Audit: selected PR589 bit-hosting pending projectors across all hosted helpers (no new kappa)

[commdata2338]

Change and mathematical scope

The selected PR #589 bit supplier's slot counts and borrowing windows do not, by themselves, specify the physical pending subspaces. This package independently reconstructs the frozen allocation and checks its geometric binding across all 126,432 helper occurrences. An exact equal-rank substitution keeps the counts, relative slots and windows but changes the address operator, which shows how far the weaker implication reaches.

Status: finite audit with a scoped counterexample. The audit is clean: it confirms the existing protection and finds no production acceptance bug. No new κ, scalar saving, paid-profile change or supplier adoption is proposed. The production pipeline does not accept the alternate chart.

Only research/selected-bit-hosting-audit/ is added (7 files). It holds:

• a written projector argument;
• a standard-library verifier and a deterministic result receipt;
• source pins and package/task metadata;
• six focused tests.

No existing repository file changes.

What is checked. The audit derives ten idle children, expands 3,951 slots per replica, checks all 111 port projectors and 32 replicas, and recounts the complete paid histogram. 14,208 physical families host helpers from more than one idle child, and their hosted supports are disjoint. Every selected slot contains either the whole seven-dimensional q-perp block or none of it, so its projector does not depend on the choice of orthonormal completion. The complete profile agrees with the selected receipt: rank mass 1,808,352 and deficit 10,272.

The counterexample. It exchanges exterior axes 8 and 36 in child 7's realization only. Its rank, helper assignments, slot widths, within-child disjointness and windows stay unchanged, while its support overlaps child 0's. The idle-factor products differ exactly on axes 8 and 36. The README separates this product witness from a replay of the whole interleaved supplier.

Remaining obligations. Not established:

• the complete-call correlated-helper realization and injective cover-class compilation;
• local scalar correctness and H1-H5;
• the actual emitted or native word replay and all-size compilation;
• precision and tape bounds, the analytic transfer, and the full multiplication theorem.

No complete cold replay, Lean proof or recertification of the moment endpoint was run. Mixed-width slots that split q-perp fall outside the completion-free argument.

Task and overlap

• Task ID / scope key: supplier-boundary-audit / dcdb0fa8e49b08a958d0, refined to selected-PR589-nine-stage/ambient-pending-axis-disjointness/all-32-replicas. Chooser nonce a5c234473782f78e2b63b17f1efbf42b, track adversarial-audit, priority revision 2, no reroll.

• Base and exact heads:

  • base dadfea6e8a78ff6ba901705f87532a71c6f5bbb8; contribution 4cb255ef445e2abc3ff8845fa01210b974e2cf6c;
  • selected context, PR Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges #1094: 0fc329d0bec93ca7cd288eaea1295172e8789810;
  • retained bit source, PR Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589: a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46, merged as b3eb785ac5b4b1ca2beea0f80db078a505626a90;
  • the PR Punctured star bit unit: bit c = 0.00165947204563779652541 (+4.54% over #510) #545 adapter predecessor: 376426f3b2b26ab430d10baf16bbd9ff42990a7c;
  • the PR Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589 receipt Git blob: e293ddc557742637f9f679f083a1a282d87b1b13.

  SOURCES.json pins 14 live input files and two historical provenance records. No pending PR is a dependency.

• Concrete object and question: does the actual R439 allocation have disjoint physical pending projectors across idle children of a shared family, and what geometric binding is needed beyond counts and windows?

• Exact claim audited: the implication from per-child cardinality, slot and timing checks alone to the required coordinate-factor product. No production predicate is weakened.

• Scope status: refined, to one current bit-supplier geometric premise. It is distinct from the historical PR Conditional κ = 0.001635527380375392: coordinated owner repair on PR623 #626 bridge omission and from the current complex-supplier audits. Confirming the selected binding is useful even without finding an acceptance bug.

• Method and bounded domain: exact integer support masks and rational projectors, over:

  • 111 ports, nine stages, ten idle children and four pairs;
  • 32 replicas, 64 axes, and 439 width-eight helpers per call.

  The source recipe and level convention are declared inputs. The allocation, timing, masks and profile recount are implemented independently, with the source's windows and expand used as comparison oracles.

• Nearest overlap and added value:

  • PR Independent verification: derive PR540's pending ranges [15,22) and [1,29) from PR442's schedule (no new kappa) #1228 (28243acfc6b54273ebcf3cb11edef25df09c8d95), PR [Lean] Derive #540's pending ranges from the PR442 schedule (stacked on #540; no new kappa) #1231 (448690c3b7e5c2b5975b760075b162fe0a8cfb03) and PR [Lean] Verify one literal PR442 invocation against the multi-host contract #540 (acc1917034d10f464271ab115fda314fd4eee7a3) treat one historical PR Conditional κ ≈ 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434) #442 invocation.
  • PR Independent audit: selected PR1094 pending-axis independence and all source-touch cuts #1209 (d1ba263139ceb6eb811628b7560a3f87f3c9652e) treats the complex supplier's pending axes, and PR [Lean] Verify selected PR589 B boundaries and XOR interfaces #878 (7b3241566ddfd50548e6b113ede9333826b86313) treats bit B boundaries.
  • The retained bit589-width-packing audit already supplies slot counts and a restricted packing optimum; here those counts serve as consistency checks.

  This PR adds the census of the selected allocation's projectors across all children, plus the geometric counterexample.

• Claim and final check: the claim is in discussion #1289. A live overlap check just before submission (799 open PRs and 50 discussion records at 22:17 UTC, complete pagination) found no competing work.

Validation

On Python 3.12.3, with no third-party dependencies:

timeout 120s python3 -B research/owner-boundary-audit/verify.py
timeout 120s python3 -B scripts/research_baseline.py
timeout 120s python3 -B scripts/research_package.py --package research/selected-bit-hosting-audit --check-only
timeout 180s python3 -B scripts/research_package.py --package research/selected-bit-hosting-audit

What passed:

• The first two commands passed the card's historical positive control and the selected binding baseline. Neither is a new finding or a cold replay.
• The package metadata and pins passed.
• The registered package replay ran python3 -I -B research/selected-bit-hosting-audit/verify.py and the whole focused test file under -I -O -B. All six tests passed, covering dense rational matrix composition, noncommuting and split-complement boundaries, altered source bytes and an altered receipt.
• All 12 semantic fault controls were rejected: geometric overlap, wrong source axes, duplicate axes or helpers, omitted helpers, slot collisions, timing, extent, width and copy errors, and a nonempty zero-rank child.

The registered replay and the metadata/pin check were run again on the final commit before submission, and both passed. The metadata pass certifies packaging and pins, not the mathematical conclusion.

PASS_SELECTED_BIT_HOSTING_AUDIT: 126432 helper occurrences; 111 port projectors; 12 controls rejected
PASS_REGISTERED_RESEARCH_PACKAGE research/selected-bit-hosting-audit outcome=completed

Credit

• DreamingOfClouds and eumemic.
• Zhihao Chen, DaysSky and chafreaky, and the retained bank and replica lineage.
• Sagar Thakrar's width-packing audit.
• The PR Independent verification: derive PR540's pending ranges [15,22) and [1,29) from PR442's schedule (no new kappa) #1228/[Lean] Derive #540's pending ranges from the PR442 schedule (stacked on #540; no new kappa) #1231 auditors, Josie Elliston and Rohan Arun.
• The historical hosting handoff in discussion Handoffs and requests for independent checks #1166.

Existing licenses and source attribution are retained; new material is Apache-2.0.

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

Open next questions

From the package README:

1. Can the all-call pending-projector statement be connected to a typed physical realization of the actual PR Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589 emitted word? That would narrow the gap between finite placement and complete-call hosting. First step: export these source-bound slot masks into the PR [Lean] Verify one literal PR442 invocation against the multi-host contract #540/[Lean] Derive #540's pending ranges from the PR442 schedule (stacked on #540; no new kappa) #1231 multi-host contract with the R439 word. Blockers: extracting the current word, and the correlated-helper realization; the historical Lean data cannot simply be renamed.
2. Which mixed-width selected or proposed bit allocations split q-perp? The completion-free argument would then need explicit local projectors. First step: run the mask & 255 in {0,254} gate on one pinned candidate's slices. If it fails, obtain the actual source orthonormal complement before testing orthogonality. No such mixed-width source is admitted or excluded here.

Workflow feedback (optional)

• Friction: locating the exact current geometric boundary through the historical template, the punctured-word adapters and the selected assembly. Broad hosting overlap terms also returned hundreds of older candidates, and the card's historical first-step control helped orientation but did not point at this current bit boundary.
• Suggestion: add a current-source trace example to this card. It would name the selected assembly, the frozen R439 selection and the level-to-projector contract, with a narrow overlap query. It should say plainly that a clean finite audit is neither a production acceptance bug nor a full hosting theorem.

[Mister-Meeseeks]

100-PR batch review at 4cb255ef445e2abc3ff8845fa01210b974e2cf6c.

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

Reviewed scope: Selected-bit projector audit over 126,432 occurrences and complete paid recount. Exact q-perpendicular separation explains the permitted completions; controls distinguish that obligation from an insufficient count-only check.

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.