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{"admissible_edges":[{"dimensions":[9],"roles":[0,1]},{"dimensions":[9],"roles":[0,2]},{"dimensions":[9],"roles":[1,2]}],"all_concave_prices_certified":true,"coefficients":[-1,1],"contacts_bases":[[1,2,4,8,16,32,64,128,256],[1,2,4,8,16,32,64,128,256]],"ends_bases":[[1,2,4,8,16,32,64,128,256],[1,2,4,8,16,32,64,128,256],[1,2,4,8,16,32,64,128,256]],"field_partitions":[[[]],[[1]],[[]]],"incumbent_partition":[1],"index":12655,"mandatory_bridges":[],"phase":"cleanup_tail","relaxed_partitions":[[1]],"required_dimension_sets":[[[9]],[[9]],[[9]]],"roles":[40,18,226],"starts_bases":[[1,2,4,8,16,32,64,128,256],[1,4,10,16,34,64,128,256],[1,2,4,8,16,32,64,128,256]]} + ] +} diff --git a/research/receiver-contact-floor/README.md b/research/receiver-contact-floor/README.md new file mode 100644 index 0000000000..f29e9c6f38 --- /dev/null +++ b/research/receiver-contact-floor/README.md @@ -0,0 +1,260 @@ +# Arbitrary-length contact floor for PR4470 receiver windows + +**Result (author-checked scoped proof and exact certificate):** none of the 128 +eligible forward receiver windows of the pinned PR4470 construction admits a +cheaper paid rank profile through a finite scalar-shear word on the same three +persistent fields, with the same monotone entrance/exit frame contract. This +holds for **every price `r^t`, `0 < t <= 1`**, including the predecessor's +`t = 1 - 0.00302015`. Word length and nonzero scalar coefficients are unrestricted. +The original two-shear word attains the lower bound in each window. + +This closes the explicit arbitrary-length gap in +[#4567](https://github.com/CrocSwap/integer-mult-bounds/pull/4567), following +[#4546](https://github.com/CrocSwap/integer-mult-bounds/pull/4546). It uses necessary +information-flow contacts and graph bridges, rather than another word census. +It is **not** a global supplier ceiling, a new kappa, or supplier admission. +Overlapping window conclusions cannot be added. + +Concurrent investigations [#4572](https://github.com/CrocSwap/integer-mult-bounds/discussions/4572), +[#4573](https://github.com/CrocSwap/integer-mult-bounds/discussions/4573), and +[#4577](https://github.com/CrocSwap/integer-mult-bounds/discussions/4577) pursue +the same conclusion through finite-state relaxations. They appeared after the +initial overlap snapshot and were found before publication. This package is a +parallel static-contact proof/checker with no priority claim; it does not claim +to have reviewed their code or to provide independent human review. + +## Contract and statement + +Fields are `a, b, x`, numbered `0, 1, 2`. They contain arbitrary independent +initial data. The logical endpoint is + + a' = a + ca*x, b' = b + cb*x, x' = x, ca, cb in {-1, 1}. + +A candidate uses any finite sequence `y_i += c*y_j`, `i != j`, with nonzero +scalar `c` (over the rationals, or any characteristic-zero field), and has that +same endpoint. Each field has an initial binary subspace `S_i` and final +subspace `E_i` of `F_2^9`. Its frames grow by inclusion. Both operands of every +shear occupy one common frame. Every positive dimension increment, including +the last movement to `E_i`, is charged as a separate child rank. Additional +nonnegative scalar costs are omitted in the candidate's favor. +The scalar endpoint is evaluated in transported logical coordinates: a frame +movement changes representation, preserving the field's scalar coefficient +vector. This is the common-frame model used in #4546/#4567. + +Only these three fields are available. Extra or owned fields, a decreasing +frame step, a changed boundary, internal warps, and changes across nonadjacent +or multiple windows are outside the statement. This package does not claim a +backward-orientation result or recheck the full native/phase/outer construction. + +More generally the proof works for any nonnegative concave price `f` on integer +ranks `0,...,9`, with `f(0)=0`. The machine check uses only exact set operations +and integer inequalities; no logarithmic approximation or sampled exponent +stands in for the quantified price statement. + +## Proof + +**1. Admissible contacts and forced edges.** A contact between fields `i,j` +has a common frame `F` satisfying + + S_i + S_j <= F <= E_i intersect E_j. (1) + +Define the undirected admissible-contact graph `G` by including `ij` exactly +when the left subspace is contained in the right. Every used contact lies on +an edge of `G`. The graph of contacts actually used must connect `x` to both +receivers: otherwise the component not containing `x` cannot acquire any +coefficient of the arbitrary initial `x`. Thus it is a connected spanning +subgraph of `G`. Every bridge of `G` must be used at least once. For such an +edge, each incident field must visit a contact dimension in + + [dim(S_i + S_j), dim(E_i intersect E_j)]. (2) + +This conclusion is independent of word length, coefficient size, cancellations, +and the direction of a contact. The source windows have either a triangle +(96 cases) or a two-edge tree (32 cases). + +**2. A contact carrying original `x`.** At any time, if a field's current +logical value has a nonzero coefficient of initial `x`, its current frame +contains `S_x`. This is an induction: it is true initially; monotone moves +preserve it; and a shear's common frame contains the old frames of both +operands. A newly nonzero coefficient must come from an operand with a nonzero +coefficient. Cancellation can remove a coefficient but cannot violate the +implication. The source and target of a shear have distinct roles; all data +are arbitrary, so this coefficient argument is legitimate. + +Each receiver starts with coefficient zero and finishes with coefficient +`ca` or `cb`, which is nonzero. At a contact where it first acquires original +`x`, the common frame contains `S_x`. The field `x` itself must participate in +some contact, or no receiver could acquire its initial value; any such contact +also contains `S_x`. Consequently **each of the three fields** has at least +one contact on an incident edge `ij` with dimension in + + [dim(S_i + S_j + S_x), dim(E_i intersect E_j)], (3) + +where the interval is included only when the subspace containment holds. +For a field, take the union over its incident edges. This is a necessary +dimension set, not an assertion that every dimension choice is realizable. + +**3. Finite coarsening of every arbitrarily long path.** On each field select +one witness contact for (3), and one for every incident bridge requirement +(2). Different requirements may use the same contact. Retain their dimensions +together with the entrance and exit dimensions; sort and remove duplicates. +Successive differences give a partition of `dim(E_i)-dim(S_i)`. + +The actual paid path refines that partition. For a concave `f` with `f(0)=0`, +`f(u)+f(v) >= f(u+v)` for nonnegative `u,v` in the domain (apply concavity +between 0 and `u+v` twice). Therefore coarsening cannot increase the bill. +Enumerating the finite dimension choices from (2),(3) contains a coarsening +of every actual path, regardless of its length. Ignoring simultaneous frame +incidences, scalar endpoint feasibility, and contact order only enlarges this +relaxation. The checker never asserts those relaxed choices are constructions. + +**4. Exact comparison for every concave price.** Let `P` be the incumbent's +list of positive ranks and `Q` any relaxed coarsened list. The certificate +checks equal rank mass and, for every integer `k=1,...,9`, + + sum_{r in P} min(r,k) <= sum_{r in Q} min(r,k). (4) + +These inequalities imply `sum f(P) <= sum f(Q)`. To see this without any +numerical exponent calculation, set `d_k=f(k)-f(k-1)` and use + + f(r) = r*d_9 + sum_{k=1}^8 (d_k-d_{k+1})*min(r,k). + +Concavity makes every `d_k-d_{k+1}` nonnegative. The linear term cancels by +equal rank mass; (4) handles the rest. The checker can stop at the largest +rank in either list, since subsequent inequalities are equal rank-mass +identities. Combining steps 3 and 4 gives + + incumbent cost <= relaxed coarsening cost <= actual cost. + +All 128 reconstructed incumbents have legal nested frames, the required +two-shear endpoint, and an attained partition in the relaxation. Thus the +minimum is attained by the incumbent. This last assertion is per window; +it does not combine incompatible changes in overlapping windows. + +## Why both necessary constraints matter + +Window 10557 has entrance dimensions `(0,0,1)` and exit dimensions `(2,1,1)`. +Merely requiring each field to participate would allow a spurious `(2,1)` +bill in place of the incumbent `(1,1,1)`. The contact that supplies original +`x` must already contain its rank-one entrance, forcing the split. + +In window 11073, the receiver/source entrance dimensions are `(2,4,2)` and +exit dimensions `(3,4,4)`. The first receiver cannot meet the second, whose +entrance has dimension four. The two source-receiver edges are both bridges. +The source must pass through dimension three to reach the first receiver and +then dimension four to reach the second, so its rank-two growth cannot be +merged into one payment. Dropping the bridge constraint again admits the +false optimistic partition `(2,1)` instead of `(1,1,1)`. + +## Evidence and reproduction + +Base: canonical main `f626db5c3a3d781d8f7695038776c621651f75e1`, priority +revision 7. `SOURCES.json` pins the seven executable/data inputs needed by +`research/joint-helper-lattice/native_joint.py:construct`, including its two +compressed original artifacts. They are authenticated **before** construction +in an isolated Python process with a fresh bytecode cache. No #4546/#4567 +acceptance, enumeration, interval, or relaxation function is imported. + +The source constructor is reused for data, so this is not an independent +implementation or validation of that constructor or the complete supplier. +The new window extraction, floor, concave comparison, and controls are separate +code. The pinned constructor is small enough for this bounded replay; its +expensive full native/phase `run()` path is not invoked. + +`CERTIFICATE.json` contains every window's index, phase, roles, signs, actual +binary bases, incumbent partition, admissible contacts, bridge requirements, +and every coarsened partition. The normal verifier compares every field to +fresh output and does not rewrite the certificate. + +```sh +python -B scripts/research_package.py --package research/receiver-contact-floor +python -I -O -B research/receiver-contact-floor/verify.py +``` + +CPython 3.12.0 on Windows; standard library only. Direct replay is about two +seconds on the contribution host. Expected status: `PASS_RECEIVER_CONTACT_FLOOR`. + +Registered and optimized replays passed, as did committed-byte comparison and +an isolated Git-free export replay. In the private exported copy, changing a +rank, changing a certificate boolean to an integer, deleting a certificate +field, and modifying/removing the constructor were all rejected. These are +local validation results, not a claim about upstream CI or formal acceptance. +The portable replay can be repeated with `scripts/export_research_package.py` +as described in `docs/research/package-export.md`, followed by the second command +above in the extracted tree. + +| Evidence | Coverage | +| --- | --- | +| Source windows | 128 total: 123 phase B, 5 cleanup_tail | +| Admissible graphs | 96 triangles, 32 two-edge trees | +| Price check | Exact integer (4), every relaxed partition in every window | +| Geometric controls | All 84 unit-shear words of length at most four with endpoint `a+=x; b+=x`, against three small frame contracts | +| Actual control paths | 106, 15 and 2,868 (2,989 total), each with checked source-information invariant and an admissible coarsened lower bound | +| Essential-rule ablations | Remove (3) at 10557 or bridges at 11073: the claimed floor fails | +| Scope-positive fixture | With all entrances zero and exits the same plane, `(2,1,1,1,1)` can improve to `(2,2,2)`; the checker admits it | +| Rejections | Decreasing frame contact and omitted rank mass | + +The tiny word enumeration tests the lemma's geometric relaxation; it is not +the reason the all-length statement follows. That statement follows from the +proof above plus the finite boundary comparisons. + +## Selection, overlap, limitations and credit + +Canonical investigation: [Discussion #4574](https://github.com/CrocSwap/integer-mult-bounds/discussions/4574), +taken from the #4567 all-length gap in the central handoff. The initial helper +refresh covered 355 open PRs and 3,470 Discussion records, with incomplete +sparse local-note coverage. The nearest results are #4546 (first twelve +windows through four unit shears), #4567 (all 128 through bounded lengths and +coefficient alphabets), and #4504 (chronological frame and invoice audit). +No claim of exhaustive historical novelty follows from that search. + +The submission refresh at 2026-10-22 08:06 UTC covered 357 open PRs and 3,489 +Discussion records. Canonical main was still the pinned base. In addition to +the concurrent claims credited above, #4567 had advanced to +`5ac594d1bc1e6d91f20ef8157f38bb9b29768bfd`, adding nonadjacent and single-contact +tests. Its all-length explanation remained unproved in that version. This +package retains its original adjacent forward-window scope and earlier +predecessor attribution; no scientific input was repinned. + +This is a refined `independent-moment` task: prove a previously unproved +cost implication at a specific newer caller, rather than recompute a root. +The family decision is to stop length/coefficient expansion within this +model. Reopening requires a changed boundary or operation model. This is +research guidance from a scoped result, not a change to the task catalogue, +the selected frontier (still conditional kappa 0.0023), or maintainers' decisions. + +The default orientation baseline was attempted but could not run in the sparse +checkout because the full selected package was omitted. The selected record, +review, source manifest and reproduction entry point were read; selected +cold replay, full native phases, backward windows, hosting, stock, precision, +and compiler/outer admission were not checked. No global lower bound or +practical multiplication speedup is established. The proof is author-checked, +not formally verified or independently reviewed by another agent or human. + +Credit Chris R / **Clear1nsight**, #4546 at +`55b8d34c82fc4df6499c5037e156db6e990b96fe`, for the fixed-boundary model and +initial ceiling; **Ryanson Jonathan / pinterbanget**, #4567 at +`50fedd98cda709707e4291c542e20ead96bcc786`, for the all-window extension and +explicit all-length question; **Cinna Davis / 1337isnot1337**, #4470 at +`b9a13c1673e0e9697de410de16e8bbf3207a7363`, for the retimed native data; +**zxv** for receiver sharing and productive helpers; and the original native, +Clifford, geometry, mixed-target (Jacob Alan Sussman), and outer contributors +retained in the source notices. The package-generator and replay infrastructure +retain Douglas Colkitt and their credited contributors' attribution. + +Prepared for **Mihir Srivastava**, with substantial **OpenAI Codex** assistance +for the argument, code and checks. Apache-2.0; predecessor files remain unchanged. + +## Open next questions + +- Can one additional, explicitly priced field avoid these mandatory contacts? + This matters because extra workspace changes the information paths. First + specify its entrance, exit, ownership and restoration, then test an optimistic + four-field floor on one window. Its costs are unknown, not zero. +- Can changing one boundary jointly with its actual neighboring consumer yield + a saving? First price a concrete combined interval, including the movement + paid outside these two gates. The fixed-boundary theorem does not cover that + contract, and overlapping local gains cannot simply be summed. +- An independent proof review can check steps 2 and 3 against the same common-frame + model and replay the seven pinned inputs. No further length census is needed + unless that review finds a gap or changes a hypothesis. diff --git a/research/receiver-contact-floor/SOURCES.json b/research/receiver-contact-floor/SOURCES.json new file mode 100644 index 0000000000..70a88c8c48 --- /dev/null +++ b/research/receiver-contact-floor/SOURCES.json @@ -0,0 +1,60 @@ +{ + "schema_version": 1, + "base_commit": "f626db5c3a3d781d8f7695038776c621651f75e1", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + }, + { + "path": "research/fresh-helper-boundary/CHANGES.json", + "usage": "input", + "git_blob": "45744fedd0e28967aa72586048b8bc0c72f419a9", + "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624" + }, + { + "path": "research/fresh-helper-boundary/native.py", + "usage": "input", + "git_blob": "1b36f6cb5f205c33bf48811e0b1b3621c55e8154", + "sha256": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29" + }, + { + "path": "research/joint-helper-lattice/PATCH.json", + "usage": "input", + "git_blob": "51304a6601061ed4e698f910b09135ef109555e3", + "sha256": "296d0e8c58cc70febe042c681ef30d6bb469818c0835fbcaac8aa8d330f5b727" + }, + { + "path": "research/joint-helper-lattice/native_joint.py", + "usage": "input", + "git_blob": "0315f80e2fdef5e0eef13e3e9b8f72066238164d", + "sha256": "50869b1bcad7493e6b4cb2a4cd5d2fd9a193a5921100483fa2c3f2c999ddfd46" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "usage": "input", + "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784", + "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "usage": "input", + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39" + }, + { + "path": "research/missing-join-frame/PATCH.json", + "usage": "input", + "git_blob": "f96d295d40014d4dd503f58eb3cdabcbb4b8e101", + "sha256": "9ab5328245ff02c9d0be21d39bcc375f50bc5d7909e9f7b9a3a9a6f812f5bd6e" + } + ] +} diff --git a/research/receiver-contact-floor/TASK.json b/research/receiver-contact-floor/TASK.json new file mode 100644 index 0000000000..abe6cef8a2 --- /dev/null +++ b/research/receiver-contact-floor/TASK.json @@ -0,0 +1,156 @@ +{ + "schema_version": 1, + "task_id": "independent-moment", + "priority_revision": 7, + "base_commit": "f626db5c3a3d781d8f7695038776c621651f75e1", + "original_card": { + "id": "independent-moment", + "question": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/staged-fourth-mixture-ceiling/README.md", + "research/r437-two-window-carrier/README.md" + ], + "methods": [ + "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.", + "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls." + ], + "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.", + "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.", + "allowed_variations": [ + "Reconstruct either a source ledger or a numeric enclosure with a different method." + ], + "scope_change_triggers": [ + "Importing the primary function and calling its output independent verification.", + "Calling an aggregate histogram or source archive an independently accepted physical supplier." + ], + "overlap_terms": [ + "independent moment", + "rank histogram", + "exact enclosure", + "2979", + "rank7 joint endframes", + "paired extraction", + "joint lowering", + "4088", + "4091", + "4067", + "staged544-mixed-fourth-entry", + "staged-fourth-mixture-ceiling", + "r437-two-window-carrier" + ], + "existing_checks": [ + { + "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.", + "evidence": "research/staged-fourth-mixture-ceiling/README.md", + "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.", + "status": "author-checked", + "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.", + "evidence": "research/r437-two-window-carrier/README.md", + "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.", + "status": "author-checked", + "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "refined", + "actual_scope": "Prove an arbitrary-length, arbitrary-scalar-coefficient paid-rank floor for all 128 forward PR4470 receiver windows under the fixed three-field monotone common-frame contract.", + "scope_change_reason": "Handoff-first selection: #4567 explicitly leaves an all-length explanation unproved after the finite #4546/#4567 censuses. This checks a missing cost implication at a newer caller, not another root evaluation.", + "bottleneck_link": "A source-bound sharp obstruction prevents more length/coefficient scans inside this fixed invoice and identifies boundary or field-count changes needed to escape it.", + "budget_minutes": 60, + "stop_rule": "Stop after exact contact floors and semantic controls on the 128 pinned boundaries; if the floor fails, report the residual contract instead of inferring a universal barrier from a finite search.", + "outcome": "negative-result", + "evidence": "README.md contains the quantified proof; CERTIFICATE.json records every exact boundary and concave-price comparison; verify.py authenticates seven data/constructor inputs, reconstructs all windows, and exercises 2989 actual tiny paths plus essential-rule ablations.", + "author": "Mihir Srivastava, with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance for reasoning, implementation, documentation and verification. One agent; no independent human or multi-agent proof review claimed.", + "open_questions": [ + { + "question": "Can one additional, fully priced field escape the contact floor?", + "why_it_matters": "An additional field can change the paths carrying source information.", + "first_step": "Specify one four-field window with entrance/exit, ownership, all frame costs and restoration, then derive an optimistic complete bill.", + "blocked_by": "No paid additional-field contract or favorable completed invoice is supplied." + }, + { + "question": "Can a changed boundary save work after its actual neighboring consumer is paid?", + "why_it_matters": "The theorem freezes boundaries; moving costs outside the window is not a gain.", + "first_step": "Choose one combined interval and account for every entrance, contact and exit movement.", + "blocked_by": "Joint neighboring-boundary realization and complete cost are not established." + }, + { + "question": "Does an independent review confirm the source-information and coarsening implications?", + "why_it_matters": "The all-length claim uses the written lemma, not finite word enumeration.", + "first_step": "Review README proof steps 2-3 and replay the seven pinned inputs.", + "blocked_by": "No independent reviewer has yet audited this package." + } + ], + "coordination_url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4574", + "predecessors": [ + { + "pr": 4546, + "head": "55b8d34c82fc4df6499c5037e156db6e990b96fe", + "credit": "Chris R / Clear1nsight: fixed-boundary relaxation and twelve-window ceiling" + }, + { + "pr": 4567, + "head": "50fedd98cda709707e4291c542e20ead96bcc786", + "credit": "Ryanson Jonathan / pinterbanget: all-window bounded census and all-length question" + }, + { + "pr": 4470, + "head": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "credit": "Cinna Davis: native retimed constructor, retained at the pinned main base" + } + ], + "overlap": { + "checked_at_utc": "2026-10-22T07:49:28Z", + "open_prs": 355, + "discussion_records": 3470, + "remote_pagination_complete": true, + "local_note_inventory_complete": false, + "limitation": "Sparse local notes; not an exhaustive historical novelty claim. Latest source PR heads were read directly." + }, + "orientation_baseline": "Attempted scripts/research_baseline.py; blocked by omitted selected package in sparse checkout. Read selected record, review, source manifest and reproduce command; no selected cold replay.", + "submission_refresh": { + "checked_at_utc": "2026-10-22T08:06:31Z", + "canonical_main": "f626db5c3a3d781d8f7695038776c621651f75e1", + "priority_revision": 7, + "open_prs": 357, + "discussion_records": 3489, + "remote_pagination_complete": true, + "local_note_inventory_complete": false, + "latest_pr4567_head": "5ac594d1bc1e6d91f20ef8157f38bb9b29768bfd", + "concurrent_claims": [ + 4572, + 4573, + 4577 + ], + "decision": "Continue as a parallel static mandatory-contact/bridge proof, complementary to concurrent finite-state approaches; no priority claim or claimed review of their packages. Preserve the frozen 128 adjacent forward-window baseline." + }, + "validation_environment": "CPython 3.12.0, Windows, standard library; registered replay, isolated optimized replay, committed bytes and private Git-free export replay passed. Private-export mutations of rank, boolean type, missing certificate field and modified/missing constructor were rejected." +} diff --git a/research/receiver-contact-floor/VERIFY.json b/research/receiver-contact-floor/VERIFY.json new file mode 100644 index 0000000000..5146b52509 --- /dev/null +++ b/research/receiver-contact-floor/VERIFY.json @@ -0,0 +1,27 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/fresh-helper-boundary/CHANGES.json", + "research/fresh-helper-boundary/native.py", + "research/joint-helper-lattice/PATCH.json", + "research/joint-helper-lattice/native_joint.py", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/missing-join-frame/PATCH.json" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Seven source hashes; 128 source-derived boundaries; exact all-concave-price floor; 2989 actual geometric paths; information/bridge ablations; changed-boundary positive case; nonmonotone and rank-mass controls; complete certificate comparison." + } + ] +} diff --git a/research/receiver-contact-floor/verify.py b/research/receiver-contact-floor/verify.py new file mode 100644 index 0000000000..0c52828d88 --- /dev/null +++ b/research/receiver-contact-floor/verify.py @@ -0,0 +1,344 @@ +#!/usr/bin/env python3 +"""Contact floors independent of the #4546/#4567 search engines. + +Mihir Srivastava with substantial OpenAI Codex assistance. Apache-2.0. +The inherited #4470 constructor supplies data only; README.md proves the bound. +""" +from collections import Counter +from functools import lru_cache +import hashlib +import itertools +import json +from pathlib import Path +import subprocess +import sys +import tempfile + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +CERTIFICATE = HERE / "CERTIFICATE.json" + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +@lru_cache(None) +def span(vectors): + values = {0} + for vector in vectors: + values |= {value ^ vector for value in tuple(values)} + return frozenset(values) + + +def join(*spaces): + return span(tuple(sorted(set().union(*spaces)))) + + +def dim(space): + need(len(space) > 0 and len(space) & (len(space) - 1) == 0, "subspace size") + return len(space).bit_length() - 1 + + +def basis(space): + result, generated = [], frozenset({0}) + for vector in sorted(space): + if vector not in generated: + result.append(vector) + generated = span(tuple(result)) + need(generated == space, "binary subspace") + return result + + +def authenticate_inputs(): + manifest = json.loads((HERE / "SOURCES.json").read_text(encoding="utf-8")) + pins = [row for row in manifest["files"] if row["usage"] == "input"] + need(len(pins) == 7, "seven constructor input pins") + for row in pins: + need(hashlib.sha256((ROOT / row["path"]).read_bytes()).hexdigest() == row["sha256"], + "source hash: " + row["path"]) + return manifest["base_commit"] + + +def construct(): + # A fresh cache namespace prevents a stale .pyc from replacing pinned source. + with tempfile.TemporaryDirectory(prefix="contact-floor-") as cache: + code = ("import json,sys;sys.path.insert(0,sys.argv[1]);import native_joint;" + "c,p,_,_,_=native_joint.construct();print(json.dumps([c,p['forward']]))") + run = subprocess.run( + [sys.executable, "-I", "-B", "-X", "pycache_prefix=" + cache, "-c", code, + str(ROOT / "research/joint-helper-lattice")], + check=True, capture_output=True, timeout=60) + return json.loads(run.stdout) + + +def participants(event): + if event[0] != "scalar": + return [] + operation = event[1] + return operation[1:3] if operation[0] in ("add", "copy") else operation[1:2] + + +def extract_windows(canonical, program): + """Read entrance, two contacts, and the next external use for each field.""" + frames = [span(tuple(b)) for b in canonical["frames"]] + events = [event for event in program if event[0] != "climb"] + current = list(canonical["start"]) + phase, windows = None, [] + for index, first in enumerate(events): + if first[0] == "phase": + phase = first[1] + if phase in ("B", "cleanup_tail") and index + 1 < len(events): + second = events[index + 1] + if first[0] == second[0] == "scalar" and first[1][0] == second[1][0] == "add": + f, g = first[1], second[1] + roles = (f[1], g[1], f[2]) # a, b, x + eligible = (f[2] == g[2] and all(r[0] == "L" for r in roles) + and len(set(map(tuple, roles))) == 3 + and f[3] in (-1, 1) and g[3] in (-1, 1) + and f[4] == g[4] == 1) + if eligible: + owners = [r[1] for r in roles] + starts = [frames[current[r]] for r in owners] + ends = [] + for role in roles: + label = canonical["final"][role[1]] + for later in events[index + 2:]: + if role in participants(later): + label = later[2] + break + if later[0] == "warp" and later[1] == role: + label = later[3] + break + ends.append(frames[label]) + windows.append({"index": index, "phase": phase, "roles": owners, + "coefficients": [f[3], g[3]], "starts": starts, "ends": ends, + "contacts": [frames[first[2]], frames[second[2]]]}) + if first[0] == "scalar": + for kind, role in participants(first): + if kind == "L": + current[role] = first[2] + elif first[0] == "warp": + current[first[1][1]] = first[4] + need(len({w["index"] for w in windows}) == len(windows), "unique window indices") + return windows + + +def path_partition(starts, ends, word, contacts): + need(len(word) == len(contacts), "one common frame per shear") + current, gaps = list(starts), [] + for (i, j, coefficient), contact in zip(word, contacts): + need(i != j and coefficient != 0, "nonzero two-field shear") + for role in (i, j): + need(current[role] <= contact <= ends[role], "monotone contact inside fixed exit") + if current[role] != contact: + gaps.append(dim(contact) - dim(current[role])) + current[role] = contact + for before, after in zip(current, ends): + need(before <= after, "monotone terminal movement") + if before != after: + gaps.append(dim(after) - dim(before)) + need(sum(gaps) == sum(map(dim, ends)) - sum(map(dim, starts)), "complete paid rank mass") + return tuple(sorted(gaps, reverse=True)) + + +def connected(edges): + reached = {2} + while True: + updated = reached | {v for edge in edges if reached.intersection(edge) for v in edge} + if updated == reached: + return len(reached) == 3 + reached = updated + + +def relaxed_partitions(starts, ends, *, use_information=True, use_bridges=True): + """Necessary contact dimensions only; no scalar word is enumerated.""" + need(all(s <= e for s, e in zip(starts, ends)), "nested boundaries") + edges = {} + for i, j in itertools.combinations(range(3), 2): + required, cap = join(starts[i], starts[j]), ends[i] & ends[j] + if required <= cap: + edges[i, j] = list(range(dim(required), dim(cap) + 1)) + need(connected(edges), "admissible contact graph must connect all fields") + bridges = [edge for edge in edges if not connected([e for e in edges if e != edge])] + field_choices, requirements_by_field = [], [] + for role in range(3): + # Each receiver must acquire original x; x must export it at some contact. + witnessed = set() + for i, j in edges: + if role not in (i, j): + continue + required = join(starts[i], starts[j], starts[2]) if use_information else join(starts[i], starts[j]) + cap = ends[i] & ends[j] + if required <= cap: + witnessed.update(range(dim(required), dim(cap) + 1)) + requirements = [sorted(witnessed)] + if use_bridges: + requirements += [edges[edge] for edge in bridges if role in edge] + need(all(requirements), "required contact has no feasible dimension") + choices = set() + for contacts in itertools.product(*requirements): + marks = sorted({dim(starts[role]), dim(ends[role]), *contacts}) + choices.add(tuple(sorted((b - a for a, b in zip(marks, marks[1:])), reverse=True))) + field_choices.append(sorted(choices)) + requirements_by_field.append(requirements) + partitions = sorted({tuple(sorted(sum(parts, ()), reverse=True)) + for parts in itertools.product(*field_choices)}) + return partitions, { + "admissible_edges": [{"roles": list(edge), "dimensions": ds} for edge, ds in edges.items()], + "mandatory_bridges": [list(edge) for edge in bridges], + "required_dimension_sets": requirements_by_field, + "field_partitions": [[list(p) for p in choices] for choices in field_choices], + } + + +def dominates(cheaper, dearer): + """Exact concave-price comparison, including equality at linear price.""" + if sum(cheaper) != sum(dearer): + return False + return all(sum(min(r, k) for r in cheaper) <= sum(min(r, k) for r in dearer) + for k in range(1, max((*cheaper, *dearer), default=0) + 1)) + + +IDENTITY = (1, 0, 0, 0, 1, 0, 0, 0, 1) + + +def act(matrix, gate): + i, j, coefficient = gate + result = list(matrix) + for column in range(3): + result[3 * i + column] += coefficient * matrix[3 * j + column] + return tuple(result) + + +def subspaces(ambient_dimension): + found = {frozenset({0})} + while True: + expanded = found | {join(s, frozenset({0, v})) for s in found + for v in range(1 << ambient_dimension)} + if expanded == found: + return sorted(found, key=lambda s: (len(s), sorted(s))) + found = expanded + + +def controls(windows): + by_index = {w["index"]: w for w in windows} + failures = {} + for index, disabled in [(10557, "use_information"), (11073, "use_bridges")]: + w = by_index[index] + old = path_partition(w["starts"], w["ends"], ((0, 2, 1), (1, 2, 1)), w["contacts"]) + candidates, _ = relaxed_partitions(w["starts"], w["ends"], **{disabled: False}) + failures[disabled] = [list(p) for p in candidates if not dominates(old, p)] + need(failures[disabled], "ablation must reveal missing cost: " + disabled) + need(not dominates((1,), (1, 1)), "rank-mass mismatch rejected") + zero, line, plane = span(()), span((1,)), span((1, 2)) + # Changed boundaries admit a cheaper path: the checker must not always return zero. + starts, ends = [zero] * 3, [plane] * 3 + word = ((0, 2, 1), (1, 2, 1)) + old = path_partition(starts, ends, word, (line, plane)) + better = path_partition(starts, ends, word, (plane, plane)) + candidates, _ = relaxed_partitions(starts, ends) + need(better in candidates and dominates(better, old) and not dominates(old, better), + "positive headroom in changed boundary fixture") + rejected = False + try: + path_partition([line, zero, line], [plane] * 3, word, [zero, plane]) + except ValueError: + rejected = True + need(rejected, "decreasing contact rejected") + + # Exhaust actual small geometric paths, not copies of the dimension rules. + gates = tuple((i, j, s) for i in range(3) for j in range(3) if i != j for s in (-1, 1)) + target = act(act(IDENTITY, word[0]), word[1]) + matching = [] + for length in range(5): + for candidate in itertools.product(gates, repeat=length): + matrix = IDENTITY + for gate in candidate: + matrix = act(matrix, gate) + if matrix == target: + matching.append(candidate) + need(len(matching) == 84, "small exact endpoint census") + full3 = span((1, 2, 4)) + fixtures = [(2, [zero, zero, line], [plane, line, line]), + (3, [line, full3, span((2,))], [plane, full3, full3]), + (2, [zero] * 3, [plane] * 3)] + checked = [] + for ambient, starts, ends in fixtures: + all_frames = subspaces(ambient) + candidates, _ = relaxed_partitions(starts, ends) + count = 0 + for candidate in matching: + def visit(position, current, matrix, contacts): + nonlocal count + for role in range(3): + if matrix[3 * role + 2]: + need(starts[2] <= current[role], "source-information frame invariant") + if position == len(candidate): + paid = path_partition(starts, ends, candidate, contacts) + need(any(dominates(p, paid) for p in candidates), "every actual path has a relaxed lower bound") + count += 1 + return + i, j, _ = candidate[position] + for contact in all_frames: + if current[i] <= contact <= ends[i] and current[j] <= contact <= ends[j]: + state = list(current) + state[i] = state[j] = contact + visit(position + 1, state, act(matrix, candidate[position]), contacts + [contact]) + visit(0, starts, IDENTITY, []) + need(count > 0, "positive geometric fixture") + checked.append(count) + return {"ablations": failures, "rank_mass_mismatch_rejected": True, + "decreasing_contact_rejected": True, + "changed_boundary_positive": {"old": list(old), "better": list(better)}, + "tiny_endpoint_words": len(matching), "tiny_actual_paths": checked} + + +def build_certificate(): + base = authenticate_inputs() + windows = extract_windows(*construct()) + need(len(windows) == 128, "exact forward eligible-window count") + need(Counter(w["phase"] for w in windows) == {"B": 123, "cleanup_tail": 5}, "window phases") + rows, graph_counts = [], Counter() + for w in windows: + ca, cb = w["coefficients"] + incumbent = path_partition(w["starts"], w["ends"], ((0, 2, ca), (1, 2, cb)), w["contacts"]) + candidates, details = relaxed_partitions(w["starts"], w["ends"]) + need(all(dominates(incumbent, p) for p in candidates), "concave floor at window " + str(w["index"])) + need(incumbent in candidates, "incumbent attains floor at window " + str(w["index"])) + graph_counts[len(details["admissible_edges"])] += 1 + row = {key: w[key] for key in ("index", "phase", "roles", "coefficients")} + row.update({key + "_bases": [basis(s) for s in w[key]] for key in ("starts", "ends", "contacts")}) + row.update(details) + row.update({"incumbent_partition": list(incumbent), "relaxed_partitions": [list(p) for p in candidates], + "all_concave_prices_certified": True}) + rows.append(row) + return {"schema_version": 1, "status": "PASS_RECEIVER_CONTACT_FLOOR", "base_commit": base, + "scope": "All finite three-field scalar shear words, fixed monotone boundaries, forward windows", + "windows": rows, "window_count": len(rows), + "contact_graph_counts": {str(k): v for k, v in sorted(graph_counts.items())}, + "controls": controls(windows), "new_kappa_claimed": False} + + +def main(): + import argparse + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--write", action="store_true", help="explicit authoring only; replace local certificate") + args = parser.parse_args() + result = build_certificate() + serialized = json.dumps(result, indent=2, sort_keys=True) + "\n" + if args.write: + summary = json.dumps({k: v for k, v in result.items() if k != "windows"}, indent=2, sort_keys=True) + rows = ",\n".join(" " + json.dumps(row, sort_keys=True, separators=(",", ":")) for row in result["windows"]) + formatted = summary[:-2] + ',\n "windows": [\n' + rows + "\n ]\n}\n" + CERTIFICATE.write_text(formatted, encoding="utf-8", newline="\n") + else: + # Canonical JSON preserves types/list order and checks every proof-relevant field. + stored = json.dumps(json.loads(CERTIFICATE.read_text(encoding="utf-8")), indent=2, sort_keys=True) + "\n" + need(stored == serialized, "complete committed certificate equality") + print(json.dumps({key: value for key, value in result.items() if key != "windows"}, sort_keys=True)) + + +if __name__ == "__main__": + main()