+1))/2 for j in range(n)] for i in range(n)] + need(all(sum(G[i][k]*H[k][j] for k in range(n)) == (i == j) + for i in range(n) for j in range(n)), "Clique inverse differs") + clique8 = [[h, s] for h in range(9) for s in range(-h, h+1, 2) + if 9*h-s*s == 18] + need(clique8 == producer["clique_eight_projection_cases_h_s"], "Eight-clique cases differ") + need(28+7*max(x[0] for x in clique8)+21 == 91, "Eight-clique edge bound differs") + high = [[s, str(Q(s*s-32, 4))] for s in range(-6, 7, 2) if s*s >= 32] + need(high == [[-6, "1"], [6, "1"]], "High-root cases differ") + expected = {(0, 0, "4"): 7, (1, 1, "9/4"): 6, (2, 0, "0"): 2, + (2, 2, "1"): 7, (3, 3, "1/4"): 4, + (4, 4, "0"): 3, (5, 5, "1/4"): 2} + cases = Counter() + comparisons = 0 + for epsilon in product((-1, 0, 1), repeat=7): + h, s = sum(x != 0 for x in epsilon), sum(epsilon) + residual4 = s*s-8*h+16 + if h > 5 or residual4 < 0: + continue + a2 = isqrt(residual4) + need(a2*a2 == residual4, "A low-root residual needs another case") + key = (h, abs(s), str(Q(residual4, 4))) + need(key in expected, "Unlisted low-root case") + allowed = [] + for index in range(7): + dots2 = {s-4*epsilon[index]+sign*a2 for sign in (-1, 1)} + allowed.append(dots2 & {-4, 0, 4}) + possible_edges = sum(bool(values & {-4, 4}) for values in allowed) + need(possible_edges == expected[key], "The low-root table differs") + for t in range(8): + if t <= sum(bool(values) for values in allowed): + need(h+min(t, possible_edges) <= max(7, t+2), "Combined degree bound fails") + comparisons += 1 + cases[key] += 1 + need(sum(cases.values()) == 281 and set(cases) == set(expected), "Low cases are incomplete") + bounds = [21+6*t+5*(8-t)+28 if t < 2 else + 21+6*t+comb(t, 2)+(8-t)*max(7, t+2)+comb(8-t, 2) + for t in range(8)] + need(bounds == [89, 90, 91, 87, 85, 85, 89, 93], "Seven-clique total differs") + need(bounds == producer["clique_seven_bounds_for_t_zero_through_seven"], "Receipt cases differ") + need((Q(1)-Q(1, 6))*225/2 < 94, "Small-clique bound fails") + return {"epsilon_patterns": sum(cases.values()), "degree_checks": comparisons, + "low_table": [[*key, expected[key], cases[key]] for key in sorted(cases)], + "seven_clique_bounds": bounds, "eight_clique_bound": 91, + "fifteen_root_edge_bound": 93} + + +def log_bounds(argument, terms=64): + """Use direct rational powers and an explicit positive tail bound.""" + x = Q(argument) + need(x > 0, "Nonpositive logarithm") + if x < 1: + lo, hi = log_bounds(1/x, terms) + return -hi, -lo + exponent = 0 + while x > 2: + x /= 2 + exponent += 1 + z = (x-1)/(x+1) + lower = sum((2*z**j/Q(j) for j in range(1, 2*terms, 2)), Q(0)) + upper = lower + 2*z**(2*terms+1)/((2*terms+1)*(1-z*z)) + if exponent: + lo2, hi2 = log_bounds(Q(2), terms) + lower, upper = lower+exponent*lo2, upper+exponent*hi2 + return lower, upper + + +def rational_floor(x, scale=10**9): + return str(Q((x*scale).numerator//(x*scale).denominator, scale)) + + +def spectral_cases(receipt): + lo44, _ = log_bounds(44) + lo2, hi2 = log_bounds(2) + log44_32, _ = log_bounds(44, 32) + _, log2_32 = log_bounds(2, 32) + rows = [] + for row in receipt["rows"]: + v = row["additional_columns"] + trace = 4*v + edge = min(comb(v, 2), 7*v*v//16) + if v >= 15: + edge = min(edge, 93*comb(v, 2)//comb(15, 2)) + moment = 16*v+8*edge + discr = 7*(8*moment-trace*trace) + root_upper = isqrt(discr*256**2) + root_upper += (root_upper**2 != discr*256**2) + cap = min(Q(2*v+2), Q(4)+Q(7*v, 4), (trace+Q(root_upper, 256))/8) + need(0 < cap < 44 and Q(row["largest_eigenvalue_bound"]) == cap, "Eigenvalue cap differs") + need((row["trace"], row["nonorthogonal_edge_bound"], row["square_trace_bound"]) + == (trace, edge, moment), "Moment ledger differs") + count = int(trace//cap) + leftover = trace-count*cap + need(0 <= count < 8 and 0 <= leftover < cap, "Invalid extreme spectrum") + crude = (44-cap)**count*(44-leftover)*44**(7-count) + upper = (44-Q(v, 2))**8 + ratio = Q(44)/(44-cap) + _, log_ratio_hi = log_bounds(ratio) + lower = 8*lo44-Q(trace, 44)-Q(moment)/cap**2*(log_ratio_hi-cap/44) + lower_power = max(k for k in range(60) if crude > 2**k or lower > k*hi2) + upper_power = min(k for k in range(60) if upper < 2**k) + remaining = list(range(lower_power+1, upper_power)) + need(Q(row["crude_determinant_lower"]) == crude and Q(row["determinant_upper"]) == upper, + "Determinant bounds differ") + need((lower_power, upper_power, remaining) == + (row["strict_lower_power"], row["strict_upper_power"], row["remaining_power_exponents"]), + "Power-of-two interval differs") + if not remaining: + _, lr32 = log_bounds(ratio, 32) + l32 = 8*log44_32-Q(trace, 44)-Q(moment)/cap**2*(lr32-cap/44) + margins = row["exact_exclusion_margins"] + need(Q(margins["log_lower_minus_previous_power"]) == l32-lower_power*log2_32, + "Saved logarithm margin differs") + need(Q(margins["crude_lower_minus_previous_power"]) == crude-2**lower_power, + "Saved crude margin differs") + need(Q(margins["next_power_minus_upper"]) == 2**upper_power-upper, + "Saved upper margin differs") + margin = lower-lower_power*hi2 + if v == 15: + need(moment == 984 and cap == Q(29815, 1024), "Critical v15 data differ") + need(margin > Q(1, 1250), "The exact v15 gap is not above 1/1250") + rows.append({"selected_size": v+16, "edge_bound": edge, + "largest_eigenvalue_bound": str(cap), + "strict_powers": [lower_power, upper_power], + "remaining_exponents": remaining, + "log_margin_lower_bound": rational_floor(margin)}) + need([r["selected_size"] for r in rows] == list(range(24, 40)), "Size range is incomplete") + excluded = [r["selected_size"] for r in rows if not r["remaining_exponents"]] + need(excluded == [24, 25, 26, 28, 29, 30, 31] == receipt["excluded_selected_sizes"], + "Exclusion list differs") + return rows + + +def main(): + blobs = {name: pinned(PRODUCER/name, pin) for name, pin in PINS.items()} + receipt = json.loads(blobs["SPECTRAL-BOUND.json"]) + need(receipt["status"] == "PASS_UNPAIRED_SPECTRAL_EXCLUSIONS", "Wrong source status") + result = {"status": "PASS_INDEPENDENT_UNPAIRED_SPECTRAL_BOUND", + "reviewed_pins": PINS, "interface_sha256": INTERFACE_PIN, + "source_reconstruction": source_matrix(), + "graph_cases": graph_cases(receipt["fifteen_root_edge_proof"]), + "logarithm_terms": 64, "rows": spectral_cases(receipt), + "critical_v15_log_margin_strictly_above": "1/1250", + "general_selected_lower_bound": 27, + "scope": "S contains the fixed A and T, and the selected baselines are retained.", + "not_repeated": ["The million-vector split-pair enumeration"], + "not_claimed": ["Existence at size 27", "A general centre-information lower bound", + "A native controller", "A supplier or kappa improvement"]} + (HERE/"SPECTRAL-BOUND-REVIEW.json").write_text(json.dumps(result, indent=2)+"\n") + print(json.dumps({"status": result["status"], "general_selected_lower_bound": 27, + "critical_v15_gap": "> 1/1250"})) + + +if __name__ == "__main__": + main() diff --git a/research/actual-query-information-bounds/payload/upstream/CANONICAL-WORD.json.gz 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+{"cover_correction":{"complete_small_cover_checks":[{"n":1,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":1},{"n":2,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":2},{"n":3,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":6},{"n":4,"nonzero_full_kernel_corrections":24,"orthogonal_matrices":48},{"n":5,"nonzero_full_kernel_corrections":600,"orthogonal_matrices":720}],"formula":"delta(g)_i = (weight(row_i(g))-1)/2 mod 2; apply X_delta(g) to EVERY final live stream in cover class g.","mandatory":true,"reason":"P_g C_all P_g^-1 = C_all X_delta(g) exactly. Orthogonality cancels all quadratic cross terms; both sides fix the uniform vector."},"global_phase_argument":"Every C_q and every linear address permutation fixes the uniform vector. Equality of the exact Z4 Fourier multiplier therefore fixes the scalar phase as 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