Independent verification: PR589 paid rank ledger by exact rational projectors (no new kappa)

[commdata2338]

Change and mathematical scope

This adds an independent exact-projector path from the frozen PR #555/#589 bit words to the retained nine-stage rank invoice. Existing supplier checks already verify the construction. The contribution is a separate geometric implementation, a complete operation-to-ledger reconstruction, and failure controls.

Status: an independent finite audit with a written exact projector-rank argument. The selected numbers are reproduced unchanged. No supplier, packing ceiling or κ improvement is claimed, and no defect in the retained checkers is claimed.

Only seven files under research/bit589-projector-ledger/ are added. Existing tracked bytes, frozen sources and the selected record are unchanged.

What is reconstructed.

• 636 rational label-frame projectors per word, with symmetric idempotence, closure, exact nesting and rank-as-trace checked without floating point or modular rank.
• Both full orientations: 27,234 records, 24,305 ADDs, 2,911 MOVEs, nine COPY/ERASE pairs, all 661 dirty-input columns and a clean restored temporary.
• Local rank mass 5,129, and the PR Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589-minus-PR Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555 delta +2 H1 - H3 - 3 H4 + H6 + H7.
• Idle capacities derived from the schedule levels. The selection counts independently give {2:435,4:444,6:444,7:666,42:9} per replica. The 288 local calls give the global profile {1:381024,2:400416,3:22752,4:26880,5:29376,6:17376,7:26784,42:288}, with mass 1,808,352 and deficit 10,272.
• Wrong-frame witness: it preserves the scalar program and the entire dimension-only histogram, but fails projector nesting. It is a control against a weakened implication, not a finding that the original checkers accept it.

Remaining obligations.

• Not established:
  • a complete selected cold replay, a native cohort run or a word-generator rebuild;
  • a full lattice classification, or every H1-H5 implication;
  • the physical owner and chart realization, or global emitted-program equivalence;
  • precision/tape bounds, the all-size compiler, the analytic, moment and surcharge transfer, or a Lean theorem.
• The fixed schedule is a pinned-source transcription, not a proof of the Python compiler for every parameter.
• Existing mathematical and interface assumptions remain in force.

Task and overlap

• Task ID / scope key: independent-moment / c6f2494b197df3bc3591, refined to PR589/orthogonal-projector-local-ledger/PR555-delta/nine-stage32. Chooser nonce 941551c5c8443ceafec83371687af2c5, track independent-verification, priority revision 2.

• Base and exact heads: base bce54fb3f895cbe5cd4c0eb477c3afeed100190f; contribution a79ffd1571fff90f0d1dfbbed97e8ae7483e3e42. Retained PR Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589 a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46; selected PR Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges #1094 0fc329d0bec93ca7cd288eaea1295172e8789810. There is no pending code dependency, and all eleven consumed inputs are individually pinned by Git blob and SHA256 in SOURCES.json.

• Current-main compatibility: main advanced to cd91ac8e2652bfee6bf09da3b8724253bcf78f5f during the session. All eleven live input blobs, the selected record, the contribution guidance and the package tooling are unchanged. The patch applies to a source export of those latest-main inputs, and the patched standalone audit passes.

• Concrete object and question: independently derive the local paid ranks and the selected global bit histogram from the compact gates, rational frame spans, stage recipe and frozen selection.

• Exact claim audited: the implication from operations to the invoice. In the independent decision path, orthogonal projectors replace the predecessor's span and nullspace routines.

• Scope status: refined. The card's source-ledger method is kept and narrowed to the bit supplier; the complex ledgers, endpoint engines and packing ceilings already covered elsewhere are credited, not repeated.

• Method and domain: exact Q^8 projectors, all 661 scalar F2 inputs, both frozen words and both orientations, with L=9, K=4, T=32, v=111 and m=64. No heuristic search.

• Nearest work:

  • PR Independent verification: the selected frontier1094 complex rank ledger, rebuilt from its emitted program (no new kappa) #1262: the complex emitted ledger.
  • PR Independent verification: prove and certify the a < D/E diagnostic for the selected complex and bit ledgers (no new kappa) #1293: aggregate pricing and D/E; PR Audit PR1293 logarithm enclosures with exact counterexamples and fail-closed repair #1405 audits its enclosure.
  • PR Audit: bind retained PR589 supplier identity and COPY deficit #1329: identity binding.
  • This account's PR Audit: selected PR589 bit-hosting pending projectors across all hosted helpers (no new kappa) #1307: the pending-axis census.
  • PR Research: exact one-family physical host realization for selected PR589 (no new kappa) #1351 and PR Independent verification: PR589 family map by exact projector algebra #1371: one physical family's operator identity.
  • PR Independent verification: R439 frame-509 matrix replay (no new kappa) #1344: a frame-509 scalar replacement; PR Scoped negative result: PR589's bit word is exactly transport-locally optimal (no new kappa) #1345 and the newer Research: seed 5 exact joint-boundary census for PR589 r659 (no kappa) #1404/Scoped negative: PR589 A-triple fixed single-move options (210 cases) #1413: transport censuses.
  • The retained bit589-width-packing optimum.

  This is deliberately independent corroboration of the complete local-to-global bit invoice, and claims no priority for those methods.

• Claim and final check: the claim is in discussion #1166. A live overlap check just before submission (785 open PRs and 145 discussion records at 00:34 UTC, complete pagination) found no competing ledger audit.

Validation

python3 -I -B research/bit589-projector-ledger/verify.py
python3 -B scripts/research_package.py --package research/bit589-projector-ledger --check-only
python3 -B scripts/research_package.py --package research/bit589-projector-ledger
python3 -I -O -B research/bit589-projector-ledger/verify.py

Run on CPython 3.12.3 / Linux. The registered replay takes about five seconds and runs the seven focused tests and all 16 rejection controls. Also checked:

• real copied-source byte corruption and real saved-receipt corruption;
• an unchanged read-only relocation;
• patch application and replay against the latest-main source inputs.

Secondary tests match both predecessor binary exports and every basis and annihilator operator; the main verifier imports no predecessor implementation. The registered replay and the metadata/pin check were run again on the final commit before submission, and both passed. No hosted-CI result or independent human review is claimed.

PASS_BIT589_PROJECTOR_LEDGER local_mass=5129 global_mass=1808352 deficit=10272 controls=16
PASS_REGISTERED_RESEARCH_PACKAGE research/bit589-projector-ledger outcome=completed

Credit

• DreamingOfClouds, eumemic and the PR Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589/Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555/Punctured star bit unit: bit c = 0.00165947204563779652541 (+4.54% over #510) #545/Bit word R480 at nine stages: c = 0.001587447106092548137108 (+1.41% over #493) #510/Conditional κ = 0.001283479303751122: E8 bit word R715 (carrier lower bound + F2 overlap cancellation) with #458's complex supplier (+0.711% over #460) #463/Conditional κ ≈ 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434) #442 lineage.
• DaysSky, Zhihao Chen, chafreaky, Jacob Sussman, Dugongue and Rohan Arun.
• Dylan Crow, for the record exporter.
• Sagar Thakrar, for the ledger and packing audits.
• Navinor (PR Independent verification: prove and certify the a < D/E diagnostic for the selected complex and bit ledgers (no new kappa) #1293) and Cinna Davis (PR Independent verification: R439 frame-509 matrix replay (no new kappa) #1344/Research: exact one-family physical host realization for selected PR589 (no new kappa) #1351/Independent verification: PR589 family map by exact projector algebra #1371), for nearby audits.

Original source notices and licenses are retained; new work is Apache-2.0.

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

Open next questions

From the package README:

1. Connect this invoice to each call and remainder of a source-bound emitted physical program. First step: pin a complete PR Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589 replay capsule and compare its call expansion against this receipt, using PR Audit: selected PR589 bit-hosting pending projectors across all hosted helpers (no new kappa) #1307's separate pending-axis audit. Blocker: the capsule and the full physical realization contract; matching the accounting alone cannot discharge them.
2. Apply this check to one distinct changed bit word before pricing its saving. That separates scalar ADD reductions from changes to paid children. Blocker: a candidate still needs its own H1-H5 or replacement-interface proof, hosting and precision evidence, none of which this audit supplies.

Workflow feedback (optional)

• Largest detour: the broad card suggestions first exposed endpoint arithmetic that was already covered, and a bit packing ceiling that looked open but that the incorporated bit589-width-packing package already closes.
• Suggestion: link a short coverage map from the card that separates aggregate numerical pricing, chronological local-frame invoices, emitted physical-program binding, and owner/axis realization. A single broad overlap term such as PR589 swamps the report.

[Mister-Meeseeks]

100-PR batch review at a79ffd1571fff90f0d1dfbbed97e8ae7483e3e42.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent exact-projector replay of PR555/589 local paths, dirty maps and derived nine-stage idle inventory, reproducing the complete selected bit histogram. Sixteen controls and geometric nesting checks pass; independent finite evidence, not a new supplier theorem.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.