Extend standalone paid-history bounds to central scalars and nonuniform words (no new κ)

docs/research/standalone-history-scalar-ceiling/EVIDENCE-INDEX.md

@@ -0,0 +1,57 @@
+# Written-proof evidence and original-label remap
+
+The twelve payloads below are unchanged LOCAL proof, acceptance, review and conditional-source snapshots. [SOURCE-MANIFEST.json](SOURCE-MANIFEST.json) records exact hashes, byte lengths and original labels. They are not registered executable inputs or claims that private source programs have been bundled or newly validated. The four new navigation/provenance documents are README, this index, the manifest and handoff.
+
+## Current written-review status
+
+| Result | Exact proof | Additive acceptance | Independent AI static review |
+| --- | --- | --- | --- |
+| Fixed-word central Laurent extension | [Lemma](proofs/central-lemma-v1.md), e4ead15d… | [Report](acceptance/central-report.md), 7508cb57…; [decision](acceptance/central-decision.json) | [Report](reviews/central-report.md), 6438f2df…; [decision](reviews/central-decision.json), 5a53ed0e… |
+| Eventual pointwise extension | [Lemma](proofs/pointwise-lemma-v1.md), ac2a5a7c… | [Report](acceptance/pointwise-report.md), c4451f41…; [decision](acceptance/pointwise-decision.json), 9c6b9514… | [Report](reviews/pointwise-report.md), c49f6c25…; [decision](reviews/pointwise-decision.json), 1177ef15… |
+
+The original PROPOSED headings and old pending-review statements in the exact lemmas remain historical. Acceptance is additive and the independent decisions require no mathematical correction. The pointwise guard is each f≥2p−1 for a fixed finite projective ordinary family; it is not a practical-width result. Both variants exclude free correlated nonordinary paid history initially.
+
+## Direct predecessor and the added scope
+
+The direct public predecessor is [#5425's standalone ordinary-module history argument](https://github.com/Clear1nsight/integer-mult-bounds/tree/00005c8c5e81c7f27b5769f9309ff88758e26f51/research/fanout-optimality-support), at head `00005c8c5e81c7f27b5769f9309ff88758e26f51`. Its cached body declares module-proof SHA256 `cfa9f3df855f96a3e73bcb8042a750a3aa41d18ec098d6a34268370f3e84d782` and explicitly allows feedback/overwrites with ordinary initial history, fixed capacity and a finite columnwise ordinary group. The monitor supplied the immutable package-tree locator and declared proof hash; no new predecessor proof fetch or scientific replay is claimed here.
+
+This note extends that principle to fixed central c·2^(n f) normalizers and to arbitrary exterior c(f) with nonuniform finite words and N(f) at each f≥2p−1. Its conditional 120-coordinate nomination is separate from the predecessor's 112-output specialization. It is an extension/application of an existing history argument, not a new general history principle.
+
+## Source nomination and link remap
+
+The [source report](source/standalone-local-report.md), 6dc97b31…, supplies the ordered T=A Jbar A^-1 nomination, 120 distinct input coordinates, nonmonomial support and surjectivity arguments, and the conditional signed-profile inequality. The [conversion obligation](source/conversion-obligation.md), 70230e2b…, makes the exact standalone resource contract explicit. These documents do not make this note a physical BC implementation or admitted supplier.
+
+The following original labels inside frozen appendices resolve to the copied artifacts here. A reference to a source program or another audit not listed below remains an inherited source premise, not a new public dependency or execution claim.
+
+| Original LOCAL label suffix | Public copy |
+| --- | --- |
+| `coded-canonical-conversion-ceiling-20261024/REPORT.md` | [Source report](source/standalone-local-report.md) |
+| `CONVERSION-OBLIGATION.md` | [Conversion obligation](source/conversion-obligation.md) |
+| `central-scalar-extension/PROPOSED-LEMMA-v1.md` | [Central proof](proofs/central-lemma-v1.md) |
+| `central-scalar-extension/REPORT.md` / `DECISION.json` | [Acceptance](acceptance/central-report.md) / [decision](acceptance/central-decision.json) |
+| `central-scalar-independent/REPORT.md` / `DECISION.json` | [Review](reviews/central-report.md) / [decision](reviews/central-decision.json) |
+| `pointwise-scalar-extension/PROPOSED-LEMMA-v1.md` | [Pointwise proof](proofs/pointwise-lemma-v1.md) |
+| `pointwise-scalar-extension/REPORT.md` / `DECISION.json` | [Acceptance](acceptance/pointwise-report.md) / [decision](acceptance/pointwise-decision.json) |
+| `pointwise-scalar-independent/REPORT.md` / `DECISION.json` | [Review](reviews/pointwise-report.md) / [decision](reviews/pointwise-decision.json) |
+
+No raw native word, provider kernel, helper census, source scan, scientific checker or constructor is imported. Original source-path labels and old publication-status statements are preserved as evidence history. The top-level narrative links to the copies above rather than to workspace paths.
+
+## Primary-reference attribution
+
+Anthony Chefles, *Unambiguous Discrimination Between Linearly Dependent States With Multiple Copies*, Physical Review A 64, 062305 (2001), [DOI](https://doi.org/10.1103/PhysRevA.64.062305), [inspected manuscript version](https://arxiv.org/abs/quant-ph/0105016v3). The sole literature worker's LOCAL fit note is SHA256 `bf92eaf26ae87303e6f1f8a893a33db48009b93b5c3ec269b2d426f2c2ad3562`; its retained inspected manuscript hash is `38f5efd58c5c4f902e40cfb6283c804650bf1d5ebd2678a89ffe7710e44ecdb9`. This note neither repeats that paper review nor claims the classical tensor observation as new.
+
+Peter Kropholler and Karl Lorensen, *Group-graded rings satisfying the strong rank condition*, Journal of Algebra 539 (2019), 326–338, [DOI](https://doi.org/10.1016/j.jalgebra.2019.08.014), [inspected manuscript version](https://arxiv.org/abs/1901.10001v2). The sole literature worker's LOCAL fit note is `170e3c9923f0c9b7543f7775b00aeda953691012d82e84ecea43ed861827e5fb`; its inspected manuscript hash is `9ed6eaa9ed0a459da9411dc4739152ff93d72f27d0d38c0b70f109e168df51f1`. The central proof is self-contained; the published theorem provides corroboration.
+
+Only short factual attribution, URLs and hashes are retained here. No third-party paper PDF/text, full bibliography or raw agent/chat coordination log is included.
+
+## Scope of inspection and overlap
+
+The retained reports record written reasoning, source-text inspection and byte hashes. No native, phase, rank, operator, calibration, numerical-power, price, Lean or other proof engine was run for this documentation note. Independent AI static review is separate from human review, formal verification, hosted tooling checks and supplier admission.
+
+The sole monitor's checkpoint 1347 was captured at 2026-10-24 13:47:44 UTC, with current all-author/all-state PR metadata coverage through 13:33:40 UTC and selective body/source review. At exact cached [PR5436 head](https://github.com/CrocSwap/integer-mult-bounds/commit/4c31fd7d4eee61ff9fd59533549a67ef1a25b449) `4c31fd7d4eee61ff9fd59533549a67ef1a25b449`, zxv's moving-support statement and four-control 2705-source corollary supplied the prompt. Their proof, count, calibration and execution claims are not independently adopted here. This bounded overlap context is not universal novelty coverage.
+
+The supplied prepublication receipt is SHA256 `3f68e99596c99eb0597baaedcc69d40b11748153f2a31df3c9a2eaf75b74ca48`, recorded at 2026-10-24 16:52:00 UTC with current metadata/body coverage through 16:50:42 UTC and a subsequent static locator addendum. It covers 100 recent all-state records, reports no changed nearby exact-scope claim in that incremental pass, and leaves main/guidance/selected unchanged. It does not exhaust Discussion history or unpublished work. The cached #5425 body is `b84a70a51002eeb5aa54c74e1e78865a79f276dee6d0defb852a68d20d0cd1ab`.
+
+Adjacent exact heads are [#5441](https://github.com/CrocSwap/integer-mult-bounds/commit/11fedb46fa199283f78282187c10aea432d8b0bb), for fixed physical transfer-table endpoint/cut bounds, and [#5442](https://github.com/CrocSwap/integer-mult-bounds/commit/19e8f0452c09cbfe99511ea697fa239c1f457314), for a finite-group all-width lifting lemma and a separately claimed complete-body certificate. The latter claim is [challenged by review comment 6385984727](https://github.com/CrocSwap/integer-mult-bounds/pull/5442#issuecomment-6385984727). This note adopts neither that executable certificate nor its body-closure claim; neither is a dependency of the conditional LOCAL nomination. A finite-width affine diagnostic for a different family supplies no replacement for this note's ordinary-group/target-coset separation. No such calibration is imported or executed here.
+
+The [handoff](HANDOFF.md) distinguishes the current local assembly from any later commit, public readback or hosted CI result.

docs/research/standalone-history-scalar-ceiling/HANDOFF.md

@@ -0,0 +1,22 @@
+HANDOFF
+
+Research discussion / PR / artifact:
+[Standalone paid-return histories with scalar extensions](README.md), with the [immutable proof/review snapshot](https://github.com/Clear1nsight/integer-mult-bounds/blob/56c52a79f7663bc59ad3a5013c242a113039a701/docs/research/standalone-history-scalar-ceiling/README.md). The upstream PR is the canonical investigation thread for this documentation contribution. The note is unregistered written mathematics with independent AI static reviews, not an executable research capsule.
+
+Exact commit:
+Proof/review snapshot: 56c52a79f7663bc59ad3a5013c242a113039a701; authenticated canonical base: 32890bc5de034ab8fc93ac88ead7279a6a416d04. A later metadata-only commit pins this handoff; the upstream PR and public handoff identify its publication head separately. The twelve original proof/review/source payloads retain their exact LOCAL byte hashes in [SOURCE-MANIFEST.json](SOURCE-MANIFEST.json); they are not fabricated canonical source roots. The canonical CI-navigation repair is already present and has no duplicate delta here.
+
+What is established:
+The ordinary-module paid-history principle is retained from [#5425 at exact head 00005c8c…](https://github.com/Clear1nsight/integer-mult-bounds/tree/00005c8c5e81c7f27b5769f9309ff88758e26f51/research/fanout-optimality-support), including feedback/overwrites, ordinary initial span and fixed capacity. This note adds the fixed-word central c·2^(n f) variant at all positive widths or a consecutive infinite tail, and the eventual pointwise arbitrary-c(f) variant with nonuniform finite words and N(f), only at each f≥2p−1 for one fixed finite ordinary G and geometry. Both yield at least q actual new returns for the stated q independent invertible target coordinates. No new history principle or transfer of the predecessor's 112-output application is claimed. The pointwise threshold may be astronomical. Independent AI reviews accept the exact scalar-extension proofs without a required correction; acceptance reports preserve the original PROPOSED headings. The q=120 source example remains a conditional LOCAL mathematical nomination, with its ordered target, nonmonomial and independent-input arguments copied for inspection. The supplied sole-monitor refresh covers current PR metadata/body records through 2026-10-24 16:50:42 UTC, bounded rather than exhaustive; main/guidance/selected are unchanged.
+
+What remains uncertain:
+The written proofs and documentation scope have separate independent AI static reviews. Independent human or formal-kernel review and a source-specific application remain open. Public readback and hosted tooling status are recorded on the upstream PR; neither supplies physical or scientific admission. The supplied prepublication refresh does not approve future byte changes. Neither theorem establishes an additional paid-call charge at an actual parent cut with cached/native/paid observations. No practical-width application, physical BC ABI/implementation, admitted supplier, new productive target, uniform recursive cost/precision/stock contract or new kappa follows. Adjacent #5441 concerns transfer endpoints/cut dimensions; #5442's claimed complete-body closure is challenged and is not a dependency here. No small-width affine corollary replaces this note's large fixed ordinary-group/target-coset separation. A shallow/shared base checkout does not prove full source history or corpus availability. The copied source premises are not freshly replayed.
+
+Smallest useful next task:
+The next distinct research question is the actual cut's versioned available-history module and target containment, including ownership, retention and opportunity costs. That question remains outside this note and with its owner. A source-specific smaller width threshold also needs a separate justified argument.
+
+Reproduction command and expected runtime:
+None for a scientific replay. Read the [two proofs and their independent reviews](EVIDENCE-INDEX.md). There is no VERIFY.json, verifier, numerical RESULT or registered command. Assembly checks are limited to copied-byte hashes, local navigation and Git diff/metadata; their results cannot certify the theorem or a supplier. No paper PDF/text, raw agent/chat log, peer-owned helper census or constructor is included.
+
+Predecessor credit:
+The #5425 finite ordinary-module proof/reviewer directly, including its feedback/overwrites argument; Anthony Chefles for classical tensor/projective independence; Peter Kropholler and Karl Lorensen and their credited strong-rank predecessors; zxv for the #5436 support-width prompt; scalar/source authors, root's localization and paid-history application question, independent reviewers and sole literature worker; and the BC/native/Clifford/product/compiler/precision/analytic lineage. Preserve Ali Romman, Dillon Amburgey/dillona, Cao Yifan, Cinna Davis, zxv, Dugongue, Jacob Alan Sussman, Chris R/Clear1nsight and the retained notices. Substantial OpenAI Codex assistance. No independent human or formal-kernel verification is claimed.