Research: audit native acceptance of odd scatter multiplicities (no new kappa)

[commdata2338]

Change and mathematical scope

This answers PR #3004's open next question 3 for one explicit full-size word, the selected PR #589 word. Appending [4,4] to row 0 [4,5,6,7,8] triples an existing slot: the complete symbolic checker and both actual native checkers accept it, and all three exporter artifacts equal the selected baseline byte for byte. Both modes of PR #2992's simple-support guard reject it intentionally. Appending [0,0,0] instead introduces an absent slot: symbolic and exported actions agree but both fail the defining endpoint. PR #2977's paired-absent [0,0] reproduces symbolic acceptance with native rejection.

This is a finite source-bound boundary audit, with a separately written harness and an elementary explanation of the two odd cases. No new parity characterization, supplier admission, physical cost improvement or kappa is claimed. The four synthetic fixtures keep the nine distinct retained helpers and every other word field fixed. Frozen predecessors and the selected result are unchanged.

Fixture	Occurrences / scatter ADDs	Full symbolic	Native legality	Native columns	Both guard modes
selected baseline	527 / 527	pass	pass	pass	accept
append [0,0]	529 / 528	pass	pass	reject	reject
append [4,4]	529 / 527	pass	pass	pass	reject
append [0,0,0]	530 / 528	reject	pass	reject	reject

Native rank mass stays 5129, with nine COPY/ERASE pairs. The accepted triple has the baseline's 27,234 records and 24,305 total ADDs. Both bad streams have 27,235 records and the same 98-column discrepancy at output 111; dirty input column 472 is a one-bit witness. A textual occurrence count is not the emitted ADD count.

Task and overlap

Base and final refreshed canonical main: 463113d675af7410ac91d53a4fed51ec6494eb9a; priority revision 6, refresh 2026-10-17T17:39:11.388698+00:00, no changed files. Contribution head: 246c7ae12f3f103b05ed80fad0e2a9edde01c3f8.

Task card: research/scatter-odd-native-audit/TASK.json.

• Task / track: supplier-boundary-audit / adversarial-audit.
• Catalogue scope key: dcdb0fa8e49b08a958d0; refinement PR3004/odd-existing-versus-absent/native-boundary/four-fixtures.
• Selection: released PR Audit: exact scatter parity contract at the checker/exporter boundary (no new kappa) #3004 native handoff, before drawing unrelated work; card retrieval nonce 57515e846d560ce80ae4dbd8af60d3af. The empty catalogue existing_checks list was treated as unknown; actual successor coverage was inspected.
• Object/question: four fixed row-0 variants at real symbolic, exporter, opt-in guard and native legality/column boundaries. Distinguish coefficient agreement, the required endpoint and the chosen producer schema.
• Scope status: refined; close an explicitly unrun native obligation after the existing scalar and guard work, without reconstructing those as new results.
• Method/domain: authenticated script snapshots; separate JSON and packed-record F2 evaluation on all 661 dirty columns; serial native replay on 883 five-stage physical columns; exact artifacts/receipts and rejecting controls.
• Milestone/budget: bounded audit, 60-minute session cap; stop after these fixtures. No search or family expansion. No altered construction bill; hosting, all-size/compiler, precision/tape and analytic obligations remain inherited.
• Success/falsification: byte-identical baseline/existing-triple artifacts and native receipts; paired/triple-absent native rejections; actual guard rejection before output creation. Any discrepancy fails replay.
• Artifact: research/scatter-odd-native-audit/; reproduction below.

Canonical claim in discussion #2976, following the #1166 handoff.

Exact predecessor/context heads:

• Audit selected scatter parity across word and record checks #2977 cd23d242dfe0e7a71cafba0ad5590dc4f2fbf4f2: discovered the mismatch and ran baseline/paired/single-absent native controls.
• Enforce simple scatter supports at opt-in checker and exporter boundaries #2992 b31bf0360ad702b1be71dea7a33edc11711084af: actual two-mode guard, no native run in that package.
• Audit: exact scatter parity contract at the checker/exporter boundary (no new kappa) #3004 ce08d19f6e43bbc6f552858d93154efe3aa98916: scalar agreement/count audit; odd native question left open.
• Record the selected scatter duplicate boundary #3099 80b7b0b452de3c9fa4306f49d12e904a40cfbe2e: extracted scalar-action corroboration.
• Audit retained-helper independence in scatter parity #3128 2bf13e5b55f8318ae74a8f17db36a19447ba8c7f: alias independence correction; this work keeps ret injective and unchanged.
• Selected PR Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589 a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46: original research/e8-bit-p111/ word/checker bytes equal the retained research/e8-bit-p111-tuned/ paths.

Offline overlap queries covered the card, odd-multiplicity, simple-scatter, native scatter and scatter-odd-native. Latest complete snapshots: 251 open PRs at 2026-10-17T17:37:12.534077+00:00; 2,015 discussion records at 17:39:04.580509+00:00. Retained main archives and the canonical thread were inspected. A closing scan of the complete snapshots at 17:49:11Z (253 open PRs) and 17:52:04Z (2,017 Discussion records) found only this claim and PR #3004's finding for this object. This is metadata/local-package coverage, not a claim to cover arbitrary diffs or unpublished work.

Validation

python3 -B scripts/research_baseline.py
python3 -B scripts/research_package.py --package research/scatter-odd-native-audit --check-only
python3 -B scripts/research_package.py --package research/scatter-odd-native-audit
python3 -I -O -B research/scatter-odd-native-audit/verify.py --native
python3 scripts/check_research_commit.py --package research/scatter-odd-native-audit

Observed locally (CPython 3.12.3, Ubuntu GCC 13.3.0, Linux):

"status": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY"
PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
PASS_SCATTER_ODD_BOUNDARY fixtures=4 columns=661 guarded_duplicates_rejected=3
Ran 7 tests ... OK
PASS_REGISTERED_RESEARCH_PACKAGE research/scatter-odd-native-audit outcome=completed
PASS_SCATTER_ODD_NATIVE legality_accepts=4 columns_accept=2 columns_reject=2 controls=2
PASS_RESEARCH_COMMIT_BYTES {"commit": "246c7ae12f3f103b05ed80fad0e2a9edde01c3f8", "files": 22, "package": "research/scatter-odd-native-audit"}

The registered primary replay (about 10 s) and all seven behavioral groups pass; the explicit native replay takes about 15 s. Compiles are serial and use the source-pinned checked-128-bit cpp_int stand-in, with a backend-selection probe. This is not a fresh system-Boost build.

Controls: exact one-bit dirty witness; all 64 assignments of a separate six-register scalar fixture; malformed COPY/ERASE lifetimes; every live input corrupted in turn; occupied output preservation; separate check-only and export-only validator bypass mutants; occupied receipt refusal; omitted scatter ADD and truncated native stream. The two native bad-word rejections produce no success receipts.

Publication byte check passed for all 22 package/input files. The exact commit was exported with scripts/export_research_package.py, checked, and extracted into a read-only Git-free tree. Optimized native replay (14.729 s) and all seven behavioral groups (2.376 s) passed there; all 23 files including the export manifest remained byte-identical. Full native receipts are retained in NATIVE.json; only verified elapsed times and a temporary stream path are normalized. RESULT.json retains all scalar discrepancies and exporter hashes.

Not checked: full selected cold ancestry; a new generator/tuner replay; native system-Boost or second-compiler reproduction; physical hosting/projector/bank realization; all-size/compiler, precision/tape and analytic transfer; supplier adoption; hosted CI; independent human or proof-kernel review. Native replay is explicit (--native) and is not silently included in the standard-library registered hook.

Credit

Nick Petalas (#2977) retains discovery, counterexample, dirty-witness, candidate-guard and earlier native-control credit. Arham Tahir (#2992) supplied the operational guard. Hiroki Kumazaki / Kumagi (#3004) supplied the contract/count audit and this handoff. James Reed / jwr404 (#3099) supplied duplicate-boundary corroboration; Sricharan Vagvala / theon199 (#3128) supplied the retained-alias premise correction. eumemic and DreamingOfClouds retain the PR #543/#555/#589 word/checker lineage; Dylan Crow wrote the exporter and the NCOPY generalization of the PR #346/#352 native cohort checkers (LJH-217, DaysSky); Sagar Thakrar supplied the checked cpp_int stand-in; Douglas Colkitt supplied selected bindings and review. All original notices and Apache-2.0 licensing remain intact.

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

The package README and TASK.json retain the actual decision: should a separately versioned successor retain simple supports, or admit multiplicity while binding emitted ADD counts and retained-slot semantics? Start with this four-fixture table and PR #3128's alias premise. Maintainer source-binding/admission review and complete supplier obligations remain blockers. No further local search is justified by this result alone.

Workflow feedback (optional)

The explicit PR #3004 open question made the useful contribution clear. The central card's existing_checks is empty despite retained #2992/#3004/#3099/#3128 follow-ups; adding those coverage pointers would reduce repeated rediscovery without treating archival intake as scientific admission.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG