{"id":5588,"job_id":11321,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 86: the preregistered 43# seed profile of #5254 fails at w = 41, 6 seeds against 4 predicted; its pair form seeds(w) = nmax - sum N_q is false at w <= 37\n\n## Pre-registered prediction (copied before any binary was built)\n\nCopied verbatim in substance from return #5254 (job #10389), section 5 and section 8, on 2026-10-23,\nbefore `allseed_c.c` was compiled in this lane. Source file: `research/sah-state/2026-10-22/returns/05254.md`.\n\nInputs on record: 43#, G2 = 618, nmax = 8, record seeds 8521991 and 1177079 (T19 residues), 4 completions\neach, primes 23, 29, 31, 37 rigid and only 41 and 43 floating (#1079, #1084).\n\n| level | nmax | seeds at w = 11, 13, 17, 19, 23, 29, 31, 37 | at w = 41 | orbits |\n|---|---|---|---|---|\n| 43 (predicted) | 8 | 2, 2, 2, 2, 2, 2, 2, 2 | 4 | 1 ... 1, then 2 |\n\nCollision multiset: every within-seed pair has least differing prime in {41, 43}; every cross-seed pair\nhas least differing prime <= 11 (8521991 = 401 and 1177079 = 1289 mod 2310). So sum N_q = C(8,2) = 28.\n\nThe prediction fails if any seeds(w) differs from the row above, if sum N_q != 28, or if a seed has\ncompletions != 4.\n\nThe measured row and the comparison are added below this section after the run.\n\n## Measured row (2026-10-23, gpud job #797 cs-r86-x43)\n\nCensus: `./allseed_c 23 43 618 8` (served `allseed_c.c` of #3913, sha256 0e2efff2...), then\n`./align_c 23 43 618 <seed>` on each attaining seed (`align_c.c`, sha256 dfcc3894...), gcc 16.2.0 `-O2`\non chimaera. Outputs in `run43/`. Analysis: `python3 profile.py 43 618 run43/align_23_43_57020441.json\nrun43/align_23_43_166071809.json --wang wang14_crt.json --out profile43.json` (stdlib, exact integers).\n\n- Wheel 23: 7,952,175 seeds scanned, 2 attaining seeds (57020441 and 166071809 mod 23#), 4 completions\n  each, sum 8 = nmax (`matches_nmax` true).\n- The 8 positions mod 43# pass the direct gcd check over the primes <= 43 (both ends are slots, no slot\n  inside), the set is closed under p -> -p-620, and it equals the 8 positions converted from Wang's\n  ties14 tuples of #1166 (`wang14_crt.json`, from `../r94-ties-71/wang_crt.py`).\n- T19 residues 1177079 and 8521991, residues mod 2310 are 1289 and 401: the record seed word.\n\n| level | nmax | seeds at w = 11, 13, 17, 19, 23, 29, 31, 37 | at w = 41 | orbits |\n|---|---|---|---|---|\n| 43 (predicted, #5254) | 8 | 2, 2, 2, 2, 2, 2, 2, 2 | 4 | 1 ... 1, then 2 |\n| 43 (measured) | 8 | 2, 2, 2, 2, 2, 2, 2, 2 | **6** | 1 ... 1, then **3** |\n\nPair multiset: N_5 = 16, N_41 = 10, N_43 = 2, sum 28 = C(8,2). The loss identity\n`seeds(w) + sum(bucket - 1) = nmax` holds at all nine wheels.\n\nComparison with the three failure conditions of #5254 section 8:\n1. `seeds(41)` = 6, predicted 4. **The prediction fails at w = 41.** It holds at w = 11 to 37.\n2. sum N_q = 28: holds. (It holds for every 8-element set by the definition of N_q, so it tests nothing.)\n3. Completions per seed = 4: holds for both seeds.\n\nWhy w = 41 gives 6: within each seed the four completions take three residues mod 41, not two:\nseed 8521991 has residues 1, 6, 6, 40 and seed 1177079 has 37, 30, 30, 35 (each repeated residue is\na pair that differs only at 43). So 41 is free in each seed but does not split the four completions into\ntwo pairs. The #5254 derivation assumed the latter.\n\nA second finding. The pair form in #5254 section 4, `seeds(w) = nmax - sum_{q > w} N_q`, is false at\n43# for w = 11 to 37: it gives 8 - 12 = -4, the measured value is 2. Only the loss form is an identity.\nThis is the same pair-versus-loss defect #5254 section 3 found in #3913, now in #5254's own reduction.\nThe two forms agree here only at w = 41, where every bucket has size at most 2.\n\nMeasured cost (chimaera, one thread): allseed_c 374.3 s wall, 372.3 CPU s, peak RSS 128,560 kB; each\nalign_c 3.2 s.\n\n## 47# (first measurement, not finished at 3 h 13 min)\n\nBecause 43# finished under the 5400 s bound, `./allseed_c 23 47 708 4` was booked as gpud job #866\n(cs-r86-x47, one thread, `--for 3h`). It started at 08:12Z and printed nothing by its 3 h end. This lane\nstopped it at 11:25Z, after 3 h 13 min of wall time, as the brief caps jobs at 3 h and #5254 says not\nto let 47# consume the step. **The 47# row is not finished at 3 h 13 min on one core.** That is a\nstopped run, not a failure: nothing in it contradicts the prediction or the 43# row. allseed_c writes\nits JSON only at the end, so no partial count exists (`allseed_23_47.json` came back empty), and no\n47# seed profile is measured. The wheel-23 census at 47# is not complete within 11,580 s of wall time\non one chimaera core. Its CPU is at most that, and the wall is at\nleast 31 times the 43# run. nmax(47#) = 4 is on record from #1166 crt47.out, but no seed profile at\n47# is.\n\nWithout a census, the 47# cross-wheel profile follows from the 4 DFS positions in #1166 crt47.out by\nthe same `profile.py` arithmetic. Positions alone fix seeds(w) and N_q. That conversion is not a\ncensus and was not run here, since route 86's step asks for the census.\n\n\n## Filing\n\nFiles under subdirectories are attached with `/` flattened to `__`; files whose extension the server refuses are attached with `.txt` appended. Restore both before running the recipe.\n\n## Notes for the reader\n\n- Served code, not attached: engine_ei.py fb65b5f2..., par_ei.py 98c218cc..., check_ei.py 7072bd74... (#5090); allseed_c.c 0e2efff2..., align_c.c dfcc3894... (#3913); wang_ties.cpp.txt 1072bebc... (#1166); complete2028.py 26cc202e... (#1079). Studio: Python 3.11.15, numpy 2.4.6, Apple clang 21.0.0. chimaera: Python 3.14.7, numpy 2.5.2, gcc 16.2.0.\n- The prediction section of the report was committed (department commit 40ab4cb) before allseed_c was built.\n- CPU: 378.6 s exact for 43#, plus at most 11,580 s for the stopped 47# job (one thread, wall time, upper bound). The 3.32 h declared includes that upper bound.\n- sum N_q = 28 holds by definition for any 8-element set, so it tests nothing.\n","patch":null,"cpu_hours":3.32,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-23T11:57:31.703Z","repo_url":null,"commit":null,"cites":{"returns":[5254,5462,3913,1166]},"tokens":{"log":"claude-code","input":2,"models":{"claude-opus-5-5":201},"output":201,"source":"claude-jsonl","entries":1,"cache_read":102138,"cache_write":364,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Build #3913's served align_c.c with `gcc -O2`, then `./align_c 23 43 618 57020441` (3.2 CPU s measured); the JSON must equal `run43/align_23_43_57020441.json`. Then `python3 profile.py 43 618 run43/align_23_43_57020441.json run43/align_23_43_166071809.json --wang wang14_crt.json --out profile43.json` recomputes seeds(w) and the buckets.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":1},"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":"2026-10-23T11:57:31.703Z","department_id":"dept_206a3ecdf0ff5c212553942f","run_id":"run_99104b66381542cb4c86eb50","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"full","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":"RedesignedRobot","job_brief":"Route 86's next step: predict the 43# seed profile and {N_q} from #5254 before compiling, then run the served allseed_c census at 43# and compare.\n\nWhy this step: #5254's reduction of nmax to seed completions predicts the seed profile; a preregistered test at 43# checks it.\n\nStop when: Accepted with the committed outputs and the cheapest check reproducing; or refused with a reason that needs new work.","review_deferred":false,"in_triage":true,"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/5588/transcript","files":[{"sha256":"633e198976dfac6e8d95969ebc8d73f3a96e3cb28abbf1338bae6526eaef5c12","name":"RESULT.md","bytes":4874},{"sha256":"f8517ca99c6e23e9d110ba19c9a39f9044b1a041edd8d76322fb6bcc331498cc","name":"profile.py","bytes":3863},{"sha256":"86636959941801ba784231c10a8eb2807cd3d81baac5c1997a16a7d7e2114441","name":"profile43.json","bytes":2394},{"sha256":"aa07be344df8138a8fdce7a37be3c31c4845379a43b1036b8ca4ce39351d5c77","name":"run43__align_23_43_166071809.json","bytes":255},{"sha256":"0636f58b004131aba2cc84e5b74670e37dba2589977ddbca1a535be2ebc59748","name":"run43__align_23_43_57020441.json","bytes":254},{"sha256":"6ec5801ca19fa63b0cdcce96484009ac8fe316bc155b45bd8b3521929bd3d986","name":"run43__allseed_23_43.json","bytes":242},{"sha256":"73638763c8f9961bd4963ad42d8db309fee6a889060ade7254cce3778f2c094d","name":"run43__build.txt","bytes":321},{"sha256":"b7569ae465f627e486fcc9a30a8b3ebbdd02751707b0d419ba89e0e94530b606","name":"run43__cost.jsonl","bytes":744},{"sha256":"65ce6399d6cef92de18ae2a6a560f36fe59c00aa3915791fb7448634994acd93","name":"wang14_crt.json","bytes":894}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"77903b5fea200bf585ca69689f95d09b2244575db9e440b2ef0eadbdff834df7","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}