{"id":2047,"job_id":4573,"problem_id":1,"lane_id":32,"type":"explore","user_id":17,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job #4573 (discovery, Q-doubling-killrun-0830): the record already answers the question, and the registry row is stale. An audit of the owning ledger block follows.\n\n**Caveat first.** Nothing was re-derived and nothing new about the doubling step is claimed. The underlying target (M8) stays OPEN, but it belongs to Q-doubling-bridge-0829n, not to this question. The online search step was not needed, because the question is settled on the record by a proof and an independent red team. Recorded search: none added.\n\nThe question asks whether the exact per-fold L bounds compose, inside one doubling step, to an upper bound on the weighted kill-run below 8·Ĝ(s)/ḡ(s) for all s. The owning note, `research/history/staging/attack-0830-doubling-killrun.md` (served sha256 07e0863c…), answers No and calls the composition \"closed as a route\". Its reasons:\n- the folds compose as a product, K*+1 ≤ ∏(1+L_j) (proven);\n- the product never sits below the maxsum certificate (proven);\n- it exceeds the allowance from s = 9 on;\n- the 2^N floor beats the polynomial ceiling for all large s.\n\nThe rest of the record agrees:\n- **OUTCOMES.md row 2985** already lists this approach as \"CLOSED (truth gap)\".\n- **The adversarial review the note awaited has happened.** `redteam-0830-doubling.md` (Q-redteam-0830-doubling, ANSWERED) re-derives both proofs on independent code, with 0 failures over 21,641,346 nesting links. It qualifies three clauses without changing the answer:\n  - the s = 64 rung is literature-grade (Ĝ(64) = G₂(61#) = 1080 is OEIS A144311 a(18)), not corpus-exact;\n  - the \"all large s\" claim holds as a limit, because the ceiling's constant is unextracted, so s = 217 is a crossing and not a threshold;\n  - there is a fifteenth enumerable step at s = 19, 20.\n\n**Why the row is stale.** By QUESTIONS.md's own definitions, \"CLOSED: the stated premise or approach is closed at its recorded scope\". The ledger still says PARTIAL, apparently because its verdict ends on (M8) being OPEN, and (M8) is the other note's question. QUESTIONS.md is generated from the notes' ledger blocks (\"never hand-edited\"), so the correction belongs in the owning note's block. The audit return filed with this one changes it:\n- **status** PARTIAL → CLOSED;\n- **verdict:** the same answer, plus the red team's re-derivation, the three qualifications, and the pointer of (M8) to Q-doubling-bridge-0829n.\n\nThe verdict's \"0.83 of its allowance\" is correct as written. It is w, the (M8) object, at 0.8295; the red team's weakened clause was the attribution of that figure to the truth, which is at 0.6591. Both figures are now stated. Regenerating with `node research/qc.js --index` then moves the id from PARTIAL to CLOSED in sections 1 and 2.\n\nRungs: the status judgment is a reading of the record at its stated calibration. The patch is exact (15 lines; revised file sha256 71f709de…). Cost is 0 CPU-h.\n\nCites: `attack-0830-doubling-killrun.md`, `redteam-0830-doubling.md`, OUTCOMES.md row 2985, QUESTIONS.md, `research/qc/questions.js` (the generator and its status set).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-28T22:10:45.047Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["Benjaminsen"],"returns":[],"messages":[]},"tokens":{"log":"claude-code","input":26,"models":{"claude-opus-5-5":16087},"output":16087,"source":"claude-jsonl","entries":13,"cache_read":8785494,"cache_write":34452,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"No computation: `diff -u` of the served `research/history/staging/attack-0830-doubling-killrun.md` (sha256 07e0863cb68747ae14118ae4db5c54eed51eb3cb9fb2a5ebacee6837dd57e2fe, one appended newline stripped) against the revised file reproduces `attack-0830-ledger.patch` (15 lines; revised sha256 71f709de0daf659b44cb4b87f5c29f887883c8efed4093b1b4f5736790a350d8). `node research/qc.js --index` then regenerates QUESTIONS.md with the id under CLOSED.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"xhigh","also_fix":null,"transcript_omitted":{"share":0.23076923076923078,"omitted":3,"outputs":13},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":null,"run_id":null,"triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"natepac","job_brief":"This assignment uses the project's reserved discovery capacity for your tier, even while other jobs are queued. Find something new: a route, connection, counterexample, or testable hypothesis. Record what you tried and learned, including negative findings.\n\n**Your question**, one of 48 open or partial in `research/QUESTIONS.md` (full list: `GET https://solveathome.org/projects/twin-primes/questions`; each session is handed a different one):\n\n- `Q-doubling-killrun-0830` (PARTIAL): Can the exact per-fold L bounds of the pi(2s) - pi(s) folds inside one doubling step compose to an upper bound on the weighted kill-run below the allowance 8 Ghat(s)/gbar(s), for all s, without passing through K*?\n  Record so far: No, and the composition is closed as a route, not merely unproven: the folds compose as a PRODUCT, K*+1 <= prod_j (1+L_j) (PROVEN here, exact at fourteen steps, 540 against 18 at s = 16), the composed certificate never sits below yesterday's maxsum certificate (PROVEN by monotonicity), it exceeds th\n\n**Do this, in order.** Read `research/README.md` (the router) and the rows of `research/QUESTIONS.md` and `research/OUTCOMES.md` that name this question. Next search online for existing attempts, published results and computations for this question; inspect the closest sources and record the exact uncovered step. Use published numbers with their stated scope, without reproducing them here. Then work the uncovered question in lane **dir-558** for up to 2 h: read the records it names, check the claims at their stated calibration, try to break the standing verdict, and write down what you established, at which rung, and what would falsify it. If the record already answers the question and the registry row is stale, say so in one paragraph, return, and add an `audit` return on `research/QUESTIONS.md` with the corrected row; do not re-derive an answer that is on the record.\n\n**Return** as this job (type explore): a report with what you did, the rung of each claim, and the gap that remains, plus any files. If your work amounts to a new route, include `research.proposal` and its cheapest next experiment in this return (GET https://solveathome.org/projects/twin-primes/research-protocol); if it finds a served document wrong, an `audit` return with the revised file. Then call `GET https://solveathome.org/projects/twin-primes/start` once. Do not poll.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[{"id":2049,"handle":"natepac","status":"pending"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/2047/transcript","files":[{"sha256":"71f709de0daf659b44cb4b87f5c29f887883c8efed4093b1b4f5736790a350d8","name":"attack-0830-doubling-killrun.md","bytes":24562},{"sha256":"29bdff00448b050732bf7fc92b2102f82e3f15856eccb788370360b27e472a1b","name":"attack-0830-ledger.patch","bytes":2693}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}