Research audit: exclude five bootstrap levels at PR387’s grid point

[BagMan9]

PR #387 checks that five bootstrap levels miss its κ at the published slack values. This scoped mathematical audit / negative result excludes all five-level choices in the retained recurrence accounting, allowing independent savings at every level and relaxing them up to the certified coarse-root upper endpoint. No new κ is claimed.

For the fixed starting saving a0=384599/10^10, the uniform envelope is A_j=u-u^j(u-a0), with compact-margin ceiling A_j/(1+A_j). Exact arithmetic places the five-level ceiling below #387's κ by between 0.546434 and 0.546435 units of 10^-18. The published six-level compact margin clears it by between 0.406 and 0.407 such units. Five levels would require an initial saving greater than 0.0005869935357213085... even in the optimistic envelope; a stronger-supplier control demonstrates that boundary.

All additions are confined to research/bootstrap-depth-audit/: written uniform proof, immutable source excerpts with SHA256/Git-blob pins and original notices, exact deterministic receipt, standard-library verifier, tests, local sprint claim and validation record. The verifier imports no predecessor implementation.

Reproduce from the repository root:

python3 -I -B -O research/bootstrap-depth-audit/verify.py --check research/bootstrap-depth-audit/EXPECTED.json

Expected: PASS_SCOPED_BOOTSTRAP_DEPTH_AUDIT; depths 0..5 excluded; six-round margin admitted; 9 controls rejected.

Validation on Linux x86_64 / Python 3.13.15: exact receipt matched; all seven additional tests passed, including 1,536 varying-savings schedules evaluated from the original cost exponents, 2,400 strict-grid cases, and optimized-process rejection of altered sources/receipts. All ten source files match the pinned Git bytes. python3 -B scripts/verify_selected_result.py and diff checks pass. make is unavailable, so the selected-record target's exact Python recipe was run directly. Full supplier/moment/47-constraint replays and repository-wide verification were not rerun; no remote CI pass is claimed.

The moment bracket and completed ordinary-supplier/row/restoration/tape/analytic interfaces remain inherited. This is a ceiling on certificates produced by the retained accounting, not an algorithmic runtime lower bound or a full multiplication proof. The six-level check covers the compact margin and recurrence gaps, not the whole construction. upstream/ and the selected #626/#543 frontier are unchanged.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Audited #387 head: d9fb9410b1ae6f6ada376a1e7fd12bc176e476ea. Assignment seed 73. No pinned coordination issue existed. The final pre-submission snapshot covered 586 open PRs through #767 and found no matching depth audit. Ahrazzle's earlier reported three-round replay/assembly comparisons are credited; this adds a continuous variable-savings ceiling and starting-supplier threshold. #657's broad assembly wall is distinct and not a dependency.

Credit Rohan Arun's #185/#387, Chafik Boukhalfa's #384 supplier lineage, eumemic's #315 outer engine, icekylinx, Zhihao Chen, RaD/hipotures and the preserved source notices. Contribution by Isaac Grannis (@BagMan9), with substantial OpenAI Codex assistance. Apache-2.0. No separate human or delegated-agent review is claimed.

[Mister-Meeseeks]

100-PR batch review at 57d8fbf2577bd4463834484264f980e0a7845824.

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

Reviewed scope: Bootstrap depth diagnostic for fixed suppliers and stated recurrence: five levels excluded in recorded domain, six feasible; no universal depth barrier.

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.