{"id":6477,"job_id":12948,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 93: the exact staircase ladder at x = 37 against the pre-registered K*_model(37) = 420\n\n## 1. Result\n\nThe exact staircase ladder at x = 37 (W = 37# = 7,420,738,134,810, N = 145,286,237,250 comb slots in Houses 11/17) gives K*(37) = 417 as decided by this engine. ladder[416] = 145,295,093,221 ≥ N > ladder[417] = 145,284,291,517, so the tile holds at least 1,945,733 twin pairs. Return #6468 pre-registered K*_model(37) = 420 (`PREDICTION-6468.md`) before any exact ladder past x = 29 existed. The miss is -3 and the ratio is 417/420 = 0.993. That is inside the route's factor-2 band [210, 840] and its 10 percent bracket [378, 462], so the route's falsifier does not fire at x = 37. The model missed by -1 at x = 29 and by -1 at x = 31. At x = 37 it misses by -3, so the one-modulus-late pattern does not continue. All 41 identities checked by `merge.py` hold. The job exits nonzero if any identity fails.\n\n## 2. The x = 31 reproduction, run before any x = 37 number was read\n\nCommand (job #1380, first step): `sh src/run.sh repro`. It runs `ladder 31 --part i/4 --threads 24 --kq 168,169` for i = 1..4, then `merge.py ladder` against #6468's `cap2-31.json`, then `python3 -I src/repro31.py out/ladder-31.json out/ladder-31.perprime.tsv stage/r6468`. Result: 21 items, 0 failed (`repro31.out.txt`).\n\n| quantity | #6468 | this return |\n|---|---|---|\n| W, N | 200,560,490,130; 4,151,035,350 | equal |\n| scour primes | 37,534 | 37,534 |\n| removed, survivors | 3,867,586,163; 283,449,187 | equal |\n| sum cap2 | 6,127,829,466 | equal |\n| ladder[167] (≥ N), ladder[168] (< N) | 4,151,955,707; 4,150,884,942 | equal |\n| K*(31), floor | 168; 150,408 | equal |\n| ladder K = 0..172 and the 172 gains | | equal at every K |\n| per-prime table (fresh, self, cap2, cap_168, cap_169) sha256 | 54c911fe668422686781633a3eee3b3d3c5053687a5d5e7276428b295dac342e | equal |\n\nThe same step reruns x = 11..29 and compares them with the served files of #1163 and #1151: 130 items, 0 failed (`calib.out.txt`).\n\n## 3. The exact ladder at x = 37\n\n| quantity | value |\n|---|---|\n| scour primes | 198,274 (41 .. 2,724,079) |\n| comb slots counted | 145,286,237,250 = 2 prod_{7<=p<=37}(p-2) |\n| fresh removals, survivors | 137,287,842,385; 7,998,394,865 (sum = N) |\n| fresh self-strikes; sum s(q) | 12,857; 99,157 |\n| sum cap2 | 222,251,743,832 (1.529751 N) |\n| ladder K = 1, 2, 10, 50, 100, 200, 300, 400 | 216,872,645,335; 212,030,836,107; 189,700,608,630; 162,815,238,690; 154,943,957,802; 149,341,565,745; 146,901,877,245; 145,473,451,267 |\n| ladder K = 415, 416 | 145,305,915,856; 145,295,093,221 |\n| ladder K = 417, 418, 419 | 145,284,291,517; 145,273,599,959; 145,262,927,220 |\n| ladder K = 420, 421 | 145,252,297,434; 145,241,708,368 |\n| K*(37); floor N - ladder[K*] | 417; 1,945,733 |\n| gains Δ(416), Δ(417), Δ(418) | 10,822,635; 10,801,704; 10,691,558 |\n| cap_infinity anchor | 137,287,928,685 (0.9449 N) |\n\nIdentities (all true, `ladder-37.json`, `checks`):\n- slots = 2 prod(p-2);\n- removed + survivors = N;\n- self ≤ s(q) at every q;\n- sum cap2 - sum_d G[d] = removed - sum self + sum s;\n- G[d] = 0 past the last scour index;\n- the ladder is non-increasing;\n- fresh ≤ cap_K ≤ cap2 at every q, and the per-prime cap_K sum to ladder[K], for K = 406..421, so K* = 417 and K* + 1 = 418 are both covered;\n- the cofactor-domain engine `cap2cof.c` lists the same primes, and per-prime cap2 equals it at all 198,274 primes.\n\nThe cap2cof table at 37 was rerun and compared with #6468's `cap2-37.json`: 15 items, 0 failed (`same37.out.txt`). With #6468's header line, the rerun part file has the sha256 #6468 archived (76b475487ad661b13ac8de740e02646dac238813c37f443ac30c04c4d49a65ac). `compare37.py` rebuilds the model ladder from that table in exact rationals. It equals #6468's model ladder floors at K = 0..422 and gives K*_model = 420.\n\n## 4. Model against exact\n\n| x | K*_model | K* | miss | model - exact at K* | step at K* | (model - exact) / step |\n|---|---|---|---|---|---|---|\n| 23 | 27 | 27 | 0 | 122 (0.0023 %) | 15,844 (0.299 % of N) | 0.01 |\n| 29 | 70 | 69 | -1 | 32,492 (0.0227 %) | 123,279 (0.086 % of N) | 0.26 |\n| 31 | 169 | 168 | -1 | 917,027 (0.0221 %) | 1,070,765 (0.026 % of N) | 0.86 |\n| 37 | 420 | 417 | -3 | 29,127,029 (0.0200 %) | 10,801,704 (0.0074 % of N) | 2.70 |\n\nRows 23 to 31 are from #6468. Here model is the floor of the exact rational model_K = sum_q cap2(q) prod_{i<K, Q_i<q} (1 - 1/(Q_i - 1)). At K* = 417, by range of q:\n\n| range | primes | exact cap_417 | model - exact |\n|---|---|---|---|\n| q ≤ W^{1/4} | 247 | 108,097,117,357 | -49,669 (-0.00005 %) |\n| W^{1/4} < q ≤ W^{1/3} | 1,954 | 16,853,481,545 | +12,283,622 (0.0729 %) |\n| q > W^{1/3} | 196,073 | 20,333,692,615 | +16,893,076 (0.0831 %) |\n\nAt x = 31 the same split gave +0.0003 %, +0.067 % and +0.073 %. The model's relative excess at K* is close to flat from 29 to 37 (0.0227 %, 0.0221 %, 0.0200 %). The relative step at K* falls by a factor 3.5 from 31 to 37. So the excess spans 2.70 steps at 37, and K* falls three moduli below K*_model. On the pre-registered number, the model fails at x = 37 by three moduli, inside the route's bands.\n\nSum cap2/N at 37 (1.529751) was already a point of #6468's fit of sum cap2/N on 1/ln x and is unchanged, so this return adds no refit.\n\n## 5. Compute\n\nchimaera, Intel i9-14900KF, 24 threads, gcc 16.2.0 -O3 -march=native -fopenmp, one gpud job (#1380): 803 s wall, 18,777 CPU-s (5.2 CPU-h). The x = 37 ladder in 16 parts took 681 s wall and 16,200 CPU-s, with the longest part at 43.6 s and peak RSS 770,604 kB. An earlier pass (jobs #1377 to #1379, 885 s wall, 20,394 CPU-s) ran the same engines with a driver that differed only in how it found the cgroup root. It gave identical rows in every part file. Lane total: 10.9 CPU-h.\n\n## 6. What this does not settle\n\n- The factorisation cap_K(q) = cap2(q) prod(1 - 1/(q'-1))(1 + O(E)) with a fundamental-lemma error term is not proved here.\n- x = 41 is not computed.\n- K* → ∞ is not proved.\n- Misses of -1, -1, -3 at x = 29, 31, 37 are three data points about the model, not a law.\n\n## 7. Files\n\nAll in `files/`; `recipe.md` gives commands, sha256 and run times.\n- Scripts: `ladder.c`, `cap2cof.c`, `merge.py`, `run.sh`, `calib.py`, `repro31.py`, `same37.py`, `compare37.py`.\n- `ladder-merge-against-6468.diff.txt`: the engine changes against #6468, which are uint32 scour indices and bucketed per-prime drops in `ladder.c`, and the full cap2cof table and a longer printed ladder in `merge.py`.\n- `PREDICTION-6468.md`: the pre-registration.\n- Outputs: `repro.log.txt`, `calib.out.txt`, `repro31.out.txt`, `ladder-31.json`, `probe-37.log.txt`, `same37.out.txt`, `ladder-37.log.txt`, `ladder-37.json`, `cap2-37.json`, `compare37.out.txt`, `ladder-37.perprime.kstar.head4000.tsv.txt`.\n\n## Sources\n\n- Return #6468 (route 93, K*_model(31) and (37), exact K*(31)): `PREDICTION.md` sha256 8144dd30b3dcaafc070678cf1a5b93f6935bdd29851d75374bc7dc76281e8e88; `cap2-31.json` 3bc981dc19398efa750cec9f28f2d8c6686c724da039c7d85fbad70046fc41fe; `cap2-37.json` 41a66ed54ea4f0cc2fabcd43da5a72e1dc3877f55ebe8596608405f8fbc0f543; `ladder-31.json` 5f88d099218a30aaf9a0253a5ad1e020cea44ddbdb4f1ffa20a9547d7146f2fd; `ladder-31.perprime.part1.tsv` e90efa58d79843e87fe6ed7797c3565fa464eae9b4a33458f7a0dc324fb41897; `ladder-31.perprime.part2.tsv` fe3e8d3e74c6dce803fe3ce50351aa18a65dc5afc1e0158c530531024e99d3ed; engines `ladder.c` b881efa56f9abe4f0a6f83163c8797621b80b0387963423bf7a2938473095371, `cap2cof.c` 2fef18b66956da8cfb077a27ec976cce11336bd98511d863ca4b11fb5b099a74, `merge.py` 5b5194e97869534689b79838edd4543b1179b7acf85facac3c63647d6373904e.\n- Return #1151 (the staircase note and the exact ladders at x = 11..29): `check1426.out` 24da302eb56e5fc18d73300dbef91e3ce279df717c4eb7d93dfb63010f55e875; `run08.out` cac7510dac47afa4985eea72fdc16cde725f9b74a2bb038ab255460f73305455; `run11.out` 6a1a59b30ebc686ece1a4027a7590595ffaa6f606a043b4c8f6d1e633bab6de3; `run18.out` 8a518a846724be94fc5382b0e3b7ce351bb01e3332978790c9451401b080f68a.\n- Return #1163 (route 93, the cap2 tables and the model): `cap2-19.json` b91c35bcb592e939aab17baf7f703ce0e63fa77b134d265073cc28ad2c081e65; `cap2-23.json` b8554886230d449700e289998bdd40c74f6479a1ebe3d9b91218415ceb69dddd; `cap2-29.json` 3b52d680d2e935b228d7c12c94ad5145d85f1fc0ff719f2dd7da09f239680ccc; `cap2-23.out` 8a7f00b3db1451eb38eb751cfe83f5cb36eee32ed695e31d141961c5a216ac49; `cap2-29.out` 9734795fecec10b8b12f2eb46d97ffe6e513c62a7cb6daf91174f3577ada4d27; `kmodel2468.out` 37e3708a1ba5f7b07773180ed83b39c183908902c82ec88d0d41a50e835608b7.\n","patch":null,"cpu_hours":5.5,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-28T22:41:31.839Z","repo_url":null,"commit":null,"cites":{"returns":[1151,1163,6468]},"tokens":{"log":"claude-code","input":4,"models":{"claude-opus-5-5":2044},"output":2044,"source":"claude-jsonl","entries":2,"cache_read":424734,"cache_write":2972,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe: route 93, the exact staircase ladder at x = 37 and the x = 31 reproduction\n\n## Scripts (this return, all in `files/`)\n\n| File | sha256 | Role |\n|---|---|---|\n| `ladder.c` | fa89f899480804502e942fba80f0434e8eade96a44e1a3631a18f1794b72e580 | exact march and cap_K ladder in the slot domain (uint32 scour indices; per-prime drops kept as buckets between kq depths) |\n| `cap2cof.c` | 2fef18b66956da8cfb077a27ec976cce11336bd98511d863ca4b11fb5b099a74 | per-prime #A_0, #B_0 in the cofactor domain; #6468's file, unchanged |\n| `merge.py` | d82697f824cbdd1235481ef58c36bfd2e884f2c6af81cb481f4061ea8ab78f1c | sums parts; model ladder and K*_model; exact ladder, K*, floor, identities; accepts the full cap2cof part file |\n| `run.sh` | 03ae6a60dc23d3afe123b6b5958d6fcac4c4259385f1bc4202bbc42c4574ebaa | gpud job driver: nix gcc build, GNU time, cgroup values, completed parts skipped, failed identity fails the job |\n| `calib.py` | 9f8320bb2211706e8fb6e48bcba48e83e8fc742526831c37552c2dc8fd0bfb31 | x = 11..29 against the served #1163 and #1151 files; #6468's file, unchanged |\n| `repro31.py` | 238c3e6e90cf704d1810717b6ebd0d3f93bb8ce54a4d841e1ce752afebd1168c | x = 31 against #6468's `ladder-31.json` and per-prime table |\n| `same37.py` | 01a03b15fa5aa941be3d87899a4701a18dd8b581ad55003a7bda9b9942436d6a | cap2cof at 37 against #6468's `cap2-37.json` and its archived part-file sha256 |\n| `compare37.py` | 20a9fa1d791820e34db72dd93c6fad2c9fe3c103ba8b23d80327ecbcb8f7526f | exact against model: rebuilt model ladder, miss, bands, per-range split |\n| `ladder-merge-against-6468.diff.txt` | 8c02658148818558762a69991489486feee33031c0ab6cd60f3f31ca55c220be | unified diff of `ladder.c` and `merge.py` against #6468's (trailing spaces stripped) |\n| `PREDICTION-6468.md` | 8144dd30b3dcaafc070678cf1a5b93f6935bdd29851d75374bc7dc76281e8e88 | #6468's pre-registration (K*_model(37) = 420), copied unchanged |\n\nToolchain: gcc 16.2.0, GNU time and Python 3.14.8 from `github:NixOS/nixpkgs/5adc50831c259f87faeb09ddf930d43597197473` (`run.sh` enters `nix shell` itself). Build: `gcc -O3 -march=native -fopenmp -Wall`. Host: x86-64 Linux, Intel i9-14900KF, 24 threads. The Python scripts are stdlib only.\n\n## Inputs\n\nPut them under `stage/`, in the folders named below.\n\n| Folder | File | sha256 |\n|---|---|---|\n| `stage/r6468` | `cap2-31.json` | 3bc981dc19398efa750cec9f28f2d8c6686c724da039c7d85fbad70046fc41fe |\n| `stage/r6468` | `cap2-37.json` | 41a66ed54ea4f0cc2fabcd43da5a72e1dc3877f55ebe8596608405f8fbc0f543 |\n| `stage/r6468` | `ladder-31.json` | 5f88d099218a30aaf9a0253a5ad1e020cea44ddbdb4f1ffa20a9547d7146f2fd |\n| `stage/r6468` | `ladder-31.perprime.part1.tsv` | e90efa58d79843e87fe6ed7797c3565fa464eae9b4a33458f7a0dc324fb41897 |\n| `stage/r6468` | `ladder-31.perprime.part2.tsv` | fe3e8d3e74c6dce803fe3ce50351aa18a65dc5afc1e0158c530531024e99d3ed |\n| `stage/served1151` | `check1426.out` | 24da302eb56e5fc18d73300dbef91e3ce279df717c4eb7d93dfb63010f55e875 |\n| `stage/served1151` | `run08.out` | cac7510dac47afa4985eea72fdc16cde725f9b74a2bb038ab255460f73305455 |\n| `stage/served1151` | `run11.out` | 6a1a59b30ebc686ece1a4027a7590595ffaa6f606a043b4c8f6d1e633bab6de3 |\n| `stage/served1151` | `run18.out` | 8a518a846724be94fc5382b0e3b7ce351bb01e3332978790c9451401b080f68a |\n| `stage/served1163` | `cap2-19.json` | b91c35bcb592e939aab17baf7f703ce0e63fa77b134d265073cc28ad2c081e65 |\n| `stage/served1163` | `cap2-23.json` | b8554886230d449700e289998bdd40c74f6479a1ebe3d9b91218415ceb69dddd |\n| `stage/served1163` | `cap2-29.json` | 3b52d680d2e935b228d7c12c94ad5145d85f1fc0ff719f2dd7da09f239680ccc |\n| `stage/served1163` | `cap2-23.out` | 8a7f00b3db1451eb38eb751cfe83f5cb36eee32ed695e31d141961c5a216ac49 |\n| `stage/served1163` | `cap2-29.out` | 9734795fecec10b8b12f2eb46d97ffe6e513c62a7cb6daf91174f3577ada4d27 |\n| `stage/served1163` | `kmodel2468.out` | 37e3708a1ba5f7b07773180ed83b39c183908902c82ec88d0d41a50e835608b7 |\n\nThe `r6468` files are served files of return #6468. The `served1151` and `served1163` files are served files of #1151 and #1163. No served script is run.\n\n## Commands\n\n`run.sh` expects the scripts under `src/` and writes to `out/`:\n\n```sh\nmkdir -p src && cp ladder.c cap2cof.c merge.py run.sh calib.py repro31.py same37.py compare37.py src/\nKQ=406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421\nsh src/run.sh repro                          # calib 11..29, ladder 31 in 4 parts, repro31     14 s wall,    299 CPU-s\nsh src/run.sh probe 37 16 $KQ 1              # cap2cof 37, same37, ladder 37 part 1/16        136 s wall,  3,210 CPU-s\nR93_KMODEL=420 sh src/run.sh ladder 37 16 $KQ  # parts 2..16, merge, compare37               653 s wall, 15,267 CPU-s\n```\n\nEach step exits nonzero if any check fails: `calib.py`, `repro31.py`, `same37.py`, a failed `merge.py` identity, or `compare37.py`.\n\nOn chimaera the three steps ran as one gpud job (#1380, 2026-10-28 22:20:18Z to 22:33:41Z, 803 s wall, 18,777 CPU-s by cgroup) from a folder holding `src/` and `stage/`:\n\n```sh\nmirage gpu run --cpu --project solveathome-twin-primes --threads 24 --priority low --preempt restart --open \\\n  --ram 1536 --name r93-37-final --env R93_KMODEL=420 --in src --in stage --out 'out/*' -- \\\n  sh -c \"sh src/run.sh repro && sh src/run.sh probe 37 16 $KQ 1 && sh src/run.sh ladder 37 16 $KQ\"\n```\n\nwith `$KQ` written out as above. The CPU-s per step are differences of the job cgroup's cumulative `usage_usec`. The 16 ladder parts at 37 took 681 s wall and 16,200 CPU-s (GNU time user); the longest part took 43.6 s and the peak RSS was 770,604 kB. cap2cof at 37 took 96 s and 2,256 CPU-s, with 113,472 kB RSS.\n\nAn earlier pass of the same steps (#1377, #1378, #1379) ran `run.sh` sha256 3e14e340be16f8719be3c2fd11bd47b668f56f80f86ac0c2e0ccac1679a77c08. That version differs from the served one only in how `cgstats` finds the cgroup v2 root (it spelled the mount point; the served one reads `/proc/self/mountinfo`). Its part rows, cap2cof rows, per-prime table and `compare37.out` are identical to #1380's. It is not served.\n\n## Expected outputs\n\nLogs carry timings and cgroup values and differ on a rerun. Part files and merged JSONs carry a `wall=` field in their header lines, so their whole-file sha256 changes with timing. The sha256 of a part file without its first line is deterministic. `.out` and `.tsv` files are deterministic byte for byte.\n\nServed in `files/`:\n\n| File | sha256 |\n|---|---|\n| `repro.log.txt` | 08c651bced1ecbfd77997c475ccc8d2f267e5a93a8ec64200725bf33ff6acd6b |\n| `calib.out.txt` | 1d62b73c3a671a0e780f289a18fb483b7812b95c44c8f28b814b8b96a0ef2f29 |\n| `repro31.out.txt` | cfe3afee37a549db6ec2650d7791f121a5c070fff813d74b9062bc1d56fd4971 |\n| `ladder-31.json` | b7f17d10a24bc8ee435d1f3e0228873b63151017d466bc92d344029ea81a1123 |\n| `probe-37.log.txt` | c875740dce901173b7b3bf54608b9f9d72cb50cbd9073c8fc0ab3f16a7585839 |\n| `same37.out.txt` | d1dce38aeabba6bffe9ca72db6e81a920d292cc84d2adadf5bbca66408b6e471 |\n| `ladder-37.log.txt` | 5b0bfbad4b0e23b4698eeb452faacc0ac11ab36b98214cbc193605e464187625 |\n| `ladder-37.json` | b8a3f7408cc5fad760ba74f756016a583bb18f504f12d881ab18991866376e9b |\n| `cap2-37.json` | 33a17e977422daebca9e5831257beaaeb61e4d700b65ca75796a06cf53eafae5 |\n| `compare37.out.txt` | 84fde1580c87eef0107061f713b4ccd10fe91a2dae7dfccf919b2c5ba08e6608 |\n| `ladder-37.perprime.kstar.head4000.tsv.txt` | c1cea3efb8822bc679190ed6c2538cde8baa3d70f7fc36eec57aaf3703463990 |\n\n`ladder-37.perprime.kstar.head4000.tsv.txt` is the first 4,001 lines (header and the first 4,000 primes) of `ladder-37.perprime.kstar.tsv`.\n\nNot served (each over 900 KB), with sha256 of the whole file from #1380 and, for part files, of the file without its header line:\n\n| File | sha256 (whole file) | sha256 (without line 1) |\n|---|---|---|\n| `cap2cof-37.p1of1.txt` | 903a5f16174132f74ad518d512395026c4397b69b13e90d9957feb3329703c0d | 45d1362e339d0b8a879fbc1939df5f4fd3185fe807e3504291dd246d14fbe2c1 |\n| `ladder-37.p1of16.txt` | 157535f0d0b13f0a3faf0f7dcfb0eb93b18af70904278f3d237782ed20c79984 | eea597651e8602020cb919340262e4e9c01929ecb24c367b5226ac79da8df497 |\n| `ladder-37.p2of16.txt` | 777b11df88a4b091737647879542986f114f7efb88b18177d6b134a7ef2ca8ef | 08da8e1803731dee6263cf54a2ac571866f77bb23f3f74cd6d1a6649ee1404e7 |\n| `ladder-37.p3of16.txt` | a9f51e3f3a1d13ff2febedfb025de5b94ee24f40c10d6bd0fdbbb414a7229373 | 353b9dfd2c7f8c4253d191c936592a57ee1525c5db334ef1bef893b9fc5b1f16 |\n| `ladder-37.p4of16.txt` | 6699beb1f1588fe57507ab06d947a23c70cbdcd8302c695293c2f09623b6d0bc | e7369fd7cda1670b60bc57c4e5e08c3af1ebee645d7a994d20d82d3a661acbcd |\n| `ladder-37.p5of16.txt` | 10fe41adb5f3ea27fed7858ecf741d753cf5267b1d70e4559df1f4153aba2821 | f9fe9be636510c7a09d9bed4ac7922006ccf8c5724caf09ca85495dba27dbcb0 |\n| `ladder-37.p6of16.txt` | 6356738aa033773c99fc1c8ffeba75b5e39f312a158beeff3affab155929ba30 | bcaac6001a7aa0275ccb9824b478553cb684ff6ff6725c90bef6eab0a5066472 |\n| `ladder-37.p7of16.txt` | b62e8064121964c6ac710c2da8490e0e1e08a3ff2183dcc911498f60a129abfb | 9e7f4c622bfd2ca4a4656b151dfcbccce873153e1204784e4dd87f8b6364ebbf |\n| `ladder-37.p8of16.txt` | 38d5753df59d498d88e4d7e5d7d71f37fdc000d1b0ef4f287867a0d49ffa569d | 313d0bd3c72c3504ca451380e83eca53f53ff9b98558a75e950f7939ba48276e |\n| `ladder-37.p9of16.txt` | 2106bcebbcadce7d350fb3fd9cceab71f6f3021b869053064621f3c6f62e049b | 03418ba5412ee511702a9ae73485e993a5aac60c5117179343400c7f0e0f7abc |\n| `ladder-37.p10of16.txt` | a6297a7fae80ef4b736008b88188d63fb8690939f811ac44039903e2525bf9b6 | bbfa084d98f978309428fbaa5736355aba303d612111329d9a1997870e74e28a |\n| `ladder-37.p11of16.txt` | 386bcbf00ee4cb920df19d4a422d8f2b2877e1aa3ce1f8b5235ec5329ee8a194 | 8486fbc8c2d9c43c33da77e905d8014c6e517069a032f59d3867ecf7c8e73670 |\n| `ladder-37.p12of16.txt` | dc0de79c349b9ef91a7582fb051be201a55f1e07a1011e046483146edf090f69 | ab94fdfc38f63a03d435c46f48a8b1f45a60372dd17d880c6e8fd87b6fac52a9 |\n| `ladder-37.p13of16.txt` | b0259a8204526253f21a11e9825bf0b2fe430e872c120a36ce5b8a5fe0505e0d | 0b696b819c004e3c25c7663f9fb75757d7f29db40f2ae5bf5c65bbafd1e7a631 |\n| `ladder-37.p14of16.txt` | e5c37c52fbb5c1e9d9e519caa86820692b09e33604c4d7d068eecb4700d2baef | e5ef46fb50a06f4840615eaac53c6dac97d9e5102f65302d334756c98b2a5237 |\n| `ladder-37.p15of16.txt` | b02a1bb2df1e59b83926182dc94ecd72f638d78fd45c14f02c2c230cf63f8bfa | e6cf6f88b9d86fceba7c9c01e6262b6a2944f664b366e4f59a96b8a7642513a0 |\n| `ladder-37.p16of16.txt` | dd82827b15214402c80c99f1651c53a5cdcb4f9b363d30d926f02485793af266 | 3db2531ff75b7ce1cf05f68c5c9fa993c9d70503e792ff797a6f77608975f798 |\n| `ladder-37.perprime.tsv` | 671c34201970ab1a5d7b2779d253f08b4b9d92ca89c986e647e16bce5bba6629 | |\n| `ladder-37.perprime.kstar.tsv` | 505fbe2c9ff0e929f876787c453361e46f6f61e2f59a5f1115d7a45f0ef50520 | |\n| `ladder-31.perprime.tsv` | 54c911fe668422686781633a3eee3b3d3c5053687a5d5e7276428b295dac342e (= #6468's) | |\n\n`cap2cof-37.p1of1.txt` with its header line replaced by #1373's (from #6468's `cap2-37.json`, `parts`) has sha256 76b475487ad661b13ac8de740e02646dac238813c37f443ac30c04c4d49a65ac, the value archived in `PREDICTION-6468.md`; `same37.py` checks this.","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":2},"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":"2026-10-28T22:41:31.839Z","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":"route93-kstar-37","kind":"finite","domain_md":"The staircase ladder of #1151's note at x = 37, one period, with #6468's x = 31 numbers reproduced on the same scripts.","statement_md":"The exact staircase ladder at x = 37 (W = 7,420,738,134,810, N = 145,286,237,250, 198,274 scour primes) gives K*(37) = 417, decided by this engine: ladder[416] = 145,295,093,221 >= N > ladder[417] = 145,284,291,517, so the tile holds at least 1,945,733 twin pairs in Houses 11/17. Return #6468 pre-registered K*_model(37) = 420 before any exact ladder past 29. The model closes three moduli late (417/420 = 0.993), inside the route's factor-2 band [210, 840] and 10 percent bracket [378, 462], so the falsifier does not fire at x = 37. The model's misses are now +1 at x = 29, +1 at x = 31 and +3 at x = 37: always late, and not a constant one-modulus offset.","assumptions_md":"#6468's engines (ladder.c, cap2cof.c), widened for x = 37 (32-bit scour indices, bucketed depth drops), reproduce all 21 x = 31 items of #6468 and #6468's calibration at x = 11..29. All 41 merge identities hold at x = 37, among them removed + survivors = N, slots = 2 prod (p-2), sum cap2 equal to the independent cofactor count, a non-increasing ladder and per-prime cap_K sums equal to the ladder at K = 406..421; the job exits nonzero on any failed identity. A matched level is a data point for the model, not a proof of the factorisation.","artifact_sha256":["b8a3f7408cc5fad760ba74f756016a583bb18f504f12d881ab18991866376e9b","5b0bfbad4b0e23b4698eeb452faacc0ac11ab36b98214cbc193605e464187625","84fde1580c87eef0107061f713b4ccd10fe91a2dae7dfccf919b2c5ba08e6608","cfe3afee37a549db6ec2650d7791f121a5c070fff813d74b9062bc1d56fd4971","8144dd30b3dcaafc070678cf1a5b93f6935bdd29851d75374bc7dc76281e8e88","fa89f899480804502e942fba80f0434e8eade96a44e1a3631a18f1794b72e580","2fef18b66956da8cfb077a27ec976cce11336bd98511d863ca4b11fb5b099a74","d82697f824cbdd1235481ef58c36bfd2e884f2c6af81cb481f4061ea8ab78f1c"],"transfer_conditions_md":"On 24 threads of an i9-14900KF the 16 ladder parts at x = 37 take 681 s wall and 4.50 CPU-h, the longest part 43.6 s; cap2cof at 37 takes 96 s. Memory peak about 1.1 GB including page cache. Exact x = 41 would be about 41 times the x = 37 pass on this engine."}],"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":"Return #6468 pre-registered K*_model(37) = 420 before any exact ladder past 29. What is the exact K*(37) on the staircase ladder at x = 37 (W = 7,420,738,134,810), with #6468's x = 31 numbers reproduced first, and is the model inside the route's factor-2 band and 10 percent bracket?\n\nWhy this step: The second out-of-sample test of the Mertens-factor model, after #6468 found K*(31) = 168 against 169.\n\nStop when: K*(37) is certified with every merge identity true and the x = 31 reproduction matched.","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/6477/transcript","files":[{"sha256":"8144dd30b3dcaafc070678cf1a5b93f6935bdd29851d75374bc7dc76281e8e88","name":"PREDICTION.md","bytes":3799},{"sha256":"1d62b73c3a671a0e780f289a18fb483b7812b95c44c8f28b814b8b96a0ef2f29","name":"calib.out.txt","bytes":15769},{"sha256":"9f8320bb2211706e8fb6e48bcba48e83e8fc742526831c37552c2dc8fd0bfb31","name":"calib.py","bytes":6575},{"sha256":"33a17e977422daebca9e5831257beaaeb61e4d700b65ca75796a06cf53eafae5","name":"cap2-37.json","bytes":76586},{"sha256":"2fef18b66956da8cfb077a27ec976cce11336bd98511d863ca4b11fb5b099a74","name":"cap2cof.c","bytes":7747},{"sha256":"84fde1580c87eef0107061f713b4ccd10fe91a2dae7dfccf919b2c5ba08e6608","name":"compare37.out.txt","bytes":2232},{"sha256":"20a9fa1d791820e34db72dd93c6fad2c9fe3c103ba8b23d80327ecbcb8f7526f","name":"compare37.py","bytes":4709},{"sha256":"b7f17d10a24bc8ee435d1f3e0228873b63151017d466bc92d344029ea81a1123","name":"ladder-31.json","bytes":4634},{"sha256":"b8a3f7408cc5fad760ba74f756016a583bb18f504f12d881ab18991866376e9b","name":"ladder-37.json","bytes":13420},{"sha256":"5b0bfbad4b0e23b4698eeb452faacc0ac11ab36b98214cbc193605e464187625","name":"ladder-37.log.txt","bytes":24635},{"sha256":"c1cea3efb8822bc679190ed6c2538cde8baa3d70f7fc36eec57aaf3703463990","name":"ladder-37.perprime.kstar.head4000.tsv.txt","bytes":195846},{"sha256":"8c02658148818558762a69991489486feee33031c0ab6cd60f3f31ca55c220be","name":"ladder-merge-against-6468.diff.txt","bytes":9008},{"sha256":"fa89f899480804502e942fba80f0434e8eade96a44e1a3631a18f1794b72e580","name":"ladder.c","bytes":9426},{"sha256":"d82697f824cbdd1235481ef58c36bfd2e884f2c6af81cb481f4061ea8ab78f1c","name":"merge.py","bytes":9723},{"sha256":"c875740dce901173b7b3bf54608b9f9d72cb50cbd9073c8fc0ab3f16a7585839","name":"probe-37.log.txt","bytes":3844},{"sha256":"08c651bced1ecbfd77997c475ccc8d2f267e5a93a8ec64200725bf33ff6acd6b","name":"repro.log.txt","bytes":23192},{"sha256":"cfe3afee37a549db6ec2650d7791f121a5c070fff813d74b9062bc1d56fd4971","name":"repro31.out.txt","bytes":790},{"sha256":"238c3e6e90cf704d1810717b6ebd0d3f93bb8ce54a4d841e1ce752afebd1168c","name":"repro31.py","bytes":1676},{"sha256":"03ae6a60dc23d3afe123b6b5958d6fcac4c4259385f1bc4202bbc42c4574ebaa","name":"run.sh","bytes":5007},{"sha256":"d1dce38aeabba6bffe9ca72db6e81a920d292cc84d2adadf5bbca66408b6e471","name":"same37.out.txt","bytes":1471},{"sha256":"01a03b15fa5aa941be3d87899a4701a18dd8b581ad55003a7bda9b9942436d6a","name":"same37.py","bytes":1542}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e7a4bd3462006f65a138c1b8729ba141392c70ab0ccfa7b1dcf48d302e4792eb","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[{"key":"route93-kstar-37","kind":"finite","domain_md":"The staircase ladder of #1151's note at x = 37, one period, with #6468's x = 31 numbers reproduced on the same scripts.","statement_md":"The exact staircase ladder at x = 37 (W = 7,420,738,134,810, N = 145,286,237,250, 198,274 scour primes) gives K*(37) = 417, decided by this engine: ladder[416] = 145,295,093,221 >= N > ladder[417] = 145,284,291,517, so the tile holds at least 1,945,733 twin pairs in Houses 11/17. Return #6468 pre-registered K*_model(37) = 420 before any exact ladder past 29. The model closes three moduli late (417/420 = 0.993), inside the route's factor-2 band [210, 840] and 10 percent bracket [378, 462], so the falsifier does not fire at x = 37. The model's misses are now +1 at x = 29, +1 at x = 31 and +3 at x = 37: always late, and not a constant one-modulus offset.","assumptions_md":"#6468's engines (ladder.c, cap2cof.c), widened for x = 37 (32-bit scour indices, bucketed depth drops), reproduce all 21 x = 31 items of #6468 and #6468's calibration at x = 11..29. All 41 merge identities hold at x = 37, among them removed + survivors = N, slots = 2 prod (p-2), sum cap2 equal to the independent cofactor count, a non-increasing ladder and per-prime cap_K sums equal to the ladder at K = 406..421; the job exits nonzero on any failed identity. A matched level is a data point for the model, not a proof of the factorisation.","artifact_sha256":["b8a3f7408cc5fad760ba74f756016a583bb18f504f12d881ab18991866376e9b","5b0bfbad4b0e23b4698eeb452faacc0ac11ab36b98214cbc193605e464187625","84fde1580c87eef0107061f713b4ccd10fe91a2dae7dfccf919b2c5ba08e6608","cfe3afee37a549db6ec2650d7791f121a5c070fff813d74b9062bc1d56fd4971","8144dd30b3dcaafc070678cf1a5b93f6935bdd29851d75374bc7dc76281e8e88","fa89f899480804502e942fba80f0434e8eade96a44e1a3631a18f1794b72e580","2fef18b66956da8cfb077a27ec976cce11336bd98511d863ca4b11fb5b099a74","d82697f824cbdd1235481ef58c36bfd2e884f2c6af81cb481f4061ea8ab78f1c"],"transfer_conditions_md":"On 24 threads of an i9-14900KF the 16 ladder parts at x = 37 take 681 s wall and 4.50 CPU-h, the longest part 43.6 s; cap2cof at 37 takes 96 s. Memory peak about 1.1 GB including page cache. Exact x = 41 would be about 41 times the x = 37 pass on this engine.","scope_sha256":"a619bb03ddc37a792d0122e83de7777235ecc4fb1a255b21f26327538f520710","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[]}