Complete two-pivot caller readers and certify fixed-chart retiming costs

[RossRichardson]

Summary

• Complete both dirty-pivot readers and every original-input reader in the two-pivot caller. For n=2q+2, the all-q histogram is H_(2f)=n²+2, H_(4f)=1: full stock plus 8f.
• Certify the fixed six-bank native-product chart floor at 72f using 36 edge-disjoint odd Eulerian subgraphs, with a matching word. Complete eight-bank quadratic retimings improve 138f to 130f against stock 128f; they remain unfavorable.
• Add only research/two-pivot-caller-readers/. The evidence index maps every retained file to its verification role: 14 mathematical JSON dependencies, one status-only dependency, 12 archival mathematical receipts, and two attribution JSON files. All 59 retained files remain mandatory for the integrity gate. The original 277,041-line import was 98.4% JSON; this follow-up adds only the index and README link, preserving every frozen byte and pin.

Scope and limits

The all-q construction covers integers q≥2 and f≥1. The 72f floor applies only to the retained six-bank skeleton and native-product chart compiler. It is not a bound for changed callers, new charts, or all eight-bank words. Finite exact replays and written all-parameter proofs are separate evidence.

The broader favorable-supplier target remains open: literal selected-native lowerings, contracting splits, compatible BIT, owners, precision, storage, fixed-tape costs and complete recursive/outer admission are unresolved. No new κ, selected-frontier change or formal-kernel theorem is claimed.

See the proof, coverage and limits, and task, scope change and open next questions.

Test plan

• At documentation head 6ea9d3a06275225f0ef2bdc306618842f09bccf7, python3.12 -B scripts/check_research_commit.py --package research/two-pivot-caller-readers --check-source-history and python3.12 -B scripts/research_package.py --package research/two-pivot-caller-readers --check-only pass: committed bytes, source history, metadata and pins.
• python3.12 -B scripts/research_package.py --package research/two-pivot-caller-readers passes both registered commands (normal and optimized Python) at that head.
• Index links, complete 59-file binding coverage, category counts and byte/line totals checked against the retained inventory, static consumers and an observed direct replay. All 70 pre-existing package files other than README are byte- and mode-identical to 896e2a2e89fd2b54d4defafaef3b91bb4b33b493; the verifier and BINDINGS are unchanged. Separate AI review checked the index's coverage distinctions, including status-only reads and imported helpers versus unexecuted audits.
• Automatic CI run 39324524356 completed successfully at documentation head 6ea9d3a06275225f0ef2bdc306618842f09bccf7, including planning and registered package replay. The final workflow status, conclusion and source SHA were read back. No manual GitHub check rerun was requested.
• The original scoped AI review checked the all-q derivation and independently rebuilt the fixed-chart graph/certificate and matching word maps at 896e2a2e89fd2b54d4defafaef3b91bb4b33b493; those scientific files remain unchanged.

The earlier author-reported Git-free export checks are recorded in the canonical finding; export was not repeated for this documentation-only change. AI review and finite replay are not independent human or formal-kernel acceptance.

Sources and credit

Canonical base 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. SOURCES, BINDINGS and RELATED-WORK retain exact ancestry and explain the changed task scope and nearest overlaps. Live Discussion/open-PR overlap coverage is partial, not a novelty certificate. Canonical publication.

Ross Richardson with substantial OpenAI Codex assistance; Apache-2.0. Preserve icekylinx/PR531 and Rohan Arun/kernel92 compiler notices and recorded ancestry; Chris R/Clear1nsight #3987 and ToikY #4002 signed-lift/phase credit; and Clear1nsight's distinct #3989/#4045 interface/volume work. Earlier #3630/#3632/#3645/#3649/#3655 and separate BIT #4021/#4023 are excluded from these new claims. No merge requested.

[RossRichardson]

Reviewed exact head 896e2a2e89fd2b54d4defafaef3b91bb4b33b493 against canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90.

No actionable mathematical defect found in the scoped all-q reader proof, fixed native-product chart floor, or reported retiming invoices. A separate AI checking context independently reconstructed the signed graph (295 nodes, 624 edges), checked all 36 odd Eulerian edge-disjoint subgraphs (508 used edges), and independently replayed the six-bank original/retimed and eight-bank retimed words against diag(E). Bills recount to 72f/128f, with both changed eight-bank invoices 138f -> 130f. Native lowering, contracting splits and full physical/recursive admission remain open.

Size: 277,041 added lines across 71 files; 272,613 lines (98.4%) are JSON, versus 3,535 Python lines. Total package bytes: 4,930,357. The large diff is chiefly frozen receipts. No repository line-count cap was found; size alone is not a correctness objection. Preserve original byte bindings rather than minifying frozen inputs. A useful optional follow-up is a replay-input versus archival-only index and a dedicated assertion that each fixed-chart original word equals diag(E); the latter equality was independently checked here.

Fresh checks: committed bytes/source-history and registered metadata/source pins pass. Existing CI run 39248120264 was read back completed/success at this exact head. No full-suite rerun was needed or requested. This review combines written-proof/source inspection with the small independent checks above; it is not independent human, formal-kernel, or complete multiplication-theorem acceptance.

Presentation correction: use Summary, Scope and limits, Test plan, Sources and credit; remove the invalid -standalone suffix from the purported commit SHA; link the canonical finding and exact proof/manifest. Prepared by Ross Richardson with substantial OpenAI Codex assistance.