From 548f96032c7203953bcf3a3458b92f59b3e9261d Mon Sep 17 00:00:00 2001 From: Cinna Davis <1337isnot1337@users.noreply.github.com> Date: Tue, 13 Oct 2026 19:04:20 -0500 Subject: [PATCH] Research: locate helper468 rank-eight suffix bound at B88 --- research/r439-helper468-late-cut/CLAIM.json | 44 + research/r439-helper468-late-cut/LICENSE | 201 + research/r439-helper468-late-cut/OVERLAP.json | 55 + research/r439-helper468-late-cut/PROOF.md | 223 + research/r439-helper468-late-cut/README.md | 147 + research/r439-helper468-late-cut/SOURCES.json | 53 + research/r439-helper468-late-cut/TASK.json | 60 + .../r439-helper468-late-cut/VALIDATION.json | 33 + research/r439-helper468-late-cut/VERIFY.json | 50 + research/r439-helper468-late-cut/engine.py | 303 + .../generated/CERTIFICATE.json | 39 + .../generated/CUTS.jsonl | 4874 +++++++++++++++++ .../generated/EVENTS.json | 1 + .../generated/GEOMETRY.json | 326 ++ .../r439-helper468-late-cut/independent.py | 287 + .../inputs/PR1256-CERTIFICATE.json | 1302 +++++ .../inputs/PR589-NOTICE.md | 62 + .../inputs/PR589-WORD.json.gz | Bin 0 -> 42353 bytes .../r439-helper468-late-cut/test_package.py | 175 + research/r439-helper468-late-cut/verify.py | 72 + 20 files changed, 8307 insertions(+) create mode 100644 research/r439-helper468-late-cut/CLAIM.json create mode 100644 research/r439-helper468-late-cut/LICENSE create mode 100644 research/r439-helper468-late-cut/OVERLAP.json create mode 100644 research/r439-helper468-late-cut/PROOF.md create mode 100644 research/r439-helper468-late-cut/README.md create mode 100644 research/r439-helper468-late-cut/SOURCES.json create mode 100644 research/r439-helper468-late-cut/TASK.json create mode 100644 research/r439-helper468-late-cut/VALIDATION.json create mode 100644 research/r439-helper468-late-cut/VERIFY.json create mode 100644 research/r439-helper468-late-cut/engine.py create mode 100644 research/r439-helper468-late-cut/generated/CERTIFICATE.json create mode 100644 research/r439-helper468-late-cut/generated/CUTS.jsonl create mode 100644 research/r439-helper468-late-cut/generated/EVENTS.json create mode 100644 research/r439-helper468-late-cut/generated/GEOMETRY.json create mode 100644 research/r439-helper468-late-cut/independent.py create mode 100644 research/r439-helper468-late-cut/inputs/PR1256-CERTIFICATE.json create mode 100644 research/r439-helper468-late-cut/inputs/PR589-NOTICE.md create mode 100644 research/r439-helper468-late-cut/inputs/PR589-WORD.json.gz create mode 100644 research/r439-helper468-late-cut/test_package.py create mode 100644 research/r439-helper468-late-cut/verify.py diff --git a/research/r439-helper468-late-cut/CLAIM.json b/research/r439-helper468-late-cut/CLAIM.json new file mode 100644 index 0000000000..15fff435e3 --- /dev/null +++ b/research/r439-helper468-late-cut/CLAIM.json @@ -0,0 +1,44 @@ +{ + "seed": 17, + "track": "bit supplier", + "start_utc": "2026-10-13T23:13:28.854690+00:00", + "previous_pr": 1347, + "previous_head": "64fd5f9e91961dedc16118fcc7ad71ee82efe28f", + "state": "claimed", + "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "worktree": "/home/cinna/int-bounds/seed17-bit-supplier", + "branch": "research/seed17-bit-supplier", + "selected_record_sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32", + "budget_minutes": 60, + "expected_finish_utc": "2026-10-14T00:13:28Z", + "verification_reserve_start_utc": "2026-10-13T23:58:28Z", + "candidates": [ + { + "object": "Semantic zero-frame D contract for composed R439", + "disposition": "PR1194 proves it and PR1311 independently applies it; duplication avoided." + }, + { + "object": "Nonabelian binary affine register model with restored helpers", + "disposition": "PR1333 already closes the complete priced alphabet; not reopened." + }, + { + "object": "All original B/C literal cuts for helper468 rank-seven retirement", + "disposition": "Chosen: extends PR1256 fixed post-scatter boundary to every later cut, including completed target reads." + } + ], + "seed_use": "Select helper468 from [465,466,468,469,476] at index17 mod5. Coverage within this one-helper domain is exhaustive.", + "domain": "Original PR589 D/A/scatter prefix; every MOVE and individual ADD boundary through original B, C and final frame moves; helper468; arbitrary rank-at-most-seven one-common-frame restore-and-isolate blocks with arbitrary block length, scalar mixing and independent dirty auxiliaries. No earlier lower-frame preparation, new copies, descent or changed prefix.", + "initial_body": "CLAIM \u2014 bit supplier track, OS seed 17.\n\nBase `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. Exact object: helper 468 in the selected PR589 bit word, after every later literal MOVE/ADD boundary from the original D/A/scatter cut through B/C. PR1256 (`d6d5a994fcdcd8d04ec439ff988daa8f37b17ece`) proves its obstruction at the initial cut, and explicitly leaves later target-read cuts open; PR1128 (`df29b159239b79d7e451d6ddda826a73e0e50a67`) supplies the two-sided footprint contract.\n\nMethod: incrementally update all 661 binary input rows and the inverse, exact rational frame spans, helper dirty support, restoration row, and every remaining target dependency. Test any one-common-frame restore-and-isolate block of rank at most 7, with arbitrary scalar mixing/block length and independent dirty auxiliaries; no earlier preparation or new transport. This covers one helper across all later cuts, not another replay of the two old cuts. Seed17 selects helper 468 at index 17 mod 5 among the five initially blocked helpers.\n\nOptimistic screen: ending its residual width at 7 instead of 8 can free a host coordinate; helpers, restoration and source access will be counted for a concrete candidate. Information-access failure rules a cut out even if all added work is free. Expected deliverable: complete exact cut ledger and scoped obstruction or a fully checked narrow candidate, with source pins and negative controls. No new kappa assumed.\n\nExpected finish 2026-10-14 00:13 UTC; final quarter reserved for verification. Claim expires 2026-10-14 01:13 UTC. Cinna Davis with substantial OpenAI Codex assistance.", + "discussion": { + "id": "D_kwDOU-508s4AqAs8", + "number": 1362, + "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1362" + }, + "result": { + "status": "verified", + "cuts": 4874, + "statement": "Every original cut excludes a one-common-frame rank-seven isolation block. From cut 177 (B88 MOVE 208:0->152), PR1128's two-sided lemma excludes any permitted reversible linear suffix ending helper 468 below rank eight. The earlier 177 cuts are not existence certificates.", + "command": "python3.12 scripts/research_package.py --package research/r439-helper468-late-cut", + "verification": "Both engines and all ten tests pass on Python 3.12.15 and 3.14.7; four source archives match exact Git blobs." + } +} diff --git a/research/r439-helper468-late-cut/LICENSE b/research/r439-helper468-late-cut/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/r439-helper468-late-cut/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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PR1128 supplies the general two-sided lemma; PR1256 supplies the initial-cut fixture. PR1253 is a different first-contact kernel entrance. Head/Discussion refresh completed before publication. Literal body/comment coverage does not prove novelty." +} diff --git a/research/r439-helper468-late-cut/PROOF.md b/research/r439-helper468-late-cut/PROOF.md new file mode 100644 index 0000000000..cb9add3179 --- /dev/null +++ b/research/r439-helper468-late-cut/PROOF.md @@ -0,0 +1,223 @@ +# No rank-seven common-frame isolation of helper 468 at a later PR589 cut + +## 1. Statement and exact scope + +Fix DreamingOfClouds' PR589 tuned R439 word, with 111 source/target pairs and +439 arbitrary dirty helpers. All 661 formal input coordinates are independent. +The exact input bytes are archived and pinned in +`SOURCES.json`. Use its listed rational frame spaces, original register roles, +and final output convention: source/helper r returns its original input, and +target t returns `u_t + u_(t-111)` at its specified target hyperplane. +The proposed change is helper 468's terminal frame, which may be any rational +space of rank at most seven. Its required output remains its original input. + +The starting cut is just after the original D/A/scatter prefix and all nine +retained COPY/ERASE pairs. Continue the original B/C word, interpreting each +listed donor in its listed order. The ledger includes the starting cut and +every boundary after a literal MOVE or individual ADD, including final MOVEs: +4,873 events and 4,874 cuts in total. + +**Theorem.** At none of those cuts can an inserted scalar block at one common +rational frame F of rank at most seven both restore helper 468 to its original +dirty input and remove that dirty input from every other register, while +admitting a completion with the original output roles/target frames. The block +may have arbitrary length, arbitrary invertible scalar mixing, target feedback, +and any number of independent dirty auxiliaries at F. The remaining completion +need not be the original B/C continuation. + +The allowed completion uses scalar operations at common frames and monotone +frame enlargements. New COPY transport, descent/reset, an earlier lower-frame +preparation, altered prefix, different output roles, and restoration without +immediate complete isolation are outside the theorem. An auxiliary's initial +dirty input is independent; it does not provide an extra copy of a boundary +coordinate. This is a scoped finite-word obstruction, not a barrier for all +width-seven interfaces or bit suppliers. + +**Stronger later-cut corollary.** Starting at cut **177**, immediately after +the MOVE of target 208 from frame 0 to frame 152 at zero-based B gate **88**, +no reversible linear suffix in the inherited monotone/common-frame model can +restore helper 468 at any terminal frame of rank at most seven. This permits +arbitrarily many frames, arbitrary suffix length and extra restored dirty +auxiliaries. All 4,697 cuts from 177 onward have a rank-eight two-sided footprint +or an already rank-eight helper. The first 177 cuts pass that two-sided rank +test; no existence conclusion is drawn for them. Their single-frame isolation +blocks remain excluded by the theorem above. + +Ross Richardson's PR1256 proves the initial-cut footprint obstruction and +explicitly leaves later target-read cuts open. Ali Romman's PR1128 supplies +the two-sided restoration/dirty-column condition and two earlier cut analyses. +This contribution evaluates the changing condition at every later literal cut +for one seed-selected helper. It does not reopen their fixed-cut exclusions. + +## 2. Scalar information required by an isolating block + +At a cut write `w = M u`, where M is the 661-by-661 binary scalar matrix. The +prefix and every suffix ADD are invertible; all scatter snapshots have been +erased. Thus the coordinates of w are independent arbitrary bits. The scalar +matrix concerns formal inputs, not a reduction of rational frame coordinates +modulo two. + +For h = 468, let + +``` +a_h = e_h^T M^-1, +d_h = {r : M[r,h] = 1}, +P_h = support(a_h) union d_h union {h}. +``` + +Every coordinate of `support(a_h)` must participate in a block that outputs +`u_h`. If a coordinate p with a nonzero coefficient is not read, two boundary +states differing only at p give the block identical inputs but require different +restored helper values. Independent dirty auxiliaries cannot distinguish them. +Every other register in d_h must also participate: leaving it unchanged retains +its nonzero coefficient of u_h, contradicting complete isolation. Include h +itself even when its current coefficient or restoration-row coefficient is zero. +This necessity allows arbitrary scalar mixing rather than assuming the short +restore/clear star used as a predecessor fixture. + +All participants must reach F. Let J be the rational span of their current +frame spaces. Monotone frame legality forces `J subset F`. Consequently: + +- if helper h has already reached rank eight, a rank-seven F is impossible; +- if `dim J = 8`, no F of rank at most seven contains the footprint; +- if a target in P_h has a final frame V_t that does not contain J, forcing + that target to F makes its required final frame unreachable. + +The third condition alone excludes every low-rank footprint in the census: +target **208** is always such a forced participant. + +The ledger also recomputes the broader missing-information condition. The +required target row in current boundary coordinates is + +``` +b_t = (e_t + e_(t-111))^T M^-1. +``` + +If J is not contained in V_t and `support(b_t)` meets P_h, two states differing +only in one such forced coordinate have different desired target values. After +the block, all information about that coordinate lies in registers at F or +descendant frames containing F. No common-frame scalar dependency path can +reach target t at V_t. Extra participants can only enlarge J. These are +information-access failures even if all additional work is free. + +## 3. Complete cut enumeration and inverse updates + +The primary engine constructs M from every D/A ADD and scatter read, then +inverts it exactly over F2. For `w_t ^= w_s`, write `S = I + e_t e_s^T`. Since +`S^-1 = S`, the new matrix and inverse are + +``` +M' = S M, +M'^-1 = M^-1 S. +``` + +Hence every inverse row containing coordinate t toggles coordinate s. A MOVE +changes frames but not scalar rows. The primary engine updates all 661 forward +and inverse rows after every event, reconstructs P_h, and joins its rational +frames. The final forward matrix and inverse both equal the full required +dirty-input/output map. This also checks the entire B/C tail after helper h has +already become too large, rather than ending coverage at the first obstruction. + +The independent engine uses sets for scalar expressions, a descending-column +set inverse, and explicit integer minor/normal witnesses for the nine footprint +joins. It imports no primary or predecessor program. Both implementations agree +on all events, all cut fields, the full ledger/certificate, and all 661 final +forward and inverse columns. Both are from this AI-assisted contribution; this +does not claim independent human review or proof-assistant formalization. + +| Exclusion | Cuts | +|---|---:| +| Footprint rank seven, but target 208 cannot reach its required final frame | 177 | +| Footprint already spans rank eight | 1,557 | +| Helper 468 itself has already reached rank eight | 3,140 | +| Not excluded by the necessary conditions | 0 | + +There are 1,310 suffix MOVEs and 3,563 scalar ADDs. Helper h's current-rank +counts are 890 cuts at rank four, 710 at rank six, 134 at rank seven, and 3,140 +at rank eight. These counts sum to the entire 4,874-cut domain. + +For a rank-eight join, the certificate gives eight contained root lines and a +nonzero 8-by-8 integer determinant. For the rank-seven join it gives a nonzero +7-by-7 minor and a nonzero normal annihilating every line of the join, certifying +both rank bounds. A separate target normal annihilates target 208's final frame +and detects a line of the footprint. All nine cases are exact; no floating-point +rank tolerance is used. The independent engine checks their determinants by +fraction-free Bareiss elimination and their normal equations by integer dots. + +The listed MOVE order is target followed by the listed donors. No alternative +ordering of those MOVEs inside a gate can rescue a cut: before its first ADD, +scalar rows and P_h are fixed, while each MOVE only enlarges participating +frames. Any exclusion before those MOVEs persists throughout their reordering. +The theorem fixes the original listed order of scalar donor ADDs; arbitrary +donor permutations or gate reorderings are not searched. + +Thus the finite census instantiates the footprint proof at every specified cut. +This is stronger than a failed circuit search in that domain: each cut has a +necessary-condition failure excluding arbitrary block length and coefficients. +It is not an impossibility theorem for the excluded mechanisms in Section 1. + +## 4. Arbitrary suffixes after the first rank-eight footprint + +We apply Ali Romman's PR1128 two-sided boundary lemma, crediting the lemma to +that predecessor. Suppose h ends in a rational frame U. The restoration +argument requires every frame on `support(a_h)` to be contained in U: otherwise +an essential independent boundary coordinate cannot reach the restored output. + +For erasure, call a register high when its current frame is not contained in U, +and take the F2 span S of all current high-register scalar rows. A low-to-high +MOVE adds a row to S; an already-high register cannot become low. A common-frame +invertible linear operation either acts entirely on low registers or, after +its operand MOVEs, entirely on high registers. In the latter case it preserves +their row span. Thus S never loses a vector. + +At completion h is low. Every other required output, including every restored +extra dirty auxiliary, has zero coefficient of the original u_h. The final S +therefore has zero u_h coefficient on every vector. Any boundary register with +nonzero u_h coefficient must initially be low. Hence every frame in d_h, as +well as the restoration footprint and current helper frame, must lie in U. +The same J is a necessary subspace of U for **any** such suffix, without assuming +a single-frame block or immediate isolation. + +At cuts 176 and 177 the scalar restoration row and dirty column are identical. +The event between them only moves target 208, which contains u_h, from frame 0 +to frame 152. The frame join grows from seven to eight; the new eight-line minor +has determinant -32. Therefore helper 468 must end at rank eight from that cut. +The exact ledger verifies the same bound at every later cut. No new COPY, +descent/reset, different prefix or non-restored auxiliary is included in this +corollary. In particular, a staged attempt using the original prefix must start +before this MOVE; merely waiting for later target reads cannot repair it. + +## 5. Favorable accounting screen and why it does not supply a construction + +The unchanged prefix has already placed h at rank four. Its original later +path has ranks `4 -> 6 -> 7 -> 8`, contributing `H2 + 2 H1`. An ideal direct +move to a rank-seven residual instead contributes H3. The ideal local delta +at such a cut is therefore `H3 - H2 - 2 H1`. At a rank-six or rank-seven cut, +the ideal delta is `-H1`. + +As in PR1256's credited two-slot planning model, relocate the residual from +an old width-eight host into a formerly idle rank-seven slot, returning all +eight freed coordinates to an old idle remainder r. The complete ideal child +deltas, retaining every other child and all nine COPY/ERASE pairs, are + +``` +current rank 4: e3 - e2 - 2e1 - e7 + e_(r+8) - e_r, +current rank 6 or 7: -e1 - e7 + e_(r+8) - e_r. +``` + +For each inherited remainder r in {2,4,6}, rank mass is unchanged. Child count +falls by three or two respectively. Any fixed nonnegative child-count surcharge +therefore also falls. Additional preparation, source access, helper storage, +restoration, frame changes and scalar work are optimistically free in this +screen; no new copies or recursive children are omitted from a claimed actual +construction because no construction is asserted. It is a favorable scenario, +not a bound on every possible alternative invoice or a physical slot assignment. + +At the pinned bit exponent `a = 1733427039589844234749 / 10^24`, and indeed for +every `0 < a < 1`, `g(r) = r*(64/r)^a` is strictly subadditive. For the first +delta, merge old ranks 2+1 into 3 and old ranks 1+7+r into r+8. For the second, +merge 1+7+r into r+8. These merges strictly lower the weighted moment in the +ideal screen. The geometric failures above remain decisive even under that +favorable bill: a rank-seven single-frame block cannot satisfy the required +information and final-frame obligations. No native, packed precision, hosted +invoice, new endpoint or kappa follows from this screen. diff --git a/research/r439-helper468-late-cut/README.md b/research/r439-helper468-late-cut/README.md new file mode 100644 index 0000000000..c3c595705d --- /dev/null +++ b/research/r439-helper468-late-cut/README.md @@ -0,0 +1,147 @@ +# R439 helper 468: rank-eight suffix bound begins at B gate 88 + +**Scoped negative result with a written footprint proof and complete exact ledger. +No new circuit, supplier or kappa.** + +PR1256 excludes an eager restore/isolate block at the original PR589 post-scatter +cut and leaves later target-read cuts open. This contribution checks one helper, +**468**, at every original B/C MOVE and individual ADD boundary. A later cut may +have already delivered a needed target input; its inverse rows and dirty column +must be recomputed rather than reusing the original-cut obstruction. + +All **4,874 cuts** are excluded for an arbitrary restore-and-isolate block at +one common rational frame of rank at most seven: + +| Exclusion | Cuts | +|---|---:| +| Target 208 would be promoted into an incompatible frame | 177 | +| The restoration/isolation footprint has rank eight | 1,557 | +| Helper 468 itself has already reached rank eight | 3,140 | + +The starting cut and all **1,310 MOVEs plus 3,563 ADDs** are included. The +block may have arbitrary length, scalar mixing, target feedback and independent +dirty auxiliaries at its common frame. The [proof](PROOF.md) gives the exact +output/frame contract and the necessary-condition argument. It excludes any +permitted completion after such a block, not merely the original remaining C. + +The single-frame result does not rule out earlier lower-frame preparation, a block using multiple +frames, new COPY transport, descent/reset, a changed prefix/output basis, or +restoration with delayed isolation. Donor ADDs are taken in their original listed +order. Other source/helper outputs and target output roles remain fixed; helper +468 is the proposed smaller endpoint. No general bit-supplier impossibility is claimed. + +The same ledger gives a stronger later-cut result by applying PR1128's +two-sided lemma. **After B gate 88 moves target 208 from frame 0 to frame 152 +(cut 177), every permitted reversible linear suffix must end helper 468 at rank +eight**, even if it uses several frames and extra restored dirty auxiliaries. +All 4,697 later cuts have that rank-eight obstruction. The first 177 cuts still +pass the two-sided rank-seven test; their single-frame blocks are excluded, +but staged suffixes there remain undecided. This identifies the precise original +MOVE before which a changed width-seven mechanism must begin. + +The critical source gate is `B[88] = [152, 208, [19]]`. The obstruction begins +at its target MOVE, before the ADD: the restoration row and dirty column are +unchanged across the transition, while their required frame join grows from +seven to eight. The first 177 cuts are not proofs of feasible staged suffixes. + +## Reproduce + +From the repository root, standard-library Python: + +```sh +python3 -I -O -B research/r439-helper468-late-cut/verify.py +python3 -I -O -B research/r439-helper468-late-cut/independent.py +``` + +Expected markers: + +```text +PASS_R439_HELPER468_LATE_CUT cuts=4874 excluded=4874 joins=9 arbitrary_suffix_from=177 new_kappa=false +PASS_INDEPENDENT_R439_HELPER468 cuts=4874 excluded=4874 integer_geometry_cases=9 arbitrary_suffix_from=177 +``` + +`generated/EVENTS.json` is the complete ordered suffix event stream. A MOVE is +`[section, gate_index, "MOVE", register, previous_frame, new_frame]`; an ADD is +`[section, gate_index, "ADD", target, source, donor_offset]`. Before a multi-donor +gate, all operands climb in target/listed-donor order; each donor ADD gets its +own cut. Cut 0 is the original post-scatter boundary; cut k is after event k-1. + +`generated/CUTS.jsonl` stores every cut, the helper's current frame/rank and its +exclusion. For current rank at most seven it also stores restoration, dirty and +participant masks in original register coordinates, and the contributing frames. +For rank-seven footprints it includes all illegal target promotions and all +missing target-dependency masks. Rank-eight helper cuts need no further footprint +test. `generated/GEOMETRY.json` supplies the nine independent minor/normal +witnesses and a full-frame witness. `generated/CERTIFICATE.json` records all +counts and hashes. The writer refuses existing receipt directories. + +The primary checker uses rational frame elimination and packed binary rows. +The separate checker uses set-valued rows, a descending-column inverse and +integer Bareiss determinants/normal equations. It imports no primary or +predecessor executable. Both agree on every event, cut and final dirty column; +both belong to this AI-assisted contribution, not independent human review. + +The credited card's working example also passes: +`python3 -I -B research/r439-bsection-stars-seed01/verify.py`. This confirms the +historical finite word and its documented H2/K pattern; it does not adopt a new +supplier. This package uses the original PR589 word, rather than composing those +ADD savings or changing selected artifacts. + +The full registered replay passes on Python 3.12.15, and all ten tests also +pass on Python 3.14.7. Regressions check all 168 invertible binary 3-by-3 +matrices, 1,008 inverse updates and 10,080 outside-frame span cases. Controls +reject changed sources, omitted cuts/MOVEs, false minors/normals and receipt +overwriting; an isolated export passes both engines under `-I -O -S -B` without +writing files. Four frozen inputs match their exact source Git blobs. +`VALIDATION.json` records the environment and the unrun physical obligations. + +## Accounting and limits + +The ideal width-seven two-slot relocation has favorable complete child deltas +even before constructing a suffix. It retains all nine COPY/ERASE pairs, returns +all eight old host coordinates, consumes an idle rank-seven slot and accounts +for the changed helper path. For old remainder r in {2,4,6}, the rank-four-cut +delta is `e3-e2-2e1-e7+e_(r+8)-e_r`; at rank six/seven it is +`-e1-e7+e_(r+8)-e_r`. Both preserve rank mass and reduce child count. Subadditivity +proves a strict favorable moment for every exponent between zero and one. + +This is an optimistic planning scenario with every other child retained and +added preparation/storage/source/restoration/frame/scalar charges set to zero. +It is not a realized invoice or physical owner assignment. The exact geometry +still prevents the one-common-frame block even when all that work is free. +Packed precision/tape, native compiler, hosting, analytic transfer and a complete +outer multiplication theorem are not verified or supplied by this audit. + +## Open next questions + +Can a staged mechanism clear helper 468's dirt from target 208 at a compatible +lower frame before isolating the helper at rank seven? A feasible first step is +one explicitly priced two-frame block with a full 661-column replay and legal +continuation. It must also preserve the source/target dependencies identified +by PR1256 and replace any later reads of the changed helper. It must begin before +the original target 208 MOVE at B gate 88; every later original cut has a general +rank-eight terminal bound. The initial-cut theorem +excludes a single common-frame block at an original cut; it does not decide this +changed mechanism. Physical hosting and all preparation/restoration work must +be paid if a finite construction is found. + +## Provenance and credit + +Base: `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. OS assignment seed **17**, +bit supplier track, selects helper 468 from the five initially blocked helpers +at index `17 mod 5`. The within-helper cut domain is exhaustive and deterministic. +Coordination: [discussion1362](https://github.com/CrocSwap/integer-mult-bounds/discussions/1362). + +Ross Richardson's PR1256, head `d6d5a994fcdcd8d04ec439ff988daa8f37b17ece`, +supplies the initial-cut footprint argument, exact helper468 fixture, helper470 +exception and stated later-cut question. Ali Romman's PR1128, head +`df29b159239b79d7e451d6ddda826a73e0e50a67`, supplies the two-sided boundary model; +his PR1043, head `e309e17f83f5759b1ea1fa24a76f24838784cb4d`, deletes helper470 by +changing an earlier source boundary. Those constructions are not combined here. +DreamingOfClouds' PR589 on eumemic's PR555/543 supplies the selected bit word and +interface lineage. Sagar Thakrar's PR1023 motivates rank-seven hosting. The +original NOTICE is retained, along with the exact compressed word bytes. + +New work by **Cinna Davis (@1337isnot1337)** with substantial **OpenAI Codex +assistance** in mathematics, code, experiments, verification and writing. +Apache-2.0. Exact Git blobs, hashes, source heads and scope metadata are retained. diff --git a/research/r439-helper468-late-cut/SOURCES.json b/research/r439-helper468-late-cut/SOURCES.json new file mode 100644 index 0000000000..60eaace7cc --- /dev/null +++ b/research/r439-helper468-late-cut/SOURCES.json @@ -0,0 +1,53 @@ +{ + "schema_version": 1, + "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "c05fafaa25ba95b2d5af86b1800427198e3d20eb", + "sha256": "89b5928bc92c81e2647b6d702a7ad85a6795b8f44e2eb267b2ff3145d8f2b2ce" + } + ], + "archives": [ + { + "local_path": "inputs/PR589-WORD.json.gz", + "source_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "source_path": "research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz", + "git_blob": "85a4499bf9e4911a705d50567a2c2ef6cf23739a", + "sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f" + }, + { + "local_path": "inputs/PR589-NOTICE.md", + "source_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "source_path": "research/e8-bit-p111-tuned/NOTICE.md", + "git_blob": "b589500c8ae02a0a4c476e61dfdd1b79dcbf7cad", + "sha256": "5b88eb2b7de76aa2a3288ee3c7a08d18a5eadfa82f5e7a99e207d232aed71221" + }, + { + "local_path": "inputs/PR1256-CERTIFICATE.json", + "source_commit": "d6d5a994fcdcd8d04ec439ff988daa8f37b17ece", + "source_path": "research/bit-early-retirement-cut/CERTIFICATE.json", + "git_blob": "b7a8d17755711ccb901742c59dd775c586be1c8d", + "sha256": "735c507caf32715f978e9c0ca67cb056184c751593cd8c58e9dd97232def7a46" + }, + { + "local_path": "LICENSE", + "source_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "source_path": "LICENSE", + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4" + } + ], + "predecessors": { + "PR1256": "d6d5a994fcdcd8d04ec439ff988daa8f37b17ece", + "PR1128": "df29b159239b79d7e451d6ddda826a73e0e50a67", + "PR1043": "e309e17f83f5759b1ea1fa24a76f24838784cb4d" + } +} diff --git a/research/r439-helper468-late-cut/TASK.json b/research/r439-helper468-late-cut/TASK.json new file mode 100644 index 0000000000..2c717168a3 --- /dev/null +++ b/research/r439-helper468-late-cut/TASK.json @@ -0,0 +1,60 @@ +{ + "schema_version": 1, + "task_id": "bit-helper-contract", + "priority_revision": 2, + "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "original_card": { + "id": "bit-helper-contract", + "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?", + "starting_points": [ + "research/r439-bsection-stars-seed01/README.md", + "research/r439-copy-path-sharing-barrier/README.md" + ], + "methods": [ + "Derive a replacement interface lemma and price its implementation.", + "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement." + ], + "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient.", + "first_step": { + "command": [ + "python3", + "-B", + "research/r439-bsection-stars-seed01/verify.py" + ], + "expected": "PASS_R439_BSECTION_STARS", + "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.", + "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.", + "allowed_variations": [ + "Choose one helper-star or quartet instance; narrow to one boundary implication." + ], + "scope_change_triggers": [ + "Changing only source count or scalar addition count without an interface argument." + ], + "overlap_terms": [ + "H2_D_frame0_targets_from_helpers", + "K_equals_D", + "helper-star" + ] + }, + "scope_status": "changed", + "actual_scope": "All original B/C literal MOVE/ADD cuts of PR589 for a one-common-frame rank-seven restoration and complete isolation of helper468, permitting arbitrary block length and independent dirty auxiliaries. Apply PR1128's two-sided lemma to the exact rank-eight transition at B88 and all 4697 later cuts, allowing arbitrary-frame suffixes in its full restored-workspace model.", + "scope_change_reason": "PR1194 and PR1311 already cover the immediate H2/K contract. The assigned bit track is retained while testing the explicit later-cut question in PR1256 and PR1128. This audit concerns rank-seven residual/H4 boundary capability, not a replacement H2 proof.", + "bottleneck_link": "A legal residual below width eight could enter rank-seven idle slots and alter paid profile. The optimistic child bill is favorable, but each original cut violates a necessary frame condition. Complex supply remains binding at the selected base.", + "budget_minutes": 60, + "stop_rule": "Exhaust the one-helper original literal suffix domain (4874 cuts) and stop construction at exact necessary-condition failure; reserve final quarter for separate replay, rejection controls and handoff.", + "outcome": "negative-result", + "evidence": "PROOF.md and generated/{EVENTS.json,CUTS.jsonl,CERTIFICATE.json,GEOMETRY.json}; both complete engines agree.", + "author": "Cinna Davis (@1337isnot1337)", + "ai_assistance": "Substantial OpenAI Codex assistance in mathematical analysis, implementation, experiments, verification and writing.", + "open_questions": [ + { + "question": "Can a staged or transported mechanism isolate helper468 without one common rank-seven frame?", + "why_it_matters": "Every original literal cut fails the single-frame condition, while the ideal width-seven hosting bill is favorable. A changed mechanism must address the forced target208 or rank-eight footprint.", + "first_step": "Specify one two-frame block with a legal changed continuation, preserving all 661 dirty columns and pricing source access, preparation, frame changes, copies and restoration. The changed mechanism must start before the original target 208 MOVE at B88.", + "blocked_by": "No staged candidate or source/copy transport is constructed; later reads of helper468 and target/source dependencies must be preserved. Native hosting, precision and all-size obligations remain." + } + ] +} diff --git a/research/r439-helper468-late-cut/VALIDATION.json b/research/r439-helper468-late-cut/VALIDATION.json new file mode 100644 index 0000000000..6720fc7d28 --- /dev/null +++ b/research/r439-helper468-late-cut/VALIDATION.json @@ -0,0 +1,33 @@ +{ + "status": "PASS", + "local_python": "3.14.7", + "registered_python": "3.12.15", + "standalone_release": "20261009", + "runtime_asset": { + "browser_download_url": "https://github.com/astral-sh/python-build-standalone/releases/download/20261009/cpython-3.12.15%2B20261009-x86_64-unknown-linux-gnu-install_only_stripped.tar.gz", + "digest": "sha256:ffa8f85f1b56e88b687f08d743d817015524b86a9365fd921243132b80f1a36d", + "name": "cpython-3.12.15+20261009-x86_64-unknown-linux-gnu-install_only_stripped.tar.gz" + }, + "runtime_validation": "Pinned public release asset hash matches the verified release digest; private extracted runtime. The unchanged artifact is retained by SHA256 in the local cache.", + "tests": 10, + "local_test_seconds": 9.597, + "registered_test_seconds": 9.129, + "mathematical_regressions": { + "GL3_binary_matrices": 168, + "inverse_transvection_updates": 1008, + "outside_frame_span_cases": 10080 + }, + "cut_domain": { + "cuts": 4874, + "MOVE_events": 1310, + "ADD_events": 3563, + "general_suffix_rank8_from_cut": 177, + "general_suffix_excluded_cuts": 4697, + "earlier_single_frame_excluded_cuts": 177, + "join_geometry_cases": 9 + }, + "source_archives_checked_against_git_blobs": 4, + "command": "python3.12 scripts/research_package.py --package research/r439-helper468-late-cut", + "working_example": "PASS_R439_BSECTION_STARS blocks=10 gates=388->254 ADDs=11783->11515->11500 guard_rejections=24->0 columns=661 controls=8 no_new_kappa", + "scope": "Final registered replay includes the arbitrary-suffix corollary, exact B88 transition and all ten tests. No native, new supplier/host invoice, selected cold replay, remote CI or full multiplication formalization claimed." +} diff --git a/research/r439-helper468-late-cut/VERIFY.json b/research/r439-helper468-late-cut/VERIFY.json new file mode 100644 index 0000000000..c6098a7c02 --- /dev/null +++ b/research/r439-helper468-late-cut/VERIFY.json @@ -0,0 +1,50 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/r439-helper468-late-cut/inputs/PR589-WORD.json.gz", + "research/r439-helper468-late-cut/inputs/PR589-NOTICE.md", + "research/r439-helper468-late-cut/inputs/PR1256-CERTIFICATE.json", + "research/r439-helper468-late-cut/LICENSE" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-S", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 90, + "checks": "Complete 4874-cut rational geometry/inverse replay and predecessor initial-cut fixture." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-S", + "-B", + "{package}/independent.py" + ], + "timeout_seconds": 90, + "checks": "Independent set scalar replay and explicit integer minor/normal geometry witnesses." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-S", + "-B", + "{package}/test_package.py" + ], + "timeout_seconds": 180, + "checks": "Ten mathematical/rejection groups, inverse updates, outside-frame span monotonicity, exact B88 transition, false certificates, omitted cuts/MOVEs and portable export." + } + ] +} diff --git a/research/r439-helper468-late-cut/engine.py b/research/r439-helper468-late-cut/engine.py new file mode 100644 index 0000000000..86895f4145 --- /dev/null +++ b/research/r439-helper468-late-cut/engine.py @@ -0,0 +1,303 @@ +# SPDX-License-Identifier: Apache-2.0 +# Cinna Davis, with substantial OpenAI Codex assistance. +"""Exact late-cut ledger; footprint argument follows Ross Richardson / PR1256.""" +from collections import Counter +from fractions import Fraction +from functools import lru_cache +import hashlib +import itertools +import json +import math + +HELPER = 468 + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def bits(mask): + while mask: + bit = mask & -mask + yield bit.bit_length()-1 + mask ^= bit + + +def invert(matrix): + left = matrix[:] + right = [1 << i for i in range(len(left))] + for col in range(len(left)): + pivot = next((i for i in range(col, len(left)) if left[i] & (1 << col)), None) + require(pivot is not None, "singular scalar boundary") + left[col], left[pivot] = left[pivot], left[col] + right[col], right[pivot] = right[pivot], right[col] + for i in range(len(left)): + if i != col and left[i] & (1 << col): + left[i] ^= left[col] + right[i] ^= right[col] + require(left == [1 << i for i in range(len(left))], "inverse residual") + return right + + +def rref(vectors): + rows = [] + for vector in vectors: + row = list(map(Fraction, vector)) + for pivot, basis in rows: + coefficient = row[pivot] + row = [a-coefficient*b for a, b in zip(row, basis)] + pivot = next((i for i, value in enumerate(row) if value), None) + if pivot is None: + continue + coefficient = row[pivot] + row = [value/coefficient for value in row] + rows = [(p, [a-basis[pivot]*b for a, b in zip(basis, row)]) + for p, basis in rows] + rows.append((pivot, row)) + rows.sort() + return tuple(tuple(row) for _, row in rows) + + +def contains_basis(small, large): + pivots = [(next(i for i, x in enumerate(row) if x), row) for row in large] + for vector in small: + row = list(vector) + for pivot, basis in pivots: + coefficient = row[pivot] + row = [a-coefficient*b for a, b in zip(row, basis)] + if any(row): + return False + return True + + +class Geometry: + def __init__(self, word): + self.word = word + self.bases = [rref(word["lines"][i] for i in frame) for frame in word["frames"]] + + def rank(self, frame): + return len(self.bases[frame]) + + @lru_cache(maxsize=None) + def contained(self, small, large): + return contains_basis(self.bases[small], self.bases[large]) + + @lru_cache(maxsize=None) + def join(self, frame_ids): + return rref(row for f in frame_ids for row in self.bases[f]) + + @lru_cache(maxsize=None) + def join_contained(self, frame_ids, terminal): + return contains_basis(self.join(frame_ids), self.bases[terminal]) + + def separation(self, frame_ids, terminal): + """A rational annihilator of the target frame detecting the join.""" + import math + large = self.bases[terminal] + pivots = {next(i for i, x in enumerate(row) if x): row for row in large} + for free in range(self.word["h"]): + if free in pivots: + continue + normal = [Fraction(i == free) for i in range(self.word["h"])] + for p, row in pivots.items(): + normal[p] = -row[free] + scale = 1 + for x in normal: + scale = math.lcm(scale, x.denominator) + normal = [int(x*scale) for x in normal] + for f in frame_ids: + for line in self.word["frames"][f]: + dot = sum(x*y for x, y in zip(normal, self.word["lines"][line])) + if dot: + return dict(normal=normal, frame=f, line=line, dot=dot) + raise ValueError("no separating normal for an excluded join") + + +def add(rows, inverse, target, source): + require(target != source, "self ADD") + rows[target] ^= rows[source] + tbit, sbit = 1 << target, 1 << source + for i, row in enumerate(inverse): + if row & tbit: + inverse[i] ^= sbit + + +def initial_boundary(word, geometry): + n, v = 2*word["v"]+word["R"], word["v"] + require((n, v, word["h"]) == (661, 111, 8), "wrong pinned dimensions") + frames = word["start"][:] + rows = [1 << i for i in range(n)] + for section in ("D", "A"): + for frame, target, sources in word[section]: + for register in [target, *sources]: + require(geometry.contained(frames[register], frame), "prefix frame descent") + frames[register] = frame + for source in sources: + require(target != source, "prefix self ADD") + rows[target] ^= rows[source] + require(all(frames[i] == 0 for i in range(v, 2*v)), "wrong scatter target frame") + for i, sources in enumerate(word["scatter"]): + for index in sources: + rows[v+i] ^= rows[word["ret"][index]] + require(len(word["ret"]) == 9, "retained COPY/ERASE inventory changed") + return frames, rows, invert(rows) + + +def suffix_events(word, initial, geometry): + frames = initial[:] + events = [] + for section in ("B", "C"): + for gate, (frame, target, sources) in enumerate(word[section]): + require(len(set([target, *sources])) == len(sources)+1, "invalid gate operands") + for register in [target, *sources]: + previous = frames[register] + require(geometry.contained(previous, frame), "suffix frame descent") + if previous != frame: + require(geometry.rank(frame) > geometry.rank(previous), "redundant frame alias") + events.append([section, gate, "MOVE", register, previous, frame]) + frames[register] = frame + for offset, source in enumerate(sources): + events.append([section, gate, "ADD", target, source, offset]) + for register, frame in enumerate(word["final"]): + previous = frames[register] + require(geometry.contained(previous, frame), "final frame descent") + if previous != frame: + require(geometry.rank(frame) > geometry.rank(previous), "redundant final alias") + events.append(["final", register, "MOVE", register, previous, frame]) + frames[register] = frame + return events + + +def inspect_cut(word, geometry, frames, rows, inverse, event_index): + current = frames[HELPER] + record = dict(cut=event_index, helper_frame=current, helper_rank=geometry.rank(current)) + if record["helper_rank"] > 7: + record["reason"] = "helper_already_rank8" + return record + restore = inverse[HELPER] + dirt = sum(1 << i for i, row in enumerate(rows) if row & (1 << HELPER)) + participants = restore | dirt | (1 << HELPER) + frame_ids = tuple(sorted({frames[i] for i in bits(participants)})) + joined = geometry.join(frame_ids) + record.update(restore_hex=format(restore, "x"), dirt_hex=format(dirt, "x"), + participants_hex=format(participants, "x"), join_frames=list(frame_ids), + join_rank=len(joined)) + if len(joined) > 7: + record["reason"] = "footprint_rank8" + return record + lost, illegal = [], [] + for target in range(word["v"], 2*word["v"]): + if geometry.join_contained(frame_ids, word["final"][target]): + continue + if participants & (1 << target): + illegal.append(target) + missing = (inverse[target] ^ inverse[target-word["v"]]) & participants + if missing: + lost.append([target, format(missing, "x")]) + record.update(illegal_target_promotions=illegal, lost_target_inputs=lost) + record["reason"] = ("illegal_target_promotion" if illegal else + "lost_target_input" if lost else "not_excluded") + return record + + +def ledger_bytes(records): + return "".join(json.dumps(row, sort_keys=True, separators=(",", ":"))+"\n" + for row in records).encode() + + +def determinant(matrix): + a = [list(map(Fraction, row)) for row in matrix] + value = Fraction(1) + for column in range(len(a)): + pivot = next((i for i in range(column, len(a)) if a[i][column]), None) + if pivot is None: + return Fraction(0) + if pivot != column: + a[column], a[pivot] = a[pivot], a[column] + value = -value + entry = a[column][column] + value *= entry + for i in range(column+1, len(a)): + factor = a[i][column]/entry + a[i] = [x-factor*y for x, y in zip(a[i], a[column])] + return value + + +def geometry_witness(word, geometry, frame_ids): + union = sorted({i for f in frame_ids for i in word["frames"][f]}) + chosen = [] + for i in union: + if len(rref(word["lines"][j] for j in chosen+[i])) > len(chosen): + chosen.append(i) + dimension = len(chosen) + columns = next(c for c in itertools.combinations(range(word["h"]), dimension) + if determinant([[word["lines"][i][j] for j in c] for i in chosen])) + value = determinant([[word["lines"][i][j] for j in columns] for i in chosen]) + result = dict(frames=list(frame_ids), rank=dimension, basis_lines=chosen, + minor_columns=list(columns), minor_determinant=str(value)) + if dimension == 7: + joined = geometry.join(frame_ids) + pivots = {next(i for i, x in enumerate(row) if x): row for row in joined} + free = next(i for i in range(word["h"]) if i not in pivots) + normal = [Fraction(i == free) for i in range(word["h"])] + for p, row in pivots.items(): + normal[p] = -row[free] + scale = math.lcm(*(x.denominator for x in normal)) + normal = [int(x*scale) for x in normal] + divisor = math.gcd(*normal) + normal = [x//divisor for x in normal] + if next(x for x in normal if x) < 0: + normal = [-x for x in normal] + require(all(sum(x*y for x, y in zip(normal, word["lines"][i])) == 0 for i in union), + "join normal is not an annihilator") + result["annihilating_normal"] = normal + result["target208_separation"] = geometry.separation(frame_ids, word["final"][208]) + return result + + +def census(word): + geometry = Geometry(word) + frames, rows, inverse = initial_boundary(word, geometry) + events = suffix_events(word, frames, geometry) + records = [inspect_cut(word, geometry, frames, rows, inverse, 0)] + for index, event in enumerate(events, 1): + if event[2] == "MOVE": + _, _, _, register, previous, frame = event + require(frames[register] == previous, "MOVE chronology disagreement") + frames[register] = frame + else: + _, _, _, target, source, _ = event + add(rows, inverse, target, source) + records.append(inspect_cut(word, geometry, frames, rows, inverse, index)) + expected = [(1 << i) ^ ((1 << (i-word["v"])) if word["v"] <= i < 2*word["v"] else 0) + for i in range(len(rows))] + require(rows == expected and inverse == expected, "full dirty endpoint or inverse changed") + require(frames == word["final"], "final frame inventory changed") + counts = Counter(record["reason"] for record in records) + general_start = next(record["cut"] for record in records + if record["helper_rank"] == 8 or record.get("join_rank") == 8) + require(all(record["helper_rank"] == 8 or record.get("join_rank") == 8 + for record in records[general_start:]), "later proper-frame footprint unexpectedly returns") + frame_sets = sorted({tuple(record["join_frames"]) for record in records if "join_frames" in record}) + geometry_certificate = dict( + cases=[geometry_witness(word, geometry, frame_ids) for frame_ids in frame_sets], + full_frame=geometry_witness(word, geometry, (1,))) + summary = dict(helper=HELPER, registers=len(rows), targets=word["v"], cuts=len(records), + events=len(events), event_kinds=dict(Counter(e[2] for e in events)), + reasons=dict(sorted(counts.items())), not_excluded=[r["cut"] for r in records + if r["reason"] == "not_excluded"], + complete_forward_and_inverse_endpoint=True, + first_rank8_cut=next(r["cut"] for r in records if r["helper_rank"] == 8), + arbitrary_suffix_rank8_from_cut=general_start, + arbitrary_suffix_excluded_cuts=len(records)-general_start, + first_rank8_footprint_event=events[general_start-1], + earlier_two_sided_rank7_cuts=general_start, + eligible_current_rank_histogram=dict(Counter(r["helper_rank"] for r in records + if r["helper_rank"] <= 7)), + geometry_cases=len(frame_sets), + geometry_sha256=hashlib.sha256(json.dumps(geometry_certificate, sort_keys=True, + separators=(",", ":")).encode()).hexdigest(), + ledger_sha256=hashlib.sha256(ledger_bytes(records)).hexdigest(), + events_sha256=hashlib.sha256(json.dumps(events, separators=(",", ":")).encode()).hexdigest()) + return events, records, summary, geometry_certificate diff --git a/research/r439-helper468-late-cut/generated/CERTIFICATE.json b/research/r439-helper468-late-cut/generated/CERTIFICATE.json new file mode 100644 index 0000000000..173a6d5de6 --- /dev/null +++ b/research/r439-helper468-late-cut/generated/CERTIFICATE.json @@ -0,0 +1,39 @@ +{ + "arbitrary_suffix_excluded_cuts": 4697, + "arbitrary_suffix_rank8_from_cut": 177, + "complete_forward_and_inverse_endpoint": true, + "cuts": 4874, + "earlier_two_sided_rank7_cuts": 177, + "eligible_current_rank_histogram": { + "4": 890, + "6": 710, + "7": 134 + }, + "event_kinds": { + "ADD": 3563, + "MOVE": 1310 + }, + "events": 4873, + "events_sha256": "43717ad9dd0b268fc887de82572393c6bc3569b877aea270e5fe210c3960ae4f", + "first_rank8_cut": 1734, + "first_rank8_footprint_event": [ + "B", + 88, + "MOVE", + 208, + 0, + 152 + ], + "geometry_cases": 9, + "geometry_sha256": "9847f5ad492bec2ab7f2d1a233168245f93313962f4ad29289f58a33b5683817", + "helper": 468, + "ledger_sha256": "fa256db2c039bda75daec90dbb6446bdfd84de55d9c11cf3d0d2eb3fe1746b8c", + "not_excluded": [], + "reasons": { + "footprint_rank8": 1557, + "helper_already_rank8": 3140, + "illegal_target_promotion": 177 + }, + "registers": 661, + "targets": 111 +} diff --git a/research/r439-helper468-late-cut/generated/CUTS.jsonl b/research/r439-helper468-late-cut/generated/CUTS.jsonl new file mode 100644 index 0000000000..65b8cd25ad --- /dev/null +++ b/research/r439-helper468-late-cut/generated/CUTS.jsonl @@ -0,0 +1,4874 @@ 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+1,287 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +# Cinna Davis, with substantial OpenAI Codex assistance. +"""Set-valued scalar replay and integer minor/normal geometry certificates.""" +from collections import Counter +from functools import lru_cache +import gzip +import hashlib +import json +import math +from pathlib import Path +import sys + +HERE = Path(__file__).resolve().parent +HELPER = 468 + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def mask_hex(values): + return format(sum(1 << i for i in values), "x") + + +def primitive(row): + divisor = math.gcd(*row) + if not divisor: + return row + row = [x//divisor for x in row] + if next(x for x in row if x) < 0: + row = [-x for x in row] + return row + + +def integer_basis(vectors): + matrix = [primitive(list(row)) for row in vectors if any(row)] + if not matrix: + return () + rank = 0 + for col in range(len(matrix[0])): + pivot = next((i for i in range(rank, len(matrix)) if matrix[i][col]), None) + if pivot is None: + continue + matrix[rank], matrix[pivot] = matrix[pivot], matrix[rank] + selected = matrix[rank] + entry = selected[col] + for i, row in enumerate(matrix): + if i != rank and row[col]: + factor = row[col] + matrix[i] = primitive([entry*x-factor*y for x, y in zip(row, selected)]) + rank += 1 + return tuple(tuple(row) for row in matrix[:rank]) + + +def bareiss(matrix): + """Exact determinant using integer divisions; no rational elimination.""" + a = [row[:] for row in matrix] + if not a: + return 1 + sign, previous = 1, 1 + for col in range(len(a)-1): + pivot = next((i for i in range(col, len(a)) if a[i][col]), None) + if pivot is None: + return 0 + if pivot != col: + a[col], a[pivot] = a[pivot], a[col] + sign = -sign + entry = a[col][col] + for i in range(col+1, len(a)): + for j in range(col+1, len(a)): + numerator = a[i][j]*entry-a[i][col]*a[col][j] + quotient, remainder = divmod(numerator, previous) + require(remainder == 0, "nonexact Bareiss division") + a[i][j] = quotient + a[i][col] = 0 + previous = entry + return sign*a[-1][-1] + + +def inverse_sets(rows): + left = [set(row) for row in rows] + right = [{i} for i in range(len(rows))] + for col in reversed(range(len(rows))): + pivot = next((i for i in range(col+1) if col in left[i]), None) + require(pivot is not None, "independent singular boundary") + left[col], left[pivot] = left[pivot], left[col] + right[col], right[pivot] = right[pivot], right[col] + for i in range(len(rows)): + if i != col and col in left[i]: + left[i].symmetric_difference_update(left[col]) + right[i].symmetric_difference_update(right[col]) + require(left == [{i} for i in range(len(rows))], "independent inverse residual") + return right + + +class Geometry: + def __init__(self, word, certificate): + self.word = word + self.bases = [integer_basis(word["lines"][i] for i in frame) for frame in word["frames"]] + self.cases = {} + for case in [*certificate["cases"], certificate["full_frame"]]: + self.validate_case(case) + self.cases[tuple(case["frames"])] = case + for i in range(word["v"]): + target_frame = word["final"][word["v"]+i] + normal = word["lines"][i] + require(self.rank(target_frame) == 7 and any(normal), "target is not a hyperplane") + require(all(sum(x*y for x, y in zip(normal, word["lines"][j])) == 0 + for j in word["frames"][target_frame]), "wrong target normal") + require(self.rank(1) == 8 and all(word["final"][i] == 1 for i in range(661) + if not 111 <= i < 222), "non-target final contract changed") + + def rank(self, frame): + return len(self.bases[frame]) + + @lru_cache(maxsize=None) + def contained(self, small, large): + return len(integer_basis([*self.bases[small], *self.bases[large]])) == self.rank(large) + + def validate_case(self, case): + word = self.word + union = {i for f in case["frames"] for i in word["frames"][f]} + lines, columns, dimension = case["basis_lines"], case["minor_columns"], case["rank"] + require(dimension in (7, 8) and len(lines) == len(set(lines)) == dimension and + set(lines) <= union and len(columns) == len(set(columns)) == dimension and + all(0 <= i < 8 for i in columns), "bad determinant witness dimensions") + value = bareiss([[word["lines"][i][j] for j in columns] for i in lines]) + require(value != 0 and str(value) == case["minor_determinant"], "minor witness disagreement") + if dimension == 7: + normal = case["annihilating_normal"] + require(len(normal) == 8 and any(normal) and + all(sum(x*y for x, y in zip(normal, word["lines"][i])) == 0 for i in union), + "invalid rank-seven upper-bound normal") + witness = case["target208_separation"] + target = word["final"][208] + require(witness["frame"] in case["frames"] and + witness["line"] in word["frames"][witness["frame"]] and + len(witness["normal"]) == 8 and any(witness["normal"]), "invalid separating witness") + require(all(sum(x*y for x, y in zip(witness["normal"], word["lines"][i])) == 0 + for i in word["frames"][target]), "separator does not annihilate target208") + value = sum(x*y for x, y in zip(witness["normal"], word["lines"][witness["line"]])) + require(value != 0 and value == witness["dot"], "separator does not detect the join") + + def join_rank(self, frames): + require(frames in self.cases, "missing explicit geometry case") + return self.cases[frames]["rank"] + + def join_contained_in_target(self, frames, target): + normal = self.word["lines"][target-self.word["v"]] + return all(sum(x*y for x, y in zip(normal, self.word["lines"][i])) == 0 + for i in self.cases[frames]["basis_lines"]) + + +def replay(word, geometry): + n, v = 661, 111 + frames = word["start"][:] + rows = [{i} for i in range(n)] + for section in ("D", "A"): + for frame, target, sources in word[section]: + for register in [target, *sources]: + require(geometry.contained(frames[register], frame), "independent prefix descent") + frames[register] = frame + for source in sources: + rows[target].symmetric_difference_update(rows[source]) + require(all(frames[i] == 0 for i in range(v, 2*v)), "independent scatter frame changed") + snapshots = [set(rows[i]) for i in word["ret"]] + require(len(snapshots) == 9, "wrong retained snapshots") + for i, sources in enumerate(word["scatter"]): + for index in sources: + rows[v+i].symmetric_difference_update(snapshots[index]) + inverse = inverse_sets(rows) + events, records = [], [] + + def cut(): + current = frames[HELPER] + record = dict(cut=len(events), helper_frame=current, helper_rank=geometry.rank(current)) + if record["helper_rank"] > 7: + record["reason"] = "helper_already_rank8" + records.append(record) + return + restore = inverse[HELPER] + dirt = {i for i, row in enumerate(rows) if HELPER in row} + participants = restore | dirt | {HELPER} + frame_ids = tuple(sorted({frames[i] for i in participants})) + dimension = geometry.join_rank(frame_ids) + record.update(restore_hex=mask_hex(restore), dirt_hex=mask_hex(dirt), + participants_hex=mask_hex(participants), join_frames=list(frame_ids), join_rank=dimension) + if dimension == 8: + record["reason"] = "footprint_rank8" + else: + illegal, lost = [], [] + for target in range(v, 2*v): + if geometry.join_contained_in_target(frame_ids, target): + continue + if target in participants: + illegal.append(target) + missing = (inverse[target] ^ inverse[target-v]) & participants + if missing: + lost.append([target, mask_hex(missing)]) + record.update(illegal_target_promotions=illegal, lost_target_inputs=lost) + record["reason"] = ("illegal_target_promotion" if illegal else + "lost_target_input" if lost else "not_excluded") + records.append(record) + + cut() + for section in ("B", "C"): + for gate, (frame, target, sources) in enumerate(word[section]): + require(len(set([target, *sources])) == len(sources)+1, "independent gate operands") + for register in [target, *sources]: + previous = frames[register] + require(geometry.contained(previous, frame), "independent suffix descent") + if previous != frame: + require(geometry.rank(frame) > geometry.rank(previous), "independent redundant MOVE") + frames[register] = frame + events.append([section, gate, "MOVE", register, previous, frame]) + cut() + for offset, source in enumerate(sources): + rows[target].symmetric_difference_update(rows[source]) + for row in inverse: + if target in row: + row.symmetric_difference_update({source}) + events.append([section, gate, "ADD", target, source, offset]) + cut() + for register, frame in enumerate(word["final"]): + previous = frames[register] + require(geometry.contained(previous, frame), "independent final descent") + if previous != frame: + require(geometry.rank(frame) > geometry.rank(previous), "independent final alias") + frames[register] = frame + events.append(["final", register, "MOVE", register, previous, frame]) + cut() + expected = [{i, i-v} if v <= i < 2*v else {i} for i in range(n)] + require(rows == expected and inverse == expected and frames == word["final"], + "independent full dirty/inverse endpoint changed") + return events, records + + +def main(): + try: + sources = json.loads((HERE / "SOURCES.json").read_text()) + for source in sources["archives"]: + name = Path(source["local_path"]) + require(not name.is_absolute() and ".." not in name.parts, "unsafe archive path") + require(hashlib.sha256((HERE/name).read_bytes()).hexdigest() == source["sha256"], "source archive drift") + word = json.loads(gzip.decompress((HERE / "inputs/PR589-WORD.json.gz").read_bytes())) + geometry_certificate = json.loads((HERE / "generated/GEOMETRY.json").read_text()) + geometry = Geometry(word, geometry_certificate) + events, records = replay(word, geometry) + require(events == json.loads((HERE / "generated/EVENTS.json").read_text()), "independent event coverage changed") + recorded = [json.loads(row) for row in (HERE / "generated/CUTS.jsonl").read_text().splitlines()] + require(records == recorded, "independent complete cut ledger changed") + raw = "".join(json.dumps(row, sort_keys=True, separators=(",", ":"))+"\n" for row in records).encode() + counts = Counter(row["reason"] for row in records) + general_start = next(row["cut"] for row in records + if row["helper_rank"] == 8 or row.get("join_rank") == 8) + require(all(row["helper_rank"] == 8 or row.get("join_rank") == 8 + for row in records[general_start:]), "independent late footprint returns below eight") + summary = dict(helper=HELPER, registers=661, targets=111, cuts=len(records), events=len(events), + event_kinds=dict(Counter(e[2] for e in events)), reasons=dict(sorted(counts.items())), + not_excluded=[row["cut"] for row in records if row["reason"] == "not_excluded"], + complete_forward_and_inverse_endpoint=True, + first_rank8_cut=next(row["cut"] for row in records if row["helper_rank"] == 8), + arbitrary_suffix_rank8_from_cut=general_start, + arbitrary_suffix_excluded_cuts=len(records)-general_start, + first_rank8_footprint_event=events[general_start-1], + earlier_two_sided_rank7_cuts=general_start, + eligible_current_rank_histogram=dict(Counter(row["helper_rank"] for row in records + if row["helper_rank"] <= 7)), + geometry_cases=len(geometry_certificate["cases"]), + geometry_sha256=hashlib.sha256(json.dumps(geometry_certificate, sort_keys=True, + separators=(",", ":")).encode()).hexdigest(), + ledger_sha256=hashlib.sha256(raw).hexdigest(), + events_sha256=hashlib.sha256(json.dumps(events, separators=(",", ":")).encode()).hexdigest()) + require(json.loads(json.dumps(summary)) == json.loads((HERE / "generated/CERTIFICATE.json").read_text()), + "independent summary changed") + require(not summary["not_excluded"], "independent cut survives") + print("PASS_INDEPENDENT_R439_HELPER468 cuts=4874 excluded=4874 integer_geometry_cases=9 arbitrary_suffix_from=177") + except (OSError, ValueError, KeyError, TypeError) as error: + print("REJECT_INDEPENDENT_R439_HELPER468: " + str(error), file=sys.stderr) + return 1 + return 0 + + +if __name__ == "__main__": + raise SystemExit(main()) diff --git 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b/research/r439-helper468-late-cut/inputs/PR589-NOTICE.md new file mode 100644 index 0000000000..b589500c8a --- /dev/null +++ b/research/r439-helper468-late-cut/inputs/PR589-NOTICE.md @@ -0,0 +1,62 @@ +# Notice + +Apache-2.0 (`LICENSE`, copied from #493's package). Prepared by eumemic with substantial Anthropic Claude +assistance. + +## New in this package + +- `code/gen_p3.py` (the generator of the punctured word: the L3 skeleton of #543 restricted to the live lines, the + pseudo-target totals, the phase-A mini-nodes and extra carriers), `code/pwordl.py` (word builder for a live subset + of the 120 lines; output in the bitE8/1 layout with the `ports_geom` and `punctured` fields introduced by #545), + `data/bitE8mut-p111.json.gz` (the word), `data/punct.json` (its frozen parameters), `discovery/choose.py` and + `discovery/search.py` (the nomination of P and of the parameters; not run by `verify.sh`). +- `code/gen_p3.py` carries `derive`, `ex_part` and `plan_thirds` from #543's `code/gen_l3.py` (eumemic), and + `data/plan-l3.json` is #543's CP-SAT plan, unchanged. `code/nodeopt.py`, `code/planio.py`, `code/mutants.py`, + `code/mutrec_b.py` and `code/provenance.py` are #543's files, unchanged. +- `code/xcheck_p.py`: #543's independent checker `code/xcheck.py` with nine listed edits for v <= 120 live labels + (root-line enumeration of the lattice, frame closure and target frames over the live labels) and a new part T (the + frame and COPY rank of every retained total at the scatter, and whether it is the hyperplane of a punctured line). +- `code/mutants_p.py` (punctured-design controls), `code/adapt9p.py` (#510's nine-stage files parameterised for + v <= 120 and any copy ranks, the way #545's `adapt.py` parameterises #493's eleven-stage files), `code/cited.py`, + `code/receipt_kappa.py`, `code/summary.py`, `verify.sh`, `EXPECTED.json`, `DEPENDS.json`, `requirements.txt`, + `data/complex-b.json`, `data/selection9-p111.json` and `data/hosting11-p111.json` (frozen nominations of #442's + hosting programme, rediscovered by `verify.sh`), `.github/workflows/e8-bit-p111.yml`. + +## Vendored, byte-identical (git blob ids in `SOURCE-pr*.json`, checked by `code/provenance.py`) + +- **PR #510 (DreamingOfClouds, with Claude Opus 5.5 via Claude Code), commit 64edee1** (`vendor/pr510/`): the same 19 + files as #543's package (#510's nine-stage chain with the files it vendors from #463, #443, #442 and #315, and #503's + R480 word). Their notices are listed in #543's NOTICE and in the files. +- **PR #545 (DreamingOfClouds, with Claude Opus 5.5 via Claude Code; draft), commit 376426f** (`vendor/pr545/`): + `code/adapt.py` and `code/punct_cfg.py`, run unchanged on this package's word; `data/bitE8mut-v111-r489.json.gz`, + `data/hosting-v111-r489.json` and `EXPECTED.json` (a control). +- **PR #548 (Dugongue), commit 66dbc2b** (`data/complex/pr548/`): `EXPECTED.json` and `evidence/EXACT-ASSEMBLY.json`. +- **PR #544 (chafreaky, with OpenAI Codex assistance), commit 4858bb3** (`data/complex/pr544/`): `EXPECTED.json` and + the Linux exact-assembly receipt. +- **PR #535 (icekylinx, with GPT-6 Astra assistance), commit 8b758a1** (`data/complex/pr535/`): `EXPECTED.json` and + `evidence/audit/EXACT-ASSEMBLY-PR493.json`. + +## Used from main, unchanged (pinned in `DEPENDS.json`) + +- `research/e8-bit-carrier-skeleton` (PR #493, eumemic): the skeleton modules and D4 partition the generator imports, + #370's checker (run here in #545's v <= 120 form), the official cohort checkers, `gram_frames.py`, the record + exporter, the geometries and the eleven-stage chain that #545's `adapt.py` parameterises, #442's hosting programme, + the R489 word, the control receipts and #315's engines. +- `research/direct-delivery504-global/EXPECTED.json` (PR #531, icekylinx): its complex b and kappa. + +## Cited, not rebuilt + +Complex coarse savings in `data/complex-b.json`, each bound to its PR's receipt by `code/cited.py`: PR #548 (primary; +open), PR #544 and PR #535 (open), PR #531 (merged), and PR #484, #471 and #458 (controls). + +## Ideas used + +- PR #545 (DreamingOfClouds): the punctured-star unit. Nine lines are neither sources nor targets; each retained total + is a pseudo-target that reads what the removed target would read, at frame rank 7, so the decoder constant is 63; + the rank-mass identity with v and the decoder constant as parameters; the parameterisation of the hub chain. +- PR #543 (eumemic): the R420 L3 skeleton with keepers read by targets and rewritten in phase B. +- PR #493 (eumemic), PR #503 and #510 (DreamingOfClouds), PR #425 (Zhihao Chen / jacklightChen), PR #370 (Dylan Crow), + PR #472, #445, #443 (chafreaky), PR #442 (DaysSky), PR #463 and #315 (DreamingOfClouds), PR #386 (Zhihao Chen): the + skeleton, the scalar-interface lemma, the format, and the pricing pipelines. +- PR #523 (icekylinx): the puncture pattern on the complex side, cited by #545. +- Jacob Sussman introduced the E8 unit. diff --git a/research/r439-helper468-late-cut/inputs/PR589-WORD.json.gz b/research/r439-helper468-late-cut/inputs/PR589-WORD.json.gz new file mode 100644 index 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