{"id":7067,"job_id":13961,"problem_id":1,"lane_id":32,"type":"explore","user_id":121,"model":"gpt-6-astra","provider":"openai","report_md":"The assigned Q-xchannel-closedform is already answered at its stated finite scope: xchan-at29.md sections5-6 records both blind tests, @29 HIT and @31 SURVIVES WITH A MEASURED OFFSET under the original inherited sigma, with d=-0.41% and -0.48%; the separately attributed slot-clustered comparison scores both within its HIT band. This is MEASURED historical evidence, not an exact law or an asymptotic theorem. The later37 record rejects seven registered candidates under its declared comparison, leaving the structural Q-xchannel-offset PARTIAL. No scientific computation was repeated. The stale PARTIAL question status is addressed by audit 7065 through a two-line owning-ledger revision with preserved historical body and corrected-row preview, because the platform forbids directly editing generated QUESTIONS.md. That audit is a proposal pending its ordinary review/integration, not an assertion that the live registry has changed. The uncovered analytic derivation concerns the separate offset question. A missing original test, a different registered requirement or contrary source evidence would reopen this narrow conclusion. Searched for the exact joint-deficit / 4S2 / super-W triple terminology and inspected the closest primary published work: Goldston and Yildirim, Higher correlations of divisor sums related to primes I: triple correlations, Integers 3 (2003), A05, https://math.colgate.edu/~integers/d5/d5.pdf (definitions and Theorem 1.1), also https://arxiv.org/abs/math/0111212. That work averages products of truncated divisor sums and derives singular-series main terms. It does not evaluate this natal-conditioned, mixed-sign, product-of-scour-primes-greater-than-W normalized census. No exact external match was returned by this search; this is not a claim of literature-wide absence. The genuinely uncovered analytic step is a derivation/error theory for that different statistic and its offset; it is outside the already completed two-test question. Internal import-stein.md identifies 4S2 as a full-CRT Bernoulli variance defect but supplies no transfer theorem to the super-W statistic.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-11-06T23:51:43.307Z","repo_url":null,"commit":null,"cites":{"returns":[7065]},"tokens":{"log":"summary","input":111724,"models":{"gpt-6-astra":17986},"output":17986,"source":"reported","entries":0,"cache_read":3488128,"cache_write":0,"observed_models":[]},"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":"max","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"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":"dept_2e6f65f85bbd2da1f9dae4ec","run_id":"run_f049d1d8233b4e460e7d8c6f","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"wuhongtangcha-cmd","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 47 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-xchannel-closedform` (PARTIAL): Does the zero-parameter closed form for the joint deficit survive its two blind tests at @29 and @31?\n  Record so far: 1 - J = 4S2 is the only one of the three pre-registered laws left standing and it is not exact: a clean hit at @29, z = -0.90, and 4.93 sigma low at @31 under the inherited sigma_J = 0.000024 (section 7), while item-x-offset.md section 4's calibrated slot-clustered sigma scores the same law at z = -\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. After a verified result or release, stop if your person's assignment cap or session length is reached. Otherwise call `GET https://solveathome.org/projects/twin-primes/start` once with this run's saved headers for the next authorized assignment. Do not poll.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"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/7067/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"91317a4c54f967c86e2ceac38e74643707988fe0d846521bdcbfe3281c06d533","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}