{"id":5589,"job_id":11323,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 94: Wang's tie DFS at 71# and 73#: 4 ties in 2 sigma-orbits at each, one mirror seed pair; route 86's DP confirms the DFS tie sets at 53# to 73#; n = 22 priced at 7.7 CPU h\n\n## Result\n\n`wang_ties 20 1397` (71#) and `wang_ties 21 1529` (73#) both terminated inside the 3 h job cap. At both\nlevels every printed tie converts to a position that passes certification. The positions are\nsigma-closed and their T_19 residues form a single mirror pair. n = 22 (79#) is priced, not run.\n\n| x | n | G2 | ties = nmax | sigma-orbits | T_19 seed pair (mirror) | split class at w_prev | CPU s (chimaera, measured) |\n|---|---|---|---|---|---|---|---|\n| 53 | 16 | 870 | 2 | 1 | 1984889, 7713929 | w 47: L 4, [132, 108, 210, 420] | Studio only |\n| 59 | 17 | 966 | 8 | 4 | 3259691, 6439031 | w 53: L 3, [60, 708, 198] | Studio only |\n| 61 | 18 | 1080 | 4 | 2 | 1606949, 8091659 | w 59: L 3, [90, 612, 378] | 108.2 |\n| 67 | 19 | 1284 | 2 | 1 | 3941657, 5756747 | w 61: L 4, [30, 402, 270, 582] | 144.6 |\n| **71** | 20 | 1398 | **4** | **2** | **4460219, 5238071** | w 67: L 4, [30, 708, 144, 516] | 1,358.1 |\n| **73** | 21 | 1530 | **4** | **2** | **875207, 8822951** | w 71: L 3, [420, 294, 816] | 6,917.5 |\n\nThe 71# and 73# rows are new. The 53# to 67# rows reproduce #1166: this lane's ties14 to ties18 outputs are byte\nidentical to the served files (raw sha256 in `../control/studio/raw-sha256.txt` and\n`data/cs-wang-n18/raw-sha256.txt`). At 67# (`ties19.out`) m = 2 and the attaining slot 3941657 agree with route 349's record (#5158 section 4).\n\nConversion and certification (`wang_crt.py`, stdlib, exact integers): x == 1 (mod 6), x == 2 - 6 r_p\n(mod p), position = x - 2 (mod x#). Each position is checked by direct gcd over the primes <= x: both\nends are slots, the forward gap is exactly G2, no slot inside. Then sigma closure p -> -p-G2-2, the\norbits, the T_19 residues and the split class at w_prev (the #424 / #5090 `split_class` definition).\nThe converter reproduces #1166 crt53-61.out at 53#, 59# and 61#. Outputs: `wang16_crt.json` to\n`wang21_crt.json`. Positions at 71# and 73# are in those files (mod 71#, mod 73#).\n\nThe single-pair statement (one mirror pair of T_19 seeds per level) holds at every level from 53# to\n73#. The #424 ancestry test was not run beyond the split class, because its definition beyond\n`split_class` is not in the files this lane read.\n\n## Independent completeness check: route 86's DP\n\nRoute 94 asks for route 86's DP (`complete2028.py`, return #1079, sha256 26cc202e..., H29) on one\nposition per seed at 59#, 61# and 67#. **At every level from 53# to 73# the DP confirms the DFS tie set**:\nfor each T_19 seed, the DP's completions equal the number of DFS ties with that residue, the\ncompletions sum to nmax, and the positions rebuilt from the DP's completing residue tuples are exactly\nthe DFS positions of that seed (set equality mod x#, each position certified by direct gcd).\n\n| x | G2 | seed | inner T_19 slots | DP completions | DFS ties with this seed | positions equal | CPU s (Studio, measured) |\n|---|---|---|---|---|---|---|---|\n| 53 | 870 | 1984889, 7713929 | 26 | 1, 1 | 1, 1 | yes | 0.05 (both seeds) |\n| 59 | 966 | 3259691, 6439031 | 31 | 4, 4 | 4, 4 | yes | 0.45 |\n| 61 | 1080 | 1606949, 8091659 | 34 | 2, 2 | 2, 2 | yes | 1.10 |\n| 67 | 1284 | 3941657, 5756747 | 41 | 1, 1 | 1, 1 | yes | 0.47 |\n| 71 | 1398 | 4460219, 5238071 | 49 | 2, 2 | 2, 2 | yes | 101.9 |\n| 73 | 1530 | 875207, 8822951 | 58 | 2, 2 | 2, 2 | yes | 68.3 |\n\nOutputs: `dp/dp53.json` to `dp/dp73.json` (with the residue tuples and the masks kept per stage), and\n`dp/dp<x>.time.txt` (`/usr/bin/time -l`; peak RSS 30 MB to 101 MB up to 67#, 5.8 GB at 71#, 5.0 GB at\n73#). Studio, nice 10, one process, Python 3.11.15 through `uv run --offline`.\n\nHow it was run. The served `analyse()` is not practical past 43# as written (measured at 53#): its\nforward DP keeps every reachable covered-slot mask, and the copy of that loop in `dp/probe_dp.py` held\n64,246,940 masks after the last prime and took 412.9 s at 53# for one seed (`dp/probe_dp53.out.txt`,\ncount 1). Its tuple reconstruction then scans every mask of the previous stage for each residue, which\nwas not run. With 31 to 41 inner slots at 59# to 67# the mask count is bounded only by 2^31 to 2^41;\nthis lane did not price the served loop there. So the levels ran through `dp/dp_prune.py`, which imports\n`complete2028.py` unchanged for `primorial`, `primes_between` and `slot`, builds the same per-prime\ntables and runs the same forward DP, with one prune: after the stage of prime q_i a mask is dropped\nwhen its count of uncovered inner slots exceeds the largest number of slots the later primes can kill\n(sum of each later prime's largest alive kill set). A dropped mask cannot reach the full mask, so the\nfull-mask count is unchanged. Tuples are listed by a forward walk through the masks that reach the full\nmask and turned into positions by CRT.\n\nControls for the pruned DP. (1) The served `complete2028.py`, run unchanged on the Studio, reproduces\nthe served `complete2028.out` on its six cases (37#, 41#, 43#, both seeds each) in every field except\nthe timings (`dp/complete2028_studio.out.txt`, `.json`; 19.5 CPU s, 3.1 GB peak RSS, measured).\n(2) `dp_prune.py --served` gives the same completions and the same residue tuples on those six cases\n(`dp/dp_prune_served_cases.json`). (3) At 53# the served DP loop and the pruned DP agree (count 1 for\nseed 1984889). This is a check of the arithmetic of one prune, by this lane's code. It does not\nreread the derivation of route 86's DP.\n\nWhat this confirms and what it does not. The DP counts, for a fixed T_19 seed, every alignment mod\nx#/19# that attains G2. It confirms that the DFS missed no tie that shares a residue with a tie it\nfound, at 53# to 73#. It does not test seeds the DFS never printed. At 53# to 67# that is covered by the\nengine_ei census of #5090, run in this sweep over all 378,675 T_19 slots: its COUNT(G2) position set\nequals the DFS tie set at 53# and 59# (control), at 61# (`../r15-61-census/analyze61_cs.json`) and at\n67# (`../r349-controls/run67/cert67_1278.json`, `../r344-m-ladder/data/e67/count67_1284.json`), and it\ncertifies CERT(G2) = 0 at 61# and 67#. At 71# and 73# no full-slot census was run, so a seed outside\nthe DFS output is not excluded there by this sweep.\n\n## Cost ladder and the price of n = 22\n\nMeasured, one core each. Studio wall: n = 15 2.09 s, n = 16 3.61 s, n = 17 17.67 s. chimaera CPU:\nn = 18 108.2 s, n = 19 144.6 s, n = 20 1,358.1 s, n = 21 6,917.5 s. Peak RSS is 14.7 MB at every level.\nSuccessive chimaera ratios are 1.34, 9.39 and 5.09, with geometric mean 4.0.\n\nRoute 94's own price was 1 to 4 h for n = 20 and 5 to 15 h for n = 21 (estimate). Measured: 0.38 h and\n1.92 h.\n\nn = 22 (79#, target 1709), estimate: 6,917.5 s times 4.0 gives about 27,700 CPU s, 7.7 CPU h. The\nobserved ratio range, 1.34 to 9.39, brackets it at 2.6 to 18 CPU h. Route 94 priced it at 20 to 60 h.\nThe central estimate exceeds the 3 h job cap. The served patch has no top-level branch split, so a run\nwould need one `--open` gpud job of about 8 to 18 h, which the head would have to agree to. The brief\nputs n = 22 beyond pricing out of scope, and the head ruled it out: the 2.6 to 18 CPU h range\n(estimate) breaks the 8 CPU h cap. Not run.\n\n## Run list\n\n| gpud job | command | wall s | CPU s |\n|---|---|---|---|\n| #794 cs-wang-n18 | `sh wang.sh 18 1079`: `g++ -O2`, then `./wang_ties 18 1079` | 108.6 | 108.2 |\n| #795 cs-wang-n19 | `sh wang.sh 19 1283` | 145.3 | 144.6 |\n| #796 cs-wang-n20 | `sh wang.sh 20 1397` | 1,371.2 | 1,358.1 |\n| #1093 cs-wang-n21 | `sh wang.sh 21 1529` | 7,118.6 | 6,917.5 (cgroup 6,917.5) |\n| Studio | `./wang_ties 14..17` at nice 10 (`../control/studio/ctl.sh`) | up to 17.7 | |\n\nSource: `wang_ties.cpp.txt` of #1166 (sha256 1072bebc..., the patched source), built with g++ 16.2.0 on\nchimaera and Apple clang 21.0.0 on the Studio. The patched file was read in full.\n\nThe patch against Wang's original (`../control/wang-patch/compare.txt`). `patch` applies #1166's\n`wang_ties.patch.txt` to Wang's original `a144311.cpp.txt` (oeis.org/A144311, sha256 6ddb723a...,\n4458 B) with all 5 hunks, and the result is byte-identical to `wang_ties.cpp.txt` (sha256 1072bebc...).\nSo the code this sweep ran is Wang's original plus that patch. #1166's `wang.cpp.txt` (e6bcff12...)\ndiffers from the original only in a `<cstdlib>` include and a `main()` that reads n from argv; it is a\nsibling edit, not the patch base, and the patch does not apply to it (4 of 5 hunks fail).\nExact command lines: `../jobs/submitted.txt`.\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- dp_prune.py and probe_dp.py import #1079's complete2028.py, which needs numpy, so they are not stdlib-only. wang19_crt.json and complete2028.py must sit beside the script.\n- The served complete2028.py control is 19.5 CPU s in its time file against 19.8 in the CPU table.\n- CPU: 8,528.3 s exact for wang_ties n = 18 to 21, 194.3 s for the DP runs, plus about 468 s of DP probes (wall, upper bound).\n- `control__wang-patch__compare.txt` records the patch check.\n","patch":null,"cpu_hours":2.55,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-23T11:58:09.024Z","repo_url":null,"commit":null,"cites":{"returns":[1176,1166,1079]},"tokens":{"log":"claude-code","input":2,"models":{"claude-opus-5-5":201},"output":201,"source":"claude-jsonl","entries":1,"cache_read":102752,"cache_write":359,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Build #1166's wang_ties.cpp.txt, then `./wang_ties 19 1283` (144.6 CPU s measured) and compare with `data/cs-wang-n19/ties19.out.txt`. `python3 wang_crt.py` certifies the 71# and 73# tuples in under a second. With #1079's complete2028.py beside it: `python3 dp/dp_prune.py 67 1284 wang19_crt.json dp67.json` (0.5 CPU s, Python 3.10 or later); `confirms_dfs_tie_set` must be true.","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":[{"sha":"2b2311a7f2d261230afac412288e2e8df8d626d05f9cf176953703d1696ad308","name":"dp__probe_dp.py","notes":["prints what looks like progress or timing to stdout on line 26 (\"print(q, len(dp), round(time.time() - t0, 1), flush=True)\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-23T11:58:09.024Z","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 94's next step: run wang_ties at n = 20 and 21 (and price 22), convert and certify each tie, test sigma-closure and seeds, and check completeness with route 86's DP at 59#, 61#, 67#.\n\nWhy this step: Wang's DFS with ties is the cheapest record instrument past 61#; the DP check makes its tie sets independent of one code.\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/5589/transcript","files":[{"sha256":"50457d6c807d00fa8b378fcb95bd80dd0ad239ed58bb2424fa717acc21e756dd","name":"RESULT.md","bytes":8507},{"sha256":"85c1ee3f36db2aa18bc480fc3c6f784f49bbf5d84456fe135bda756fb6a3388c","name":"control__wang-patch__compare.txt","bytes":1141},{"sha256":"28fdf3326e964b1f3ea3095d7f07aa120cfab664d623e66e81fed1dad8edf197","name":"data__cs-wang-n18__build.txt","bytes":173},{"sha256":"912a1d6dcbc26788a948a25f11de175a138a0db9d75fa065f20ee7cb5b81e5e8","name":"data__cs-wang-n18__cost.jsonl","bytes":248},{"sha256":"71a1bddc7522e48829c7d498ddf4fc6545942c6aef229f0f9df70438621857c0","name":"data__cs-wang-n18__raw-sha256.txt","bytes":156},{"sha256":"dc6c481170c40bac73a79b88100cb06e23e2fa61acd9dc2f69649d860d71c152","name":"data__cs-wang-n18__ties18.err.txt","bytes":7},{"sha256":"fa9441fe6cdf9ed03a94da84581d396f9ba7cf3b0b40bf71d5eb01ba4fbfd124","name":"data__cs-wang-n18__ties18.out.txt","bytes":445},{"sha256":"3a4d9293f30caf157a2baea14ac6ffb630ad11491253390832b9408fbd331223","name":"data__cs-wang-n19__cost.jsonl","bytes":248},{"sha256":"1abb154bf99c04b0da4e2de618df3653a63a2b9e6fa59d48ea618436b5d1d063","name":"data__cs-wang-n19__raw-sha256.txt","bytes":156},{"sha256":"c11dc1a5b0690cf3828d4778dfbf1010a1b9281704ed93cfc74480edd0459bfb","name":"data__cs-wang-n19__ties19.err.txt","bytes":7},{"sha256":"dfd8c3a0091f5f0aa4e7c7734ad4fc593e7d8913c60c3f8e3410d643917b3cd7","name":"data__cs-wang-n19__ties19.out.txt","bytes":242},{"sha256":"088b0ff32b595f24db06641f871b4b9c1d7df3863fe4a5484d520aa04417735b","name":"data__cs-wang-n20__cost.jsonl","bytes":252},{"sha256":"a66ff5d89719494ed9ddb2dde71070f169006be887747c958f042ebcbf0ef953","name":"data__cs-wang-n20__raw-sha256.txt","bytes":156},{"sha256":"73b1fb316aa894b517bf0365d6f7decde1e9874cc1c0f764f6fbb6e541fcc884","name":"data__cs-wang-n20__ties20.out.txt","bytes":486},{"sha256":"fb1e142d4d6c25657218e6e56618db74f2b4d681f04e97e1a565df66efee3b51","name":"data__cs-wang-n21__cost.jsonl","bytes":276},{"sha256":"fc21f36f2b62aab7afde9b67db83e519b4f7234f8709bff764174e57f67c82be","name":"data__cs-wang-n21__raw-sha256.txt","bytes":156},{"sha256":"1c3b95469fc25028b555b2f6da2afb24674a1039897889490f34445f0efebde0","name":"data__cs-wang-n21__ties21.out.txt","bytes":515},{"sha256":"9947ce45ef5967c1bd0a1ac4dc27f0e9b95cc4535ce04b25c59b6617c7bb24ce","name":"dp__complete2028_studio.json","bytes":3317},{"sha256":"1c2367e6b5bfdd292c60e36a45f3b9d926730875cb38a108ddc198580e544198","name":"dp__complete2028_studio.out.txt","bytes":1069},{"sha256":"e05dcf67fb5e8ea2c4a13a12bc6e7ee4f39c93bd817031152119d5a3af73610f","name":"dp__complete2028_studio.time.txt","bytes":84},{"sha256":"3b95b22aa84561954b4d1129b5118a103b961b726c9f7f80c6f2924c5756446b","name":"dp__dp53.json","bytes":1403},{"sha256":"d7a0f06205da6517eedcb431541782c66deaea9410cbf42978e34ca25cfe136c","name":"dp__dp53.time.txt","bytes":81},{"sha256":"a1e5adce106271050151088a80d31e98324f226cefa24d3ee27e7cf1300f07c9","name":"dp__dp59.json","bytes":2222},{"sha256":"689f263668ddbe4c2fb76bbb35ecf5abdbbf4c11299b3e9df8a0726d3b8a353c","name":"dp__dp59.time.txt","bytes":81},{"sha256":"cf2dcfae53a44348ca8176a51ed99f711b8d4764378875bcc6dc3a0d176f42ad","name":"dp__dp61.json","bytes":1826},{"sha256":"5089b3c6941376c06d0d52937efc96016b08a5d6ae196923469f0097dbb20184","name":"dp__dp61.time.txt","bytes":82},{"sha256":"36fca1d08d986f5f4a1a647beadce7456e5746eaa4e345c14c43e45109a02a98","name":"dp__dp67.json","bytes":1618},{"sha256":"a374af2c26d59420ca261b66b03787ffb236ed8077eaadb2e9510c8e083d44c0","name":"dp__dp67.time.txt","bytes":81},{"sha256":"78105aff8a743975ace8748fd5d0318d5a68a1de14ded444ee4903c6f0c4fbc1","name":"dp__dp71.json","bytes":2020},{"sha256":"8f0a67c0d0568c99a11087cfb6f45e85d0e928541e9192baf6c36049d16174ad","name":"dp__dp71.time.txt","bytes":85},{"sha256":"116aae9e798f3e260f2cc925ba8a20ccff3d39f07a3acbec3d7ef33ca2abb351","name":"dp__dp73.json","bytes":2109},{"sha256":"2ad69347e9b28f2f6750011a2ae268331d6e85e0138cf854455fc09fbd0fd32f","name":"dp__dp73.time.txt","bytes":84},{"sha256":"07d9a9e8281dfcab5314551d6683fc3e45fb22cbc0bdbaa57c81d7c1295a343b","name":"dp__dp_prune.py","bytes":5841},{"sha256":"ad240efac86ffbbc140bf2ccdcaa0aedf7da993677f6c705b99a093617b82dbe","name":"dp__dp_prune_served_cases.json","bytes":3573},{"sha256":"2b2311a7f2d261230afac412288e2e8df8d626d05f9cf176953703d1696ad308","name":"dp__probe_dp.py","bytes":1100},{"sha256":"13aebb3c8e1fa9bf1fc9bc67a5d76bc728975b8d4b3762e18751b958fe344fe7","name":"dp__probe_dp53.out.txt","bytes":311},{"sha256":"6dc1ae3a57905b692de89e367c94662f117bdb7f5eb0156e83d12860cb1e0102","n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