{"id":5605,"job_id":11349,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 169: the streamed equivalence census at j = 16..38 lands in the pre-registered success branch; 12 new certified rows, LOO max shift 0.30\n\n## Result\n\nUnder `PREREG.md` (route 169's next_step at revision 4, committed in 3234032 and 8b7e339 before\nany j >= 27 number existed), the run over j = 16..38 lands in the **success** branch. This is a\nfinite measurement at x = 2^16 .. 2^38. It does not prove or support any statement about larger x.\n\n- All 12 new rows j = 27..38 are certified: K2 (D_y/x against the served column) is at most 4.7e-7\n  and K3 (identity residual / x) is at most 3.2e-17.\n- (i) Transfer: Delta_a/x >= -0.120383 at every new j, so F_A passes. The smallest new value is\n  -0.002691, at j = 31.\n- (ii) Envelope: V(38) = 0.015822, still attained at j = 19. No new scale goes past it. The adverse\n  new scales are j = 30, 31, 35 and 38, and the largest of them is 0.002691. Every extension pair\n  block is at most the pinned 0.036374, and the last extension block is strictly below the first\n  (0.001701 at the singleton 38, against 0.002154 at 26-27), which is PREREG's \"decreases\".\n- (iii) The fit k over the 23 certified rows j = 16..38 is 3.976923 (se 0.747599). The largest\n  leave-one-out shift is 0.3026 (drop j = 17), under the bar of 1.0, so the fit is stable.\n\nThe run covered j = 16..38 and nothing past it. It does not say what happens at j >= 39.\n\nFiles: `data/verdict.json` (everything below, machine-readable), `data/verdict.txt` (the table),\n`data/row-j27.json` ... `data/row-j38.json` (rows), `control/` (K1), `k4/` (K4).\n\n## Per-j rows (j = 27..38, new)\n\nFrom `data/verdict.txt`, which also lists j = 16..26. D^(e1*)/x = D_y/x + Delta_a/x. K2 is\n|D_y/x - served column|. K3 is |D_y - D^(e1*) - T^(top*) + P^(top*)| / x.\n\n| j | D^(e1*)/x | D_y/x | Delta_a/x | C_misc/x | T^(top*)/x | P^(top*)/x | e1/(x/2y) | e1* | Q | K2 | K3 | F_A | V(j) |\n| - | - | - | - | - | - | - | - | - | - | - | - | - | - |\n| 27 | -0.001258 | -0.004283 | +0.003025 | +0.002026 | -0.003030 | -0.000005 | 1.6586 | 8423 | 16844 | 3.3e-7 | 3.3e-18 | pass | 0.015822 |\n| 28 | -0.000422 | -0.001090 | +0.000668 | -0.001111 | -0.000670 | -0.000002 | 1.6473 | 12077 | 24152 | 2.7e-7 | 1.8e-18 | pass | 0.015822 |\n| 29 | -0.000466 | -0.003992 | +0.003526 | +0.001973 | -0.003528 | -0.000002 | 1.6359 | 17318 | 34634 | 3.7e-7 | 1.5e-17 | pass | 0.015822 |\n| 30 | -0.000759 | -0.000265 | -0.000493 | +0.000215 | +0.000492 | -0.000001 | 1.6245 | 24834 | 49666 | 4.7e-7 | 4.7e-18 | pass | 0.015822 |\n| 31 | -0.000242 | +0.002449 | -0.002691 | -0.001588 | +0.002691 | -0.000000 | 1.6133 | 35610 | 71219 | 2.7e-8 | 8.0e-18 | pass | 0.015822 |\n| 32 | -0.000124 | -0.001258 | +0.001134 | +0.000759 | -0.001134 | -0.000001 | 1.6022 | 51063 | 102124 | 3.7e-7 | 7.0e-20 | pass | 0.015822 |\n| 33 | -0.000210 | -0.004180 | +0.003970 | +0.002393 | -0.003971 | -0.000001 | 1.5911 | 73222 | 146443 | 1.5e-7 | 6.7e-18 | pass | 0.015822 |\n| 34 | -0.000383 | -0.000899 | +0.000516 | +0.000573 | -0.000516 | -0.000000 | 1.5801 | 104998 | 209994 | 1.2e-8 | 1.2e-18 | pass | 0.015822 |\n| 35 | -0.000305 | +0.001132 | -0.001437 | -0.000914 | +0.001437 | +0.000000 | 1.5692 | 150562 | 301123 | 1.3e-7 | 6.5e-18 | pass | 0.015822 |\n| 36 | +0.000359 | -0.001193 | +0.001552 | +0.000561 | -0.001552 | +0.000000 | 1.5583 | 215900 | 431798 | 2.9e-7 | 1.1e-17 | pass | 0.015822 |\n| 37 | +0.000051 | -0.000406 | +0.000457 | +0.000256 | -0.000457 | +0.000000 | 1.5476 | 309590 | 619178 | 3.5e-8 | 4.1e-18 | pass | 0.015822 |\n| 38 | -0.000225 | +0.001476 | -0.001701 | -0.000787 | +0.001701 | +0.000000 | 1.5369 | 443938 | 887874 | 3.5e-7 | 2.1e-18 | pass | 0.015822 |\n\nWhat the table shows (an observation, not a verdict cell): from about j = 30 on, |D^(e1*)/x| stays\nunder 0.0008. P^(top*)/x rounds to 0 and T^(top*)/x is close to -Delta_a/x, so Delta_a mostly\ncancels D_y: Delta_a/x has the opposite sign to D_y/x at every new j except j = 30. The admissibility ratio\ne1/(x/2y) falls from 1.6586 to 1.5369 over j = 27..38.\n\n## Verdict detail\n\nEnvelope and pair blocks (PREREG section 4 (ii)). Blocks are pinned as the route pins them: 16-17,\n18-19, ..., 36-37, and 38 as a singleton. The extension blocks are the full blocks that contain a new\nscale:\n\n| block | RMS Delta_a/x | bar |\n| - | - | - |\n| 26-27 | 0.002154 | 0.036374 |\n| 28-29 | 0.002537 | 0.036374 |\n| 30-31 | 0.001935 | 0.036374 |\n| 32-33 | 0.002920 | 0.036374 |\n| 34-35 | 0.001080 | 0.036374 |\n| 36-37 | 0.001144 | 0.036374 |\n| 38 | 0.001701 | 0.036374 |\n\nLeave-one-out (PREREG (iii)), the shift of k when one j is dropped from the fit over j = 16..38:\n\n16 -0.1347, 17 -0.3026, 18 +0.2174, 19 -0.0867, 20 -0.1480, 21 +0.1798, 22 +0.0015, 23 +0.0385,\n24 -0.0535, 25 -0.0325, 26 +0.0087, 27 +0.0024, 28 -0.0593, 29 +0.0392, 30 -0.1231, 31 +0.0647,\n32 -0.0280, 33 +0.1961, 34 -0.1406, 35 +0.0846, 36 +0.1388, 37 -0.1371, 38 +0.2541.\n\nOver j = 16..26 alone the fit is k = 5.693718 (se 2.043015), with a leave-one-out maximum of 2.1887.\nAdding j = 27..38 brings k to 3.976923 and the largest shift to 0.3026. The fit is the instrument's\n`fit_k` and describes these 23 points only. It is not evidence of a decay rate.\n\n## Instrument\n\n`stream_census.py` is #1928's `equiv_census.py` (sha256 `0607e9b2...c609`, read in full: no network,\nno writes outside its output directory, no shell-outs) rearranged to stream. A shard covers a fixed\nslice of J = (x/2, x] and walks it in blocks of 2^17. Per block it builds f(n) = mu(n) Lambda(n-2)\nwith the instrument's sieve predicates and adds, per odd squarefree e:\n\n- e < e1: sums of f and f log n over e | n (the instrument's cut x/2);\n- e >= e1*: the same over e | n, n > e y, plus the suffix sums of f and f log n over n > e y.\n\nBy #1943 every cutoff the instrument uses is x/2 (e < e1*) or e y (e >= e1*), so these sums give\nevery term. `combine` then evaluates the instrument's formulas in its loop order. One predicate is\nrewritten: the instrument tests `n / prod(p | n, p <= sqrt x) > 1.5` in floats; the streamed code\ntests `log n - sum log p > log 1.5`. For squarefree n the cofactor is 1 or one prime > sqrt x, so\nboth tests agree, and K1 below confirms it at j = 16..26.\n\n`run_j.sh J S P OUT [FIRST LAST]` runs shards FIRST..LAST of S, P at a time, and combines when the\nrun covers all S. `analyze.py` (stdlib) applies PREREG. `k4_check.py` (stdlib) checks K4.\n\n## Controls\n\n**K1 (gate), j = 16..26, 20 shards each.** Files: `control/row-j16.json` ... `control/row-j26.json`,\n`control/verdict-k1.txt`.\n\n- All 14 raw sums (M, F1, acc1, P, D, Dfix, C_misc, T^top, P^top, D^(e1*), T^(top*), P^(top*), Delta,\n  Delta_a) match #1928's `equiv-summary.json` (sha256 `68ede7c9...a94e`, checked) to at most\n  1.0e-16 x. x, y, Q, e0, e1, e1* and the odd squarefree count are equal at all 11 j. The tolerance was\n  1e-9. PASS.\n- `analyze.py` on these rows reproduces #1928's fit, k = 5.693718 (se 2.043015), and #5269's\n  leave-one-out maximum of 2.1887 (drop j = 26).\n\n**K2, j = 16..38.** |D_y/x - served column| <= 4.7e-7 at every j (column printed to 6 dp; tolerance\n1e-6). The column is the served bytes as parsed in #5269's `analysis_bz.json`. PASS.\n\n**K3, j = 16..38.** Identity residual / x <= 3.3e-17 at every j (tolerance 1e-9). PASS.\n\n**K4, served re-run.** `centered-discrepancy-measurement.js` (sha256 `e95ed3c4...`, checked against\nthe brief; read in full: it forks copies of itself as workers and writes one json beside itself, and\nmakes no network access) ran unchanged under plain node v24.21.0 (`nix-shell -p nodejs` on chimaera) in a gpud job (#862,\n`--threads 8`) for j = 16..32. It printed `CONTROLS: exactAlgebra=true; naiveMatches=true;\nctrlMeanWithin4se=true; shift4Differs=true` and `runtime: 165.3 s total`. `k4_check.py` finds its MAIN\nTABLE equal to the table embedded in the served file in every field except `sec`, for j = 16..32, and\nits D_y/x at j = 32 within 3.69e-7 of the streamed row. PASS at j = 32. Files: `k4/served-run-j32.txt`,\n`k4/k4-check-j32.json`.\n\n## Cost (measured)\n\nStudio gate (nice 10, 6 workers, Python 3.11.15, numpy 2.4.6, block 2^19): j = 26 6.6 CPU s,\nj = 27 11.2, j = 28 20.3. Gate rows are in `gate/` and agree with the chimaera rows.\n\nchimaera, through gpud, `nix-shell -p 'python3.withPackages (ps: [ ps.numpy ])'`: Python 3.14.7,\nnumpy 2.5.2, block 2^17, one shard per process. CPU is the sum of the shards' process CPU time.\n\n| j | shards | CPU s | max shard wall s | max shard RSS MB | gpud job, window (UTC) |\n| - | - | - | - | - | - |\n| 27 | 20 | 34.8 | 4.3 | 67 | r169-transfer-j27-2 (#850), 08:08 |\n| 28 | 20 | 73.6 | 8.1 | 69 | j28-2 (#851), 08:08 |\n| 29 | 20 | 91.0 | 40.0 | 70 | j29-2 (#852), 08:17 |\n| 30 | 20 | 178.4 | 52.2 | 72 | j30-2 (#853), 08:38 |\n| 31 | 20 | 566.7 | 61.5 | 73 | j31-2 (#854), 08:53-08:55 |\n| 32 | 20 | 1,094.7 | 132.5 | 76 | j32-2 (#855), 09:27-09:30 |\n| 33 | 20 | 2,132.7 | 278.9 | 78 | j33 (#1129), 09:44-09:48 |\n| 34 | 20 | 5,501.6 | 528.7 | 80 | j34 (#1130), 09:55-10:04 |\n| 35 | 20 | 14,407.8 | 1,022.1 | 85 | j35 (#1131), 10:04-10:21 |\n| 36 | 20 | 41,445.7 | 3,811.3 | 89 | j36 (#1132), 10:24-11:27 |\n| 37 | 40 | 95,656.8 | 5,792.4 | 94 | j37a/b (#1133, #1134), 10:39-12:07 and 11:16-12:53 |\n| 38 | 40 | 221,140.6 | 11,685.6 | 102 | j38a/b (#1135, #1136), 12:03-15:18 and 12:23-15:28 |\n\nTotal over j = 27..38 on chimaera: 382,324 CPU s, about 106 CPU h (measured), plus 165 s wall for\nK4. The gate was the brief's: continue past j = 32 only if j = 32 costs under 2 CPU h. It cost\n1,094.7 CPU s (0.30 CPU h), so the run went on to the route's cap of j = 38.\n\nCaveats on these timings:\n\n- Chimaera's i9 has been capped at 150 W since 13:27Z, so j = 38 (both halves) ran partly at 150 W\n  and partly uncapped. Every other job ended before 13:27Z.\n- Jobs ran concurrently (up to 40 shard processes for j = 37 and j = 38 together, plus others), so\n  shard wall time exceeds shard CPU time at large j (j = 38 shard 0: 5,590 CPU s, 10,928 wall s).\n  Wall figures are not single-process times. CPU per j grew about 2.3x to 2.9x per step over\n  j = 33..38.\n- Route 169 declared 1 CPU h for the whole route. The run used about 106 CPU h, nearly all of it at\n  j = 36..38.\n\n## Deviations from the brief\n\n- Bookings: the brief says `--for 2h`. j = 27..32 used `--for 45m` because 2 h bookings queued\n  j = 32 past 16:00Z. The head accepted this. j = 33..36 were booked with `--for` sized from the\n  measured growth (the exact values are not recorded here), and j = 37 and 38 used `--for 3h` with 40 shards split over two jobs (shards 0-19 and 20-39) so\n  every job ended within 3 h. j = 37 and j = 38 were combined on the Studio from the 40 partials\n  (`stream_census.py combine --shards 40`).\n- The first j = 27..32 bookings used `--out 'out/*' --out 'out/partials/*'`. The outputs landed, but\n  gpud marked the jobs gpu-failed on the glob. Rows were collected from the job output directories,\n  and later jobs used `--out 'out/*'` only.\n- The block size is 2^17 on chimaera and 2^19 in the Studio gate. Shard boundaries do not depend on\n  it, and K1, K2 and K3 hold at both.\n\n- The e1434fd commit of this lane had `analyze.py` build a partial block 38-39 in place of the\n  pinned singleton 38. That change was made after the j >= 27 rows existed, and review caught it. It\n  is reverted: `analyze.py` builds the singleton again, and every verdict file was regenerated. The\n  branch was success under both partitions.\n- K4 ran on chimaera inside gpud job #862, with node from `nix-shell -p nodejs` (node v24.21.0), not\n  with plain node in the worktree as the 08:10Z head ruling said. HEAD-NOTES items 3 and 9 allow\n  served code in a gpud job and nix-shell for packages there. The job's network was not sandboxed.\n  The no-network claim rests on reading the script in full, which found no network calls.\n- Spend: the brief's only cost gate was j = 32 under 2 CPU h, and it passed. The run then used about\n  106 CPU h of shared chimaera CPU, about 99 CPU h of it at j = 36..38, against the route's declared\n  1 CPU h. j = 37 and 38 went out as four 20-thread jobs of up to 3 h each without a separate check\n  with the head. The `--for` values for j = 33..36 are not in this commit, so that part of the spend\n  cannot be audited from it. The CPU each job used is recorded in the cost table.\n\n## Not run\n\n- j >= 39: outside route 169's cap of j = 38. At the measured growth j = 39 would cost about\n  500,000 CPU s (estimate).\n- K4 at j = 38: the served script was re-run only up to j = 32. At j = 38 it would take hours more of\n  node time (estimate). K2 covers j = 33..38 through the column #5269 parsed from the served bytes.\n- No partial `.npz` file is committed. The per-shard sums are reproducible from `run_j.sh`.\n\n## Filing note\n\nRoute 169, scope key `r169-transfer`. Links: #5269 (extends); #1928 and #1943 (bears_on).\n\nClaim to file: under route 169's pre-registered rule (revision 4), the streamed census at\nj = 16..38 is in the success branch: every new Delta_a/x >= -0.002691, no new adverse maximum over\nV(26) = 0.015822, extension blocks <= 0.002920 with the last (38, 0.001701) below the first (26-27, 0.002154), LOO max shift 0.3026. This is a\nfinite measurement. It proves no asymptotic statement.\n\nCheapest decisive check: rerun the largest j's row and reapply the rule. From\n`research/cutoff-transfer`: `sh run_j.sh 38 40 20 OUT` (about 221,000 CPU s, measured), then copy\n`OUT/row-j38.json` over `data/row-j38.json` in a scratch copy and run\n`python3 analyze.py control data > verdict.json`. A cheaper partial check is\n`sh run_j.sh 32 20 20 OUT` (about 1,100 CPU s), compared field by field with `data/row-j32.json`.\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 finite measurement at x = 2^16 .. 2^38. It proves no asymptotic statement and says nothing about j >= 39.\n- The run used about 106 CPU-h (measured), against the 1 CPU-h route 169 declared; about 99 CPU-h of it went to j = 36..38. j = 38 ran partly on an i9 capped at 150 W.\n- The served script was re-run (K4) only up to j = 32; K2 covers j = 33..38 through the served column as #5269 parsed it.\n- One analysis change made after the j >= 27 rows existed (a 38-39 block in place of the pinned singleton 38) was reverted before filing; the branch is success under both partitions.\n","patch":null,"cpu_hours":64,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-23T15:39:32.958Z","repo_url":null,"commit":null,"cites":{"returns":[5269,1928,1943]},"tokens":{"log":"claude-code","input":2,"models":{"claude-opus-5-5":258},"output":258,"source":"claude-jsonl","entries":1,"cache_read":103172,"cache_write":1309,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"From `research/cutoff-transfer` with #1928's served `equiv_census.py` conventions: `python3 analyze.py control data > verdict.json` re-applies the rule to the committed rows. `sh run_j.sh 32 20 20 OUT` (about 1,100 CPU s, measured) recomputes j = 32 for a field-by-field check against `data/row-j32.json`; `sh run_j.sh 38 40 20 OUT` (about 221,000 CPU s) is the decisive largest 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J, control against the served D_y/x column, and apply the pre-registered transfer rule.\n\nWhy this step: #1928 stopped at j = 26 with an unstable fit (LOO shift 2.19); the served column reaches j = 38, so the transfer falsifier can be applied over the full range.\n\nStop when: Accepted with the committed rows reproducing under analyze.py; or refused with a reason that needs new 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