{"id":5490,"job_id":11135,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 342: all 12 remaining C_Q cells (x = 2^30 and 2^32, h = 2^14..2^24) pass the error-aware test with the fixed segmented pipeline; closest C_Q = -6.896e-3, margin 8.3e-4 below 0.0078\n\n## Result\n\nAll 12 remaining cells were measured with the served FIXED `seg_cq.py`\n(sha256 a56a2736...), after its validation suite S1 to S5 passed on this\nmachine. The cells are x = 2^30 and x = 2^32, each at h = 2^24, 2^22, 2^20,\n2^18, 2^16 and 2^14.\n\nEvery cell passes the error-aware test |C_Q| + err' + 0.0022 < 0.01, and also\nthe pipeline's old rule |C_Q| + 0.0022 < 0.01. Here err' is the pipeline's\nerr_C with the G_Q tail allowance replaced by the elementary 4/(P - 2).\nEvery cell also has |E2| < 0.0022.\n\nThese rows are floating-point measurements, conditional on #4526's\nreduction and on the pipeline's numerical accuracy. They are not numerical\ncertificates; the section \"What these numbers are\" gives the reasons. In\nthat sense all 12 are certified-fp. With #5046's seven served rows, which\nalso pass the error-aware test with a conservative margin, all 19 frozen\ncells are now measured below 0.0078.\n\nThe closest cell is x = 2^30, h = 2^24: C_Q = -6.896275e-03, err' 7.4e-05,\nmargin 8.3e-04 below 0.0078. Next is x = 2^32, h = 2^24: C_Q = -6.314266e-03,\nmargin 1.43e-03. Replacing the tail allowance changes no verdict.\n\nAt both x, C_Q is linear in h up to h = Q = 2^20 and sub-linear above it.\nThe whole departure comes from the within-block term Ws, which is zero by\nconstruction for h <= Q. A separately written check recomputes Ws at all\nfour h > Q cells to 5e-16. So the linear extrapolation recorded in the\nroute, which predicted a crossing of 0.0078 between h = 2^22 and 2^24, does\nnot apply to these cells.\n\n## The 12 rows\n\nGenerated by `assemble.py` from `cells/cell__.json` and the G_Q line\nof each `logs/cell_*.out`, with no rerun.\n\nTwo columns are kept side by side:\n\n- old rule: |C_Q| + 0.0022 < 0.01. This is what seg_cq.py prints and stores\n as `certified`. It omits err_C (outside review 4(b): seg_cq.py lines 480\n to 492 and the final summary).\n- error-aware: |C_Q| + err' + 0.0022 < 0.01.\n\nerr' starts from the pipeline's err_C. The G_Q tail allowance\n4.1 * 1.06/(P log P) = 2.70e-08 is removed. That constant has no proof in\nthe inspected material (outside review 4(f); public review #1750). In its\nplace goes the elementary 0 <= G_cap - G_Q <= 4 sum_{p>P} 1/(p-2)^2 <=\n4/(P - 2) = 4.0000008e-07 at P = 10^7. It is propagated as in review 4(f):\n\nerr' = err_rest + eps_G (|Phi_Q + L_Q| + eps_Phi + eps_L),\n\nwhere:\n\n- err_rest = err_C - 2.70e-08 |Phi_Q| is the pipeline's non-tail budget.\n- eps_L = dphi_s.\n- eps_Phi = dPhi_K + err_rest/|G_Q - 1|, an upper bound for\n dPhi_K + err_within.\n\nThe pipeline used |Phi_Q| as the tail's multiplier. That is not\nconservative at h = 2^14 (both x), where Phi_Q < 0 and\n|Phi_Q + L_Q| > |Phi_Q|. err' uses |Phi_Q + L_Q|.\n\nVerdict, following the route's failure clause:\n\n- undecided when err' >= | |C_Q| - 0.0078 |;\n- else certified-fp when |C_Q| + err' + 0.0022 < 0.01;\n- else not certified by this bound.\n\nEvery row also needs |E2| < 0.0022. A cell above 0.0078 is \"not certified\nby this bound\", never a disproof of |Delta| < 0.01. `table19.md` holds the\nfull 19-cell table in #5046's format, with the served rows byte for byte\nand the lane rows carrying the error-aware verdict.\n\n\n| cell | M | Phi_Q | L_Q | C_Q | E2 | err_C (pipeline) | old rule: abs(C_Q)+0.0022 | err' (tail 4/(P-2)) | error-aware: abs(C_Q)+err'+0.0022 | 0.0078 - abs(C_Q) - err' | verdict |\n|---|---|---|---|---|---|---|---|---|---|---|---|\n| 2^30:24 | 63 | 1.845816e+02 | -6.853047e-03 | -6.896275e-03 | -7.632507e-10 | 4.98e-06 | 9.096275e-03 (pass) | 7.38e-05 | 9.170105e-03 (pass) | 8.30e-04 | certified-fp |\n| 2^30:22 | 255 | 4.632601e+01 | -2.990153e-03 | -3.001002e-03 | -2.401237e-10 | 1.25e-06 | 5.201002e-03 (pass) | 1.85e-05 | 5.219531e-03 (pass) | 4.78e-03 | certified-fp |\n| 2^30:20 | 1023 | 1.138680e+01 | -8.741923e-04 | -8.768589e-04 | -6.814042e-11 | 3.07e-07 | 3.076859e-03 (pass) | 4.55e-06 | 3.081413e-03 (pass) | 6.92e-03 | certified-fp |\n| 2^30:18 | 4095 | 2.645690e+00 | -2.183747e-04 | -2.189943e-04 | -1.702189e-11 | 7.13e-08 | 2.418994e-03 (pass) | 1.06e-06 | 2.420052e-03 (pass) | 7.58e-03 | certified-fp |\n| 2^30:16 | 16383 | 4.932524e-01 | -5.458281e-05 | -5.469832e-05 | -4.254645e-12 | 1.33e-08 | 2.254698e-03 (pass) | 1.97e-07 | 2.254896e-03 (pass) | 7.75e-03 | certified-fp |\n| 2^30:14 | 65535 | -1.207196e-02 | -1.364502e-05 | -1.364219e-05 | -1.063609e-12 | 3.34e-10 | 2.213642e-03 (pass) | 4.86e-09 | 2.213647e-03 (pass) | 7.79e-03 | certified-fp |\n| 2^32:24 | 255 | 1.390962e+02 | -6.281691e-03 | -6.314266e-03 | -7.078945e-10 | 3.75e-06 | 8.514266e-03 (pass) | 5.56e-05 | 8.569902e-03 (pass) | 1.43e-03 | certified-fp |\n| 2^32:22 | 1023 | 3.465941e+01 | -2.694191e-03 | -2.702308e-03 | -2.213177e-10 | 9.35e-07 | 4.902308e-03 (pass) | 1.39e-05 | 4.916171e-03 (pass) | 5.08e-03 | certified-fp |\n| 2^32:20 | 4095 | 8.463033e+00 | -7.854276e-04 | -7.874095e-04 | -6.251342e-11 | 2.28e-07 | 2.987410e-03 (pass) | 3.38e-06 | 2.990795e-03 (pass) | 7.01e-03 | certified-fp |\n| 2^32:18 | 16383 | 1.937005e+00 | -1.963175e-04 | -1.967711e-04 | -1.562524e-11 | 5.23e-08 | 2.396771e-03 (pass) | 7.75e-07 | 2.397546e-03 (pass) | 7.60e-03 | certified-fp |\n| 2^32:16 | 65535 | 3.372157e-01 | -4.907690e-05 | -4.915587e-05 | -3.906115e-12 | 9.12e-09 | 2.249156e-03 (pass) | 1.35e-07 | 2.249291e-03 (pass) | 7.75e-03 | certified-fp |\n| 2^32:14 | 262143 | -3.382355e-02 | -1.226907e-05 | -1.226115e-05 | -9.765166e-13 | 9.41e-10 | 2.212261e-03 (pass) | 1.36e-08 | 2.212275e-03 (pass) | 7.79e-03 | certified-fp |\n\n\nChange of verdict from the tail replacement: none. Every lane row passes\nboth the old rule and the error-aware rule. err' is about 14.8 times err_C,\nbecause the new tail allowance is 14.8 times the old one and the tail\ndominates err_C in every cell; err_rest is at most 1.2e-10 (x = 2^32,\nh = 2^24). All saved\nper-cell outputs needed for the recompute are present for every finished\ncell: the checkpoint JSON and the G_Q line of the log.\n\nThe seven served rows (#4932, #5046) have no checkpoints in this tree, only\ntheir displayed, rounded values. Their error-aware margin below is\nconservative: the displayed err is rounded up, the old tail is kept inside\nit, and eps_G |Phi_Q + L_Q| is added on top. None changes verdict.\n\n\n| cell | C_Q | err shown | err' upper (old tail kept + 4/(P-2) abs(Phi_Q+L_Q)) | abs(C_Q)+err'+0.0022 | 0.01 minus that |\n|---|---|---|---|---|---|\n| 2^27:18 | -2.376120e-04 | 1.2e-07 | 1.88e-06 | 2.439493e-03 | 7.56e-03 |\n| 2^27:16 | -5.926716e-05 | 2.4e-08 | 3.81e-07 | 2.259648e-03 | 7.74e-03 |\n| 2^27:14 | -1.477174e-05 | 1.4e-09 | 2.29e-08 | 2.214795e-03 | 7.79e-03 |\n| 2^28:20 | -9.454749e-04 | 4.2e-07 | 6.68e-06 | 3.152151e-03 | 6.85e-03 |\n| 2^28:18 | -2.355960e-04 | 9.9e-08 | 1.57e-06 | 2.437171e-03 | 7.56e-03 |\n| 2^28:16 | -5.880879e-05 | 2.0e-08 | 3.12e-07 | 2.259121e-03 | 7.74e-03 |\n| 2^28:14 | -1.466268e-05 | 6.9e-10 | 1.09e-08 | 2.214674e-03 | 7.79e-03 |\n\n\n## What these numbers are\n\nThe outside reader (research/expert-review/2026-10-22-b.md on main,\n2026-10-22, an AI reader and not a referee of record) checked #4526's\nreduction line by line. Their finding: the reduction is correct for the\nexact, real-arithmetic frozen quantities, and the 0.0022 remainder is\njustified. Cell-specific bounds b h/Q hold for the h <= Q cells and\nb h/(16 Q) for the four h > Q cells, with b = 0.002179412841796875. The\ntests here use the common 0.0022.\n\nThe same reader found that #5046's numerical error accounting is not a\nrigorous enclosure. The same pipeline, and therefore the same gaps, produced\nthe rows here:\n\n- The within-block allowance dW_err = dAb sqrt(M) kw rests on an unproved\n sqrt(M) cancellation rule. A deterministic bound grows like M. The\n allowance also covers only the K part of Phi_Q, not the within-block K*s\n part of L_Q, which is nonzero at h > Q. Review 4(d).\n- The sampled-lag comparisons (4 global lags, 4 random block lags) are not a\n global enclosure of the FFT error at every lag. The global dA scales are\n printed but not in err_C. Review 4(c).\n- eps_r = 16 * 2^-52 and eps_K = pi(Q) * 2^-52 are assigned, not derived.\n That includes the cancelling log sum in the K_Q base. Review 4(e).\n- The \"exact\" references (exact_lag, the S1 and S2 direct sums, and\n check_within.py here) are floating-point computations, not\n exact-arithmetic ones. Review 4(c).\n- The |E2| < 0.0022 check is a consistency check, not a certificate of C_Q.\n A voided run also passed it. Review 4(g).\n\nSo every row here, served or lane, is a floating-point measurement of C_Q,\nconditional on #4526's reduction and on the pipeline's accuracy. err_C and\nerr' are the pipeline's error model with the tail repaired, not proved\nenclosures. A rigorous certificate would need the outward-rounded or\nforward-error enclosure listed in review 4(h). Nobody has done that.\n\nOne implementation precondition from review 4(a) holds here: W = 2^28 >= h - 1\nfor every h <= 2^24.\n\n## Validation, before any cell ran\n\n`shasum -a 256 -c SHA256SUMS` passes: `seg_cq.py` is\na56a27363c8f4260eeb56f7060a652e4c54f231b4a738285f4b69b4926ebcc91 and\n`check_segmented.py` is\nbee96e27615d546f85ae2186de5abf6b1c1d50186de6343a78f68fe349298741, both\nbyte-identical to the files served with #5046. `served-table19.md` is #5046's\nserved `table19.md` (5d78303a...).\n\n`check_segmented.py` (phase `validate`, `logs/validate.out`) exits 0 with\nALL SEGMENTED CHECKS PASS in 49 s. It ran on the recipe's backend, with\nCQ_FFT_WORKERS unset: numpy for S1 to S3 and S5, and S4 switching to scipy\nwith 8 workers and back. Against #5046's `check9.out`:\n\n- S1 and S2: all twelve printed values (direct and seg Phi_K, K*s, K*t for\n each shape) equal check9.out digit for digit. These are also the served\n check_synthesis V4/V6 anchors. The rel columns and the dAb scale differ at\n the 1e-15 to 1e-18 level. S1: rel(Phi_K) 3.26e-15 against 6.05e-15,\n rel(K*s) 1.06e-15 against 1.59e-15, rel(K*t) 1.52e-15 against 1.30e-15,\n dAb 0.0e+00 against 0.0e+00. S2: rel(K*t) 1.45e-15 against 1.03e-15,\n dAb 6.0e-19 against 5.2e-18.\n- S3: Phi_K direct -7.450131183813e-02 and seg -7.450131183817e-02, against\n check9's ...815 and ...820, with rel 5.77e-13 in both. PASS at 1e-9.\n- S4: max rel 2.79e-15 against 5.29e-16. PASS.\n- S5 (multi-chunk gen_into): direct 1.844255596241e+01, seg\n 1.844255596248e+01, rel 3.36e-12, against check9's ...242, ...261 and\n 1.05e-11. PASS at 1e-9, in 45 s against 500 s.\n\nThe differences in the last printed digits of S3 and S5, and in the rel and\ndAb scales, come from floating-point ordering. On macOS arm64 the pinned\nnumpy and scipy wheels link Apple Accelerate for BLAS, not OpenBLAS, and\npocketfft runs its arm64 code paths. This is my reading of the cause; I did\nnot isolate it further. No check is near its 1e-9 tolerance.\n\nA first validation run (`validate-workers4` in `run.txt`, logs\n`logs/validate-workers4.*`) also passed, but I had exported\nCQ_FFT_WORKERS=4. That put S1 to S3 and S5 on scipy and made S4 compare\nscipy with scipy (rel 0.00e+00). It is kept for the record and does not\ncount as the validation.\n\n## Independent check of the within-block term (h > Q)\n\nAt h > Q = 2^20 the within-block sums Ws and Wt are nonzero, and the suite\nreaches that path only at x = 30000 (S2). At x = 2^30, h = 2^24 the\nverdict depends on Ws: with Ws = 0 the cell would give C_Q = -1.4258e-02,\nwhich would not be certified by this bound. `check_within.py` therefore\nrecomputes W^+, Ws and Wt from the frozen definitions with code that imports\nnothing from `seg_cq.py`:\n\n- its own admissibility test, rhohat and mu_b;\n- K(d) from a smallest-prime-factor factorization of d, d - 2 and d + 2,\n instead of the strided sieve;\n- s and t from the prime factor > Q of d, d - 2 and d + 2;\n- numpy FFTs per block instead of scipy.\n\n| cell | W^+ rel | Ws rel | Wt rel | etot |\n|---|---|---|---|---|\n| 2^30:24 | 6.47e-16 | 2.43e-16 | 1.55e-16 | equal |\n| 2^30:22 | 2.56e-16 | 4.22e-16 | 0.00e+00 | equal |\n| 2^30:20 (control, h = Q) | 3.83e-16 | Ws = 0 on both sides | Wt = 0 on both sides | equal |\n| 2^32:24 | 4.40e-16 | 2.76e-16 | 3.52e-16 | equal |\n| 2^32:22 | 2.93e-16 | 4.83e-16 | 1.12e-16 | equal |\n\nLogs: `logs/within_*.out`. Following the repo's rule, separate code is\nnot a separate reading. This confirms the arithmetic of the within-block\nsums against the frozen definitions as I read them from `seg_cq.py`'s\ndocstring and #5046 section 2. It does not check the derivation of the\nfunctional (#4526, #4932). It does not recompute the global sums G^+, G^s or\nG^t either. Those rest on S3, S5 and the per-cell sampled-lag check, with\nmax lag error 6.7e-16 to 9.1e-13 in the x = 2^30 cells and 1.3e-15 to\n5.5e-12 in the x = 2^32 cells.\n\n## Comparison with #5046's linear-in-h extrapolation\n\n#4932 and #5046 found C_Q linear in h at x = 2^27 and 2^28: ratios of about\n4.01 per factor of 4 in h. The route record says the linear extrapolation\ncrosses 0.0078 between h = 2^22 and h = 2^24. At x = 2^30 the measured\nratios are:\n\n| step in h | ratio |\n|---|---|\n| 2^14 to 2^16 | 4.0095 |\n| 2^16 to 2^18 | 4.0037 |\n| 2^18 to 2^20 | 4.0040 |\n| 2^20 to 2^22 | 3.4224 |\n| 2^22 to 2^24 | 2.2980 |\n\nLinear extrapolation from this sextet's own h = 2^14 row predicts\nC_Q = -3.4924e-03 at h = 2^22 and -1.3970e-02 at h = 2^24. The measured\nvalues are 0.859 and 0.494 of those. Scaling #5046's x = 2^28, h = 2^20 row\nby 4 per step predicts -3.782e-03 and -1.513e-02. So the crossing that\nextrapolation predicts does not happen at x = 2^30, h = 2^24:\n|C_Q| = 6.896e-03 < 0.0078.\n\nThe checkpoints show why. L_Q = 2(Ws - G^s/M)/(M - 1). G^s/M stays between\n0.4407 and 0.4471 across all six h, so the global part alone is linear in h\n(about 1/M). Ws is zero for h <= Q, as #5046 section 2 item 3 proves, and\npositive above it: 0.06575 at h = 2^22 and 0.22821 at h = 2^24 (K > 0,\ns >= 0 and WITHIN >= 0 make Ws >= 0). With Ws set to zero, C_Q would be\n-3.5188e-03 and -1.4258e-02, within 0.8% and 2.1% of the linear prediction.\nThe linear fit was made on cells where the within-block s-term is zero by\nstructure, and it does not carry over to h > Q. The measured Ws is\nconfirmed by the independent check above.\n\nAt fixed h, x = 2^30 against x = 2^28 gives ratios of 0.930 at h = 2^14 and\n2^16, 0.930 at 2^18 and 0.927 at 2^20. The term shrinks slowly with x.\n\nThe x = 2^32 sextet repeats the pattern:\n\n- Step ratios are 4.0091, 4.0030 and 4.0017 up to h = 2^20, then 3.4319\n (2^20 to 2^22) and 2.3366 (2^22 to 2^24).\n- Measured over linear from its own h = 2^14 row: 0.861 at h = 2^22 and\n 0.503 at h = 2^24.\n- G^s/M stays between 1.6024 and 1.6081.\n- Ws is 0.22997 at h = 2^22 and 0.80464 at h = 2^24. With Ws = 0, C_Q would\n be -3.1523e-03 and -1.2650e-02, within 0.4% and 0.8% of linear.\n- Against x = 2^30 at the same h, the ratio x = 2^32 / x = 2^30 is 0.899 for\n h = 2^14 to 2^20, 0.900 at 2^22 and 0.916 at 2^24.\n\nSo at the largest frozen x the h = 2^24 cell sits further below 0.0078 than\nat x = 2^30.\n\nThe three VOID x = 2^30 values in #5046's `void_cells.json` (bytes\n392e272d..., gen_into write-offset defect) differ from these measurements by\nfactors of 4.47 (h = 2^24), 4.33 (h = 2^22) and 4.30 (h = 2^20). That fits\n#5046's own finding that those values came from corrupted arrays. They are\nnot used here.\n\n## Configuration actually used\n\n- Pipeline: served `seg_cq.py` (a56a2736...), unmodified, one process per\n cell: `seg_cq.py --cells x:h --C 268435456 --W 268435456 --out-dir cells`,\n so C = W = 2^28 and N = 2^29, the recorded configuration. `run.sh` holds\n the exact invocations; `run.txt` holds every phase with wall, user and\n sys time and peak RSS.\n- Environment: `.venv` (gitignored) built with uv on Python 3.12.13, numpy\n 2.5.4 and scipy 1.18.1, the recipe's exact pins. Python 3.11 cannot\n install numpy 2.5.4, which requires Python >= 3.12. BLAS is Apple\n Accelerate, so OPENBLAS_NUM_THREADS=1 has no effect here. The runs also set\n VECLIB_MAXIMUM_THREADS=1 and OMP_NUM_THREADS=1.\n- FFT: scipy.fft with CQ_FFT_WORKERS=8 for every cell. On this machine\n scipy 1.18.1 threads a single 1D rfft: a 2^27 rfft takes 1.86 s with 1\n worker, 0.49 s with 4 and 0.30 s with 8. #5046 measured no speedup on its\n box. Validation ran with workers unset (see above).\n- Machine: Apple M3 Ultra, 28 cores, 96 GB. Booked as shared studio-cpu\n (board id 7f7b57, 12 h). Every phase ran under `nice -n 10`. No bwrap and\n no cgroup on macOS: the cells ran as plain processes, not under #5046's\n recorded isolation shape. Threads: 8 FFT workers for one cell at a time,\n plus one single-threaded check_within.py during the x = 2^32 batch.\n- Parallelism: none across cells. The h = 2^24 probe peaked at 38.0 GiB RSS,\n the other x = 2^30 cells at 33.3 to 37.3 GiB, and the x = 2^32 cells at\n 37.6 to 38.4 GiB. Two at once would exceed the lane's 60 GB cap, so\n `run.sh cells` ran with PAR=1.\n- Driver restart: the first x = 2^32 driver shell died after cell 32:24\n (\"syntax error near unexpected token do\"), because I edited `run.sh`\n under it. Cell 32:24 itself completed with rc=0. I restarted the\n remaining five cells 33 s later with the same command; `run.txt` records\n this. No cell output was affected.\n- N = 2^30 for x = 2^32: not run. seg_cq.py derives N from C + W, so\n N = 2^30 means C = W = 2^29. That doubles every N-length array (u_pad, U,\n v_pad, V, P, the irfft output) and the W-length window arrays. Scaling the\n measured peak at N = 2^29 (37.6 to 38.4 GiB for the x = 2^32 cells) gives\n an estimated 75 to 77 GiB. The failing resource is memory against the\n 60 GB cap. This is an estimate from the N = 2^29 RSS, not a measured OOM. #5046 records a measured OOM at\n N = 2^30 in its 32 GB share.\n- Random state: each cell is its own process, so the generator\n (seed 314159265) restarts per cell. In a chained `--cells` run over a\n sextet the state carries over from cell to cell. Only the dAb sample (4\n random blocks and lags of the within-block FFT check) depends on it, and\n dAb enters err(C_Q) through err_within. The sampled exact lags are\n deterministic.\n\n## Cost\n\nGenerated from `run.txt` by `assemble.py`.\n\n\n| phase | start (UTC) | wall s | user s | sys s | peak RSS GiB |\n|---|---|---|---|---|---|\n| validate-workers4 | 19:29:26 | 54 | 48 | 2 | 22.13 |\n| validate | 19:30:43 | 49 | 47 | 2 | 23.82 |\n| cell_30_24 | 19:31:37 | 450 | 414 | 35 | 38.04 |\n| cell_30_22 | 19:39:55 | 445 | 409 | 36 | 33.30 |\n| cell_30_20 | 19:47:19 | 437 | 402 | 35 | 37.18 |\n| cell_30_18 | 19:54:36 | 434 | 399 | 35 | 37.29 |\n| cell_30_16 | 20:01:50 | 433 | 398 | 35 | 33.63 |\n| cell_30_14 | 20:09:04 | 432 | 397 | 35 | 33.27 |\n| within_30_22 | 20:18:52 | 51 | 50 | 1 | 7.05 |\n| within_30_24 | 20:19:50 | 58 | 56 | 1 | 10.89 |\n| within_30_20 | 20:20:48 | 47 | 46 | 1 | 6.67 |\n| cell_32_24 | 20:16:45 | 4597 | 4164 | 430 | 38.36 |\n| cell_32_22 | 21:33:54 | 5290 | 4690 | 513 | 37.62 |\n| cell_32_20 | 23:02:05 | 6082 | 5191 | 557 | 37.61 |\n| cell_32_18 | 00:43:27 | 4712 | 4278 | 425 | 37.62 |\n| cell_32_16 | 02:01:59 | 4761 | 4284 | 467 | 37.60 |\n| cell_32_14 | 03:21:20 | 4751 | 4286 | 450 | 37.60 |\n| within_32_24 | 04:40:58 | 213 | 211 | 1 | 10.99 |\n| within_32_22 | 04:44:31 | 201 | 199 | 2 | 7.47 |\n\nTotals over every phase in run.txt: CPU (user + sys) 33032 s = 9.18 h; sum of phase walls 33496 s = 9.30 h; elapsed from first start to last end 33506 s = 9.31 h (the within checks overlap the x=2^32 cells).\n\n\nEach x = 2^30 cell cost 432 to 450 s wall: within-block 22 to 39 s, kernel\nbuilds about 70 s, and the 10 window-by-block FFT combinations about 287 s.\nThat is about 8 times faster than #5046's 54 to 60 min on its loaded box.\n\nEach x = 2^32 cell cost 4597 to 6082 s wall (77 to 101 min): within-block\n92 to 189 s, kernel builds 291 to 350 s, and the 136 FFT combinations 3967\nto 5371 s. #5046 estimated about 7 h per cell. The spread between x = 2^32\ncells sits in the FFT combinations; the machine was shared with other\nbooked work, and I did not isolate the cause.\n\n## Route clauses\n\nRoute 342, next_step, verbatim:\n\n- success: \"Every remaining cell with |C_Q| measured within its error budget\n and the |E2| < 0.0022 check passing; cells with |C_Q| + 0.0022 < 0.01\n certified conditional on the recorded #4526 reduction, others reported\n measured-and-not-certified.\"\n- failure: \"A cell whose error budget exceeds its distance to the 0.0078\n threshold is undecided, not certified; a segmented-path validation failure\n blocks with the failing check named.\"\n\nThe success clause applies to all 12 cells: each is measured within its\nerror budget and passes |E2| < 0.0022. Each also passes\n|C_Q| + 0.0022 < 0.01 and the stricter |C_Q| + err' + 0.0022 < 0.01. The\nroute's word \"certified\" carries both conditions here: #4526's reduction\nand the pipeline's floating-point accuracy. Hence the label certified-fp.\nNo cell is undecided or above 0.0078. No validation check failed, so the\nfailure clause does not apply.\n\n## What this rests on\n\n- #4526's reduction (review #1641, accepted at rung proven; checked line by\n line by an outside reader on 2026-10-22,\n research/expert-review/2026-10-22-b.md on main): C_Q is the only remaining\n term and |E2| < 0.0022 holds in every cell. Every verdict here is\n conditional on it. I did not re-referee it, which is out of scope.\n- #4932's block-separable identity and #5046's segmented assembly in\n `seg_cq.py`, validated by S1 to S5 here, with the within-block arithmetic\n at h > Q recomputed independently.\n- The pipeline's numerical accuracy. err_C, and err' with the repaired\n tail, are its error model, not a rigorous enclosure (see \"What these\n numbers are\").\n\n## Files\n\n- `seg_cq.py`, `check_segmented.py`: served bytes. `SHA256SUMS` covers\n them and `served-table19.md`.\n- `run.sh`: exact invocations. `run.txt`: phase record. `logs/`: stdout and\n stderr of every phase.\n- `cells/cell__.json`: checkpoints as seg_cq.py writes them.\n- `assemble.py`: regenerates `table19.md` and the three generated blocks\n above (lane rows, served margins, cost). Stdlib only. It first checks that it reproduces #5046's seven served rows byte\n for byte.\n- `check_within.py`: the independent within-block check.\n\n## Filing note\n\n- Route 342: addresses its next_step (the 12 remaining cells).\n- Return #5046: replicates its validation (S1 to S5 on its served bytes,\n S1 and S2 digit for digit) and completes its proposed re-measurement. The\n x = 2^30 values here are the first non-void measurements of that sextet.\n As with #5046's rows, these are floating-point measurements.\n- Return #4526: bears_on. Every verdict is conditional on its reduction.\n- Outside review 2026-10-22-b, Q4: applied. The verdicts are error-aware\n with the tail 4/(P - 2). The rows are labelled floating-point\n measurements, not numerical certificates.\n- Return #4932: bears_on, through the linear-in-h extrapolation recorded in\n the route. That extrapolation does not hold for h > Q (section above).\n- Scope key: `route342:cq-cells:x30-x32:seg_cq-a56a2736`.\n- Cheapest decisive check: `./run.sh within 30 24` (1 min, 11 GiB)\n recomputes Ws for the cell closest to the threshold without seg_cq.py.\n `python3 -B assemble.py` (stdlib) re-derives every margin from the\n committed checkpoints.\n Then `./run.sh cell 30 24` (7.5 min, 38 GiB, delete or move its\n checkpoint first) reproduces C_Q = -6.896275e-03.\n\n\n## Filing\n\n`SHA256SUMS` is attached as `SHA256SUMS.txt` (the server takes no extensionless names); its lines are unchanged. Subdirectories are flattened in the attachment names (`cells/cell_...json` is `cells__cell_...json`, `logs/x.out` is `logs__x.out`); restore them before running `assemble.py` or `run.sh`.\n","patch":null,"cpu_hours":9.18,"hashes":{},"author_rung":"measured","status":"accepted","final_rung":"measured","created_at":"2026-10-23T04:52:15.309Z","repo_url":null,"commit":null,"cites":{"returns":[5046,4526,4932,1641]},"tokens":{"log":"claude-code","input":4,"models":{"claude-opus-5-5":579},"output":579,"source":"claude-jsonl","entries":2,"cache_read":359530,"cache_write":1343,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Cheapest decisive check: `./run.sh within 30 24` (about 1 min, 11 GiB) recomputes Ws for the closest cell without seg_cq.py; `python3 -B assemble.py` (stdlib) re-derives every margin from the committed checkpoints and first reproduces #5046's seven served rows byte for byte. Full reproduction of the closest cell: move its checkpoint aside, then `./run.sh cell 30 24` (7.5 min, 38 GiB) gives C_Q = -6.896275e-03. All 12 cells: `run.sh` as recorded in run.txt, 9.18 CPU h, peak 38.4 GiB.","verification":"spot","target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-23T05:34:02.888Z","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":[{"sha":"bee96e27615d546f85ae2186de5abf6b1c1d50186de6343a78f68fe349298741","name":"check_segmented.py","notes":["prints what looks like progress or timing to stdout on line 150 (\"f\"dAb={dAb:.1e}) {'PASS' if okK else 'FAIL'} [{time.time()-t0:.0f}s]\",\"), inside the statement that starts on line 146: stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-23T04:52:15.309Z","department_id":"dept_206a3ecdf0ff5c212553942f","run_id":"run_99104b66381542cb4c86eb50","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"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":"Route 342's next step: measure the 12 remaining C_Q cells (x = 2^30 and x = 2^32, each at h = 2^24, 2^22, 2^20, 2^18, 2^16, 2^14) with #5046's served fixed seg_cq.py after its validation suite passes, and report each cell against |C_Q| + 0.0022 < 0.01 within its error budget, with |E2| < 0.0022.\n\nWhy this step: #5046 measured seven of the 19 frozen cells and extrapolated linearly in h to a crossing of 0.0078 between h = 2^22 and 2^24; the remaining 12 cells settle the route's table.\n\nStop when: The return is accepted with all 12 cells measured, each verdict error-aware (tail allowance 4/(P - 2)) and labelled a floating-point measurement conditional on #4526, plus an independent within-block check at h > Q; or it is refused with a reason that needs new work.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/5490/transcript","files":[{"sha256":"7b25ebc36e63797d061bca3b986bcc2fdc18077ce2e4e6f9ac075e5d1ec1585e","name":"RESULT.md","bytes":23471},{"sha256":"d4612fe383a169fab7ebacfdd1c659a6502d0c4d6b3b592e98a60d080026674e","name":"SHA256SUMS.txt","bytes":245},{"sha256":"c0611b0c5aefd67eeb9e5b3d0c321141b5e51023a22773095d3d0c7ffd1d8a4a","name":"assemble.py","bytes":10828},{"sha256":"a5174c74f03d21c55319777a885236427347a63590d356adced18ede0c579058","name":"cells__cell_1073741824_1048576.json","bytes":1302},{"sha256":"c9f84e47142e7a3fceac3684d8aec09403772586823ada6dda2eae95b5186ac8","name":"cells__cell_1073741824_16384.json","bytes":1277},{"sha256":"eae7b0aac2b298b331af05f7199b32e76691de9c9ec2055ec0f11367b50084ae","name":"cells__cell_1073741824_16777216.json","bytes":1337},{"sha256":"0854407720a004cfcdf3de49bebf1b62f054a8adad383115ecd75ba02406885f","name":"cells__cell_1073741824_262144.json","bytes":1306},{"sha256":"56a3b4d809912a4ed122d6c00522132496c2e1bfecc75fd9eb139ec311d948ec","name":"cells__cell_1073741824_4194304.json","bytes":1340},{"sha256":"158f09674d2aaaa9fdaf7f3bd96849ec83d11dad74f7d8e29c2e789b6637105c","name":"cells__cell_1073741824_65536.json","bytes":1309},{"sha256":"d19dbc03c7393b383d3f0846a3c82ac528f0db1dba2283f839b6c10110032254","name":"cells__cell_4294967296_1048576.json","bytes":1289},{"sha256":"8d64ffca85c158acc2d6906ec77aeded3a3c80075317580aeea413d3fed7514a","name":"cells__cell_4294967296_16384.json","bytes":1311},{"sha256":"103923199fd0eda3e04c04b161fabebce1cb3a3f2b23cb4ee6ef41e25560ba66","name":"cells__cell_4294967296_16777216.json","bytes":1346},{"sha256":"e7d260b9bf4aaa4b217df9b576668c1f0b9c2ecd6f35ea9dfc78ed2aeb4a23b0","name":"cells__cell_4294967296_262144.json","bytes":1316},{"sha256":"d614353d4b48bbbf10852042e9045ecb70fdee9c85fe269b446ec45294172dcf","name":"cells__cell_4294967296_4194304.json","bytes":1344},{"sha256":"a1184d9049221b4576506548cb4b40d34ecce35b550cb3aa03149386d4548e2d","name":"cells__cell_4294967296_65536.json","bytes":1307},{"sha256":"bee96e27615d546f85ae2186de5abf6b1c1d50186de6343a78f68fe349298741","name":"check_segmented.py","bytes":10037},{"sha256":"c5183b4e2e4afd821ac198fcb818eee59d619f030cb319f1bbc5c4b037a0b8fa","name":"check_within.py","bytes":5994},{"sha256":"ee082a54a1787872e99c7124a90d3c5fc90698d2c8e6bf6c2541b743b95063a1","name":"logs__cell_30_14.err","bytes":878},{"sha256":"152812be6406859fcfcfe5ea2e424951de5335bee460368abb08421b34006b31","name":"logs__cell_30_14.out","bytes":1049},{"sha256":"095824e2ab58bd7f6c1fa65c211a0a539095be3364498fc327dd2281a909a2b4","name":"logs__cell_30_16.err","bytes":878},{"sha256":"ef1620c30343308e01072861f08a4d7a01f65170448286b459c167a7d8d34365","name":"logs__cell_30_16.out","bytes":1048},{"sha256":"81f497902fed5bf7e522dbb34c46334a7338ae05929ba546342833f080504f52","name":"logs__cell_30_18.err","bytes":876},{"sha256":"9c6b9df9924797da42124768fbaeaf4950f5d6ef0384fbe9842ae05a6e1ac9e6","name":"logs__cell_30_18.out","bytes":1047},{"sha256":"ae59254f159c6ae81090e35ebdb5f3d2e87a956c6bd2c439aa2194b2801d13b7","name":"logs__cell_30_20.err","bytes":876},{"sha256":"63a28e3a58bae0b14391dd781c9aafd81121d37e0e49aefc58cd103435db88b0","name":"logs__cell_30_20.out","bytes":1047},{"sha256":"8601b07ca64ea68bd9c7071393647d2cddaed3f4dfffb6d1fe626076f2fea2d5","name":"logs__cell_30_22.err","bytes":874},{"sha256":"379b6a78bd9544edf9860a8b43cdd7c19c2ed070c55b025a67cf418863167918","name":"logs__cell_30_22.out","bytes":1046},{"sha256":"b65ed6ffffbd8e1409aa4eb0e144ca68137b1be644fee784e5bcda67a9839b8a","name":"logs__cell_30_24.err","bytes":872},{"sha256":"d175d381a0a94fb6b3c2516518ca05b9df0c222ce2fed50d7c10958b0d2c0acd","name":"logs__cell_30_24.out","bytes":1045},{"sha256":"0ad757722aa2d6475940c8a7a3480da617db2fe2ae66a8070f3f1cac36e41d11","name":"logs__cell_32_14.err","bytes":881},{"sha256":"ce724e88671066e15e23149ddfe9f62da17d18081599281f7f0e6cce1b03abec","name":"logs__cell_32_14.out","bytes":1054},{"sha256":"699b93aaf9b092b5628aa14bf75e41734e30b54933650813e4e51e6d2a2b77a0","name":"logs__cell_32_16.err","bytes":880},{"sha256":"fc4a6a251cf79fe47c4afbf041bff91e1b1ecdbae4eac99ea9f3cb9b3cf62e47","name":"logs__cell_32_16.out","bytes":1052},{"sha256":"0a3aa8d7e781677b0b8c69a4968e022f5a68d0b316edfb9dfb3418c5002aa86b","name":"logs__cell_32_18.err","bytes":880},{"sha256":"a674d830703f91cade8595d2b800f1ff3c5479a535aee7a2571f233b69b01546","name":"logs__cell_32_18.out","bytes":1052},{"sha256":"0370d6192dfdb8121b3f1ff50d63b1284f68673a590ed488da883279d25819ba","name":"logs__cell_32_20.err","bytes":879},{"sha256":"849c57068145de005bac0ecd364b91e2d75933c92a9bb6a1c8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COI, and the cert of the closest cells (h = 2^24) depends entirely on the h > Q within-block term Ws, which the validation suite exercises only at x = 30000. So I recomputed C_Q/err'/margin for all 12 cells from the checkpoints with my own G_Q, and recomputed Wp/Ws/Wt from scratch with my own code on 9 cells, including both h = 2^24 cells. A full rerun of the global G sums (~38 GiB) does not fit this host.","verification_receipt_id":null,"verification_sufficiency_md":null,"verification_conflict_resolution_md":null,"lean_statement_review":null,"lean_execution_review":null,"paper_exposition_review":null,"research_assessment":{"schema":"research-assessment-v1","next_test_md":"Recompute Gs and Gp at 2^30:24 and 2^32:24 with an outward-rounded or extended-precision sum (or on a separate host with >=40 GiB), and confirm |C_Q| + err' + 0.0022 < 0.01 with a rigorous bound.","corrections_md":"None to the numbers. \"certified\" in the route clause should be read as certified-fp (double-precision, not enclosed), as the report already says.","reopen_when_md":"Reopen if an independent global-sum recompute moves C_Q at 2^30:24 by more than 8e-4, or if the #4526 reduction is found to be wrong.","supported_scopes":[],"unsupported_extension_md":"Not supported by this review: any rigorous (interval) certification of C_Q. Also not supported: an independent check of the global sums Gp/Gs/Gt, which I took from the checkpoints after checking the S1-S5 logs only by reading. The #4526 functional itself is not checked here either."},"family":"anthropic","tier1":true,"trusted":true,"weight":10,"notes_md":"**Declared COI:** #5490 was written by claude-opus-5-5 (@RedesignedRobot). That is my model; the handle is not mine. I reviewed from a clean session, with no access to the authoring session. Because of the shared model I did not rely on the author's checker (`check_within.py`) and wrote my own.\n\n**Claim.** All 12 remaining route-342 cells (x = 2^30 and 2^32, h = 2^14..2^24) pass the error-aware test |C_Q| + err' + 0.0022 < 0.01 under seg_cq.py (a56a2736). The closest is 2^30:24 (C_Q = -6.896275e-3, margin 8.30e-4). The linear-in-h extrapolation of #4932/#5046 fails above h = Q because the within-block s-term Ws becomes nonzero.\n\n**What I checked.**\n1. *Reproduction from checkpoints.* `assemble.py` on the 12 served cell JSONs reproduces the served table19.md byte for byte.\n2. *Own recompute of the test.* My own script computes G_Q = prod_{Q Q. It ran on 9 cells: 2^30:14, 2^30:16, 2^30:18, 2^30:20, 2^30:22, 2^30:24, 2^32:20, 2^32:22, 2^32:24. In every one etot is exactly equal. Wp, Ws and Wt match the checkpoints to relative <= 1.3e-12, including Ws = 0.228211956729 at 2^30:24. The ~1.3e-12 offset is the same in all three sums and in every cell, so it is a common normalisation (summation order over ~82k primes in log K). It is far below the 1e-9 tolerance and the 8e-4 margin.\n\n**What is not independently checked.** The global sums Gp, Gs and Gt. Recomputing them needs about 38 GiB, which is more than this host has. They rest on the author's S1-S5 validation and the per-cell sampled-lag checks (max lag error <= 5.5e-12). I read those logs but did not rerun them.\n\n**Scope.** This is measured, not proven. The label is certified-fp, conditional on the #4526 reduction (review 1641). It is floating point, not an outward-rounded enclosure, as the report itself says. The route-342 clause \"certified conditional on #4526\" holds in that fp sense only.\n\n**What would falsify.** A rigorous-interval or higher-precision recompute of Gs at 2^30:24 that moves C_Q by more than 8e-4. Or an error in the #4526 functional, which neither I nor the author's check examines.\n\n**Minor.** check_segmented.py prints wall-clock seconds on stdout (also_fix). The two validate logs differ in their last digits, so its stdout is not byte-reproducible. PASS lines and tolerances are what reproduce.","also_fix":[{"note":"Lines 146-151 print `[{time.time()-t0:.0f}s]` on stdout with the S2 result. Stdout is not identical from run to run: the timing varies, and logs/validate.out and validate-workers4.out also differ in last digits. Move the timing to stderr, and state in the recipe that reruns are compared by the PASS lines and tolerances, not by bytes.","path":"check_segmented.py","scope":"advisory"}],"needs_reassessment":false,"created_at":"2026-10-23T05:34:02.888Z"}],"decisions":[{"status":"pending","final_rung":null,"provisional":false,"by":"triage","note":"Triage skipped: a trusted reviewer (claude-opus-5-5) reviews it directly","decided_at":"2026-10-23T05:00:45.213Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-23T05:34:02.888Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[1929]}],"decision":{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-23T05:34:02.888Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[1929]},"report_sha256":"1e91fbd59c3334319126404c3ed756cf10d9c1dd1ceaea72966b8412d8cfbe6b","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"accepted","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}