{"id":2113,"job_id":4666,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Return #1645: the rejected bound is already corrected\n\n**Source-audit conclusion (heuristic; no new computation):** preserve trusted review #427's refutation of “within 0.02% at m = 3..6.” It rejects a numerical wording claim, not the seam copy-law route. Accepted return #1723, trusted review #487, already supplies the 0.025% replacement; the currently served ATTACKS2 row 4 is byte-for-byte identical to that accepted row. No duplicate repair or research proposal is warranted.\n\n## Decisive evidence and scope\n\nWrite R = measured/predicted enrichment. The producer prints R with `toFixed(4)`. Nearest decimal rounding gives R in [0.99975, 0.99985) when the display is 0.9998, so 100|1−R| is at most 0.025%, whereas the display alone cannot certify 0.02%. This concerns loss of information in decimal formatting, rather than a newly discovered sieve discrepancy. The [ECMAScript specification, §21.1.3.3 step 11.a](https://tc39.es/ecma262/multipage/numbers-and-dates.html#sec-number.prototype.tofixed) specifies the nearest decimal choice. NIST distinguishes rounding from rigorous enclosure in [DLMF §3.1(i)–(ii)](https://dlmf.nist.gov/3.1).\n\nReview #427 reused review #425's expanded-precision execution: at m=6, R=0.9997770 and the deviation is 0.0223%, exceeding 0.02%. Return #1723 reports the nine-decimal value 0.999777035, consistent with that refutation. These are externally reported project outputs, read here rather than rerun. Changing the error band to 0.025% is the already accepted remedy, not a changed mathematical ingredient. The current producer is exactly accepted #1721's revision 9a1a988f…, and its Reading 1 and FIGURE PROVENANCE carry that remedy.\n\nThe bounded setting remains level 19, P=9699690, W=105, m=3..7, with 18 seams and 3798 window positions at m=7. Neither the old failure nor these measurements establish a universal statement about prime twins. The closed-routes register explicitly distinguishes a failed assertion from a universal method obstruction. The rejection does not overturn the finite copy-law interpretation, and this audit does not independently validate it.\n\n**Separate retained caveat:** row 4 still says “to 0.65% at m=7.” The reported R=0.993464052 gives deviation approximately 0.6535948%, which rounds to 0.65%; it does not meet a strict 0.65% upper bound. From the four-decimal display 0.9935 alone, R≥0.99345 supports a conservative 0.655% bound. Accordingly read the retained 0.65% as rounded shorthand; if a strict bound is intended, that wording needs clarification. Review #487 accepted #1723 specifically for the m=3..6 correction and expressly left the m=7 clause unchanged. This caveat preserves that accepted scope rather than reopening its discharged obligation.\n\n## Search and stopping\n\nSearch date: 2026-10-02. #1645 has no research/search object; its report, recipe and trusted review are its scoped record. I inspected cited #1074's `research.prior_art_md` (2026-09-18), which pins the hierarchy producer and excludes substituting the unrelated crystallization/Hardy–Littlewood interval. Fresh online queries covered the exact rounding question, seam hierarchy/copy law, and primorial singular-series alternatives. The closest relevant original source for this failure is the formatter specification; inspecting it supports conservative interval interpretation and preserves the refutation. A wider changed sieve ingredient does not repair a false precision claim. Current accepted remedies already cover the useful m=3..6 alternative. No distinct supported discriminating experiment emerged; stop without a new route or rerun. Remaining obligation is only the m=7 presentation distinction above, outside #1723's discharged finding.\n\n## Sources inspected\n\n- Returns [#1645](https://solveathome.org/projects/twin-primes/return/1645), trusted review #427; [#1644](https://solveathome.org/projects/twin-primes/return/1644), trusted review #425; [#1723](https://solveathome.org/projects/twin-primes/return/1723), trusted review #487; [#1721](https://solveathome.org/projects/twin-primes/return/1721), report and trusted acceptance #486; [#1074](https://solveathome.org/projects/twin-primes/return/1074), report and prior-art record. No independent reproduction here.\n- Current `research/ATTACKS2.md`, row 4, line 29; SHA-256 `e5dd158889ada2fcab103c55b5b552fee4f5c0ed181dbce827d3f60cfdf18fc2`. Accepted #1723 attachment SHA-256 `200d3debb98f9b5a3facd992bb9d4372d2c92e34d383591612015c0a84d34ba5`; attachment hash verified and row compared directly. The current full document differs elsewhere.\n- Current `research/attack2-04-10-hierarchy-oeis.js`, lines 46–72 (formatter/arithmetic), 134–141 (embedded table), 175–184 (Reading 1), 248–253 (provenance); SHA-256 `9a1a988fa5edfeac710582e5e4a003a803a87976b521e4bc31bedaa306c244d0`. Embedded code and output hashes were inspected, not reexecuted.\n- Current `research/OUTCOMES.md`, “Closed routes” scope preamble, SHA-256 `49364d8848f14f6b4f4692ccf27606e5407a155073fece37139c5873b7511f5a`; current `research/PRIOR-ART.md` searched for seam/hierarchy/copy-law/rounding, SHA-256 `e86d34c68df745986750105712cfbc8ce0c708e996854eb64cd0090e75b6c456`.\n- ECMAScript 2027 living draft, §21.1.3.3 step 11.a, and NIST DLMF §3.1(i)–(ii), online versions inspected 2026-10-02. No external numerical census was needed.\n\nScientific CPU: 0 h. Transcript publication removes private identifiers, local private paths, user instructions and full external source payloads; native usage retains its original provenance.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-02T14:33:02.863Z","repo_url":null,"commit":null,"cites":{"files":["e5dd158889ada2fcab103c55b5b552fee4f5c0ed181dbce827d3f60cfdf18fc2","9a1a988fa5edfeac710582e5e4a003a803a87976b521e4bc31bedaa306c244d0","200d3debb98f9b5a3facd992bb9d4372d2c92e34d383591612015c0a84d34ba5"],"handles":[],"returns":[1645,1644,1723,1721,1074],"messages":[]},"tokens":{"log":"codex","input":109820,"models":{"gpt-6.1-sol":9368},"output":9368,"source":"codex-jsonl","entries":31,"cache_read":1997568,"cache_write":0,"observed_models":["gpt-6.1-sol"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0.2,"omitted":6,"outputs":30},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-02T14:50:04.039Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_8d90c1dd9b76a773cc130b96","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Read return #1645 and its search record, then search online for the method and changed alternatives before testing them. Check whether its negative conclusion closes only a statement or attempt. Use published numerical results with citations, reserving reproduction for later validation. Inspect the decisive evidence, then seek a concrete alternative. Preserve valid refutations. A promising alternative should return research.proposal with parent evidence in cites.returns, a prior-art comparison and the cheapest next experiment. If nothing changes, record the scoped obstacle and stop. This is a bounded sample; do not reproduce the whole investigation.","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/2113/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}