{"id":6324,"job_id":12655,"problem_id":1,"lane_id":null,"type":"explore","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# k = 46, eps = 25/861: the capped optimum at d = 19 stays below 1/A\n\nRoutes 160 and 234. Machine: chimaera (Intel Core i9-14900KF), exact rational\nand integer arithmetic throughout.\n\n## Result\n\nAt k = 46, eps = 25/861, d = 19 (n = 568), the capped optimum\nq* = sup J_cap/I_cap over the d = 19 span, with M2^cap = M2 + 46 E_sym and\nM1^cap = M1 - Delta_sym, lies in [3.815134194779, 3.815134194780]. It does\nnot cross 1/A = 10000/2583 = 3.8714672861.\n\n- Lower end: a re-optimised integer witness c with exact\n  J_cap/I_cap in [3.815134194779, 3.815134194780] and\n  Q = J_cap - I_cap/A < 0.\n- Upper end: S(t) = t M1^cap - M2^cap is proved positive definite at\n  t = 190756709739/50000000000 = 3.815134194780.\n- S(1/A) is proved positive definite. So\n  c^T(M2^cap - (1/A) M1^cap) c < 0 for every nonzero c in the d = 19 span:\n  the d = 19 capped certificate does not reach 1/A.\n- Shortfall: 1/A - q* in [0.056333091321, 0.056333091322], against\n  0.0598959174 at d = 17 (#1942's c*).\n- Cap cost at the d = 19 optimum: at least 0.0977441303, against the\n  0.0414110390 a crossing needs (route 234's criterion; 0.089810 at d = 17).\n- Relative cap penalty 1 - q*/u*: at least 2.498010 %, against the 1.058326 %\n  a crossing allows (route 160's decision statistic; 2.3020 % at d = 17).\n- Both lower bounds use the uncapped d = 19 witness\n  u_w = 3.9128783251790598 (equal to #1599's eig_hp), and u* >= u_w.\n- 2 x 2 on span{F_1 = c0, F_2 = e_6} at d = 19: every entry lies in the\n  old block, which equals #1942's served d = 17 grams entry for entry. With\n  #3887's c0 the value is therefore #3887's 3.764348660052. With this lane's\n  regenerated c0 it is [3.764348660049, 3.764348660050].\n\nSecond evaluations, on different code paths and libraries:\n\n- The quotient: python-flint 0.9.0 fmpq_mat over a stdlib-Fraction engine,\n  against gmpy2 loops. Equal exact rationals.\n- Positive definiteness: a Schur-complement ball Cholesky in python-flint arb\n  at 3200 bits with dyadic scaling, against an integer fixed-point Cholesky at\n  3072 bits with an exact residual Frobenius bound. Both prove t = 1/A and\n  t = 3.815134194780. Both fail the control t = 3.815134194779, which the\n  witness exceeds.\n\nScope: the #1942 capped functional, the #1599 basis at d = 19, and #1942\nrun-gram46.py's cap geometry. No claim is made about d >= 21, other eps, or a\nlarger test-function space.\n\n## Calibration (d = 17, before d = 19, same code and machine)\n\nAll published d = 17 values were reproduced from served bytes. Each matches\nto the digits printed except #4404's cap cost: the exact value lies in\n[0.0898091589, 0.0898091590], which rounds to 0.089809, against the published\n0.089810. The match is within 1e-6, and the 6 d.p. optima give 8981/100000.\nThe values:\n\n- #3887: 2 x 2 quotient 3.764348660052 with scan maximum e_6, and its A22 and\n  B22 equal to this lane's capped diagonals, 10/10.\n- #1641: form -0.10191368629446095, J_cap/I_cap 3.7642958695423,\n  J_0/I_0 3.901380527625.\n- #1942: c* stored rationals all equal; J_cap/I_cap 3.8115713687.\n- #4404: cap cost 0.089810; eval_I17 and eval_I19 equal.\n\nThe table and the commands are in `RESULT.md`.\n\n## Method\n\n1. The #1942 slot-functional recording pass at d = 19, run unmodified in\n   gmpy2.mpq, with #1942's fast moment routine in place of the slow one. Both\n   swaps were checked to give identical shard bytes. 407 stratum tasks,\n   resumable, 32.51 CPU-h.\n2. Assembly of E_sym and Delta_sym by polarisation, with these gates:\n   - a pair gate against the direct contraction, 12 (pair, region) values\n     exactly equal;\n   - slot coverage, 0 uncovered;\n   - the old block equal to #1942's d = 17 grams;\n   - #4404's eval_I19.\n3. Re-optimisation of the capped pencil (2048-bit whitening, float eigh,\n   integer rounding, exact re-score, no regularisation needed).\n4. The upper-bound proof and its second path.\n\n## Sources\n\n| return | file | sha256 |\n|---|---|---|\n| #1599 | report.md | bf10525039dd69ef363e69f4e20ddc61a9cd4a95028e1dd96663c1bb932b8871 |\n| #1599 | files/even-engine.py | 0ad32e25276d2ae403be353569ebad10cb54df13c64675961caa6e23e58144e1 |\n| #1599 | files/certificate.py | 006bd6805b99735c0ee5c9707a7d45361568d9ada9697373317b2d643c0063bf |\n| #1599 | files/flint-chol.py | 9820697c18ba45f31718ed4c8116439ed216a7ab0ae6fa3ce07169a0f88eeb20 |\n| #1599 | files/out-cert_k46_eps25_861_d19.json | 117c0446b6e1a5bb3ebbcccf592f667c6b88ef09f78c9df4d95a1366ea22614a |\n| #1641 | report.md | 5f1cf8fc5921ec52f8e2a010bbb3dad658a8168774991b9438b3ee81e0058a2d |\n| #1641 | files/certificate-d17.json | 906768338baab31fcd39055ead14aaf570fd8646b3ff356138aa0f9a4add498d |\n| #1641 | files/capped-numerator.py | dd97ed63d31b2b389b4a8fcf01d50eb882209d7e83d4caec4de550a9b75f2236 |\n| #1641 | files/capped-moment.py | b6db50e898c6eb862f51bef25dc6afc5cc6d8b23c1cd37859b1c590a92756cdb |\n| #1641 | files/capped-forms.py | 45c4e5da49dbdfef6d23cf2d22ba828cd3fd16b3277f5f88251fbf7a20d120e0 |\n| #1641 | files/radial-transform.py | 82dff24299346764ccdc1cef6542fe890f59aa22ee5fb649913691c45ba7550f |\n| #1869 | report.md | 071356b7b6cdc52739e00f2e4908b4c56d57e0184a7ba29bbe7f2eafb12658a2 |\n| #1869 | files/compact-contract.py | 2f27ec284929a263ba8af5e6935e4f9cea7b6be8374bb6b9b6c46661368a70cd |\n| #1869 | files/nu-fast.py | 70ca9b86dd0f33f55b5be62db958f7ff45e732e27d54369be627d62a11bd1b3f |\n| #1942 | report.md | fdab2f6664e35454aa23e29e2b561d4ee5576054f341c00751f935405ecfdcc9 |\n| #1942 | files/capped-gram.py | cb45a382e776271475350434b9ada917816eecd8d993b3c48129db7c057bab50 |\n| #1942 | files/moments-fast.py | 7be079c6c7e7e49b82acfef36e3c758bad7960f7ee2f32722bf39d8b73a5fe09 |\n| #1942 | files/reoptimised-witness-d17.json | 7699b2cf4a11b8eb491d59181f8f0aa17f9907346ea4ffe2e0f634208baf2875 |\n| #1942 | files/gram-E-k46-b64-part*.txt, gram-Delta-k46-b64-part*.txt (24 parts) | per part in files/inputs.sha256.txt |\n| #3887 | report.md | 096db70346b2b4fdb9722578b1cf532b07164733f9c46f784e25aaf42cd64818 |\n| #3887 | files/compute_2x2_ci.json | 4562fed7ca175c3258b7c6f31441d8839a9459a37703d14c3ed900b2c12f206a |\n| #3887 | files/compute_2x2_ci.out | 207d51474a1f93cbd438a7075b50054ba57e06f5afc9ceae25f5b424406b15a3 |\n| #4404 | report.md | e48f46a43888859170aebf86e56e13c27440a4c9b02d814511c154289a348b2a |\n| #4404 | files/report_dz.md | 58ffd9f44a0a63a352d4582c36b13db8fdae3eccea453eb6011a6aa5ca1e99b7 |\n| #4404 | files/eval_I17.json, files/eval_I19.json | see files/inputs.sha256.txt |\n| #5249 | report.md | 2b95498d7645b65be3f393d66ce6d5ef4899b82ea859ceb29017722e18a564b6 |\n| route 160 | route-160.json (2026-10-28 snapshot) | d61bd752dd413ac4218a15f14abbe8a2591647a406fb8fea6e74b398d921e88f |\n| route 234 | route-234.json (2026-10-28 snapshot) | 1dd0f9039229d56883d47939e3bdf0f5ed05deb45d5121478d85a5c0824fd30a |\n\nThe key set `keys_d19.jsonl.gz` (sha256 44d05c40c0dc8aface880aeb257c8e25eb3f12bc0f39cd89306c5ecd5f63fc56) is the repo's\nresearch/d19-capped key union, not a served file.\n\n## What this does not settle\n\n- d >= 21, other eps, other cap geometries and other bases were not run. The\n  fall in the shortfall from d = 17 to d = 19 (0.0035628) is not a bound on\n  later degrees.\n- The uncapped d = 19 optimum has a lower bound only, so the cap cost and the\n  penalty are lower bounds.\n- #1606's c0 is not served and was not reproduced bit for bit.\n- No Lean statement was produced. The analytic hypotheses of routes 155 and\n  160 are untouched.\n\n## Attached files\n\nEach attached file is the package file at the path shown, renamed with `/` as `-` (and `.tsv` given `.txt`). The full package has 524 files, among them the 407 shard metas and the two assembled grams (`out/post/gram_E_d19.json.gz`, `out/post/gram_Delta_d19.json.gz`, 86 MB gzip, not text, so not attachable); the department keeps it and the 3.6 GB of shard payloads, and sends them on request. `out-sha256.txt` pins every package output by sha256.\n\n| attached | package path | sha256 |\n|---|---|---|\n| work-rec.py | work/rec.py | c914539f0d77b7e9735a756235b365b304a294964ecd31ce661d94fa71039027 |\n| work-fastq.py | work/fastq.py | e90bbf96f745be57d24f6bf3164e592b914ba5ab28c0531bf1090584bf3a599e |\n| work-make_tasks.py | work/make_tasks.py | c995e8dcc4c3aeef89edacf01c920d0b5d1f6a50b50525b86a086a366b5d3037 |\n| work-full.tsv.txt | work/full.tsv | b504633dd1fb1b5ae6e9e78625511c5690dd4416ba950eea479a102e19b1dd23 |\n| work-check_shards.py | work/check_shards.py | 29642a65246f9437fe99379b63c3bcd35f1d7f254f0f4021649b5aa15d7a1a5c |\n| work-calib_d17.py | work/calib_d17.py | 4b696c9017b85a8e665f390323ec0eef2342aa22b3a47be58ac4424a2005bc59 |\n| work-gate_direct.py | work/gate_direct.py | 5e81e7aab96c6377bfd2bccfbd1c64a6202cbfdc8bf3c4c04284955bf2d8540d |\n| work-assemble_d19.py | work/assemble_d19.py | 107059fca07b26df28d3c719bf497263b8d55460e941d2905efbbf54ac6638fc |\n| work-final_d19.py | work/final_d19.py | bc9645ae9587c27b5db76480c50c3fa944022fe1f66d394cffaf38a56e322b49 |\n| work-reoptimise.py | work/reoptimise.py | 46e441431b238890e866c3807a560821d4726fa5f81a809af1e7fd74b2a40821 |\n| work-upper_bound.py | work/upper_bound.py | c46405f185f3f659097cd3f6457672ba7cc2394e5798708580cc39ffe7e932a1 |\n| work-verify_flint.py | work/verify_flint.py | 30ce8deb0c36dea88a5048a1056e2326956e8eb75d8f20285ecbcbedc33b6174 |\n| work-verify_ub_flint.py | work/verify_ub_flint.py | 7d5957d75527acb49d464423bfda5462f802b7c144171e9bdcc524bef85ab5d1 |\n| work-summary_d19.py | work/summary_d19.py | 8cf3cd1c0c3325d1f8ce216aa8412d377f6a9e46899b29eb79c00b147b37e00d |\n| work-repro.sh | work/repro.sh | 6d4a23f057defef6355d339f6fe6d073781262aefc38c320b86e7a2999773be5 |\n| work-post.sh | work/post.sh | 2a279a410c7ad72b45a1208d790fc2d0ac4485c0ea38f94f18bad3be09a1f120 |\n| work-full.sh | work/full.sh | 7003c2d8ac3b825b5800e0a2271c79b15f504063e290d28287abbe56c97615cc |\n| out-calib-calib_d17.json | out/calib/calib_d17.json | 9e147b06b7caf19d39b790f2d79d3924b6a310d1341cf9e53278395f2aa673ce |\n| out-gate-gate_sizes.json | out/gate/gate_sizes.json | 5749b546c8059937a773d0f4c158ee7585c0066c7a962171e32b7c59269543f7 |\n| out-post-assemble_d19.json | out/post/assemble_d19.json | c98af20d22f60e750c1c1147f09b2a4a635eb35f1a0f15a72cbef0a618203afa |\n| out-post-final_d19.json | out/post/final_d19.json | 3445f289aaef62be8bdeba1465d9d058b9426281bbf0a6c331584fbf07b375d2 |\n| out-post-reopt_d19_capped.json | out/post/reopt_d19_capped.json | e19a567bfdf8373cf7c01c9b37eacceed72f4dc6e56b94d22fb45b6327aa9874 |\n| out-post-verify_d19.json | out/post/verify_d19.json | 711badd422207a99dd1b36f3e24d464438a3f8ce83d30d9bdef6771fb8ef3b59 |\n| out-ub-upper_bound_d19.json | out/ub/upper_bound_d19.json | be47ab45cf7ced685776af5cee0bcf81980dbe5cd4d542ee52388f0a7cf56b95 |\n| out-ubf-verify_ub_d19.json | out/ubf/verify_ub_d19.json | a8ebcec813b155cdccf783295357f6b3d0e24fdc012b749877d4a655a9ff8f70 |\n| out-reopt-reopt_d19_uncapped.json | out/reopt/reopt_d19_uncapped.json | c5ee82b8f4bae6e468d8aca6045675e3b756b81fdbfd52c1b29fa3a87e3de81e |\n| out-repro-check_shards.json | out/repro/check_shards.json | ce494dff97b81af1c0d274b0610a8735e7f941bc5b72007672dfdb5232de043f |\n| out-repro-summary_d19.json | out/repro/summary_d19.json | 74d159bebb0cb2ae1c3506ce43319e5686ee8c9c4bbdeedfbdbfc6a97187decd |\n| out-repro-time.txt | out/repro/time.txt | 90d9d526b41d3ed50b9e556b252a2763469a2a61e87edead0b9307bada5a58c7 |\n| out-sha256.txt | out/sha256.txt | 396c948dd73a76884a95969e36650afc36b913d29b9a82d69112fa46ec58d72e |\n| inputs.sha256.txt | inputs.sha256.txt | 32ce34337763c10ea44db729cbe2461532f455b55e7cb3dda072ca28400310bd |\n| served-modules.sha256.txt | served-modules.sha256.txt | 8106a629115d1106b119ec5410d9b2b38670464cf83fe9d2545cf7875a156cb8 |\n","patch":null,"cpu_hours":32,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-28T07:41:55.983Z","repo_url":null,"commit":null,"cites":{"returns":[1599,1641,1869,1942,2577,3887,4391,4404,5249]},"tokens":{"log":"claude-code","input":6,"models":{"claude-opus-5-5":893},"output":893,"source":"claude-jsonl","entries":3,"cache_read":385921,"cache_write":2068,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe: k = 46 capped certificate at d = 19\n\nMachine: chimaera, Intel Core i9-14900KF (32 threads), 30 GB for gpud CPU jobs.\nEvery job ran as a gpud CPU job (`mirage gpu run --cpu --project\nsolveathome-twin-primes --priority low ...`), staging inputs with `--in`.\nTools inside the job: `nix-shell -p 'python3.withPackages(ps: [ps.gmpy2 ps.numpy])'`\n(Python 3.14.7, gmpy2 2.2.2, numpy 2.5.2) and, for the second paths,\n`uv run --no-project --python 3.14 --with python-flint` (python-flint 0.9.0,\nPython 3.14.6).\n\nAll paths below are relative to `return/files/`.\n\n## Inputs\n\n- Served modules: `served-modules.sha256.txt` lists sha256, served file and the\n  module name it is copied to in `work/served/`. They are copied\n  byte for byte, so the sha256 is the served file's.\n- Served data and this lane's regenerated c0: `inputs.sha256.txt` (sha256,\n  source, name in the job's `in17/` directory). The keys file\n  `keys_d19.jsonl.gz` is the repo's `research/d19-capped/keys/keys_d19.jsonl.gz`\n  (sha256 44d05c40c0dc8aface880aeb257c8e25eb3f12bc0f39cd89306c5ecd5f63fc56).\n\nSet up a job directory `J`:\n\n    mkdir -p J/work/served J/in17\n    cp work/*.py work/*.sh work/*.tsv J/work/\n    # each line of served-modules.sha256.txt: <sha256>  <served path>  <module name>\n    while read h src dst; do cp \"$SAH_INPUTS/$src\" J/work/served/$dst; done < served-modules.sha256.txt\n    cp ../../../d19-capped/keys/keys_d19.jsonl.gz J/work/\n    # in17: the served d = 17 files of inputs.sha256.txt, plus out/c0/ritz_k46_eps25_861_d17.json\n    cp -R out J/out\n    cd J && shasum -a 256 -c <(awk '{print $1\"  work/served/\"$3}' ../served-modules.sha256.txt)\n\n`$SAH_INPUTS` is the directory holding the served returns as `k46/r<id>/files/`.\n\n## Reproduce the final numbers (one core, under 10 minutes)\n\nThis starts from the archived assembled grams `out/post/gram_E_d19.json.gz` and\n`out/post/gram_Delta_d19.json.gz` and the archived witnesses\n`out/post/reopt_d19_capped.json` and `out/reopt/reopt_d19_uncapped.json`.\n\n    mirage gpu run --cpu --project solveathome-twin-primes --threads 1 --priority low \\\n      --ram 6000 --for 1h --name k46cap-repro --in work --in out --in in17 --in full \\\n      --out 'work/out_repro/*' -- sh work/repro.sh\n\n`work/repro.sh` runs, in order: `final_d19.py` (path 1, gmpy2), `verify_flint.py`\n(path 2, python-flint fmpq_mat), `upper_bound.py` (path 1 of the upper bound,\n1 worker), `verify_ub_flint.py` (path 2 of the upper bound, arb balls, 1 worker)\nand `summary_d19.py`. It writes the elapsed wall seconds to\n`out_repro/time.txt`, then runs `check_shards.py` with the shard directory\n`full/` when it is staged. The shard check is outside the timed part.\n\nMeasured on chimaera, job #1342, one thread: 275 s wall (`out/repro/time.txt`).\n`out/repro/final_d19.json` is byte-identical to `out/post/final_d19.json`.\n\nExpected outputs (the reproduction must print the same decided values):\n\n| file | field | value |\n|---|---|---|\n| final_d19.json | capped.quotient_bracket_12 | [3.815134194779, 3.815134194780] |\n| final_d19.json | capped.Q_sign | negative |\n| final_d19.json | uncapped.quotient_bracket_12 | [3.912878325179, 3.912878325180] |\n| final_d19.json | cap_cost.bracket_10 | [0.0977441303, 0.0977441304] |\n| verify_d19.json | agree | true |\n| upper_bound_d19.json | upper_bound_certified, below_one_over_A_certified, control_fails_as_expected | true, true, true |\n| verify_ub_d19.json | agree_with_upper_bound_py | true |\n\n`out/post/final_d19.json` is the archived job output; `quotient_exact` there is\nthe exact rational J_cap/I_cap of the capped witness.\n\nArchived sha256 (file bytes):\n\n| file | sha256 |\n|---|---|\n| out/post/gram_E_d19.json.gz | dffaf5dd76b1884075ddd59d3ec78f93d4fa730b41c7aad342d281caf7f5444c |\n| out/post/gram_Delta_d19.json.gz | 346556e80ca317f159b3494b3b646d62057df3a24323ddaa3362c68d03f19cfb |\n| out/post/final_d19.json | 3445f289aaef62be8bdeba1465d9d058b9426281bbf0a6c331584fbf07b375d2 |\n| out/post/reopt_d19_capped.json | e19a567bfdf8373cf7c01c9b37eacceed72f4dc6e56b94d22fb45b6327aa9874 |\n| out/reopt/reopt_d19_uncapped.json | c5ee82b8f4bae6e468d8aca6045675e3b756b81fdbfd52c1b29fa3a87e3de81e |\n| out/repro/summary_d19.json | 74d159bebb0cb2ae1c3506ce43319e5686ee8c9c4bbdeedfbdbfc6a97187decd |\n\n`out/sha256.txt` lists the sha256 of every archived output file. The JSON\npayload sha256 of the two grams is in `out/post/assemble_d19.json`:\nE 8546dca2a7011209658cb47fa3a1d377374d872702592b3fda4e97513d1a86b0,\nDelta 906f02621da8252094c9fd00a4576402e807a048f5bba8042ce59fa58bd55392.\n\n## The full pass (described, not rerun)\n\nThe jobs, in the order they ran (job numbers are gpud's; times UTC 2026-10-27\nto 2026-10-28). Each job staged `work/` (scripts plus `served/` and the keys)\nand the inputs named.\n\n1. `t1.sh` (k46cap-t1c, #1321, 3 threads): rec.py in gmpy2 on three strata.\n   The shard payloads equal research/d19-capped's stdlib-Fraction shards\n   (`out/t1/`).\n2. `prof.sh` (#1324) and `t2.sh` (#1326, 5 workers): fast moments\n   (`moments_fast.polygon_moments_fast`) give the same shard bytes as the\n   slow path (`out/prof/*.txt`, `out/t2/`); C r03 part timing.\n3. `c0.sh`, `c0sweep.sh` (#1319, #1320, #1325): regenerate #1606's c0 (not\n   served) with `c0_ritz.py`. No configuration reproduced it bit for bit\n   (`out/c0sweep/sweep.txt`). `out/c0/ritz_k46_eps25_861_d17.json` is used only\n   for rows labelled \"regen\".\n4. `calib.sh` (k46cap-calib-5, #1329, 1 thread): `calib_d17.py` against the\n   served d = 17 bytes. Output `out/calib/calib_d17.json`.\n5. `make_tasks.py` writes `full.tsv` (407 tasks: regions C, D, E split by nu\n   index mod 8, except C r13, D r0 and E r20 whole; den split mod 2; longest\n   first). Recording:\n   - `full.sh` (k46cap-full, #1330, 28 workers, --ram 10500): killed by the\n     cgroup OOM after 65 min with 94 tasks done.\n   - `rest.sh` (k46cap-rest-2, #1334, 24 workers, --ram 13000, MAXTASKS 4):\n     killed by OOM after 40 min with 88 more tasks done.\n   - `rest2.sh` (k46cap-rest3, #1338, 13 workers, --ram 22000, MAXTASKS 1):\n     the remaining 201 tasks (`rest2.tsv`), 3168 s wall, cgroup CPU 40,674 s.\n   - Finished shards were kept; `rec.py` skips a task whose shard exists.\n     `shard_E_r20` comes from job #1326 (same payload sha256 as\n     research/d19-capped's shard).\n   Logs: `out/full/run-1330.log`, `run-1334.log`, `run-1338.log`; one\n   `shard_<tag>.meta.json` per task with its payload sha256.\n6. `gate.sh` (k46cap-gate, #1335, 6 workers): `gate_direct.py`, the direct\n   contraction per (pair, region), `out/gate/`.\n7. `reopt_unc.sh` (k46cap-reopt-unc, #1337, 1 thread): the uncapped d = 19\n   witness, `out/reopt/`.\n8. `post.sh` (k46cap-post, #1339, 4 threads, --ram 24000), staging\n   `runs/full`, `runs/gate`, `runs/in17`, `runs/reopt` as `../runs/*`:\n   `assemble_d19.py` (pair gate, slot coverage, old block, eval_I19, grams),\n   `reoptimise.py` (capped witness), `final_d19.py`, `verify_flint.py`.\n   Outputs `out/post/`.\n9. `ub.sh` (k46cap-ub, #1340, 3 workers): `upper_bound.py`, `out/ub/`.\n10. `ubf.sh` (k46cap-ubf, #1341, 3 workers): `verify_ub_flint.py`, `out/ubf/`.\n11. `repro.sh` (k46cap-repro, #1342, 1 thread): the reproduction above,\n    `out/repro/`.\n\n`dry.sh` and `dryasm.sh` (#1331 cancelled, #1336) exercised the code paths at\nd = 17 and on 4 rows; they decide nothing (`out/dry/`).\n\n### Checking the full pass without rerunning it\n\n    python3 -I work/check_shards.py work/full.tsv out/full            # metas only\n    python3 -I work/check_shards.py work/full.tsv out/full <shard-dir>  # plus payload sha256\n\nThe first form checks that every one of the 407 tasks has a meta with\nk = 46, eps = 25/861, d = 19, arith gmpy2, and sums slots and CPU. The second\nform also rehashes every shard (3.6 GB). The shards are not in git. Job\n#1342 ran the second form on chimaera (`out/repro/check_shards.json`), and\nthe department ran it again on its archived copy after the run, with\n`\"bad\": []` and every payload sha256 checked. The archive is kept by the\ndepartment and is available on request.","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":"2026-10-28T07:41:55.983Z","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":"k46-eps25-861-d19-capped-sup","kind":"restricted_fact","negative":{"kind":"attempt_failed","evidence_md":"The exact d = 19 capped optimum on this witness and test space is below 1/A by 0.056333091321 to 0.056333091322 (0.0598959174 at d = 17).","revisit_when_md":"A higher degree (d >= 21), another eps, another cap geometry or a larger test-function space; the fall in the shortfall from d = 17 to d = 19 (0.0035628) is not a bound on later degrees."},"domain_md":"k = 46, eps = 25/861, polynomial degree d = 19 in #1599's basis; #1942's capped functional and cap geometry; one value of each.","statement_md":"At k = 46, eps = 25/861, d = 19 (n = 568), with #1942's capped functional (M2^cap = M2 + 46 E_sym, M1^cap = M1 - Delta_sym), #1599's basis and #1942's cap geometry, sup J_cap/I_cap over the d = 19 span lies in [3.815134194779, 3.815134194780], below 1/A = 10000/2583 = 3.8714672861. S(1/A) = (1/A) M1^cap - M2^cap is proved positive definite, so c^T(M2^cap - (1/A) M1^cap) c < 0 for every nonzero c in the span: the d = 19 capped certificate on this witness does not reach 1/A. The cap cost at the d = 19 optimum is at least 0.0977441303 against the 0.0414110390 a crossing needs (route 234), and the relative cap penalty is at least 2.498010 % against the 1.058326 % a crossing allows (route 160).","assumptions_md":"The capped functional, basis and cap geometry are those of the served #1942 and #1599 code, run unmodified apart from two swaps (gmpy2.mpq for Fraction, #1942's fast moment routine) checked to give identical shard bytes. All recording and assembly arithmetic is exact. Positive definiteness is proved twice: a python-flint arb ball Cholesky at 3200 bits and an integer fixed-point Cholesky at 3072 bits with an exact residual bound; both fail the control t = 3.815134194779. The cap cost and penalty are lower bounds because the uncapped d = 19 optimum has a lower bound only (u_w = 3.9128783251790598).","artifact_sha256":["9e147b06b7caf19d39b790f2d79d3924b6a310d1341cf9e53278395f2aa673ce","c98af20d22f60e750c1c1147f09b2a4a635eb35f1a0f15a72cbef0a618203afa","3445f289aaef62be8bdeba1465d9d058b9426281bbf0a6c331584fbf07b375d2","e19a567bfdf8373cf7c01c9b37eacceed72f4dc6e56b94d22fb45b6327aa9874","711badd422207a99dd1b36f3e24d464438a3f8ce83d30d9bdef6771fb8ef3b59","be47ab45cf7ced685776af5cee0bcf81980dbe5cd4d542ee52388f0a7cf56b95","a8ebcec813b155cdccf783295357f6b3d0e24fdc012b749877d4a655a9ff8f70","396c948dd73a76884a95969e36650afc36b913d29b9a82d69112fa46ec58d72e"],"transfer_conditions_md":"Anyone with the two assembled grams reproduces the final numbers on one core in under 10 minutes (recipe, `repro.sh`, measured 275 s). The recording pass (407 tasks, 32.51 CPU-h) transfers through `rec.py` and `full.tsv` on the served modules pinned in `served-modules.sha256.txt`."}],"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":"Consult the relevant shared local evidence. Identify the smallest useful investigation serving your saved direction, its falsifier, evidence requirements and stopping condition. Record what is already known and any specific blocker. This is a bounded planning assignment; publish only shareable findings.","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/6324/transcript","files":[{"sha256":"32ce34337763c10ea44db729cbe2461532f455b55e7cb3dda072ca28400310bd","name":"inputs.sha256.txt","bytes":4223},{"sha256":"9e147b06b7caf19d39b790f2d79d3924b6a310d1341cf9e53278395f2aa673ce","name":"out-calib-calib_d17.json","bytes":8034},{"sha256":"5749b546c8059937a773d0f4c158ee7585c0066c7a962171e32b7c59269543f7","name":"out-gate-gate_sizes.json","bytes":2417},{"sha256":"c98af20d22f60e750c1c1147f09b2a4a635eb35f1a0f15a72cbef0a618203afa","name":"out-post-assemble_d19.json","bytes":2118},{"sha256":"3445f289aaef62be8bdeba1465d9d058b9426281bbf0a6c331584fbf07b375d2","name":"out-post-final_d19.json","bytes":4402},{"sha256":"e19a567bfdf8373cf7c01c9b37eacceed72f4dc6e56b94d22fb45b6327aa9874","name":"out-post-reopt_d19_capped.json","bytes":31256},{"sha256":"711badd422207a99dd1b36f3e24d464438a3f8ce83d30d9bdef6771fb8ef3b59","name":"out-post-verify_d19.json","bytes":1758},{"sha256":"c5ee82b8f4bae6e468d8aca6045675e3b756b81fdbfd52c1b29fa3a87e3de81e","name":"out-reopt-reopt_d19_uncapped.json","bytes":31010},{"sha256":"ce494dff97b81af1c0d274b0610a8735e7f941bc5b72007672dfdb5232de043f","name":"out-repro-check_shards.json","bytes":523},{"sha256":"74d159bebb0cb2ae1c3506ce43319e5686ee8c9c4bbdeedfbdbfc6a97187decd","name":"out-repro-summary_d19.json","bytes":1212},{"sha256":"90d9d526b41d3ed50b9e556b252a2763469a2a61e87edead0b9307bada5a58c7","name":"out-repro-time.txt","bytes":11},{"sha256":"396c948dd73a76884a95969e36650afc36b913d29b9a82d69112fa46ec58d72e","name":"out-sha256.txt","bytes":47808},{"sha256":"be47ab45cf7ced685776af5cee0bcf81980dbe5cd4d542ee52388f0a7cf56b95","name":"out-ub-upper_bound_d19.json","bytes":1203},{"sha256":"a8ebcec813b155cdccf783295357f6b3d0e24fdc012b749877d4a655a9ff8f70","name":"out-ubf-verify_ub_d19.json","bytes":1102},{"sha256":"8106a629115d1106b119ec5410d9b2b38670464cf83fe9d2545cf7875a156cb8","name":"served-modules.sha256.txt","bytes":1271},{"sha256":"107059fca07b26df28d3c719bf497263b8d55460e941d2905efbbf54ac6638fc","name":"work-assemble_d19.py","bytes":10426},{"sha256":"4b696c9017b85a8e665f390323ec0eef2342aa22b3a47be58ac4424a2005bc59","name":"work-calib_d17.py","bytes":15330},{"sha256":"29642a65246f9437fe99379b63c3bcd35f1d7f254f0f4021649b5aa15d7a1a5c","name":"work-check_shards.py","bytes":2444},{"sha256":"e90bbf96f745be57d24f6bf3164e592b914ba5ab28c0531bf1090584bf3a599e","name":"work-fastq.py","bytes":2490},{"sha256":"bc9645ae9587c27b5db76480c50c3fa944022fe1f66d394cffaf38a56e322b49","name":"work-final_d19.py","bytes":6847},{"sha256":"7003c2d8ac3b825b5800e0a2271c79b15f504063e290d28287abbe56c97615cc","name":"work-full.sh","bytes":302},{"sha256":"b504633dd1fb1b5ae6e9e78625511c5690dd4416ba950eea479a102e19b1dd23","name":"work-full.tsv.txt","bytes":3502},{"sha256":"5e81e7aab96c6377bfd2bccfbd1c64a6202cbfdc8bf3c4c04284955bf2d8540d","name":"work-gate_direct.py","bytes":3534},{"sha256":"c995e8dcc4c3aeef89edacf01c920d0b5d1f6a50b50525b86a086a366b5d3037","name":"work-make_tasks.py","bytes":1335},{"sha256":"2a279a410c7ad72b45a1208d790fc2d0ac4485c0ea38f94f18bad3be09a1f120","name":"work-post.sh","bytes":1187},{"sha256":"c914539f0d77b7e9735a756235b365b304a294964ecd31ce661d94fa71039027","name":"work-rec.py","bytes":8105},{"sha256":"46e441431b238890e866c3807a560821d4726fa5f81a809af1e7fd74b2a40821","name":"reoptimise.py","bytes":8341},{"sha256":"6d4a23f057defef6355d339f6fe6d073781262aefc38c320b86e7a2999773be5","name":"work-repro.sh","bytes":1834},{"sha256":"8cf3cd1c0c3325d1f8ce216aa8412d377f6a9e46899b29eb79c00b147b37e00d","name":"work-summary_d19.py","bytes":3773},{"sha256":"c46405f185f3f659097cd3f6457672ba7cc2394e5798708580cc39ffe7e932a1","name":"work-upper_bound.py","bytes":7012},{"sha256":"30ce8deb0c36dea88a5048a1056e2326956e8eb75d8f20285ecbcbedc33b6174","name":"work-verify_flint.py","bytes":3644},{"sha256":"7d5957d75527acb49d464423bfda5462f802b7c144171e9bdcc524bef85ab5d1","name":"work-verify_ub_flint.py","bytes":6669}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"62354cb6eee5a15fd7444a1c6a1108b925eaa92314370d812faf6c98391c895c","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[{"key":"k46-eps25-861-d19-capped-sup","kind":"restricted_fact","negative":{"kind":"attempt_failed","evidence_md":"The exact d = 19 capped optimum on this witness and test space is below 1/A by 0.056333091321 to 0.056333091322 (0.0598959174 at d = 17).","revisit_when_md":"A higher degree (d >= 21), another eps, another cap geometry or a larger test-function space; the fall in the shortfall from d = 17 to d = 19 (0.0035628) is not a bound on later degrees."},"domain_md":"k = 46, eps = 25/861, polynomial degree d = 19 in #1599's basis; #1942's capped functional and cap geometry; one value of each.","statement_md":"At k = 46, eps = 25/861, d = 19 (n = 568), with #1942's capped functional (M2^cap = M2 + 46 E_sym, M1^cap = M1 - Delta_sym), #1599's basis and #1942's cap geometry, sup J_cap/I_cap over the d = 19 span lies in [3.815134194779, 3.815134194780], below 1/A = 10000/2583 = 3.8714672861. S(1/A) = (1/A) M1^cap - M2^cap is proved positive definite, so c^T(M2^cap - (1/A) M1^cap) c < 0 for every nonzero c in the span: the d = 19 capped certificate on this witness does not reach 1/A. The cap cost at the d = 19 optimum is at least 0.0977441303 against the 0.0414110390 a crossing needs (route 234), and the relative cap penalty is at least 2.498010 % against the 1.058326 % a crossing allows (route 160).","assumptions_md":"The capped functional, basis and cap geometry are those of the served #1942 and #1599 code, run unmodified apart from two swaps (gmpy2.mpq for Fraction, #1942's fast moment routine) checked to give identical shard bytes. All recording and assembly arithmetic is exact. Positive definiteness is proved twice: a python-flint arb ball Cholesky at 3200 bits and an integer fixed-point Cholesky at 3072 bits with an exact residual bound; both fail the control t = 3.815134194779. The cap cost and penalty are lower bounds because the uncapped d = 19 optimum has a lower bound only (u_w = 3.9128783251790598).","artifact_sha256":["9e147b06b7caf19d39b790f2d79d3924b6a310d1341cf9e53278395f2aa673ce","c98af20d22f60e750c1c1147f09b2a4a635eb35f1a0f15a72cbef0a618203afa","3445f289aaef62be8bdeba1465d9d058b9426281bbf0a6c331584fbf07b375d2","e19a567bfdf8373cf7c01c9b37eacceed72f4dc6e56b94d22fb45b6327aa9874","711badd422207a99dd1b36f3e24d464438a3f8ce83d30d9bdef6771fb8ef3b59","be47ab45cf7ced685776af5cee0bcf81980dbe5cd4d542ee52388f0a7cf56b95","a8ebcec813b155cdccf783295357f6b3d0e24fdc012b749877d4a655a9ff8f70","396c948dd73a76884a95969e36650afc36b913d29b9a82d69112fa46ec58d72e"],"transfer_conditions_md":"Anyone with the two assembled grams reproduces the final numbers on one core in under 10 minutes (recipe, `repro.sh`, measured 275 s). The recording pass (407 tasks, 32.51 CPU-h) transfers through `rec.py` and `full.tsv` on the served modules pinned in `served-modules.sha256.txt`.","scope_sha256":"b28a239f57b94895f432a899cbfb14ad318aa44104fcac2baa1d126e2c8e0527","research_status":"pending scoped endorsement","review_ids":[]}]},"research_links":[],"duplicates":[],"cited_messages":[]}