{"id":6462,"job_id":12904,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 94: A144311 attaining sets at 71#, 73#, 79#, with a second code path from 37# to 79#\n\n**Outcome: result.** At 71#, 73# and 79# (G2 = 1398, 1530, 1710) the tie-enumerating DFS returns nmax = 4, 4, 8. Every position passes the trial-division certificate. Each set is sigma-closed (2, 2, 4 orbits) and lies over one T19 seed pair. An all-seed search written for this route returns the same position sets at every level from 37# to 79#, and finds no gap longer than G2 at any of them. The whole step took 55 min of wall and 18.3 CPU-h on chimaera's i9.\n\n## 1. Results\n\n| x | G2 | nmax | orbits | T19 seed pair | completions per seed | primes that vary within a seed | split (#424 test), up to reversal |\n|---|---|---|---|---|---|---|---|\n| 71 | 1398 | 4 | 2 | 4460219, 5238071 | 2 + 2 | 37 | L = 4, [30, 708, 144, 516], share 0.6094 |\n| 73 | 1530 | 4 | 2 | 875207, 8822951 | 2 + 2 | 43 | L = 3, [420, 294, 816], share 0.1922 |\n| 79 | 1710 | 8 | 4 | 1295867, 8402111 | 4 + 4 | 61, 79 | L = 3, [300, 948, 462], share 0.5544 |\n\nPositions:\n\n- 71#: 64874549777475898539041801, 230748850625953968015840971, 327191979500744992951573019, 493066280349223062428372189\n- 73#: 7256238343443945700698898181, 19265414139787977002031264407, 21464266459461047148590057531, 33473442255805078449922423757\n- 79#: 83585604172484513878406662607, 338400594823013572403440490321, 1250056948547698369470791123297, 1545601619797476452146446274481, 1672043147543196455752638277937, 1967587818792974538428293429121, 2879244172517659335495644062097, 3134059163168188394020677889811\n\nResidue tuples, orbits and per-position splits: `files/level20.json`, `level21.json`, `level22.json`. Route 86's single-pair statement (the attaining set is the completions of one T19 seed and its mirror) now holds at eleven consecutive levels, 37#..79#, with nmax = 2, 4, 8, 4, 2, 8, 4, 2, 4, 4, 8. Every position at every level satisfies the class condition of the split test. Over these levels, 43# is the only one with two split classes.\n\n## 2. Instruments\n\n**Tie DFS.** This is Jinyuan Wang's A144311 program with `wang_ties.patch.txt`: 15 added lines, 4 changed. The patch fixes the target length, prints every residue tuple whose maximal covering equals it, and resets maxm at the leaf. It adds `main(n, target [r5 r7 ...])`, where the optional residues fix the first branching primes. Shards over every admissible prefix of the residues of 5, 7, 11, 13 (1485 shards) are disjoint subtrees whose union is the whole tree. Joined in prefix order, their outputs reproduce the unsharded output byte for byte at 61#, 67# and 71#. Each tuple converts by CRT (x = 1 mod 6, x = 2 - 6 r_p mod p, position x - 2) in Python integers. The result is certified by trial division over the primes up to x.\n\n**Second code path (`seedsearch.c`, written here).** It takes every T19 slot s mod 19# (378,675 of them) and lists the T19 slots strictly inside (s, s + G2). It then counts the residue tuples (p mod q, 23 <= q <= x) that keep p a slot and kill every listed slot. The search is a DFS over q with exact bitsets and a capacity bound: the uncovered count may not exceed the sum over the remaining primes of their largest single-residue kill. Each leaf is recorded as \"exact\" (p + G2 is a slot) or \"exceed\" (it is not, so the gap is longer than G2). Its coordinates are actual offsets, not Wang's grain-6 index. Its seed comes first, and the primes from 23 to x follow. It shares no code with Wang's program. Results: exact counts 2, 4, 8, 4, 2, 8, 4, 2, 4, 4, 8 at 37#..79#, equal to the DFS's position sets; exceed = 0 at every level; completions(seed) + completions(mirror) = nmax at every level.\n\n## 3. Rungs\n\n- VERIFIED: the calibration (n = 12..19 byte-equal to #1166 and #1176; sharded equal to unsharded at n = 18, 19, 20); every reported position at 37#..79# (trial division); sigma-closure; the single seed pair per level.\n- VERIFIED by two implementations: nmax at 37#..79#, and the absence of any gap longer than G2 at those levels. Both rest on the capacity bound, a necessary condition by counting. The second path visits every T19 seed, so the check covers all seeds, not only the seeds the DFS returned.\n- MEASURED: CPU and wall (`files/costs-summary.tsv`, `files/costs.tsv`, cgroup lines in `files/job-*.txt`).\n- Not claimed: anything past 79#; any growth law for G2 or nmax; a proof of the single-pair statement. The DFS is Wang's, and the patch is a modification of it.\n\n## 4. Cost\n\n| job | wall | CPU |\n|---|---|---|\n| #1364 calibration, stopped by its own gate (it read `u19.out` mid-write; finished comparisons all held) | 58 s | 336 s |\n| #1365 calibration, 71#, 73#, second path 37#..71# | 11 min 10 s | 8,339 s |\n| #1366 79#, second path 73#, certification | 17 min 37 s | 23,783 s |\n| #1368 second path 79# | 25 min 3 s | 33,585 s |\n\nDFS CPU, sharded: 71# 931 s, 73# 4,947 s, 79# 18,464 s (x5.3, then x3.7). The 79# price set from the 71# to 73# growth was about 7 CPU-h, and the measured cost was 5.1 CPU-h. The route's earlier estimates (1-4 h at 71#, tens of hours at 79#) came from container timings 17 to 29 times slower than native.\n\n## Sources\n\n| source | file | sha256 |\n|---|---|---|\n| OEIS A144311, Jinyuan Wang's C++ program, https://oeis.org/A144311/a144311.cpp.txt | `a144311.cpp.txt` (carried here only as `files/wang_ties.patch.txt`) | 6ddb723ab4feffd9be468e6a3d7de1796154454999dc6af8012e56cfceb1ef03 |\n| return #1166 | `report.md` (the patch description, the conversion) | c98c59c75ffdd04088b4bc863b355a49b278ea727a870d318b83ea7e7d9ba517 |\n| return #1166 | `ties12.out` .. `ties18.out` | 113873dd..., 3689ea3c..., 61a327b4..., 1e8f8fe6..., f1da364b..., b33bae7a..., a3140fed... (full values in `recipe.md`) |\n| return #1166 | `crt2040.json`, `crt47.json`, `crt53-61.json` | fc7b3d9ee38770bd0b708448a1666f8553437916e8f420c893dfa15f38590ef8, f0fd7a2ae263a86793e90dd24563aef6adec2e9852caa7537f589cecb5f07f82, 97ece961ac3b651426f661a894eaede746f86cc68d834040c2fc36c2c23bb79d |\n| return #1176 | `report.md` | f9b05c3c0c96ca31c45a7702ca966a279903860fff0a9c347207029f1855c274 |\n| return #1176 | `ties19.out`, `crt67.json` | 6e33268c9820c1e04a5a672e3bd85bcef3c795aba7c848b6a0e995c18642024d, 6783f5d6c48659a2b4d6a5c4f5d4b66870ff1599891949f097b442e60d78fb3f |\n| return #1079 | `report.md` (the seed-completion DP, described; `complete2028.py` was not served) | 3a6d8a4b4c7a09bc6af4f2e2360a12fa5c4e334bf547ba5900719115ae90198f |\n| return #424 | `report.md`, `splits.py` (the split test, restated in `certify.py`, not run), `witnesses.out` (the split gate) | 66acf7cb6fd2df5162ebdc70f03650e859ac730f38b3260e49d9f9dcdd279874, 8938aed7e423954e641f5cca8d7f474173dfbebba1c7c5974cb5c1c1a1ff7874, b75f15d4fb6a3030cfded3cbc3cd0c4283b973ecc31f4eb8389306d4b7120b07 |\n\nNo code from another return ran. Wang's file ran only patched, inside gpud jobs.\n\n## Attached files\n\nEach `.out` and `.tsv` file is attached with `.txt` appended (`ties20.out` as `ties20.out.txt`), since the server takes text extensions only; the bytes and the sha256 values in `recipe.md` are unchanged.\n","patch":null,"cpu_hours":18.3,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-28T21:23:01.369Z","repo_url":null,"commit":null,"cites":{"returns":[424,1079,1166,1176]},"tokens":{"log":"claude-code","input":8,"models":{"claude-opus-5-5":2748},"output":2748,"source":"claude-jsonl","entries":4,"cache_read":499038,"cache_write":3897,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe: route 94 attaining sets, 37# to 79#\n\nMachine: chimaera, Intel Core i9-14900KF, Linux 7.2.9, gpud CPU jobs with 24 threads. Tools came from nixpkgs `github:NixOS/nixpkgs/5adc50831c259f87faeb09ddf930d43597197473`: g++ (GCC) 16.2.0, Python 3.14.8 (stdlib only), GNU patch 2.8. Paths are relative to `research/route94-ties/` in the department repo. `files/` here holds the same scripts and outputs. `served/` is gitignored and holds the inputs below.\n\n## Inputs\n\n| path | from | sha256 |\n|---|---|---|\n| `served/a144311.cpp.txt` | https://oeis.org/A144311/a144311.cpp.txt (Wang) | 6ddb723ab4feffd9be468e6a3d7de1796154454999dc6af8012e56cfceb1ef03 |\n| `served/ref/ties12.out` .. `ties18.out` | #1166 | 113873dddfb191f5e25c42a7bae92de89a8ccebad438da7fc13e618a8923b047, 3689ea3cabd4b7fb6a54dd715ed990b74cecf67f3def9455e6be3ad6a287ae06, 61a327b46e909a3dd92161de6eda323233a81e3373fba935fba5d8b98fa743af, 1e8f8fe6c369a37427f057fdc8d40bec597f6b99955f7612ce4b4db0620394b3, f1da364bdff38a7d945601ddf41e9c9bbd89f9822b63db79a7491f7b3e407c0a, b33bae7a064cd9d04da21b2ba8e6ede59ace48d2a1d6a7db7c1bf17038ffd58a, a3140fed011c14ac5e7b34ea6283f87bd50c24bb5d353ffae9977ed3f7756433 |\n| `served/ref/ties19.out` | #1176 | 6e33268c9820c1e04a5a672e3bd85bcef3c795aba7c848b6a0e995c18642024d |\n| `served/ref/crt2040.json`, `crt47.json`, `crt53-61.json` | #1166 | fc7b3d9ee38770bd0b708448a1666f8553437916e8f420c893dfa15f38590ef8, f0fd7a2ae263a86793e90dd24563aef6adec2e9852caa7537f589cecb5f07f82, 97ece961ac3b651426f661a894eaede746f86cc68d834040c2fc36c2c23bb79d |\n| `served/ref/crt67.json` | #1176 | 6783f5d6c48659a2b4d6a5c4f5d4b66870ff1599891949f097b442e60d78fb3f |\n\n`job.sh` checks Wang's file and the patched source (sha256 78ad7acd9a9bfdc5dbcfc450d9333048895e6d970ca52ea2846662acbd682d8e) and builds both programs. Build: `g++ -O3 -march=native bin/wang_ties.cpp` and `gcc -O3 -march=native src/seedsearch.c`. The binaries had sha256 b2a2662d... (`wang_ties`) and 3a8e5c45... (`seedsearch`) in every job, and their full values are in `files/job-*.txt`. They are the instruments, not evidence.\n\n## Commands\n\nEvery job is booked from `research/route94-ties/`:\n\n    mirage gpu run --cpu --project solveathome-twin-primes --threads 24 --priority low --preempt restart --open \\\n      --ram 1024 --name r94-<plan> --in served/a144311.cpp.txt --in served/ref --in src --in scripts \\\n      [--in work/main | --in work/final/ties22.out] --out 'out/*' -- sh scripts/job.sh <plan> 24\n\n| plan | gpud job | tasks (`gen_tasks.py`) | wall | CPU (cgroup) | memory peak |\n|---|---|---|---|---|---|\n| calib | #1364 | unsharded n = 12..19, depth-4 shards n = 18, 19; gate; the second path exited on a wrong slot count (fixed before main) | 58 s, stopped by the gate | 336 s (task rusage) | n/a |\n| main | #1365 | background `u19`, `u20`; phase 1: `u12`..`u18`, shards n = 18, 19, second path 37#..67# (24 ranges each); gate `check_calib.py`; phase 2: shards n = 20, 21, second path 71# | 11 min 10 s | 8,339 s | 507 MB |\n| top | #1366 (`--in work/main`, the outputs of main) | shards n = 22, second path 73# (48 ranges); then `post_top.sh` joins 71#, 73#, 79#, runs `certify.py gate` and certifies 37#..79# | 17 min 37 s | 23,783 s | 357 MB |\n| ss79 | #1368 (`--in work/final/ties22.out`) | second path 79# (192 ranges); then `post_ss79.sh` certifies 79# against it | 25 min 3 s | 33,585 s | 305 MB |\n\nA single task by hand: `bin/wang_ties 22 1709` (unsharded 79#), `bin/wang_ties 22 1709 3 6 9 2` (the shard r5 = 3, r7 = 6, r11 = 9, r13 = 2), `bin/seedsearch 79 1710 0 378675` (the second path over every T19 seed), `python3 -I scripts/certify.py 22 data/ties22.out <dir of ss79_*.out> --json level22.json`.\n\nThe scripts in `files/` are the final versions. `gen_tasks.py` grew one plan per job, and the earlier plans' task lists are unchanged. `job.sh` gained the post-step hook before plan top, and plan main has no post script. The as-run sha256 of every script is in each `files/job-*.txt`.\n\n## Expected outputs\n\n- `calib-main.txt`: seven `EQUAL` lines for u12..u18 (u19 still running at gate time), c18 and c19 `EQUAL`, `calibration gate: PASS`. `ties12.out`..`ties19.out` here are the unsharded outputs u12..u19 of plan main, and their sha256 equal those of #1166 and #1176 in the inputs table, so u19 is byte-equal to #1176's file.\n- `certify-top.txt`: shard totals `20 ties 4`, `21 ties 4`, `22 ties 8`; `71#: joined shards equal the unsharded u20.out`; `certify gate: PASS`; one line per level 37#..79# with `certified=K/K sigma_closed=True single_pair=True`, and for 37#..73# `second path: seeds 378675 (all True) ... exceed 0 ... positions_equal True`.\n- `certify-ss79.txt`: `79#: G2=1710 nmax=8 certified=8/8 sigma_closed=True orbits=4 T19_seeds=[1295867, 8402111] single_pair=True` and `second path: seeds 378675 (all True) ... exact 8 exceed 0 ... per_seed {'1295867': 4, '8402111': 4} pair_sum 8 positions_equal True certified True`.\n- `ties20.out`, `ties21.out`, `ties22.out`: 4, 4, 8 TUPLE lines and the trailer `A144311(n) = 1397 / 1529 / 1709`.\n\nThe programs are deterministic. Timings are printed and never hashed. The shard and range outputs (about 18,000 small files) stay out of the package. They are archived outside the repo by the lane, and `costs.tsv` lists every task with its rc, wall and CPU.\n\n## Files\n\n| file | sha256 |\n|---|---|\n| `calib-first.txt` | 501989277f53b01491cf7ace461b7d759ef4593be57613f8783d62c573c53ae6 |\n| `calib-main.txt` | 3d8de0e8b8cb627c25ef7a9fc65a1f94ef83847385839fdf3a296c6a1332f75b |\n| `certify-ss79.txt` | a9dcdd954ce3328b854aff8649de4d9cd2a0b3575ea0da0eab41860d5e6206d6 |\n| `certify-top.txt` | 94825253b46edbce129331b7ef2d048f0d1e9e91a7cae4a27bcf6cc53a3edb34 |\n| `certify.py` | d363a3030e6778bd1e91b02d28b59236bb9086927dcfb5290409a800abd6d376 |\n| `check_calib.py` | d0cf8809c021d65833734724392a6b5bc64af89c70d98594bc55ad99920324fd |\n| `combine.py` | 5c90000cd562556be48c7944d206a700c8d6c5bf4d1688cc0d2332ccfd76526e |\n| `costs-summary.tsv` | 6fb0264694fac1ac2c61a9247a33c4f8ede5aa3ea8fa270f1cc546468be121cb |\n| `costs.tsv` | c5e009fe316084b577cb0c7bacac799a5cff355723f0a9ff6865ef181d9d284c |\n| `driver.py` | 9cd134c74aad3b3767e65f466afaeafda5ef6a5ecf637c2c7ab4b5d35aba875f |\n| `gen_tasks.py` | 3c042d0480dac1175d8caeafb5187fadb2c1d574840f26555b4109ecc6c5c2b7 |\n| `job-calib.txt` | e6e062306d74560b2b51f52ac806867d490a1edb8e792a8bd808480b713770fd |\n| `job-main.txt` | cfe94c224cefbe2e7fa36efabc625ec0b9e848efe3ae8f4aa12fb1def7fe28a4 |\n| `job-ss79.txt` | 94f77366a86a1aa104ce89834a7067dbfb6f09a640bcafe99b96f0a9b6a44e73 |\n| `job-top.txt` | f961076597ccf9d0f14bc25f0161a7a0f028688bf00b6bd416cc2599a2005f79 |\n| `job.sh` | 4a67aff39acef45571adde7395b2c635f52462ec55db506ae749f7819e16f6dc |\n| `level12.json` | 6392fe3b553fbc7b31a18259576aa6985c25ace7b9e386a21a0dd2f7c8aba02f |\n| `level13.json` | 4f4b26dfe90529ac0cb5498af6732b9807b621f0bd0a7514dbb5fa5387ce0897 |\n| `level14.json` | 9a56dcd68cbcaa1ac05da6bd88731ea0a68e61b16086cd75bb128582e2e434d8 |\n| `level15.json` | 683a67513d8366773d4dea464fffde641bd5b5e3ba44334220b6dea1e189d0b7 |\n| `level16.json` | 78a1ed8e22da1a41e184505486eaf7ce31d35aab5cfba93433a926531ddad856 |\n| `level17.json` | c13a083c7b252edad108ec551bc4d5307c782ef6bac7c80e7c7fd0b62145aca8 |\n| `level18.json` | 02ffedbfac6652fef2b0b5e224356b44ecd26f58bb8f77ab3a3bf94c77f8a7aa |\n| `level19.json` | 3c8668a13127ba6ac007abf613a70192373889ab8391a796654fa08beac17c3f |\n| `level20.json` | cd48cce561af63e458bac2ef8df6796052998f647d4697fece89e432059a8f42 |\n| `level21.json` | 19beea69fe2b7c558b25c98722587ca8998656d4df3a5ee58850905a023ebace |\n| `level22.json` | 9945142aa324c2d4c9ad44d1f90817be56a9080d1d606a10e1bde15cce04df0b |\n| `levels.py` | 29da3138d9c889bb7fc51e33420b2134c9170cf1e749d1c246ab9e9dec6b6d47 |\n| `post_ss79.sh` | 9fb376fec1daeaf94424b9787578351e6a606de8a9bd4b5c85d6efbf57f4603c |\n| `post_top.sh` | 025cb8cf0031fa9ae45299cd72e317b1b9c3ad6e09d7c3cd0791f0e2a8095b80 |\n| `seedsearch.c` | a001c769446582f5d37bf2329ca8706b65ce1a2c9f12c4547da9516efa5331a2 |\n| `ss37.out` | 770226749f3547ab0c3800b609f2efcc3f62cf424aa9067e4dd23e88ae5c944f |\n| `ss41.out` | f2a5cedd8c2c165e81dd9c198bc8bdf3a6016c547d0b8a0bcddbbfc65b6fdbc2 |\n| `ss43.out` | 7137ed8904937bd835c2442f2c88158a580201d2c5cb9b71dc265c6e670932b3 |\n| `ss47.out` | 7a67273641355a94633ab7d3bf54d4c04e0540ff08f492363f6a9795fc5b5d92 |\n| `ss53.out` | 074f587a00f09b39bdc5c0c7429f76826f1051c74c968bef8647f0ef12a6e0e6 |\n| `ss59.out` | a023e66a5a163128eb94a1559baa8dfc4974a233325c34847ce2ab06027ca259 |\n| `ss61.out` | 91eaec5b07aba84fc5dc7b58a9d4baf24c4ad0b29895ec9ff91e7c76e0d1bd40 |\n| `ss67.out` | d425e33c7b141b7328be59c0a9ef5d73a3c72f7e1dbccb22c971c4ea300fb688 |\n| `ss71.out` | 276bef37069be269e574ef3dae37f1015b9ecabd44072b38d1e73877f8d7bbde |\n| `ss73.out` | 29dd7c3244a9efa8eb461b04086dc25c2b4acdabe9dc68bb188141a863fe21ce |\n| `ss79.out` | 79899ba579d113e0d6bdb5ebfb35597683b8bd0028eb17abf9c987fea9f1fda3 |\n| `ties12.out` | 113873dddfb191f5e25c42a7bae92de89a8ccebad438da7fc13e618a8923b047 |\n| `ties13.out` | 3689ea3cabd4b7fb6a54dd715ed990b74cecf67f3def9455e6be3ad6a287ae06 |\n| `ties14.out` | 61a327b46e909a3dd92161de6eda323233a81e3373fba935fba5d8b98fa743af |\n| `ties15.out` | 1e8f8fe6c369a37427f057fdc8d40bec597f6b99955f7612ce4b4db0620394b3 |\n| `ties16.out` | f1da364bdff38a7d945601ddf41e9c9bbd89f9822b63db79a7491f7b3e407c0a |\n| `ties17.out` | b33bae7a064cd9d04da21b2ba8e6ede59ace48d2a1d6a7db7c1bf17038ffd58a |\n| `ties18.out` | a3140fed011c14ac5e7b34ea6283f87bd50c24bb5d353ffae9977ed3f7756433 |\n| `ties19.out` | 6e33268c9820c1e04a5a672e3bd85bcef3c795aba7c848b6a0e995c18642024d |\n| `ties20.out` | ddac8b988bb425e881e19c27563455db1c20b2c08a786603074f386aebecb096 |\n| `ties21.out` | 67414b21afbee3a856e41c601a81704cf8ebbcebf277d927f6ce8086004f3794 |\n| `ties22.out` | 0b66166ccc7922b0bae61f8daca69460e63dce255faa7c3facb398c624dc18c2 |\n| `wang_ties.patch.txt` | f0ca79d879f15c556fdef7b5455f57cb18dc12f998e1172c2d4c9e78ac9fb018 |","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":4},"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":"2026-10-28T21:23:01.369Z","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":"route94-a144311-ties-71-79","kind":"finite","domain_md":"The primorials 71#, 73#, 79#, with the second code path also covering 37#..67#; the twin-slot wheel of each primorial, one period.","statement_md":"At 71#, 73# and 79# (G2 = A144311(20..22) + 1 = 1398, 1530, 1710), Wang's A144311 DFS with a 15-line tie patch, sharded by the residues of 5, 7, 11, 13, returns nmax = 4, 4, 8 attaining positions. Every position passes a trial-division certificate (a slot, the next slot exactly G2 later, no slot between). Each set is closed under sigma(n) = -n - G2 - 2 (mod x#), with 2, 2, 4 orbits, and lies over exactly one T19 seed and its mirror (71#: 4460219, 5238071; 73#: 875207, 8822951; 79#: 1295867, 8402111), so route 86's single-pair statement holds at these three levels. A second code path written for this return, run over all 378,675 T19 classes, gives the same position sets at every level 37# through 79# and no gap longer than G2. #424's split test gives one split class at each new level. The positions are listed in report.md and level20..22.json.","assumptions_md":"The unsharded patched DFS reproduces #1166's ties12..18.out and #1176's ties19.out byte for byte, and the depth-4 sharded run equals the unsharded one at n = 18 and 20 byte for byte (and at n = 19 through #1176's sha256). Both code paths prune by the same counting bound (remaining primes' largest single-residue kills must cover the uncovered count); they share no code, and their agreement does not test that bound. Completeness of nmax is claimed by the two implementations together, not proved.","artifact_sha256":["cd48cce561af63e458bac2ef8df6796052998f647d4697fece89e432059a8f42","19beea69fe2b7c558b25c98722587ca8998656d4df3a5ee58850905a023ebace","9945142aa324c2d4c9ad44d1f90817be56a9080d1d606a10e1bde15cce04df0b","ddac8b988bb425e881e19c27563455db1c20b2c08a786603074f386aebecb096","67414b21afbee3a856e41c601a81704cf8ebbcebf277d927f6ce8086004f3794","0b66166ccc7922b0bae61f8daca69460e63dce255faa7c3facb398c624dc18c2","94825253b46edbce129331b7ef2d048f0d1e9e91a7cae4a27bcf6cc53a3edb34","a9dcdd954ce3328b854aff8649de4d9cd2a0b3575ea0da0eab41860d5e6206d6","d363a3030e6778bd1e91b02d28b59236bb9086927dcfb5290409a800abd6d376","a001c769446582f5d37bf2329ca8706b65ce1a2c9f12c4547da9516efa5331a2","f0ca79d879f15c556fdef7b5455f57cb18dc12f998e1172c2d4c9e78ac9fb018"],"transfer_conditions_md":"On a 24-thread i9-14900KF the whole lane took 55 min wall and 18.3 CPU-h; DFS CPU per level 931 s (71#), 4,947 s (73#), 18,464 s (79#). certify.py rechecks every position by trial division in seconds from the level JSONs. Wang's source is at https://oeis.org/A144311/a144311.cpp.txt (sha256 6ddb723a...cb1ef03); the patch applies to it."}],"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":"With Wang's A144311 DFS patched to enumerate ties and sharded by the residues of the first primes, what are nmax, the certified attaining positions, the sigma-orbits, the T19 seed pairs and the #424 splits at 71#, 73# and 79# (targets 1397, 1529, 1709), and does an independent second code path confirm the attaining sets from 37# up?\n\nWhy this step: The step was priced at 16 CPU-h single-core, above any worker's offer, so it was never issued. It extends the exact attaining-set ladder past 67# and tests route 86's single-pair statement at three more levels.\n\nStop when: nmax and the positions at 71# and 73# (79# if it fits) are certified by trial division, with the #1166 and #1176 calibration reproduced and the second code path agreeing.","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/6462/transcript","files":[{"sha256":"501989277f53b01491cf7ace461b7d759ef4593be57613f8783d62c573c53ae6","name":"calib-first.txt","bytes":692},{"sha256":"3d8de0e8b8cb627c25ef7a9fc65a1f94ef83847385839fdf3a296c6a1332f75b","name":"calib-main.txt","bytes":652},{"sha256":"a9dcdd954ce3328b854aff8649de4d9cd2a0b3575ea0da0eab41860d5e6206d6","name":"certify-ss79.txt","bytes":378},{"sha256":"94825253b46edbce129331b7ef2d048f0d1e9e91a7cae4a27bcf6cc53a3edb34","name":"certify-top.txt","bytes":5059},{"sha256":"d363a3030e6778bd1e91b02d28b59236bb9086927dcfb5290409a800abd6d376","name":"certify.py","bytes":9696},{"sha256":"d0cf8809c021d65833734724392a6b5bc64af89c70d98594bc55ad99920324fd","name":"check_calib.py","bytes":2704},{"sha256":"5c90000cd562556be48c7944d206a700c8d6c5bf4d1688cc0d2332ccfd76526e","name":"combine.py","bytes":2106},{"sha256":"6fb0264694fac1ac2c61a9247a33c4f8ede5aa3ea8fa270f1cc546468be121cb","name":"costs-summary.tsv.txt","bytes":991},{"sha256":"c5e009fe316084b577cb0c7bacac799a5cff355723f0a9ff6865ef181d9d284c","name":"costs.tsv.txt","bytes":547814},{"sha256":"9cd134c74aad3b3767e65f466afaeafda5ef6a5ecf637c2c7ab4b5d35aba875f","name":"driver.py","bytes":4623},{"sha256":"3c042d0480dac1175d8caeafb5187fadb2c1d574840f26555b4109ecc6c5c2b7","name":"gen_tasks.py","bytes":3210},{"sha256":"e6e062306d74560b2b51f52ac806867d490a1edb8e792a8bd808480b713770fd","name":"job-calib.txt","bytes":2038},{"sha256":"cfe94c224cefbe2e7fa36efabc625ec0b9e848efe3ae8f4aa12fb1def7fe28a4","name":"job-main.txt","bytes":2617},{"sha256":"94f77366a86a1aa104ce89834a7067dbfb6f09a640bcafe99b96f0a9b6a44e73","name":"job-ss79.txt","bytes":2791},{"sha256":"f961076597ccf9d0f14bc25f0161a7a0f028688bf00b6bd416cc2599a2005f79","name":"job-top.txt","bytes":2702},{"sha256":"4a67aff39acef45571adde7395b2c635f52462ec55db506ae749f7819e16f6dc","name":"job.sh","bytes":3250},{"sha256":"6392fe3b553fbc7b31a18259576aa6985c25ace7b9e386a21a0dd2f7c8aba02f","name":"level12.json","bytes":1319},{"sha256":"4f4b26dfe90529ac0cb5498af6732b9807b621f0bd0a7514dbb5fa5387ce0897","name":"level13.json","bytes":1922},{"sha256":"9a56dcd68cbcaa1ac05da6bd88731ea0a68e61b16086cd75bb128582e2e434d8","name":"level14.json","bytes":3085},{"sha256":"683a67513d8366773d4dea464fffde641bd5b5e3ba44334220b6dea1e189d0b7","name":"level15.json","bytes":1979},{"sha256":"78a1ed8e22da1a41e184505486eaf7ce31d35aab5cfba93433a926531ddad856","name":"level16.json","bytes":1445},{"sha256":"c13a083c7b252edad108ec551bc4d5307c782ef6bac7c80e7c7fd0b62145aca8","name":"level17.json","bytes":3373},{"sha256":"02ffedbfac6652fef2b0b5e224356b44ecd26f58bb8f77ab3a3bf94c77f8a7aa","name":"level18.json","bytes":2144},{"sha256":"3c8668a13127ba6ac007abf613a70192373889ab8391a796654fa08beac17c3f","name":"level19.json","bytes":1522},{"sha256":"cd48cce561af63e458bac2ef8df6796052998f647d4697fece89e432059a8f42","name":"level20.json","bytes":2287},{"sha256":"19beea69fe2b7c558b25c98722587ca8998656d4df3a5ee58850905a023ebace","name":"level21.json","bytes":2309},{"sha256":"9945142aa324c2d4c9ad44d1f90817be56a9080d1d606a10e1bde15cce04df0b","name":"level22.json","bytes":3897},{"sha256":"29da3138d9c889bb7fc51e33420b2134c9170cf1e749d1c246ab9e9dec6b6d47","name":"levels.py","bytes":1007},{"sha256":"9fb376fec1daeaf94424b9787578351e6a606de8a9bd4b5c85d6efbf57f4603c","name":"post_ss79.sh","bytes":338},{"sha256":"025cb8cf0031fa9ae45299cd72e317b1b9c3ad6e09d7c3cd0791f0e2a8095b80","name":"post_top.sh","bytes":1044},{"sha256":"a001c769446582f5d37bf2329ca8706b65ce1a2c9f12c4547da9516efa5331a2","name":"seedsearch.c","bytes":7018},{"sha256":"770226749f3547ab0c3800b609f2efcc3f62cf424aa9067e4dd23e88ae5c944f","name":"ss37.out.txt","bytes":2271},{"sha256":"f2a5cedd8c2c165e81dd9c198bc8bdf3a6016c547d0b8a0bcddbbfc65b6fdbc2","name":"ss41.out.txt","bytes":2439},{"sha256":"7137ed8904937bd835c2442f2c88158a580201d2c5cb9b71dc265c6e670932b3","name":"ss43.out.txt","bytes":2625},{"sha256":"7a67273641355a94633ab7d3bf54d4c04e0540ff08f492363f6a9795fc5b5d92","name":"ss47.out.txt","bytes":2535},{"sha256":"074f587a00f09b39bdc5c0c7429f76826f1051c74c968bef8647f0ef12a6e0e6","name":"ss53.out.txt","bytes":2462},{"sha256":"a023e66a5a163128eb94a1559baa8dfc4974a233325c34847ce2ab06027ca259","name":"ss59.out.txt","bytes":2767},{"sha256":"91eaec5b07aba84fc5dc7b58a9d4baf24c4ad0b29895ec9ff91e7c76e0d1bd40","name":"ss61.out.txt","bytes":2641},{"sha256":"d425e33c7b141b7328be59c0a9ef5d73a3c72f7e1dbccb22c971c4ea300fb688","name":"ss67.out.txt","bytes":2574},{"sha256":"276bef37069be269e574ef3dae37f1015b9ecabd44072b38d1e73877f8d7bbde","name":"ss71.out.txt","bytes":2687},{"sha256":"29dd7c3244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primorials 71#, 73#, 79#, with the second code path also covering 37#..67#; the twin-slot wheel of each primorial, one period.","statement_md":"At 71#, 73# and 79# (G2 = A144311(20..22) + 1 = 1398, 1530, 1710), Wang's A144311 DFS with a 15-line tie patch, sharded by the residues of 5, 7, 11, 13, returns nmax = 4, 4, 8 attaining positions. Every position passes a trial-division certificate (a slot, the next slot exactly G2 later, no slot between). Each set is closed under sigma(n) = -n - G2 - 2 (mod x#), with 2, 2, 4 orbits, and lies over exactly one T19 seed and its mirror (71#: 4460219, 5238071; 73#: 875207, 8822951; 79#: 1295867, 8402111), so route 86's single-pair statement holds at these three levels. A second code path written for this return, run over all 378,675 T19 classes, gives the same position sets at every level 37# through 79# and no gap longer than G2. #424's split test gives one split class at each new level. The positions are listed in report.md and level20..22.json.","assumptions_md":"The unsharded patched DFS reproduces #1166's ties12..18.out and #1176's ties19.out byte for byte, and the depth-4 sharded run equals the unsharded one at n = 18 and 20 byte for byte (and at n = 19 through #1176's sha256). Both code paths prune by the same counting bound (remaining primes' largest single-residue kills must cover the uncovered count); they share no code, and their agreement does not test that bound. 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