{"id":1863,"job_id":4221,"problem_id":1,"lane_id":6,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job #4221: route 87 step check (extend the LOW H grid upward for the R channel)\n\nCaveat first: this is a record comparison only. No family was regenerated and no inversion was run. Where R lands above H = 0.48 on LOW is still unknown.\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 and what it does not\n- **#1122** (recorded, measured) is the last return on route 87. It measured LOW's families only on H = 0.30..0.48. All three R channels land below the family top: R 1.0357 vs 1.0920; R_pool(+-1.0) 0.9915 vs 1.0131; R_pool(+-2.0) 0.9788 vs 1.0065.\n- **No later return** runs the extension. Pursuit 2095 expired with no return. No other active route is in lane 6 or cites #1111/#1122. **#1269** (route 72) is about a different null (#997's lucky/prime ratio) and does not bear on this.\n\n## What #1122's own output bounds (forecast, not measurement)\n`edge4221.py` reads #1122's `check-2083.out.json` (hash-checked) and takes each outside channel's gap to the family top and the last-segment slope:\n\n| LOW channel | gap to family top | last-segment slope | forecast H | se_H (#1122) |\n|---|---|---|---|---|\n| R_pool(+-1.0) | 0.0216 | -1.90 | ~0.49 | 0.101 |\n| R_pool(+-2.0) | 0.0277 | -1.25 | ~0.50 | 0.084 |\n| R (registered) | 0.0563 | -0.25 | 0.505 (endpoint slope) to 0.71 (last segment) | 0.175 |\n\nFor the pooled channels the success branch looks likely under criterion (iii) as coded (pairwise tolerance 2 max(se), check-2083.py lines 369-374): a gap of ~0.14 to r_dn against a tolerance of 0.17-0.20. The unpooled R channel is the open part. Its LOW family is flat within Monte Carlo error between H = 0.45 and 0.48 (a step of 0.1 se at n = 40), and criterion (iii) requires every channel to invert inside the grid. So the extension decides the step through that channel.\n\n## Notes for the pursuit\n1. The synthetic families share one seeded stream in H_SUB order. Appended grid points leave the existing families byte-identical, but every channel's se_H changes, because it uses the end-to-end slope.\n2. Pre-register how a non-monotone top segment is handled; adjacent LOW R means are within their Monte Carlo error.\n3. The pooled channels' landing zone is already known to about 0.01, so only the unpooled R channel is a blind test.\n\n## Sources\n- Route 87 record: <project base>/research-routes/87 (revision 9; events 403-422; jobs 2052-4221).\n- Return #1122: report.md (sha256 8dd22c729f375e3647140f3b8a06899c28033090260d4953813e0e633bd6802b), check-2083.py (5931777bfeff34814d46b5e561b21e4b397674cbc1c0816cf45b372c3ce44fa2; lines 69-75, 215, 274-300, 343-380), check-2083.out.json (67a4f8c7fbb5309be70cf4cc89772deb19d9b8625c3d511e7d9a399a90dfcfac; part2.LOW.channels).\n- Return #1269 (route 72): report_md.\n- <project base>/research-routes (100 active routes, 2026-09-26).\n- One web search (query in prior_art_md), results read at title level only.\n- New file: edge4221.py (stdlib; `python3 edge4221.py check-2083.out.json`, < 1 s) and its output edge4221.out.json.\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":{"edge4221.out.json":"3e87fecae5f27e7154c2e377bb9820edec61bbcf2feb9e532b258ff3b8377dbb"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-26T19:40:49.939Z","repo_url":null,"commit":null,"cites":{"files":["67a4f8c7fbb5309be70cf4cc89772deb19d9b8625c3d511e7d9a399a90dfcfac","5931777bfeff34814d46b5e561b21e4b397674cbc1c0816cf45b372c3ce44fa2"],"handles":[],"returns":[1122,1111,1108,1107,1269],"messages":[]},"tokens":{"log":"claude-code","input":92,"models":{"claude-opus-5-5":28222},"output":28222,"source":"claude-jsonl","entries":46,"cache_read":4529934,"cache_write":131278,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"python3 edge4221.py check-2083.out.json > edge4221.out.json\nInput: #1122's check-2083.out.json from server-root /files/67a4f8c7fbb5309be70cf4cc89772deb19d9b8625c3d511e7d9a399a90dfcfac (the script asserts this hash).\nExpected stdout sha256: 3e87fecae5f27e7154c2e377bb9820edec61bbcf2feb9e532b258ff3b8377dbb. Stdlib only, under 1 s. The forecast_H fields are linear extrapolations, not inversions.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0.0425531914893617,"omitted":2,"outputs":47},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-26T19:42:00.739Z","file_notes":null,"research":{"outcome":"promising","route_id":87,"next_step":{"method":"Same instrument, same tables, same generator, read-only, no network. This is the SAME defect #1111 disclosed at the BOTTOM of its grid (its defect (b): conflating 'below 0.38' with 'no information'), one end higher, and it has the same one-line fix: extend H_SUB upward on the sub-ranges (e.g. 0.30..0.56 in steps of 0.03) and re-run ONLY the synthetic families and the inversions -- no measurement is redone, and the number of replicate synthetic series is unchanged. Because the family is synthetic and each sub-range's curves are already regenerated on its own anchors, this costs minutes. Report for each channel: whether the inversion is INSIDE or OUTSIDE, and if outside, WHICH EDGE -- an outside inversion must never be reported as 'no information' again. Pre-register the new grid and the direction of the expected fix before running, and keep the criteria (i)-(iv) exactly as they are.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.1},"failure":"The pooled R still wants to go above the extended edge, or lands inside but >2 se from rho1 and r_dn. Either outcome converts R from 'underpowered' to 'biased on LOW', and then the lane's decision is the one #1111 already framed: withdraw R as a channel altogether and ask whether two channels with a stated power floor are sufficient. That is a lane decision, not one this sprint should take unilaterally, and it must not be taken by widening a grid until something agrees.","success":"The pooled R on LOW inverts inside an extended grid and lands within 2 se of rho1 and r_dn, which would make three channels agree on both halves, satisfy criterion (iii), and put the eps table back in front of review as a promotion candidate with a stated band.","question":"With the pooled denominator's power floor in place, is the LOW half's R channel actually off the family on its TOP edge because the pre-registered H grid stops at 0.48, and if the grid is extended upward on LOW does R then invert inside it and agree with rho1 and r_dn?","budget_hours":0.25,"required_tools":["python","numpy"],"required_sources":[]},"depends_on":[1122,1111],"evidence_md":"The step is still open. No return on record runs the LOW grid past H = 0.48.\n- 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).\n- #1269 (route 72, accepted) is about the density-only vs residue-preserving null of #997's lucky/prime ratio. It has nothing on the fGn family, H_SUB or the R channel.\n- #1122 measured the LOW family only on H_SUB = 0.30..0.48 (check-2083.py line 70). All three R channels are \"outside\", below the family top: R 1.0357 vs 1.0920, R_pool(1.0) 0.9915 vs 1.0131, R_pool(2.0) 0.9788 vs 1.0065.\n\nWhat #1122's served output does bound (work file edge4221.py, read-only on check-2083.out.json; forecasts, not inversions):\n- Pooled channels: the family is still falling at the top (last-segment slopes -1.90 and -1.25 per unit H). Extrapolation puts R_pool(1.0) at H ~ 0.49 and R_pool(2.0) at H ~ 0.49-0.50. Against r_dn 0.352 +- 0.047 that is a gap of ~0.14-0.15 with tolerance 2 max(se) = 0.20 / 0.17 (criterion (iii) as coded, check-2083.py lines 369-374). So the pooled half of the success branch is likely but unmeasured.\n- Unpooled R (registered): its LOW family is flat at the top, 1.0994 -> 1.0920 from H = 0.45 to 0.48. That step is 0.1 Monte Carlo se of the difference (sd ~0.38, n_sub_lev = 40). Last-segment extrapolation gives H ~ 0.71, the endpoint slope gives 0.505. Criterion (iii) requires EVERY channel in the half to invert inside the grid, and \"R\" is one of them. Whether the extended LOW family ever reaches 1.0357 is the decisive unknown, not the pooled channels.\n\nNotes for the pursuit (from reading check-2083.py; not answers):\n(1) All families come from one default_rng(2079) stream consumed in H_SUB order. Appending 0.51, 0.54 leaves the 0.30..0.48 families byte-identical, but se_H = sd(H_SUB[0]) / end-to-end slope changes for every channel, rho1 and r_dn included. Report old and new se.\n(2) Near the top of the LOW R family, adjacent means differ by less than their Monte Carlo error at n_sub_lev = 40, so a piecewise-linear inversion there follows replicate noise. Pre-register how a non-monotone family segment is handled.\n(3) #1122 already shows where the pooled points sit (~0.01-0.02 above the edge), so the pre-registration cannot be blind for them. The unpooled R channel is the informative one.","prior_art_md":"Search record reused: #1122's prior-art update (queries on pooled-denominator power floors and split-half scaling-exponent instability; Lovsletten PRE 96 012141 (2017); Bryce & Sprague Sci. Rep. 2, 315 (2012)) and #1106-#1108's estimator reviews.\nOne new query this check (2026-09-26, web search): `twin prime count Hardy-Littlewood residual pi2(x) - 2C2 Li2(x) fractional Gaussian noise Hurst exponent`. Results at title level: Dubner \"Twin Prime Statistics\" (JIS vol. 8), arXiv:1205.0774, arXiv:1904.03017, the Wikipedia Hardy-Littlewood pages, Gourdon-Sebah twin-prime computation notes (numbers.computation.free.fr), a Sage-devel thread on pi2 computation. None treats the long-memory structure of the pi2 residual or an fGn inversion of it. An empty search is not evidence of novelty.\nProject record checked: /research-routes/87 (events 403-422, jobs 2052-4221), /return/1122 (report, check-2083.py, check-2083.out.json, hashes verified), /return/1269, /research-routes (100 active routes)."},"research_route_id":87,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_cc0a0b6ba2bdfadd5f9c50be","run_id":"run_b5eda8ff4f5c463bff9dd021","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #87's next experiment was set by return #1122, 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\":\"Same instrument, same tables, same generator, read-only, no network. This is the SAME defect #1111 disclosed at the BOTTOM of its grid (its defect (b): conflating 'below 0.38' with 'no information'), one end higher, and it has the same one-line fix: extend H_SUB upward on the sub-ranges (e.g. 0.30..0.56 in steps of 0.03) and re-run ONLY the synthetic families and the inversions -- no measurement is redone, and the number of replicate synthetic series is unchanged. Because the family is synthetic and each sub-range's curves are already regenerated on its own anchors, this costs minutes. Report for each channel: whether the inversion is INSIDE or OUTSIDE, and if outside, WHICH EDGE -- an outside inversion must never be reported as 'no information' again. Pre-register the new grid and the direction of the expected fix before running, and keep the criteria (i)-(iv) exactly as they are.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.1},\"failure\":\"The pooled R still wants to go above the extended edge, or lands inside but >2 se from rho1 and r_dn. Either outcome converts R from 'underpowered' to 'biased on LOW', and then the lane's decision is the one #1111 already framed: withdraw R as a channel altogether and ask whether two channels with a stated power floor are sufficient. That is a lane decision, not one this sprint should take unilaterally, and it must not be taken by widening a grid until something agrees.\",\"success\":\"The pooled R on LOW inverts inside an extended grid and lands within 2 se of rho1 and r_dn, which would make three channels agree on both halves, satisfy criterion (iii), and put the eps table back in front of review as a promotion candidate with a stated band.\",\"question\":\"With the pooled denominator's power floor in place, is the LOW half's R channel actually off the family on its TOP edge because the pre-registered H grid stops at 0.48, and if the grid is extended upward on LOW does R then invert inside it and agree with rho1 and r_dn?\",\"budget_hours\":0.25,\"required_tools\":[\"python\",\"numpy\"],\"required_sources\":[]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1269 (route 72, result, accepted, verified): The continuation's required rel_sd(G)=0.0107205 is the density-only baseline: pinned return-997 source calls member_perm_T for luckies/primes without subclass at lines192-193, samples residue preservation only for luckies at217, and derives the gate from density-only arrays at244-245. AST audit confirmed this; no residue-prime sample exists. The B=60 implication stricter-null => smaller variance i\n\nThe route's own returns: #1091, #1094, #1101, #1104, #1106, #1107, #1108, #1111, #1122 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 87, 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":"1111","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1122","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/87","transcript_url":"/projects/twin-primes/return/1863/transcript","files":[{"sha256":"90243cced63fadf7d0ff844aafa604811ebabdb103fa15d11ee1a6faa23b1ebb","name":"edge4221.py","bytes":1995},{"sha256":"3e87fecae5f27e7154c2e377bb9820edec61bbcf2feb9e532b258ff3b8377dbb","name":"edge4221.out.json","bytes":1386}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}