# Executed briefs of the 2026-09-06 bounded round These are the briefs as they stood in `AGENT-START.md` when the round was dispatched. Outcomes: [next-transfer-review.md](../../next-transfer-review.md), [corner-branch-diagnostic.md](../../corner-branch-diagnostic.md), [next-correlation-source-map.md](../../next-correlation-source-map.md). ## 3. Copy-ready briefs (as dispatched) Use one brief per worker. Each worker owns only its named new files. Do not edit shared state, generated indexes or another worker's files. Reports carry a ledger block with the assigned id, `todo: C` and an honest `parity:` line. The coordinator integrates them in one pass. No nested delegation. Return when the acceptance criteria are met or the specified missing input is identified; do not expand the campaign. ### A. Adversarial verification of the new transfer **Question:** does `prime-band-transfer.md` (1)--(6) follow at exactly its stated scope? This is a fresh correctness check of a newly written derivation, not an instruction to strengthen it. **Read:** that note; review 21 F6--F7; the primary source arXiv:2512.01739v2 Theorem 3.1(ii), Remarks 3.2 and the definition of M. The source hashes are in the owning note. Also check MRT equation (1.12), which justifies the safe parameter L=(log X)^(1/4); do not replace it by L=log X. Do not reprove the source theorems. **Check separately:** multiplicativity on coprime inputs; the uniform O(1) pretentious-distance comparison for all Fourier parameters; integrability and the order of Tonelli; functions fixed for each outer X; no common-exceptional-set assumption; exact moving windows; CRT error versus N>=sqrt(X); the number of mesh intervals; and the final continuous-versus-dyadic distinction. Use adversarial examples to test any claimed implication. No extrapolation from finite numerical checks. **Return:** a compact per-step pass/fail table and the first actual gap, if any, with a counterexample or missing hypothesis. Do not repair a new deep analytic gap by inventing a theorem. If all steps pass, state the weaker payoff and what is still open. **Files:** `next-transfer-review.md`, optional `next-transfer-review-validation.js`. **Ledger:** `Q-next-transfer-review`. **Stop:** once the listed checks are discharged or a load-bearing counterexample is found. No new literature campaign or broader proof. ### B. Exact implementation of a branch-preserving diagnostic **Question:** can future experiments inspect the full coefficients without silently dropping small cofactors, proper powers or non-squarefree inputs? Implement the exact identity in ยง2 as a reusable local driver. **Read:** `data-reuse-audit.md`, `corner-correlation.md` sections 1.1 through 1.4, `agent-readiness-validation.js`, and the relevant OUTCOMES entries. Use `data-reuse/factor-windows.json`; preserve its source and factor hashes. Do not regenerate a large census or overwrite that input. **Requirements:** expose explicit interval and cutoff arguments; compute the direct divisor formula and the expanded prime-power formula independently; preserve the full interval defining a fiber even on an archived prefix. Split summands into P=(prime r,s=1), S=(prime r,s>1), Q=(proper prime power r), retaining the resulting 3-by-3 contribution matrix. Report signed totals, absolute term totals, grouped absolute totals and support counts separately. Report both gcd branches and non-squarefree n classes. Identify floating logarithmic sums as measured; use integer prime-log coefficient vectors for the identity check. **Controls:** deleting S/Q must break a populated fixture; count repeated powers separately; reconstruct every input integer from its factors; all categories must sum to the direct result. Reject parameter sets with empty categories as tests of those categories. The actual fixed-eta corner is often empty at retained sizes: do not call a proxy window the asymptotic corner. Include an explicit `--fixture` mode with disclosed toy cuts to exercise all branches, and label it as finite algebra only. **Return:** the driver, one bounded factor-reuse run and its embedded output, the active controls, and a short specification. No sign trend, asymptotic saving or new research closure may be inferred. This is tool preparation for a later named mechanism, not another sign-search attempt. **Files:** `corner-branch-diagnostic.js`, `corner-branch-diagnostic.md`. **Ledger:** `Q-corner-branch-diagnostic`. **Compute cap:** two minutes per run, ten minutes total; use existing factors only. Stop on a failed identity rather than running larger inputs. ### C. Bounded source lookup for a materially different interface **Question:** is there a primary-source statement with stronger scale or coefficient quantifiers than the new transfer actually used? This is source lookup and hypothesis matching, not a request for a new theorem. **Read:** `SEARCH-CONVENTIONS.md`, `prime-band-transfer.md` and relevant OUTCOMES entries. Inspect at most three candidate primary statements, including newer versions of an existing source only if its theorem changed. Search in weighted multiplicative correlations, almost-all-scale Chowla/Elliott and shifted convolution conventions. For each candidate give version/date, theorem number, actual coefficients, normalization, rate with constant dependence, scale quantifier and first unmatched hypothesis. Compare separately against the prime-cofactor subfamily and full C-product. A result on Liouville, fixed functions, bounded affine coefficients or continuous scales is not automatically a match. Do not use an abstract or a search summary as the theorem. **Return:** at most three source rows and a reason to reopen one precise step, or a scoped negative for the statements inspected. Send a genuinely new analytical requirement back to the coordinating reviewer. Do not claim no such theorem exists anywhere. **Files:** `next-correlation-source-map.md`. **Ledger:** `Q-next-correlation-source-map`. **Stop:** after three source statements or a demonstrated exact match. ## 4. Integration and stopping rule (as dispatched) The coordinating reviewer owns the complex next decision. Review A before promoting the new transfer; repair any finding locally. Review B's identity tests before using its output. A source lead from C does not authorize a theorem claim until its deduction and all errors are checked. If no matched new input remains, end the round with the precise missing estimate. Do not autonomously repeat it, enlarge the data, switch to another open conjecture or start TODO W without a separate assignment. Integrate useful results and failed steps by question in OUTCOMES. Update TODO C, CLAUDE, README Status, G2-STATE, the router and handoff together. Use the existing embed tool for producer output. Then run: ```sh node research/agent-readiness-validation.js node research/qc.js --index --strict node research/qc/selftest.js node research/audit-numbers.js git diff --check ``` Only the coordinator runs the full number audit, avoiding duplicate compute. The old six-hour campaign allowance is a total ceiling, not a fresh allowance for each worker or round. The smaller diagnostic caps above apply to this round. Make local commits after review and passing checks; do not push or circulate externally. Every final report begins with the unchanged open margin and says what was checked, what changed, which controls ran, what remains unproved and which exact input would justify another round. If only documentation or tooling changed, say so. A green gate is not a proof certificate.