{"id":5601,"job_id":11341,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Routes 160, 234, 291: the d = 19 capped recording pass priced at about 630 to 670 CPU-h from four probes, not 45 to 70; d = 17 gate and controls reproduced exactly\n\nStatus (2026-10-23, 15:1xZ): **pricing return, not a full pass.** The gate, the d = 17 control, the re-optimiser controls and four d = 19 cost probes are done. The probes price the d = 19 recording pass at about 630 to 670 CPU-h (estimate), against #4404's 45 to 70 CPU-h. Under the head's rule of 2026-10-23 (a few hundred CPU-h means stop and hand in the pricing), the full pass, the assembly and the d = 19 re-optimisation were not run. **The d = 19 capped quotient, the sign of Q and the d = 19 penalty are not known.** At d = 17 the best capped witness found (3.8130019917, re-optimised) is not certified at 1/A; nothing here says whether d = 19 is.\n\n## Pricing (the answer of this return)\n\nFour probes on chimaera, one core each, at the 150 W cap, Python 3.14.7 (measured CPU of the recording step; `pricing.py`, output `pricing.json`):\n\n| stratum | d = 19 recording CPU (measured) | max RSS (measured) | #1942 d = 17 CPU | ratio d19/d17 |\n|---|---|---|---|---|\n| C r = 7, nu part 4 of 16 (53,396 slots) | 1,344.8 s | 355 MB | | |\n| C r = 7, nu part 0 of 16 (30,900 slots) | 1,318.8 s | 324 MB | | |\n| C r = 7 whole, 16 x mean of the two parts | about 21,300 s (estimate) | | 1,661.2 s | about 12.8 (estimate) |\n| C r = 7 whole, run directly (#1138, 180 W) | not finished in 10,800 s (measured lower bound) | | 1,661.2 s | over 6.5 |\n| E r = 20 | 4,124.6 s | 211 MB | 274.0 s | 15.1 |\n| den r = 22 | 112.8 s | 395 MB | 22.8 s | 4.9 |\n\nThe two C parts cost the same to 2 % although their slot counts differ by 1.7 times, so a C stratum's cost follows its nu groups (each part holds about 100 of the 1,597), not its slots. That is why the whole C r = 7 is priced as 16 times the part mean.\n\nApplying each region's ratio to #1942's d = 17 seconds per region (C 147,054 s, D 15,539 s, E 17,186 s, den 7,120 s; D has no probe and is bounded by the smallest and largest measured ratio):\n\n| | estimate |\n|---|---|\n| CPU for the 70 strata at d = 19 | 627 to 671 CPU-h |\n| the same if #5249's 97,670 s d = 17 total is the right reading of #1942's log | 328 to 350 CPU-h |\n| wall time at three concurrent jobs | 209 to 224 h |\n| C r = 1..6 per stratum (d = 17: 20,381 to 23,255 s) | about 260,000 to 300,000 s each, so about 48 nu parts each to stay under 3 h per job |\n| RAM per job | under 400 MB measured on every probe; 8,192 MB per job is far more than needed, 1,024 MB would do |\n\nLimits of this price: one stratum per region was measured, the heavy C r = 1..6 strata may scale differently from C r = 7, the probes ran at 150 W while #1942's d = 17 seconds were taken with 6 to 8 workers on one host, and the 186,898 s versus 97,670 s reading of #1942's log is unresolved. The range above carries none of these as error bars; it is the arithmetic of the ratios.\n\n## Result so far\n## Result so far\n\n- **Gate (measured, Studio).** The served engine `EvenEngine(46, 25/861, d, 'exact')` (#1599 `even-engine.py`, sha256 `0ad32e25...44e1`) builds B_17 (n = 374) and B_19 (n = 568). B_19[:374] equals B_17, the 194 new coordinates have total degree 18 and 19, and M1, M2 agree on all 70,125 pairs i <= j < 374 (0 mismatches each, exact `Fraction` equality). The block digest in #5249's `nest_bx.py` format is `ce8094aacec46bd6b6a1bfad535251f7e6bf208168d5178026dc6e551cdff6f9`, the digest #5249 reports. This lane's own digest (`\"i j M1 M2\\n\"` lines) is `f2d07872...69e4`. File: `gate_control.json`.\n- **Control (measured, Studio).** From served bytes only (#1942's gram chunks, its witness `reoptimised-witness-d17.json`, and the d = 17 block of the gate) the exact I_0, J_0, I_cap, J_cap, J_cap/I_cap and Q = J_cap - I_cap/A all equal #1942's stored rationals exactly (6 of 6). Directed decimal print, A = 2583/10000:\n\n| quantity at d = 17, witness c* of #1942 | floor (10 d.p.) | ceil (10 d.p.) |\n|---|---|---|\n| J_cap/I_cap | 3.8115713687 | 3.8115713688 |\n| 1/A | 3.8714672861 | 3.8714672862 |\n| Q = J_cap - I_cap/A | -1.9296200187e-95 | -1.9296200186e-95 |\n| J_0/I_0 at the same witness | 3.8554999945 | 3.8554999946 |\n| witness penalty 1 - (J_cap/I_cap)/(J_0/I_0) | 0.0113937559 | 0.0113937560 |\n| optimum penalty 1 - (J_cap/I_cap)/3.901380527625 (#1641 uncapped optimum, cited, 12 digits) | 0.0230198408 | 0.0230198409 |\n\n  Q is negative: the d = 17 witness is not certified at 1/A. The optimum penalty reproduces #5249's 2.3020 %.\n- **Re-optimiser controls (measured, chimaera gpud, Python 3.14.7, numpy 2.5.2, 2048-bit fixed point, no regularisation needed).** `reoptimise.py` on the uncapped pair reproduces both served optima, and on #1942's d = 17 capped grams it finds a better capped witness than #1942's. Exact quotients of the rounded witnesses, directed print (`directed_print.py`, file `reopt/controls_directed.json`):\n\n| run | witness J/I floor | ceil | J/I - 1/A floor | ceil | sign of Q |\n|---|---|---|---|---|---|\n| d = 17 uncapped (`reopt/reopt_d17_uncapped_control.json`) | 3.9013805276 | 3.9013805277 | 0.0299132415 | 0.0299132416 | positive |\n| d = 19 uncapped (`reopt/reopt_d19_uncapped.json`) | 3.9128783251 | 3.9128783252 | 0.0414110390 | 0.0414110391 | positive |\n| d = 17 capped, #1942 grams (`reopt/reopt_d17_capped_control.json`) | 3.8130019917 | 3.8130019918 | -0.0584652944 | -0.0584652943 | negative |\n\n  The uncapped rows agree with #1641's 3.901380527625 and #1599's 3.9128783251790598 (cited) to the digits served. The capped d = 17 re-optimised witness beats #1942's witness (3.8115713687) by 0.00143 but is still not certified at 1/A. Its optimum penalty against this lane's d = 17 uncapped witness is [0.0226531442, 0.0226531443], below #5249's 2.3020 %, which used #1942's witness. A crossing at d = 19 still needs a penalty <= 1.0583 % (estimate from the cited d = 19 optimum; the exact test is the sign of Q). Q itself scales with the integer witness, so only its sign is reported; the margin J/I - 1/A carries the size.\n- **Decision rule written before d = 19 is read.** At d = 19 the capped re-optimised witness certifies J_cap/I_cap > 1/A exactly when its exact Q > 0. In penalty terms (#5249), against the uncapped d = 19 optimum 3.9128783251790598 (#1599 `out-cert_k46_eps25_861_d19.json`, cited), a crossing needs an optimum penalty <= 1.0583 %. Q's sign from the committed exact matrices is the decisive number; the penalty is the explanatory one.\n\n## Method\n\n1. `gate_control.py` (stdlib): builds both engines, compares the 70,125 old-block pairs, decodes #1942's base64 gzip gram chunks, evaluates the four quadratic forms over a common integer denominator, compares with the served strings, prints floor and ceiling at 10 decimals.\n2. `record_stratum.py` (stdlib): one (region, r) stratum of #1942's recording pass, the cap geometry of `run-gram46.py` unchanged, d = 19 slot keys from two seeded full-support random vectors on B_19 (#1599 serves no d = 19 Ritz vector, only its eigenvalue), one `shard_<region>_r<rr>.jsonl.gz` per stratum. Optional `i/m` keeps the nu groups with index = i mod m. Mode `keys` computes the d = 19 slot-key union once (`keys_d19.jsonl.gz`); stratum jobs load it through `KEYS_FILE`. `submit_strata.py` prints the gpud command of every stratum job, in chains of `--after` so at most three run at once.\n3. `split_check.py`: at k = 6 and k = 8, d = 5, every stratum recorded whole and in m = 3 nu parts; the parts are disjoint and sum to the whole, exactly, on all 54 strata (52 non-empty). This licenses splitting the long C strata (approved by the head on 2026-10-23 after this check).\n4. `assemble.py`: merges the shards, checks pair witnesses e_i + e_j against the direct contraction (`correction_compact` summed over C, D, E and `violation_F2`) bit for bit, including a pair of two new d = 19 coordinates, then assembles E_sym and Delta_sym with #1942's `assemble_gram`.\n5. `reoptimise.py` (run on chimaera through gpud under nix-shell `python3.withPackages` numpy, HEAD-NOTES 9): M2' = M2 + 46 E_sym and M1' = M1 - Delta_sym; unit-diagonal scaling, Cholesky in fixed-point integers at 2048 bits, whitening, the top eigenvector in float64 (numpy), back-substitution, rounding to integer vectors at five resolutions, and the exact J/I and Q of each. The eigen step only proposes the witness; the reported quotient and Q are exact rationals for that witness. Tested at d = 3 and 5 (uncapped): the exact quotient matches the whitened top eigenvalue to about 1e-15.\n\n## Served code checks\n\nEvery served file was checked against its `SHA256SUMS.txt` (#1599, #1942, #5249, #5442, #1641, #1869: 0 failures) and read for I/O. The modules on the recording path (`capped_gram`, `capped_numerator`, `capped_moment`, `capped_forms`, `compact_contract`, `nu_fast`, `radial_transform`, `moments_fast`, `even_engine`) import only `fractions`, `functools`, `itertools`, `math`, `collections` and `typing` on that path. flint, numpy and scipy appear only in lazy branches this lane does not call. No module opens a file, imports `os`, `socket` or `subprocess`, or calls `eval` or `exec`. Staged names and hashes: `served-modules.sha256.txt`.\n\nServed test suites on the staged copies (Studio, `nice -n 10`, measured wall): `test-nu-fast.py` NU-FAST PASS (55 s), `test-compact-contract.py` COMPACT-CONTRACT PASS (57 s), `test-moments-fast.py` MOMENTS-FAST PASS (93 s), `test-capped-gram.py` CAPPED-GRAM PASS (126 s), `test-capped-moment.py` ALL PASS (4 s) and `test-capped-numerator.py` ALL PASS (9 s), the last two under uv's offline numpy 2.4.6 (Python 3.11). Logs: `logs/`.\n\n## Run list and cost\n\n`runlist.tsv`: 70 strata, the same as at d = 17 because the stratum ranges depend only on the cap scalars (C r = 0..13, D r = 0..13, E r = 1..20, den r = 1..22). It carries #1942's per-task seconds from the served d = 17 log (measured there, with 6 to 8 workers sharing a host). Those seconds sum to 186,898 s (51.9 h), last record per stratum. #5249 quotes 97,670 s for the same log; the difference is not resolved here. Six strata, C r = 1..6, took 20,381 to 23,255 s each at d = 17, over the 3 h job limit, so they are split by nu group.\n\n| step | where | CPU | status |\n|---|---|---|---|\n| gate + control | Studio | 18.7 s user, 49 s wall, 386 MB max RSS (measured) | done |\n| served test suites | Studio | 344 s wall total (measured) | done |\n| split check | Studio | 342 s wall (measured) | done |\n| first strata E r = 20, den r = 22 | Studio, `nice -n 10` | stopped at 08:58Z for hold be846a: 104.6 s user CPU in 2,645 s wall each (4 %, the Studio's cores were busy), 215 to 229 MB max RSS, still inside the d = 19 slot-key union (measured) | not finished |\n| d = 19 slot-key union, once | chimaera gpud #1125, then loaded by every stratum job via `KEYS_FILE` | 246.5 s CPU (123.3 + 123.2 s, one per seed), measured; the job then failed writing the file (`gzip.open` takes no `mtime` on Python 3.14), fixed to `gzip.GzipFile` | rerun as gpud #1128: 234.2 s CPU, 263 MB max RSS (measured); `keys/keys_d19.jsonl.gz`, payload sha256 `0fdfcf30...6577` | done |\n| measurement stratum C r = 7, whole | chimaera gpud #1138, 8,192 MB | keys loaded in 12.8 s, then not finished in 3 h of one core (10:23Z to 13:23Z), cancelled at 13:25Z (measured). #1942's d = 17 log has 1,661 s for this stratum, so its d19/d17 ratio is over 6.5 (measured lower bound) | not finished |\n| (power note) | chimaera | the i9 is capped at 150 W from 13:27Z (180 W before, head's note). #1138 and the keys jobs ran at 180 W; the probes and E r = 20 from about 13:24Z on run at 150 W, so CPU times across the change are compared with that caveat | |\n| probe C r = 7 part 4 of 16 | chimaera gpud #1155, 150 W | 1,344.8 s CPU recording + 28.3 s engine and keys, 53,396 slots out, 355 MB max RSS (measured); `shards/shard_C_r07_p4of16.jsonl.gz` | done |\n| den r = 22 | chimaera gpud #1140, 150 W | 112.8 s CPU recording + 28.8 s, 13,955 slots out, 395 MB max RSS (measured; d = 17: 22.8 s, ratio 4.9); `shards/shard_den_r22.jsonl.gz` | done |\n| probe C r = 7 part 0 of 16 | chimaera gpud #1156, 150 W | 1,318.8 s CPU recording + 33.1 s engine and keys, 30,900 slots out, 324 MB max RSS (measured); `shards/shard_C_r07_p0of16.jsonl.gz` | done |\n| E r = 20 | chimaera gpud #1139, 150 W | 4,124.6 s CPU recording + 28.4 s, 13,955 slots out, 211 MB max RSS (measured; d = 17: 274.0 s, ratio 15.1); `shards/shard_E_r20.jsonl.gz` | done |\n| d = 17 capped re-optimisation control | chimaera gpud #863 | 312.1 s CPU (cholesky 42.5, whitening and eigh 250.5), measured | done |\n| uncapped re-optimisation d = 17 | chimaera gpud #864 | 271.4 s CPU, measured | done |\n| uncapped re-optimisation d = 19 | chimaera gpud #865 | 874.0 s CPU (cholesky 107.6, whitening and eigh 732.5), measured | done |\n| the rest of the 70 recording strata at d = 19 | chimaera gpud | 627 to 671 CPU-h (estimate, see Pricing) | **not run**, by the head's pricing rule |\n| assembly, re-optimisation at d = 19 | | not measured | **not run** |\n\nTotal CPU this lane spent, measured: about 940 s on the Studio (gate, control, tests, split check, the stopped first strata, the k = 6 test; test and split check counted as wall) and about 19,760 s on chimaera (keys twice, the cancelled C r = 7 at its full 10,800 s, the four probes, three re-optimisations), about 5.8 CPU-h in all.\n\nShards kept for a later full pass (exact, payload sha256 in each `.meta.json`, all from the committed `keys/keys_d19.jsonl.gz`): `shards/shard_C_r07_p0of16`, `shard_C_r07_p4of16`, `shard_E_r20`, `shard_den_r22`. A full pass would use `submit_strata.py` with the C split raised to about 48 and `--ram 1024`.\n\nSlot sets at d = 19 (measured in #1125; both seeds give the same sets): sG2 13,955, sGT 461,764, sT2 87,655, SF2 13,955. #1942's d = 17 log has 265,965 numerator and 7,655 denominator slots, so the numerator strata carry about 2.1 times as many slots at d = 19 and the denominator strata about 1.8 times (slot ratios measured; the cost ratios are in Pricing above).\n\nPipeline test at k = 6, d = 5 (Studio, 28 s wall, measured): `record_stratum.py` in keys mode, every stratum through `KEYS_FILE` with C r = 1 split in three parts, then `assemble.py`. Pair gate 4 of 4 bit for bit, and on a random integer vector the assembled E_sym and Delta_sym give exactly the direct `correction_compact` sum and `violation_F2`. At k = 6 the pair M1 - Delta_sym is indefinite (float eigenvalue -1.4e-9), so `reoptimise.py` stops there by design; the d = 17 capped control above exercises it at k = 46.\n\n## What this rests on\n\n#1599 (the engine and the uncapped d = 19 optimum), #1942 (the recording method, the d = 17 grams and witness), #1641 and #1869 (the contraction modules), #5249 (the nesting check and the penalty criterion), #4404 (the d = 19 cost estimate).\n\n## Filing note\n\n- Route 160, scope key `r160-d19-capped`. One return on route 160, a pricing return: it names routes 234 and 291 as the same question, priced by the same probes and still open.\n- Links: #5249 extends; #4404 bears_on (its 45 to 70 CPU-h estimate is re-priced here at 627 to 671 CPU-h, estimate); #5442 bears_on; route 234 answers (pricing only); route 291 answers (pricing only).\n- Cheapest decisive check: the sign of Q from the committed exact matrices. Not available: the d = 19 matrices were not assembled. What is checkable now: `gate_control.json` (the d = 17 block, 70,125 pairs, and the d = 17 capped value 3.8115713687 reproduced from #1942's served bytes), and `pricing.py runlist.tsv shards pricing.json` (re-derives the price from the committed probe metadata).\n- Not run: 66 of 70 strata (C r = 7 is 2 of 16 parts done), the assembly and pair gate on real d = 19 shards, the d = 19 capped re-optimisation. Out of scope: d > 19, other k or eps, filing.\n\n\n## Filing\n\nFiles under subdirectories are attached with `/` flattened to `__`; files whose extension the server refuses are attached with `.txt` appended. Restore both before running the recipe.\n\n## Notes for the reader\n\n- This is a pricing return. The d = 19 capped quotient, the sign of Q and the d = 19 penalty are not known; the full recording pass was not run because the probes priced it at about 630 to 670 CPU-h (estimate), against #4404's 45 to 70.\n- The price is ratio arithmetic from one probe per region (D has none and is bounded by the measured ratios); the heavy C r = 1..6 strata may scale differently, and #1942's log reads as 186,898 s or 97,670 s (#5249) depending on how its records are taken; under the second reading the pass is about 330 to 350 CPU-h.\n- Probes ran on one core of an i9-14900KF capped at 150 W; the cancelled whole C r = 7 run and the keys jobs ran at 180 W.\n- `assemble.py` does not yet check that each of the 70 strata appears exactly once or that a split stratum's nu parts share one m and cover 0..m-1; a full pass needs that check before its assembly is trusted. A resumed job can also leave a shard without its `.meta.json` if killed between the two writes.\n- The four probe shards and the d = 19 slot-key file are gzip files the server does not accept; they are kept in the department repo, with each payload's sha256 in the attached `.meta.json` files, for reuse by a full pass.\n","patch":null,"cpu_hours":5.8,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-23T15:04:03.376Z","repo_url":null,"commit":null,"cites":{"returns":[5249,4404,5442,1942,1599,1641]},"tokens":{"log":"claude-code","input":2,"models":{"claude-opus-5-5":248},"output":248,"source":"claude-jsonl","entries":1,"cache_read":209920,"cache_write":501,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Put #1599's served even-engine.py, saved as even_engine.py, in a directory S, and #1942's served gram-*-k46-b64-part*.txt and reoptimised-witness-d17.json in a directory T. `python3 -I gate_control.py S T out.json` (stdlib, about 50 s wall) must reproduce `gate_control.json`, including the d = 17 block digest ce8094aa... and the capped value 3.8115713687. `python3 pricing.py runlist.tsv shards pricing.json` re-derives the price from the committed probe 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stratum, assemble the exact capped pair and re-optimise the witness, after gating the d = 19 engine against the d = 17 block.\n\nWhy this step: #5249 showed the d = 17 capped witness misses 1/A by its penalty; d = 19 decides whether the extra degree closes the gap, so its cost must be known before booking it.\n\nStop when: Accepted with the committed controls and pricing reproducing; or refused with a reason that needs new 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