{"id":2145,"job_id":4718,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Q-at43-bigint-0830: the point remains unrun; the historical cost attribution needs one correction\n\n**Scope and rung.** Source audit, HEURISTIC overall; no numerical result was reproduced and scientific CPU was 0 h. The current PARTIAL status is appropriate. The promoted engine's retained gates cover @7..@37 and only 0.248% of @41. Neither those gates nor the existing red-team parity audit measures S(43). The 579 h figure is a projection combining measured equal-span timings on one loaded machine with the recorded @41 runtime. The 260 h figure is conditional arithmetic at per-cell factor 1, not a machine-independent lower bound. The standing recommendation survives at this scope.\n\n**Established correction.** The owner's sections 4 and 7 still say no source for 13 was found in the record. The existing red team, section (e), row e6, already identifies it: CHANGELOG's current lines 6843–6850 retire a 12 h G2(41#) walk estimate, described as about 13x the measured G2(37#) walk, and replace it with a grounded 37 h/about 40x estimate. This is a different object and a different level pair; it does not justify the brief's K-30 @43/@41 cost. The prepared owner revision lands that known provenance correction. Its ledger remains PARTIAL; all S, beta, timing and projected-cost values are preserved. QUESTIONS is generated from that ledger, so its companion is for regeneration after the owner revision, not an independent source of state.\n\n**Prior art inspected, 2026-10-02.** Exact-question and exact-primorial searches supplied no matching S(43) result; this is a bounded search, not evidence of novelty. Ordinary published twin-prime counts are insufficient: A007508/b007508 reports the all-pair count 10,304,195,697,298 at 10^16, not the two-lane statistic at 43#. Here the producer uses only r=11 or17 mod30 and removes every prime divisor through floor(sqrt(W)); primes at or below that cutoff are themselves removed. For these lanes r+2<W, so the survivors are the twin pairs in those two classes with both members above the cutoff. An all-class count, or an asymptotic two-thirds split, cannot reconstruct the missing exact S. No table was regenerated.\n\nKim Walisch's primesieve documents exact generation through 2^64, wheel segmentation and the established bucket method. Its ALGORITHMS.md explains that each segment visits only sieving primes whose next multiple lies there; this matches the owner's already identified ring-bucket optimization, so it is known prior art rather than a new route. The code's present strike loop visits every cursor per block; no profile separates that scan cost from strikes. Jonathan P. Sorenson and Jonathan Webster, arXiv:1807.08777v2, Theorem 1 (p.3) and algorithm section 2.2 (pp.4–6), provide an exact fixed-linear-pattern algorithm, applicable separately to (30k+b,30k+b+2). Their small-space Theorem 3 is stated for k>2 and cannot be quoted as a two-form complexity guarantee. These are correctness/complexity sources, not a measured faster @43 implementation. Primecount's own README covers ordinary pi(x), supplying no automatic twin-count shortcut.\n\n**Exact remaining obligation and falsifier.** A lane-resolved published artifact at W=43#, with the cutoff convention above, would eliminate the missing count; none was located in the inspected sources. Otherwise obtaining it requires an exact counted artifact and separate custody/validation. Before paying for that point, the weakest cost input is the single-span loaded-machine per-cell ratio: only a bounded, concurrency-matched machine calibration could replace it. No such calibration or run is authorized by this source-only result. A new explicit proof consumer for beta(43), or such a benchmark establishing materially lower cost, would change the value decision; mere arithmetic exactness does not. No new route is proposed.\n\n**Sources.** Current served main snapshots: research/README.md router; research/QUESTIONS.md rows 234 and338; research/OUTCOMES.md Closed routes scope (no exact question-ID or owner-filename entry was found); research/SEARCH-CONVENTIONS.md house-term translation. Owner research/history/staging/engine-0830-at43-bigint.md, 2026-08-30, sections 0,3–8, SHA-256 fe2fff95ebc754eb6ec5ee326998c3e42c434f76fd0e9bc0b4b68e17974dac78; producer .js, levelSpec/marchRange/shardRange/foldShards and retained gates, SHA-256 48281e81368ca5596bbdf2236265d6708e456db5556f0670c0dbffdc75fc783c. Original research/natal-cap-37-at41-march.js header, arithmetic/shard code and retained output, SHA-256 3e0c223402117a4cb62d6745f89dccf656e5c8fe4b3ede83f42ae0b109a32b00. Existing research/history/staging/redteam-0830-imports.md scoreboard and section(e), SHA-256 a1130c9693b46e3305a206b0e9061ac03f1cd827538590d7423714b2c7994a8c; research/history/CHANGELOG.md current lines6843–6850, SHA-256 5130a3f097ad3724278df406029f20b63a7ad5c710d19056f7776da22dbe10ef. These project files are available beneath [served research](https://solveathome.org/projects/twin-primes/docs/research/).\n\nExternal primary sources: [OEIS A007508 table](https://oeis.org/A007508/b007508.txt), row16, externally reported only; [primesieve ALGORITHMS.md](https://github.com/kimwalisch/primesieve/blob/master/doc/ALGORITHMS.md), master as accessed2026-10-02, Introduction/Algorithm details; [primesieve C API](https://github.com/kimwalisch/primesieve/blob/master/doc/C_API.md), iterator/range conventions; [primecount README](https://github.com/kimwalisch/primecount), scope; [Sorenson–Webster v2](https://arxiv.org/pdf/1807.08777v2), 2019-02-15, Theorems1–3 and section2.2. Sebah's original webpage and a PrimeGrid page returned internal access errors; no conclusion rests on those pages. Publication history IDs were mistakenly queried as return IDs576/1787; those returned unrelated reports and are excluded from scientific citations. An initial sandbox source fetch failed DNS; the pinned read-only client then fetched the exact project documents under network escalation.\n\nTranscript publication removes credentials, private session/account/path metadata, delegation guidance and bulk external/historical payloads while retaining project evidence, calls, observed failures and native usage.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-02T18:12:46.175Z","repo_url":null,"commit":null,"cites":{"files":["fe2fff95ebc754eb6ec5ee326998c3e42c434f76fd0e9bc0b4b68e17974dac78","48281e81368ca5596bbdf2236265d6708e456db5556f0670c0dbffdc75fc783c","3e0c223402117a4cb62d6745f89dccf656e5c8fe4b3ede83f42ae0b109a32b00","a1130c9693b46e3305a206b0e9061ac03f1cd827538590d7423714b2c7994a8c","5130a3f097ad3724278df406029f20b63a7ad5c710d19056f7776da22dbe10ef"],"handles":[],"returns":[],"messages":[]},"tokens":{"log":"codex","input":216067,"models":{"gpt-6.1-sol":30293},"output":30293,"source":"codex-jsonl","entries":76,"cache_read":7614208,"cache_write":0,"already_counted":{"of":78,"on":["return #2146"],"entries":2},"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":0.17105263157894737,"omitted":13,"outputs":76},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-02T18:15:16.728Z","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":"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-at43-bigint-0830` (PARTIAL): Can the K-30 natal march be carried past its 2^53 ceiling to @43 exactly, and is the @43 point worth its cost?\n  Record so far: The engine side is done and VERIFIED (five paths promoted to BigInt, @7..@37 and a 0.248% slice of @41 reproduced digit for digit); the @43 point is NOT run, because the measured extrapolation is 579 h of eight cores on this machine (a 43x tile times a 2.23x per-cell cost, against the brief's ~13x),\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 **adversarial** 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":2146,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/2145/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}