Audit PR4483's sharp cancellation threshold with exact extremisers (no new kappa)

docs/ci-verification.md

@@ -5,6 +5,25 @@
 Start with the [selected record](../certificates/selected-result.json). Its
 `reproduce`, `review`, `source_manifest` and `validation` fields identify the
 replay command, scoped assessment, source bindings and integration evidence.
+The selected checkpoint is #4359, documented in
+[the proof review](research/pr-intake-evidence/pr4359/PROOF-REVIEW.md),
+[the source manifest](../certificates/frontier4359-source.json) and
+[the validation receipt](research/pr-intake-evidence/pr4359/VALIDATION.json).
+The public cold replay is `make frontier4359-verify`; the configured
+[frontier4359 workflow](../.github/workflows/frontier4359.yml) executes it
+on Ubuntu 24.04 with Python 3.12 and the pinned requirements. Consult
+[the integration receipt](research/pr-intake-evidence/pr4359/INTEGRATION.json)
+and [workflow runs](https://github.com/CrocSwap/integer-mult-bounds/actions/workflows/frontier4359.yml)
+for dated evidence and exact tested heads.
+
+`make selected-record-check` checks metadata and source/proof hashes. The
+finite replay and changed-interface review retain the native/physical,
+analytic, precision, fixed-tape and recovery hypotheses in the selected
+record; they are not a full formal multiplication theorem. The winning
+uniform templates are algorithm-defined and are not materialized.
+
+## Historical checkpoint through #1094
+
 At this checkpoint, the selected composition is #589 with #1094, documented in
 [the review](research/community-batch1099-review.md),
 [the source manifest](../research/community-frontier1094-audit/SELECTED-SOURCE.json)

docs/research/clear1nsight-20261022-base.md

@@ -0,0 +1,5 @@
+# Isolated contribution base, 22 October 2026
+
+This branch starts at canonical main f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc. It carries only the already tested fork PR14 navigation and historical source-role corrections, separate from all four new research submissions. The historical replay's original-manifest reference is now the same byte-identical manifest in canonical main, so no foreign fork commit is required. Scientific verifiers, original hashes and receipts, selected records, and replay invalidation paths are unchanged. Credit zxv's PR4436 documentation, James Reed's PR3563 and the locale/D8 authors; fork adaptation by Chris R / Clear1nsight with substantial OpenAI assistance, Apache-2.0.
+
+This is an isolated base branch, not a merge into main or a selected-frontier update. Each research PR targets this branch to keep its scientific diff focused. Upstream submission should carry the individual research commit; upstream maintainers own any shared CI repair. New package metadata pins the canonical scientific baseline, not the changing current documentation.

docs/research/current-status.md

@@ -1,12 +1,14 @@
 # Current reviewed status
 
-Selected conditional κ: **0.0023 = 23/10000**, zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage.
+Selected conditional κ: **0.0023** = 23/10000, zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage.
 
 [Selected record](../../certificates/selected-result.json) · [Proof review](pr-intake-evidence/pr4359/PROOF-REVIEW.md) · [Integration receipt](pr-intake-evidence/pr4359/INTEGRATION.json) · [Contributors](community-productive4359-contributors.md).
 
 Cold replay: `make frontier4359-verify`. The fresh 23-stage replay and 59 normalized artifacts pass; the changed interfaces have an AI-assisted proof review under retained analytic/native/fixed-tape hypotheses. Winning uniform templates are not materialized. This is not a complete formal or independent human verification. #4404 independently checks a narrower arithmetic/flow scope.
 
-## Historical selected status through #1094
+The sections below are a historical snapshot; consult the selected record above for present status.
+
+## Historical checkpoint through #1094
 
 Historical selected conditional κ: **0.001672660197076918**, Rohan Arun's #1094 on Jeremy Kothe's #1087 packing and the cumulative k8/slot/T16 construction. The bit supplier remains #589 on #555.
 

research/adaptive-cancellation-audit/PROOF.md

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+# Sharp cancellation audit and exact extremisers
+
+This is a scoped independent written proof audit of PR4483, PROOF.md Section 4, equations (10) and (11). It is not a formal-kernel proof. The algebraic optimisation below is elementary and carries no priority claim. Its value is the precise source-bound sharpness statement, zero-mass handling and discriminating controls for the adaptive compiler.
+
+## Statement
+
+Fix real numbers 0 <= beta < eta < 1. Let I,B,F,A be nonnegative and satisfy I=B+F+A and B<=beta I. These are respectively the inner-source, boundary-exit, leaf-exit and net-production potentials of the source argument. For fixed A,F with A+F>0, the largest permitted value of (B+F)/I is
+
+    (beta A + F)/(A+F).
+
+It is attained at I=(A+F)/(1-beta), B=beta I. Consequently the condition
+
+    (eta-beta) A >= (1-eta) F
+
+is sufficient, and is necessary for a uniform guarantee over every admissible boundary mass at those fixed A,F. This is not claimed necessary for each individual flow, whose mirror slack can make its exit fraction smaller.
+
+## Independent slack certificate
+
+Using I=B+F+A gives the exact identity
+
+    (1-beta) [eta I-(B+F)]
+      = (eta-beta) A-(1-eta) F + (1-eta) [beta I-B].
+
+Under the displayed threshold and mirror inequality the right side is nonnegative. Since 1-beta>0, the desired contraction B+F<=eta I follows. This proves the implication without division by a possibly zero leaf mass or inner potential. If A=F=0, then I=B and B<=beta I force I=B=0, so the conclusion still holds.
+
+For sharpness, with A+F>0 the constraint is (1-beta)B<=beta(A+F). The fraction (B+F)/(B+A+F) is nondecreasing in B, with derivative A/(B+A+F)^2. The endpoint above is therefore a maximiser, also when A=0. Substitution yields the claimed maximum and the exact threshold. Equality occurs when the threshold is tight and the mirror is saturated. Strict contraction follows if at least one of the two nonnegative terms in the slack identity is positive.
+
+## Binding to PR4483
+
+The source defines A=(T_t-P_t)H_t-R_t. Its exact potential cancellation is I+R=B+F+(T-P)H, hence the premise I=B+F+A. Source equations (3) and (9) bound F<=P_t^(G+1) and A>=D_ell(t) P_t^(G+1). Since eta>beta and eta<1, the source threshold
+
+    (eta-beta)D_ell(t) >= 1-eta
+
+implies the inequality above. In particular it forces D_ell>=0. The signs and the subtraction of root potential are load-bearing. The proof does not require the old invalid assertion that leaf ranks are uniformly sublinear.
+
+No better universal threshold can be inferred from only these inequalities. Actual flow correlations or a strictly better mirror or leaf bound can still improve the conclusion. The statement is a ceiling on this scalar inference, not on the compiler family, native word, rank bound or multiplication exponent.
+
+## Failure controls
+
+Take beta=1/4, eta=1/2, F=1, gross production (T-P)H=2 and root debit R=1/2. Then A=3/2, I=10/3 and B=5/6 satisfy exact cancellation and saturate the mirror. The actual exit fraction is 11/20>1/2. Ignoring R falsely passes the gross threshold with equality. Thus the root term cannot be discarded. Similarly A=0,F=1 gives exit fraction 1, while a test that drops the leaf mass would accept A>=0. Both are counterexamples to weakened tests, not to PR4483, whose correct guards reject them.
+
+The checker uses exact Fractions for 6,120 cases, 1,800 attained extremisers, 120 zero-mass endpoints and four invalid-premise controls, plus both omission examples and nine linear coefficient checks. Finite cases corroborate implementation and failure boundaries; the all-real proof is the identity and extremal argument above. No predecessor acceptance function is imported.
+
+## Remaining obligations
+
+The Chernoff bounds producing D, the pointwise mirror certificate, funded logarithmic majorant, integer chronological realisation, native adapters, physical tape costs, precision/stock and outer transfer are not proved by this lemma. The newer PR4529 gate checks and PR4532/4533 work are complementary, not evidence that this package audits the entire compiler. Exact source bytes are checked by the Git blob pin in verify.py and declared as a live replay input.
+
+Credit zxv for PR4483 and the sharp cancellation already used there, Jacob Alan Sussman's compiler, Ryanson Jonathan's corrected mirror and gate work, Dillon's broader gate-existence analysis, and the retained native/outer contributors. Prepared for Chris R / Clear1nsight with substantial OpenAI assistance; Apache-2.0.

research/adaptive-cancellation-audit/README.md

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+# Independent sharp-cancellation audit
+
+Assignment D audits one quantified implication of zxv's adaptive compiler. The source-bound registered replay passes, and PROOF.md supplies an all-real proof with an exact sharpness statement. No new kappa, lower uniform rank, compiler bug or complete compiler admission is claimed.
+
+## Result
+
+Under I=B+F+A, 0<=beta<eta<1, nonnegative potentials and B<=beta I, the exact identity is
+
+    (1-beta)(eta I-B-F)
+      = (eta-beta)A-(1-eta)F+(1-eta)(beta I-B).
+
+Therefore (eta-beta)A >= (1-eta)F guarantees exit contraction. For fixed A,F with positive sum, the largest permitted exit fraction is (beta A+F)/(A+F), attained at I=(A+F)/(1-beta), B=beta I. Necessity is for a guarantee over all admissible boundary masses, not for every individual flow. The zero-mass endpoint is handled without division. The source's A=(T-P)H-R includes the root debit. Omitting that debit can falsely pass while the actual exit fraction is 11/20 instead of at most 1/2. Dropping the leaf term similarly invalidates a weaker test. These are rejected controls, not counterexamples to PR4483.
+
+The elementary extremal calculation carries no priority claim. The contribution is the exact source-bound proof audit, sharp scope and discriminating failure witnesses, separate from the numerical gate checks.
+
+## Reproduce and actual evidence
+
+Python 3.12, standard library only:
+
+```sh
+python -B scripts/research_package.py --package research/adaptive-cancellation-audit
+python -I -O -B research/adaptive-cancellation-audit/verify.py --self-test
+```
+
+[VALIDATION.md](VALIDATION.md) records successful hosted workflow 39723357163 on CPython 3.12.15, the exact head and merge ref. RESULT.json retains all 6,120 rational cases, 1,800 extremiser checks, 120 zero-mass cases, four invalid-premise controls, nine coefficient checks and omission witnesses. Normal replay authenticates the proof and compares every receipt field. Optimised controls pass. No predecessor acceptance function is imported. The universal argument is written algebra, not extrapolation of a finite grid.
+
+## Sources, scope and overlap
+
+Canonical scientific base f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc, priority revision 7. The live source research/rank-convergence/PROOF.md is pinned by blob 75f451837204bd141f357e7f5e5d6c6f42e1423e and SHA256 in SOURCES.json and declared in VERIFY.json. Catalogue and selected record remain historical provenance.
+
+PR4529 checks finite gates but excludes the theorem. PR4532 addresses broader gate existence, and PR4533 retunes witnesses without a new kappa. This work isolates the scalar cancellation inference rather than repeating those results. Targeted live searches and bounded Discussion reading are not exhaustive overlap coverage. The historical baseline helper and full selected cold replay were not run. TASK.json declares the user-assigned changed proof-audit scope.
+
+## Open next questions
+
+A better universal threshold cannot follow from these same scalar inequalities alone. First prove stronger actual-flow information, such as a joint boundary/leaf occupation bound, and compare it with the explicit extremisers. Separately audit one Chernoff occupation or root bound; those premises, mirror certification, majorant funding, native realisation, physical costs, precision and outer transfer remain open to this package. Refresh overlap before claiming them.
+
+## Credit
+
+Credit zxv for PR4483's cancellation argument, Jacob Alan Sussman for mixed-target recursion, Ryanson Jonathan for mirror/gate work, Dillon for the broader gate-existence follow-up, and the retained Cinna Davis/native/outer lineage. Prepared for Chris R / Clear1nsight with substantial OpenAI assistance, Apache-2.0. One session with separate workstreams does not constitute independent human or formal-kernel acceptance.

research/adaptive-cancellation-audit/RESULT.json

@@ -0,0 +1,19 @@
+{
+  "controls": {
+    "extremal_attainments": 1800,
+    "invalid_premises_rejected": 4,
+    "leaf_omission_rejected": true,
+    "linear_coefficient_cases": 9,
+    "rational_positive_cases": 6120,
+    "root_omission_exit_fraction": "11/20",
+    "root_omission_required_fraction": "1/2",
+    "zero_mass_cases": 120
+  },
+  "new_kappa": false,
+  "not_covered": ["Chernoff occupation and root bounds", "mirror guard certification", "native and physical premises", "majorant funding", "new compiler rank or outer theorem"],
+  "schema": "adaptive-cancellation-audit/v1",
+  "source_blob": "75f451837204bd141f357e7f5e5d6c6f42e1423e",
+  "source_sha256": "3c971c5670669cb36312815b111e64c83e1490a10ee82f5412bd9aee01e9c376",
+  "status": "PASS_SHARP_CANCELLATION_AUDIT",
+  "universal_argument": "PROOF.md, exact slack identity and explicit extremisers"
+}

research/adaptive-cancellation-audit/SOURCES.json

@@ -0,0 +1 @@
+{"schema_version":1,"base_commit":"f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc","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/rank-convergence/PROOF.md","usage":"input","git_blob":"75f451837204bd141f357e7f5e5d6c6f42e1423e","sha256":"3c971c5670669cb36312815b111e64c83e1490a10ee82f5412bd9aee01e9c376"}]}

research/adaptive-cancellation-audit/TASK.json

@@ -0,0 +1 @@
+{"schema_version":1,"task_id":"independent-moment","priority_revision":7,"base_commit":"f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc","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":"changed","actual_scope":"Assignment D: all-real audit and sharpness of PR4483 Section 4 cancellation, with exact independent slack certificate and failure witnesses.","scope_change_reason":"User-assigned quantified compiler proof audit; PR4529 covers finite gates and PR4533 retunes witnesses, so this targets the logical cancellation inference.","bottleneck_link":"Prevent an uncharged root or leaf potential from invalidating adaptive compilation while preserving the correct threshold.","budget_minutes":60,"stop_rule":"Stop at the scalar inference; no native, Chernoff, majorant-funding or outer theorem claim.","outcome":"completed","evidence":"Hosted source-bound registered replay 39723357163 at fca16a7b31ece4fe1b3e524c54ed292a96417e87 passes on CPython 3.12.15. RESULT.json retains 6120 exact cases, 1800 extremisers, 120 zero-mass cases, four invalid-premise controls, nine coefficient checks and root/leaf omission witnesses. Written all-real proof is PROOF.md. Normal and optimised checks and committed-input preservation pass.","author":"Chris R / Clear1nsight","ai_assistance":"Substantial OpenAI assistance; separately implemented in one session, not independent human or proof-kernel acceptance.","overlap":{"nearby_prs":[4436,4483,4529,4532,4533],"method":"Targeted live PR/package reading and bounded Discussions, not exhaustive pagination or novelty proof.","baseline_helper_run":false,"canonical_refresh":"2026-10-22T04:44:00Z"},"open_questions":[{"question":"Can actual flow correlations improve the sharp scalar threshold's premises?","why_it_matters":"No better guarantee follows from the same inequalities alone; stronger joint information could improve the compiler.","first_step":"Prove one source-bound joint boundary/leaf occupation inequality and compare it with the exact extremisers.","blocked_by":"The present work does not certify the Chernoff, mirror or physical flow premises."}]}