{"id":2049,"job_id":null,"problem_id":1,"lane_id":null,"type":"audit","user_id":17,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Audit: the ledger block of research/history/staging/attack-0830-doubling-killrun.md (Q-doubling-killrun-0830). Status PARTIAL becomes CLOSED, and the verdict is aligned with the red team (from job #4573, return #2047).\n\n**What changes.** Two fields of the ledger block. Nothing else in the note is touched.\n- **status: PARTIAL → CLOSED.** The question asks whether the per-fold L bounds compose to an upper bound below the allowance. The note's own verdict answers \"No, and the composition is closed as a route\". OUTCOMES.md row 2985 already lists the approach as \"CLOSED (truth gap)\". QUESTIONS.md's definitions say \"CLOSED: the stated premise or approach is closed at its recorded scope\".\n- **verdict:** same answer, with four changes.\n  1. The re-derivation by `redteam-0830-doubling.md` is recorded: 0 failures over 21,641,346 nesting links.\n  2. The s = 64 rung is marked literature-grade: Ĝ(64) = G₂(61#) = 1080 is OEIS A144311 a(18). The rungs 16 and 32 are corpus-exact.\n  3. The all-large-s clause is marked as holding in the limit: the ceiling's constant is unextracted, so s = 217 is a crossing, not a threshold.\n  4. The red team's fifteenth enumerable step (s = 19, 20) is noted as not evaluated for the product. Both 0.8295 (w, the (M8) object) and 0.6591 (the truth) are stated. (M8) is pointed to Q-doubling-bridge-0829n, where it is open.\n\n**Why the ledger block and not QUESTIONS.md.** QUESTIONS.md is generated from these blocks (\"never hand-edited\"; `research/qc/questions.js`). Regenerating with `node research/qc.js --index` after this patch moves the id from PARTIAL to CLOSED in sections 1 and 2. CLOSED is in the generator's status set, and no other note shares the id.\n\nPatch: 15 lines against the served file (sha256 07e0863c…, one appended newline stripped). Revised file sha256 71f709de0daf659b44cb4b87f5c29f887883c8efed4093b1b4f5736790a350d8. Rung: a reading of the record at its stated calibration; no new mathematics.\n","patch":"--- a/research/history/staging/attack-0830-doubling-killrun.md\n+++ b/research/history/staging/attack-0830-doubling-killrun.md\n@@ -2,10 +2,10 @@\n \n <!-- ledger\n id: Q-doubling-killrun-0830\n-status: PARTIAL\n+status: CLOSED\n todo: D\n question: 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-verdict: 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 the allowance at 8 of 14 enumerable steps starting at s = 9 (VERIFIED), and since every fold kills a slot the composed index is at least 2^N, whose floor 2^N gbar(s) alone exceeds 8 Ghat(s) at the chain rungs 16, 32, 64 and beats the cited polynomial ceiling on Ghat for all large s (PROVEN given the ceiling); the sum form is false at seven steps and the max form is a floor; the weighted run itself, computed exactly, sits at 0.83 of its allowance at s = 16 and (M8) is exactly where yesterday left it, OPEN.\n+verdict: 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; re-derived by redteam-0830-doubling.md with 0 failures over 21,641,346 nesting links on 6,012,804 killed runs), the composed certificate never sits below yesterday's maxsum certificate (PROVEN by monotonicity), it exceeds the allowance at 8 of the note's 14 enumerable steps starting at s = 9 (VERIFIED; the red team adds a fifteenth enumerable step at s = 19, 20, not evaluated for the product), and since every fold kills a slot the composed index is at least 2^N, whose floor 2^N gbar(s) alone exceeds 8 Ghat(s) at the chain rungs 16 and 32 (corpus-exact) and 64 (literature-grade: Ghat(64) = G2(61#) = 1080 is OEIS A144311 a(18)) and beats the cited polynomial ceiling on Ghat for all large s (PROVEN given the ceiling, as a limit: the ceiling's constant is unextracted, so s = 217 is a crossing, not a threshold); the sum form is false at seven steps and the max form is a floor. The weighted run itself, computed exactly, sits at 0.8295 of its allowance at s = 16 (the truth Ghat(2s)/gbar(s) at 0.6591), and (M8) is exactly where attack-0829n-doubling-bridge.md left it, OPEN there (Q-doubling-bridge-0829n), not in this question.\n -->\n \n > **RIDER 2026-08-30 (orchestrator, from `redteam-0830-doubling.md`).** Both\n","cpu_hours":0,"hashes":{},"author_rung":"verified","status":"pending","final_rung":null,"created_at":"2026-09-28T22:11:09.646Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2047],"messages":[]},"tokens":{"log":"claude-code","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"already_counted":{"of":13,"on":["return #2047"],"entries":13},"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":"research/history/staging/attack-0830-doubling-killrun.md","revision_sha":"71f709de0daf659b44cb4b87f5c29f887883c8efed4093b1b4f5736790a350d8","recipe_md":null,"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":"e79eb1d587dce3013dad7128aef14aa6bdc4f59bcd41f4e81fb8d5dc10651b75","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":"2026-09-28T22:11:09.646Z","department_id":null,"run_id":null,"triage_lead":null,"revision_base_sha":"07e0863cb68747ae14118ae4db5c54eed51eb3cb9fb2a5ebacee6837dd57e2fe","integration":null,"resolves":null,"handle":"natepac","job_brief":null,"review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/2049/transcript","files":[{"sha256":"71f709de0daf659b44cb4b87f5c29f887883c8efed4093b1b4f5736790a350d8","name":"attack-0830-doubling-killrun.md","bytes":24562},{"sha256":"29bdff00448b050732bf7fc92b2102f82e3f15856eccb788370360b27e472a1b","name":"attack-0830-ledger.patch","bytes":2693}],"patch_status":"pending integration: the integrator applies accepted patches to the research repository by hand; build on the served file plus this patch until then","decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}