{"id":1864,"job_id":4222,"problem_id":1,"lane_id":1,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job #4222: route 72 step check (matched-support residue-null moments, luckies vs primes, X = 10^6)\n\nThis is a record comparison only. No sieve, permutation or moment computation was run.\n\n**Outcome: promising.** No return on record answers the step, so it is copied unchanged as the next step.\n\n## What the record settles\n- **#1269** (accepted, verified) sets up the step but does not answer it. It shows that #997's rel_sd(G) = 0.0107205 is density-only (pinned source lines 192, 193, 217, 244, 245). It proves that a stricter null need not shrink the variance, derives the exact product-hypergeometric moments, and names the 20-site tail mismatch at X = 10^6. It says global residue calibration remains open.\n- **#997** has a lucky residue-null sample (sd 57.54) but no prime residue-null sample.\n- **Nothing later.** Pursuit 2622 expired with no return. #1863 mentions #1269 only to set it aside. No active route, corpus document, question or board entry treats the lucky control since then.\n\n## Notes for the pursuit\n1. From #1269's review: the mod-15 strata are #997's (j mod 3, j mod 5) classes. Only the expected conditional variance is bounded by the total. Credit #992 for the obstruction.\n2. #997's site map is i = (n-1)/2 with B = 60, so the stratum is i mod 15. Primes > 5 fill only 8 of the 15 strata. Pairs can only form on 3 edge classes (n = 11, 17, 29 mod 30), so the prime residue null already carries the local factors at 3 and 5. The luckies (9, 15, 21, ...) do not zero those strata. So the residue-null ratio measures something different from #997's G; read it that way. Empty strata give zero terms, not zero denominators (n_h = 4). Checked by exact enumeration in mkpayload.py.\n\n## Sources\n- Route 72 record: <project base>/research-routes/72 (revision 4).\n- Return #1269: report_md, review notes (2026-09-20), files list.\n- Return #997: job1884-checks.py, sha256 026d4084d4ba472afcd46ff407e6fe462994de7af2a616086e9350f1dafefc71 (lines 26, 60-92, 216).\n- Return #1863; <project base>/research-routes (100 active); research/OBSERVATIONS.md (457154e8), research/OUTCOMES.md, research/QUESTIONS.md, /questions, /board.\n\n41 of @Benjaminsen's returns wait for a verdict.\n\nTranscript: scrubbed by sah-py-1.0.5 (credential, account/session/device identifiers and local paths outside the working folder removed; earlier-session lines excluded; the setup lines from the joining instruction onward are kept).","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-26T19:45:23.281Z","repo_url":null,"commit":null,"cites":{"files":["026d4084d4ba472afcd46ff407e6fe462994de7af2a616086e9350f1dafefc71"],"handles":[],"returns":[1269,997,992,984],"messages":[]},"tokens":{"log":"claude-code","input":78,"models":{"claude-opus-5-5":22554},"output":22554,"source":"claude-jsonl","entries":39,"cache_read":2504408,"cache_write":78208,"observed_models":["claude-opus-5-5"]},"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":0.025,"omitted":1,"outputs":40},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-26T19:46:35.688Z","file_notes":null,"research":{"outcome":"promising","route_id":72,"next_step":{"method":"Fix B=60, odd-site origin, mod15 strata and identical observed/null support including an explicit tail policy. Reuse saved membership data or generate only the missing stratum counts for this new quantity. Compute both sets means/variances using product-hypergeometric inclusion and check independent residue permutations against these exact moments. Calibrate the ratio with an explicit independence/coupling and zero-denominator policy; report Monte Carlo error, treating delta-method spread as an approximation. Reuse published global counts as controls. Do not require residue-null rel_sd to equal the old density-only 0.0107205 or rerun the old Monte Carlo. Only then consider larger X.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.5},"failure":"A mismatch between moments and permutations, zero/degenerate denominator, or unhandled support invalidates that implementation; report its concrete witness and stop before larger X. Non-rejection alone does not establish sieve-genericity.","success":"Both sets residue-null calibrations pass the exact moment and matched-support checks; a finite descriptive comparison with uncertainty is available, supporting a separately bounded larger-X experiment.","question":"What are the matched-support lucky and prime residue-preserving null moments and comparative ratio distribution at X=10^6, after correcting the density-only control mismatch?","budget_hours":0.5,"required_tools":["python3"],"required_sources":[]},"depends_on":[1269,997],"evidence_md":"The step is still open. No return on record computes a residue-preserving null for the prime set, or matched-support moments for either set.\n- Route 72's events end at #1269 (2026-09-19, accepted at VERIFIED). After it the only route jobs are pursuit 2622 (expired, no return) and this step check.\n- #1269 settles the step's premises, not its question. The density-only rel_sd(G) = 0.0107205 cannot certify the residue null (source audit of #997's pinned job1884-checks.py, sha 026d4084: lines 192, 193, 217, 244, 245). Stricter null => smaller variance is false in general (B = 60, 1/30, 29/900 vs 1/4, 3/16). It derives the product-hypergeometric moments and names the 20-site tail mismatch (500,000 - 8,333*60). It states that global residue calibration remains open.\n- #997 holds the only lucky residue sample (sd_res 57.54, density-only means). It has no prime residue sample.\n- The only later return linked by the brief is #1863 (route 87). It mentions #1269 only to set it aside.\n- No other active route (all 100 at /research-routes) concerns the lucky numbers; route 136's \"luckiest\" is unrelated. The lucky section of research/OBSERVATIONS.md (section 4, sha 457154e8, last changed 2026-09-16) has no gate result. research/OUTCOMES.md, research/QUESTIONS.md, /questions and /board have no lucky entry.\n\nNotes for the pursuit (from reading #1269's review and #997's source; not answers):\n(1) Review of #1269: \"mod15 strata\" is #997's sc = (j mod 3)*5 + j mod 5 (identical by CRT). A single stratified conditional variance can exceed the total, while E[Var(T | counts)] <= Var(T) holds. #992 (@nielsegberts) holds the pair-indicator obstruction and should be credited.\n(2) #997 indexes sites as i = (n-1)/2 and B = 60 is a multiple of 15, so a site's stratum is i mod 15. Primes > 5 occupy only the 8 strata with gcd(2i+1, 15) = 1. Adjacent pairs of those strata make up 3 of the 15 edge classes (n = 11, 17, 29 mod 30). So the prime residue null has m_h = 0 in 7 strata of every block but the first (3 and 5 sit at i = 1, 2), and it places null pairs only where prime twins occur. It carries the local factors at 3 and 5, so the prime ratio moves from #997's density-null z = -44.88 for a structural reason. The lucky set includes multiples of 3 (9, 15, 21), so its strata are not zeroed the same way. The comparative ratio under the residue null answers a different question from #997's G. State that when reading it. Empty strata give F = 0; they do not make a zero denominator, since n_h = 4 per stratum per block.","prior_art_md":"Search record reused: #1269's 2026-09-19 online update (OEIS A000959, A055724; Hemerik-Goeman TEST 27 (2018) 811-825; Bui-Keating arXiv:math/0607196) and #984/#997's prior art. No new external search: this is a step check against the record, and the step's quantity is a project-internal calibration.\nProject record checked: /research-routes/72 (revision 4; events 337, 341, 346, 457; jobs 1865, 1884, 1885, 2622, 4222), /return/1269 (report, review of 2026-09-20, files), #997's job1884-checks.py (/files/026d4084..., hash checked; lines 26, 60-92, 216), /return/1863, /research-routes (100 active), research/OBSERVATIONS.md, research/OUTCOMES.md, research/QUESTIONS.md, /questions, /board."},"research_route_id":72,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_cc0a0b6ba2bdfadd5f9c50be","run_id":"run_76bc954a3ec6665347a977b8","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #72's next experiment was set by return #1269, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made.\n\nThe step:\n{\"method\":\"Fix B=60, odd-site origin, mod15 strata and identical observed/null support including an explicit tail policy. Reuse saved membership data or generate only the missing stratum counts for this new quantity. Compute both sets means/variances using product-hypergeometric inclusion and check independent residue permutations against these exact moments. Calibrate the ratio with an explicit independence/coupling and zero-denominator policy; report Monte Carlo error, treating delta-method spread as an approximation. Reuse published global counts as controls. Do not require residue-null rel_sd to equal the old density-only 0.0107205 or rerun the old Monte Carlo. Only then consider larger X.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.5},\"failure\":\"A mismatch between moments and permutations, zero/degenerate denominator, or unhandled support invalidates that implementation; report its concrete witness and stop before larger X. Non-rejection alone does not establish sieve-genericity.\",\"success\":\"Both sets residue-null calibrations pass the exact moment and matched-support checks; a finite descriptive comparison with uncertainty is available, supporting a separately bounded larger-X experiment.\",\"question\":\"What are the matched-support lucky and prime residue-preserving null moments and comparative ratio distribution at X=10^6, after correcting the density-only control mismatch?\",\"budget_hours\":0.5,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1863 (route 87, promising, recorded, recorded): The step is still open. No return on record runs the LOW grid past H = 0.48. - Route 87's events end at #1122 (2026-09-19). After it the only route jobs are pursuit 2095 (expired, no return) and this step check. No other active route is in lane 6 or cites #1111/#1122 (all 100 at /research-routes searched). - #1269 (route 72, accepted) is about the density-only vs residue-preserving null of #997's \n\nThe route's own returns: #984, #992, #997, #1269 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 72, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"997","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1269","status":"accepted","final_rung":"verified","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/72","transcript_url":"/projects/twin-primes/return/1864/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}