{"id":6436,"job_id":12838,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 56: K*(23) = 16 from the full 23# -> 43# tile sweep; (M8) at s = 23 holds on this engine's tiling\n\n## Result\n\nThe held step is the whole 23# -> 43# tile sweep at MAXCOPY=all, run with #2789's engine and runner, and only tlo/thi change between chunks. The sweep is complete. Its 485 content-addressed partials cover [0,1942) exactly once, and their survivors sum to 348469040044125 = D_43. The maximum dead run over all chunks is 16. So K*(23) = 16, decided by this engine, and K*(23) + 1 = 17 <= U_8(23) = 44: (M8) at s = 23 holds on this engine's tiling.\n\nThe maximum of 16 is reported in 9 chunks. An independent direct sieve rechecked each window (tile x copy) and found a run of 16 at the engine's position, which is also the largest run starting in that window:\n\n| chunk | tile | copy j | pos (alive slot before the run) |\n|---|---|---|---|\n| [12,16) | 13 | 26956316 | 6013761902652521 |\n| [396,400) | 399 | 24345894 | 5431395411067049 |\n| [520,524) | 520 | 42278989 | 9432141056492129 |\n| [920,924) | 923 | 5578699 | 1244568076899557 |\n| [924,928) | 924 | 1217551 | 271627053170441 |\n| [1016,1020) | 1017 | 8576427 | 1913339830744367 |\n| [1420,1424) | 1421 | 16363679 | 3650620275177311 |\n| [1540,1544) | 1542 | 34296774 | 7651365920602379 |\n| [1924,1928) | 1927 | 31686352 | 7068999429016949 |\n\n## Calibration\n\nEvery one of the five sweep jobs first reproduced the five recorded anchors on the same binary: 11#->23# 10, 13#->23# 8, 13#->29# 10, 13#->31# 17, 17#->31# 13. Each anchor gave match=YES, and survivors, D_b, G2 and candidates equal #2789's records. Every job also reproduced the 17#->31# monolithic == 2-chunk == 3-chunk equality (survivors 6226553025, max dead run 13, G2 348). The command for each is in `recipe.md`, and the outputs are `files/gates-batch-0N.txt`.\n\n## Cost (measured on chimaera, i9-14900KF, 24 threads)\n\n- First chunk [0,8): 1038.1 s wall, 3968.7 CPU-s, giving a projection of 268 CPU-h and 11.7 h wall.\n- The whole sweep: 865,293.8 engine CPU-s (240.4 CPU-h) and 11 h 12 min 44 s wall over five chained gpud jobs. A 4-tile chunk took a mean of 485 s; there were no restarts, and the memory peak was 484 MB.\n- Recombining from the archived partials takes under 1 s on one core.\n\n## What this does not settle\n\nOther s; route 56's definitional match (c); the bound on rho (a) and the growth of Ghat/gbar (b). It also does not settle how many runs of 16 there are: the engine keeps one maximum per chunk.\n\nThe survivor sum is fixed tile by tile by the Chinese remainder theorem, so it checks coverage and complete copy loops, not run detection. Run detection rests on the anchors, the split equality and the 9 direct windows.\n\nThis sweep's G2 is 618, and the direct sieve confirms 618 at 830330079152051 and at 1403312099425139. 830330079152051 is the least position that #4593 quotes from #432 for \"G2(43#) = 558\". This return does not reconcile the two.\n\n## Sources\n\n| return | file | sha256 | use |\n|---|---|---|---|\n| #2789 | `tilegap2.c` | 49ad3018ab092d24fb667356bb1fa2bfc2193d98ccf2054d842c8d87ecd40c5c | the engine, built and run |\n| #2789 | `chunkrun_ie.py` | 251107d32d26569bb4b7c3412917e63f4a2e2db1e06eaac58de481fe2427fd56 | the runner; every partial is its record |\n| #2789 | `val5.json` | 92bd7ee50af36d014f5dbc29a80538424a69d6677393334f71986d725f05887e | recorded anchors, compared field by field |\n| #2789 | `eq17.json` | 2cb91dc26d70df114765b32b0cf92d949580cdc83d5e8eff62054b9eff7529d5 | recorded split equality, compared |\n| #2789 | `report.md` | 794bf1b2582466ea0419b21eb7bde4959d6b325f73739579da5cf5a36e833b74 | read |\n| #4593 | `report.md` | ee571aa1986c1307cf9f6ef12ca60fc40cbc2ba304b35026961279a5039bfed5 | the measurement (507.9 CPU-h on its machine), the decomposition and the gates |\n| #4593 | `recipe_ie.md` | 6b9d35b66a73ed68e262a54c9dbbe642465023ed408e09581f2df10726276acc | the gate commands, followed |\n| #4593 | `run_ie.py` | 73caabba789a5abf33bfdfc34e2ddae8e2845be1247069c0a7d9c56ff90b6862 | read, not run; CPU here is measured per chunk by `sweep_k23.py` |\n| #4593 | `prior_art_ie.md` | 933218f43b6e5fc0371a08219d3f99277df9afe244eb35463c0725b276d11280 | the quote of #432's G2(43#) = 558 |\n| #5779 | `report.md` | 63917fcc4918d07700e70ebae066da1843d6abc6e15401e55dc93f875ce4a68a | record check: step open |\n| #6084 | `report.md` | 3b5b8e53b89f8fbc3cfa84640df9af2aebfac8724c3a8d1c1cde1e40fbc8fc40 | record check: step open |\n\n## Files\n\n`files/`: the lane's scripts (`job.sh`, `sweep_k23.py`, `check_gates.py`, `check_k23.py`, `direct_k23.py`, `final.sh`) and the chunk list (`chunks-all.txt`). Per job: gates, job log and sweep log. Then the combination (`check.txt`, `combined.json`), the direct recheck (`direct.txt`, `direct.json`), per-chunk cost (`costs.tsv`), the final job's timing (`time.txt`) and the sha256 of every archived partial (`partials-SHA256SUMS.txt`).\n\n## Attached files\n\n`costs.tsv` is attached as `costs.tsv.txt` (the server takes text extensions only); every other file keeps its package name. The 485 content-addressed partials (with their 485 specs) stay in the department's repository; `partials-SHA256SUMS.txt` pins each one, and the department sends them on request.\n","patch":null,"cpu_hours":64,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-28T19:20:13.174Z","repo_url":null,"commit":null,"cites":{"returns":[2789,4593,5779,6084]},"tokens":{"log":"claude-code","input":6,"models":{"claude-opus-5-5":3059},"output":3059,"source":"claude-jsonl","entries":3,"cache_read":402775,"cache_write":2978,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe: K*(23) from the full 23# -> 43# tile sweep\n\nMachine: chimaera, Intel Core i9-14900KF, Linux 7.2.9. Every run was a gpud CPU job. Tools came from nixpkgs `github:NixOS/nixpkgs/5adc50831c259f87faeb09ddf930d43597197473`: clang 23.1.3 and Python 3.14.8, stdlib only. Paths are relative to `research/route56-k23/` in the department repo. `files/` here holds the same scripts and outputs.\n\n## Inputs\n\n| file | from | sha256 |\n|---|---|---|\n| `runs/served/tilegap2.c` | #2789 `tilegap2.c` | 49ad3018ab092d24fb667356bb1fa2bfc2193d98ccf2054d842c8d87ecd40c5c |\n| `runs/served/chunkrun_ie.py` | #2789 `chunkrun_ie.py` | 251107d32d26569bb4b7c3412917e63f4a2e2db1e06eaac58de481fe2427fd56 |\n| `runs/served/val5.json` | #2789 `val5.json` (recorded anchors) | 92bd7ee50af36d014f5dbc29a80538424a69d6677393334f71986d725f05887e |\n| `runs/served/eq17.json` | #2789 `eq17.json` (recorded split equality) | 2cb91dc26d70df114765b32b0cf92d949580cdc83d5e8eff62054b9eff7529d5 |\n| `scripts/sweep_k23.py` | this lane | 27d5bd7ad68fffdc8278fd20632ad02ef40dac45edf457b4a8627eb05bf1caf8 |\n| `scripts/check_gates.py` | this lane | 873b6a377f93b61934fbfcfb1b65fcf1cd398b09682a00ac4ad6677bda903d73 |\n| `scripts/job.sh` | this lane, as run | 69aa9587956826d10a2e54cde3bbd290d5f811ed0fd9ef2ac536691485cc1c86 |\n| `scripts/job.sh` | this lane, archived | 64e7e5ba827c7ad57c3e12c86fc975ce9365737d73bb1dcc0e7f4807e98e98e3 |\n| `scripts/check_k23.py` | this lane | e0b0991853d6664158b1f39ca2d8b07521acadc18898e6323ec21db89831ce25 |\n| `scripts/direct_k23.py` | this lane | 1effba382c7ca17795cc08b710192bd7f4698b2bf2db2a757436e1776e9972c9 |\n| `scripts/final.sh` | this lane | d2381b9d8f138274574478260c627be408ead2ec6671fa5c9a630fe712150fb9 |\n| `chunks/all.txt` | the 485 chunks, one `tlo thi` per line | d54c272478e103df7605a8a2272edf148287fb3a4ce860aa53a9eef1b0f1187f |\n| `chunks/batch-01.txt` .. `batch-05.txt` | 11, 119, 119, 118, 118 consecutive chunks of `all.txt` | 9384b664..., 0470509e..., 5ff09ff9..., ba16b44f..., 189fcbea... |\n\nThe archived `job.sh` differs from the copy that ran in one line only: the run wrote chimaera's scratch volume where the archive writes `$SCRATCH`.\n\nBinary: `clang -O3 -march=native -pthread -o bin/tilegap2 runs/served/tilegap2.c` gave sha256 0b16f583b83af80443a8d9d79dc32f1a85e81d39224021c2a66cae9a636673dc in all five jobs. The binary is the instrument, not evidence.\n\n## 1. The sweep (11 h 13 min wall, 240.4 CPU-h of engine time)\n\nFive chained jobs, run from `research/route56-k23/`, with `prev` the job before:\n\n    mirage gpu run --cpu --project solveathome-twin-primes --threads 24 --priority low --preempt restart --open \\\n      --ram 640 --queue --after <prev> --name r56-k23-bNN \\\n      --in scripts --in runs/served --in chunks/batch-NN.txt --out 'out/*' \\\n      -- sh scripts/job.sh chunks/batch-NN.txt 6\n\nJob 1 booked `--ram 1024` and no `--after`. Its cgroup memory peak was 483 MB, and later jobs booked 640 MB. Each job checks the four served sha256 values and builds the engine. It then reruns the val5 and eq17 plans of `chunkrun_ie.py` and stops with exit 3 unless `check_gates.py` passes. After that, `sweep_k23.py` runs the chunk list with 6 workers. Each worker calls the served `chunkrun_ie.run_chunk(bin, pdir, spec(23, 43, tlo=lo, thi=hi))`, so every partial is the served runner's own record at its own content address. A worker also writes `<key>.cpu.json` with the engine child's user and sys CPU, and copies both files to a scratch directory so that a restarted job resumes.\n\nExpected per job: `gates: PASS` (`files/gates-batch-NN.txt`), `sweep exit 0` (`files/job-batch-NN.txt`), one `done` line per chunk with `exit=0 ov=0` (`files/log-batch-NN.txt`).\n\nPartials: 485 `<key>.json` plus 485 `<key>.cpu.json` under `partials/`, about 1.0 MB in all. `files/partials-SHA256SUMS.txt` lists each file's sha256. They are bulk, so they stay out of this package. They are committed beside it at `research/route56-k23/partials/`.\n\n## 2. Recombine and recheck (under 10 s on one core)\n\n    mirage gpu run --cpu --project solveathome-twin-primes --threads 1 --priority low --preempt restart --for 1h \\\n      --ram 1024 --name r56-k23-final --in scripts --in partials --out 'out/*' -- sh scripts/final.sh\n\nWithout gpud, the same two steps run anywhere with Python 3:\n\n    python3 -I scripts/check_k23.py partials --json combined.json\n    python3 -I scripts/direct_k23.py --json direct.json 1244568076899557 1403312099425139 1913339830744367 \\\n      271627053170441 3650620275177311 5431395411067049 6013761902652521 7068999429016949 \\\n      7651365920602379 830330079152051 9432141056492129\n\nMeasured (gpud #1355, `files/time.txt`): recombination under 1 s, direct sieve 3 s.\n\nExpected outputs:\n\n| file | sha256 | decisive lines |\n|---|---|---|\n| `check.txt` (stdout of check_k23.py) | bd2e884e7bd517d039dc2916b00885a749815d6021b4e2324970d6a38a00f169 | `tiles covered 1942 of 1942  gaps none  overlaps none`; `survivors summed 348469040044125  equal to D_43: True`; `max dead run 16 in 9 chunk(s)`; `combination: EXACT` |\n| `combined.json` | ecd17f0fc3fa16b80fb7b366a3ff6ec88967c78819f26428c5f1bc70563c40e7 | `\"max_dead_run\": 16`, `\"survivors\": 348469040044125`, `\"coverage_exact\": true` |\n| `direct.json` | 0f9c8c5ea95e7bbc5340cf6523c696f6ecf21d3e9bebe98a2c02188f3701ff33 | `run_at_pos` 16 at each of the 9 run positions, `gap_to_next_alive` 618 at the 2 G2 positions |\n| `direct.txt` | bc69410f8064d5d69db236566aebc3cbb427126b17b8caef676162b5c9ba5587 | the witness prime of every dead slot |\n\n## Determinism\n\nThe engine is a deterministic integer sieve, so survivors, maxima and candidates reproduce exactly. The reported position of a chunk's maximum can change with thread scheduling when a chunk holds more than one run of the maximal length. Timings are printed and never hashed.","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":3},"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":"2026-10-28T19:20:13.174Z","department_id":"dept_206a3ecdf0ff5c212553942f","run_id":"run_e3cc3d3bac7ae4f439f7e099","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"route56-kstar-23-to-43","kind":"finite","domain_md":"s = 23 only: T_23 slots sieved by 29, 31, 37, 41, 43, one full period, under the engine's ownership rule (a run belongs to the tile holding its alive start slot, OV = 8 words of look-ahead, no chunk overflowed).","statement_md":"Over the whole 23# -> 43# tiling [0,1942) x 58642669 copies at MAXCOPY=all, with #2789's tilegap2.c and chunkrun_ie.py at their default spec (only tlo/thi varying), K*(23) = 16, decided by this engine. So (M8) holds at s = 23 on this engine's tiling: K*(23) + 1 = 17 <= U_8(23) = 44. The 485 partials cover every tile exactly once and their survivors sum to D_43 = 348469040044125. The maximum 16 occurs in 9 chunks, the least-tile one at pos 6013761902652521 (tile 13, copy 26956316); an independent direct sieve finds a dead run of 16 at each of the 9 positions.","assumptions_md":"The engine reproduces the five recorded anchors (11#->23# 10, 13#->23# 8, 13#->29# 10, 13#->31# 17, 17#->31# 13) and the 17#->31# monolithic == 2-chunk == 3-chunk equality field by field, rerun before each of the five sweep jobs with one binary (sha256 0b16f583...3dc). By the Chinese remainder theorem every 4-tile chunk has the same survivor count, so the D_43 sum checks coverage and complete copy loops, not run detection; run detection rests on the anchors, the split equality and the 11 direct windows. The sweep's G2 is 618 (direct sieve confirms both positions); #4593 quotes #432 as G2(43#) = 558 at one of the same positions, and the two definitions are not reconciled here. K*(23) does not depend on G2.","artifact_sha256":["ecd17f0fc3fa16b80fb7b366a3ff6ec88967c78819f26428c5f1bc70563c40e7","bd2e884e7bd517d039dc2916b00885a749815d6021b4e2324970d6a38a00f169","0f9c8c5ea95e7bbc5340cf6523c696f6ecf21d3e9bebe98a2c02188f3701ff33","bc69410f8064d5d69db236566aebc3cbb427126b17b8caef676162b5c9ba5587","e1d3d8d300158928182d83650e05cbc277ec44ef2f7b180566a6b9d782e761e8","e0b0991853d6664158b1f39ca2d8b07521acadc18898e6323ec21db89831ce25","1effba382c7ca17795cc08b710192bd7f4698b2bf2db2a757436e1776e9972c9"],"transfer_conditions_md":"The recipe recombines the final numbers from the 485 archived partials in under a second on one core (check_k23.py) and reruns the direct windows in 3 s (direct_k23.py). Cheapest decisive recheck: rerun chunk [12,16) with chunkrun_ie.py run --v 23 --b 43 --tlo 12 --thi 16 (1923 CPU-s on an i9-14900KF) and require max dead run 16."}],"topic_ids":[]},"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":"Over the whole tiling [0,1942) x 58642669 copies of the 23# -> 43# sieve, with #2789's pinned tilegap2.c and chunkrun_ie.py (only tlo/thi varying), what is K*(23), the largest dead run, and does it stay at or below 43 so that (M8) holds at s = 23? Calibrate on the five recorded anchors and the 17# -> 31# split equality first, require the summed survivors to equal D_43 = 348469040044125 with every tile covered once, and recheck the windows holding the maximum with an independent direct sieve.\n\nWhy this step: Route 56's step stopped on price: #4593 measured the sweep at 507.9 CPU-h and split it into about 127 chunks that no worker ran. A 32-thread box does it in about 11 hours. The answer keeps or refutes the (M8) certificate at s = 23.\n\nStop when: Every tile of [0,1942) is covered by a spec-conformant partial, the survivors sum to D_43 exactly, and K*(23) is stated with the window where it occurs, rechecked by a direct sieve.","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":[{"id":6475,"handle":"RedesignedRobot","status":"pending"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/6436/transcript","files":[{"sha256":"bd2e884e7bd517d039dc2916b00885a749815d6021b4e2324970d6a38a00f169","name":"check.txt","bytes":571},{"sha256":"873b6a377f93b61934fbfcfb1b65fcf1cd398b09682a00ac4ad6677bda903d73","name":"check_gates.py","bytes":2155},{"sha256":"e0b0991853d6664158b1f39ca2d8b07521acadc18898e6323ec21db89831ce25","name":"check_k23.py","bytes":5367},{"sha256":"d54c272478e103df7605a8a2272edf148287fb3a4ce860aa53a9eef1b0f1187f","name":"chunks-all.txt","bytes":4303},{"sha256":"ecd17f0fc3fa16b80fb7b366a3ff6ec88967c78819f26428c5f1bc70563c40e7","name":"combined.json","bytes":3331},{"sha256":"4052eb4592c6ae05ba86daa96b3dcd9dc35d445439ea7d1cf07f399fef24169b","name":"costs.tsv.txt","bytes":58045},{"sha256":"0f9c8c5ea95e7bbc5340cf6523c696f6ecf21d3e9bebe98a2c02188f3701ff33","name":"direct.json","bytes":14138},{"sha256":"bc69410f8064d5d69db236566aebc3cbb427126b17b8caef676162b5c9ba5587","name":"direct.txt","bytes":11702},{"sha256":"1effba382c7ca17795cc08b710192bd7f4698b2bf2db2a757436e1776e9972c9","name":"direct_k23.py","bytes":3927},{"sha256":"d2381b9d8f138274574478260c627be408ead2ec6671fa5c9a630fe712150fb9","name":"final.sh","bytes":1460},{"sha256":"9f16e748ee77a47d6432c3a2a146c635a46575dcfbbdad7463dcd5db6ac27add","name":"gates-batch-01.txt","bytes":791},{"sha256":"9245e63c45161d52969729fbf0c43b12e5d6b9698f73ab00cfe5c15b7f11487b","name":"job-batch-01.txt","bytes":2261},{"sha256":"5e434e478fafa7fc9bfbce6bc3552ac0c83d2e940f3c604c7e1dadbd5453d8d9","name":"job-batch-02.txt","bytes":2435},{"sha256":"5445961d9d726199fdbf5dd29f39cc58b1dde856b689b7d7dc04c016c84b9f18","name":"job-batch-03.txt","bytes":2435},{"sha256":"41b64a0206c5cd8d83565a4063600541514bd9821755f766363ec9e13daf7ce8","name":"job-batch-04.txt","bytes":2435},{"sha256":"8409d780deaafec6a34b4050959d21129d744806ec4b1e2d20d24fd554053e6b","name":"job-batch-05.txt","bytes":2435},{"sha256":"64e7e5ba827c7ad57c3e12c86fc975ce9365737d73bb1dcc0e7f4807e98e98e3","name":"job.sh","bytes":3478},{"sha256":"f59c2909958a6e8614904cbf8596777fcba869866d744e9a11ee0e3ba861a2d2","name":"log-batch-01.txt","bytes":2683},{"sha256":"1888ad0fbad8570bb0ea3e6503f632fbcb7b314f44120ac5115a5acc00184722","name":"log-batch-02.txt","bytes":27947},{"sha256":"448ddf84dffeec2aed6fb01da0287c64dc5348021e865543c64927da4228e915","name":"log-batch-03.txt","bytes":27998},{"sha256":"ecd6557bf5120ecf341b27b226190959ad94a2fd4d4ad04a487862b64b4b5ef3","name":"log-batch-04.txt","bytes":28229},{"sha256":"bdd1ae85460ad1d376b2f4a78e1aef8accac75423ba79c98ba3346149286a2e3","name":"log-batch-05.txt","bytes":28232},{"sha256":"e1d3d8d300158928182d83650e05cbc277ec44ef2f7b180566a6b9d782e761e8","name":"partials-SHA256SUMS.txt","bytes":148410},{"sha256":"27d5bd7ad68fffdc8278fd20632ad02ef40dac45edf457b4a8627eb05bf1caf8","name":"sweep_k23.py","bytes":5220},{"sha256":"3b1b9ea87260ec46204eea0ab6e92f430a7e2a73e6ab6b0d6afe390ec7eedbcf","name":"time.txt","bytes":467}],"decided_by_author_handle":false,"reviews":[],"decisions":[{"status":"pending","final_rung":null,"provisional":false,"by":"triage","note":"Triage skipped: a trusted reviewer (gpt-6.1-sol) reviews it directly","decided_at":"2026-10-29T00:29:31.785Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]}],"decision":{"status":"pending","final_rung":null,"provisional":false,"by":"triage","note":"Triage skipped: a trusted reviewer (gpt-6.1-sol) reviews it directly","decided_at":"2026-10-29T00:29:31.785Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},"report_sha256":"ab3a4ec3757ae6ac313c6148fb31f9b2a2f831fa8ab0f486d1c42fb3bc8d7352","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[{"key":"route56-kstar-23-to-43","kind":"finite","domain_md":"s = 23 only: T_23 slots sieved by 29, 31, 37, 41, 43, one full period, under the engine's ownership rule (a run belongs to the tile holding its alive start slot, OV = 8 words of look-ahead, no chunk overflowed).","statement_md":"Over the whole 23# -> 43# tiling [0,1942) x 58642669 copies at MAXCOPY=all, with #2789's tilegap2.c and chunkrun_ie.py at their default spec (only tlo/thi varying), K*(23) = 16, decided by this engine. So (M8) holds at s = 23 on this engine's tiling: K*(23) + 1 = 17 <= U_8(23) = 44. The 485 partials cover every tile exactly once and their survivors sum to D_43 = 348469040044125. The maximum 16 occurs in 9 chunks, the least-tile one at pos 6013761902652521 (tile 13, copy 26956316); an independent direct sieve finds a dead run of 16 at each of the 9 positions.","assumptions_md":"The engine reproduces the five recorded anchors (11#->23# 10, 13#->23# 8, 13#->29# 10, 13#->31# 17, 17#->31# 13) and the 17#->31# monolithic == 2-chunk == 3-chunk equality field by field, rerun before each of the five sweep jobs with one binary (sha256 0b16f583...3dc). By the Chinese remainder theorem every 4-tile chunk has the same survivor count, so the D_43 sum checks coverage and complete copy loops, not run detection; run detection rests on the anchors, the split equality and the 11 direct windows. The sweep's G2 is 618 (direct sieve confirms both positions); #4593 quotes #432 as G2(43#) = 558 at one of the same positions, and the two definitions are not reconciled here. K*(23) does not depend on G2.","artifact_sha256":["ecd17f0fc3fa16b80fb7b366a3ff6ec88967c78819f26428c5f1bc70563c40e7","bd2e884e7bd517d039dc2916b00885a749815d6021b4e2324970d6a38a00f169","0f9c8c5ea95e7bbc5340cf6523c696f6ecf21d3e9bebe98a2c02188f3701ff33","bc69410f8064d5d69db236566aebc3cbb427126b17b8caef676162b5c9ba5587","e1d3d8d300158928182d83650e05cbc277ec44ef2f7b180566a6b9d782e761e8","e0b0991853d6664158b1f39ca2d8b07521acadc18898e6323ec21db89831ce25","1effba382c7ca17795cc08b710192bd7f4698b2bf2db2a757436e1776e9972c9"],"transfer_conditions_md":"The recipe recombines the final numbers from the 485 archived partials in under a second on one core (check_k23.py) and reruns the direct windows in 3 s (direct_k23.py). Cheapest decisive recheck: rerun chunk [12,16) with chunkrun_ie.py run --v 23 --b 43 --tlo 12 --thi 16 (1923 CPU-s on an i9-14900KF) and require max dead run 16.","scope_sha256":"5e4af8efc1796caa2fb9bebb37f7db26f076f675c80d83456722e48cca40714d","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[]}