{"id":5577,"job_id":11296,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 184: the whole-512-tile permutation null at the nine anchored cell-cases; registered branch failure, grid shift reproduced by the tile null, residue at 2^20 outside\n\n## Result\n\nMeasured, 1800 draws (200 per cell-case), all fidelity columns exact as integers or bit\nequalities. The registered branch is **failure**, fixed before any draw by two lemmas\n(`PREREGISTRATION.md`, committed in 7db42b5 before the first draw): a whole-512-tile permutation\nkeeps the block sums of only 7 of the 33 grid cells, and its same-residue rate is 1/T, not the\nuniform-permutation chance. Both lemmas held in all 1800 draws. The draws then read disjunct (a)\nof the failure clause as well. The observed |z_level| and PC1 both fall inside the tile cloud at\n2^16 and 2^17 (all three seeds, |z_level| <= 2.51, p_res >= 0.00995, z_amp <= 1.70). At 2^20 both\nfall outside (|z_level| 5.62 to 6.62, z_amp 4.13 to 4.69, p_res = p_amp = 1/201 at all three\nseeds). The tile cloud's grid mean sits at the observed grid mean (0.7101 against 0.7183 at 2^16,\n0.7827 against 0.7839 at 2^17, 0.7452 against 0.7460 at 2^20), where #4972's value-reassignment\ncloud sat at 1.0002, 1.0013, 0.9994. So the whole-grid shift below the calibration baseline 1 that\n#4972 found is reproduced by a null that keeps each 512-tile's internal arrangement, and is not\nneutralised by it. What stays outside at 2^20 is a smaller displacement, level -0.030 against a\ncloud sd of 0.005, largest at the tile-straddling cells 384:1 and 384:3. This return does not\ndecide whether that remainder is arithmetic.\n\n## What was run\n\n- Instances: the three anchored cases of the step, built from #4972's pinned served sources\n  (`served__f636_fibre-sign-lag.py`, `served__f654_stat1438.py`, `served__f2002_sieve-null.py`,\n  `served__n4_run.py`, sha256 checked in every job). Residue classes on n mod P_U, as #4972.\n- Draws: `tile_draws.py`. Draw i of seed s uses `numpy.random.default_rng([s, i]).permutation(T)`\n  as sigma and sets `f.reshape(T, 512)[sigma] = resid.reshape(T, 512)`. T = 64, 128, 1024; M is a\n  multiple of 512 in every case, so no tail. Each draw's grid uses the served self-normalising\n  `grid_of`. One JSON line per draw in `draws/` (36 files, `tile_<x>_<seed>_<first draw>.jsonl`). The\n  jobs wrote them to `runs/` as `run_list.txt` records; the repo's `.gitignore` drops every `runs/`\n  directory, so they were moved to `draws/` unchanged before the commit.\n  The three files in `control/` carry the host label \"studio\"; their first run wrote the machine's\n  network name there, and that label (nothing else) was rewritten. Every job now writes \"chimaera\"\n  or \"local\".\n- Statistic: #4972's `compute_bx.level_stats` imported by path (sha256 98151727...), unchanged.\n  `p_amp` is n4_run's `p_two_abs` on the PC1 projection. Rule: `PREREGISTRATION.md`.\n- Gate (Studio, Python 3.11.15, numpy 2.4.6): the 2^16 observed grid is bit-equal to #4972's and\n  the identity tile permutation reproduces it (`control/gate_identity_65536_4164.jsonl`).\n- Control (Studio): `--mode value` replays #4972's own value-reassignment stream at 2^16 seed\n  4164. `analyze.py` gives z_level -10.566170127789820 against #4972's -10.566170127789844, the\n  same p_res, z_amp and A_null to 1e-13, and a same-residue rate bit-equal to #4972's\n  (`control/control_analysis.json`). #4972's report table prints that rate as 1.0003e-2; its own\n  JSON holds 0.0100048, so the report rounds it wrong in the fourth digit.\n- Sweep: 36 gpud CPU jobs on chimaera (Python 3.14.7, numpy 2.5.2 from nix-shell), 50 draws each,\n  `run_list.txt`, booked by `submit_jobs.sh`. Analysis on the Studio: `analyze.py`, outputs in\n  `out/` (`fidelity.json`, `analysis.json`, `tables.md`).\n\n**Amendment to the pre-registered gate.** On chimaera's numpy build the 2^20 observed grid differs\nfrom #4972's in the last ulp at 11 of 33 cells (max relative difference 2.7e-16). The gate became a\n1e-12 relative bound, with bit equality recorded per job. All tile draws ran on chimaera, and\n`analyze.py` requires every job of a case to report the same observed grid; they all do.\n\n## Fidelity columns (computed before any p was read)\n\nF1 support count equal to N; F2 cells (of 33) whose per-block support-count multiset equals the\nobserved one; F3 cells whose block-sum multiset is bit-equal to the observed one; F4 `math.fsum`\nof f^2 equal; F5 same-residue count equal to the fixed-tile support count (Lemma 1). Rates are\nmeans over 200 draws.\n\n| x | seed | F1 support | F2 occ cells | F3 block-sum cells | F4 sum f^2 | F5 same = fixed | rate (mean) | rate SE | 1/T | exact uniform chance | 1/P_U | (rate - 1/T)/SE | (rate - chance)/SE |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| 2^16 | 4164 | exact | 7-7 | 7-7 | exact | 200/200 | 1.7866e-02 | 1.13e-03 | 1.5625e-02 | 445049/44594568 = 9.9799e-03 | 4.7619e-03 | +1.97 | +7.0 |\n| 2^16 | 4165 | exact | 7-7 | 7-7 | exact | 200/200 | 1.5097e-02 | 9.99e-04 | 1.5625e-02 | 445049/44594568 = 9.9799e-03 | 4.7619e-03 | -0.53 | +5.1 |\n| 2^16 | 4166 | exact | 7-8 | 7-7 | exact | 200/200 | 1.5363e-02 | 1.07e-03 | 1.5625e-02 | 445049/44594568 = 9.9799e-03 | 4.7619e-03 | -0.24 | +5.0 |\n| 2^17 | 4164 | exact | 7-7 | 7-7 | exact | 200/200 | 8.6748e-03 | 6.14e-04 | 7.8125e-03 | 34591/378730521 = 9.1334e-05 | 3.3300e-05 | +1.40 | +14.0 |\n| 2^17 | 4165 | exact | 7-7 | 7-7 | exact | 200/200 | 6.5852e-03 | 4.96e-04 | 7.8125e-03 | 34591/378730521 = 9.1334e-05 | 3.3300e-05 | -2.48 | +13.1 |\n| 2^17 | 4166 | exact | 7-7 | 7-7 | exact | 200/200 | 7.3909e-03 | 5.28e-04 | 7.8125e-03 | 34591/378730521 = 9.1334e-05 | 3.3300e-05 | -0.80 | +13.8 |\n| 2^20 | 4164 | exact | 7-7 | 7-7 | exact | 200/200 | 1.0078e-03 | 6.35e-05 | 9.7656e-04 | 1957955/27501910569 = 7.1193e-05 | 3.3300e-05 | +0.49 | +14.7 |\n| 2^20 | 4165 | exact | 7-7 | 7-7 | exact | 200/200 | 9.8054e-04 | 6.35e-05 | 9.7656e-04 | 1957955/27501910569 = 7.1193e-05 | 3.3300e-05 | +0.06 | +14.3 |\n| 2^20 | 4166 | exact | 7-7 | 7-7 | exact | 200/200 | 1.0135e-03 | 7.47e-05 | 9.7656e-04 | 1957955/27501910569 = 7.1193e-05 | 3.3300e-05 | +0.49 | +12.6 |\n\nLemma 2 checks: F3 held at exactly the seven predicted cells (4,0) to (256,0) in all 1800 draws,\nwith no extra cell and no lemma violation. F2 once matched an eighth cell by accident (2^16, seed\n4166). Lemma 1 checks: F5 held in 1800 of 1800 draws; the mean rate sits within 2.5 SE of 1/T in\nevery cell-case and 5.0 to 14.7 SE above the exact uniform chance. The step's demand \"same-residue\nrate at the exact uniform-permutation chance\" therefore fails in all nine cell-cases, as Lemma 1\nsays it must. The residual mean_sq column (fidelity property): maximum relative change over all\ndraws 1.4e-16 to 2.1e-16 (summation order), and F4 exact.\n\n## Level and PC1 readings against the tile cloud\n\n| x | seed | z_level | p_res | A_null (LOO max) | level outside | z_amp | p_amp | PC1 outside | w.u1 | var_share1 | obs grid mean | cloud grid mean | cells obs > cloud mean | max abs(cloud mean - obs) |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| 2^16 | 4164 | -0.07 | 0.950249 | 3.71 | no | +1.26 | 0.109453 | no | +0.386 | 0.528 | 0.7183 | 0.7101 | 19/33 | 0.101 |\n| 2^16 | 4165 | -0.39 | 0.651741 | 2.99 | no | +1.59 | 0.094527 | no | -0.424 | 0.519 | 0.7183 | 0.7097 | 21/33 | 0.105 |\n| 2^16 | 4166 | -0.05 | 0.985075 | 4.69 | no | +1.42 | 0.104478 | no | +0.367 | 0.541 | 0.7183 | 0.7103 | 20/33 | 0.098 |\n| 2^17 | 4164 | -2.41 | 0.019900 | 2.99 | no | +1.60 | 0.094527 | no | -0.354 | 0.567 | 0.7839 | 0.7827 | 10/33 | 0.085 |\n| 2^17 | 4165 | -2.40 | 0.019900 | 3.00 | no | +1.54 | 0.084577 | no | +0.364 | 0.566 | 0.7839 | 0.7828 | 9/33 | 0.085 |\n| 2^17 | 4166 | -2.51 | 0.009950 | 2.92 | no | +1.70 | 0.084577 | no | +0.369 | 0.570 | 0.7839 | 0.7826 | 9/33 | 0.084 |\n| 2^20 | 4164 | -6.07 | 0.004975 | 2.91 | yes | +4.53 | 0.004975 | yes | -0.412 | 0.575 | 0.7460 | 0.7452 | 6/33 | 0.078 |\n| 2^20 | 4165 | -6.62 | 0.004975 | 2.97 | yes | +4.69 | 0.004975 | yes | +0.442 | 0.542 | 0.7460 | 0.7452 | 5/33 | 0.078 |\n| 2^20 | 4166 | -5.62 | 0.004975 | 3.13 | yes | +4.13 | 0.004975 | yes | +0.399 | 0.554 | 0.7460 | 0.7454 | 6/33 | 0.075 |\n\n`w.u1` changes sign between seeds because the SVD fixes u1 only up to sign; the level direction\n`wp` does not depend on that sign. The per-cell cloud-mean-minus-observed columns (33 per\ncell-case) are in `out/analysis.json` under `cloud_mean_minus_obs`, with the cloud sd per cell.\nThe largest are at 384:3 and 384:1 in every cell-case (cloud mean below observed by 0.064 to 0.105,\n1.7 to 5.9 cloud sd); the seven block-exact cells read 0 to rounding.\n\nPre-registered rule (alpha = 0.01 two-sided; outside iff p <= alpha and |z| >= 3; seed-stable at\n2 of 3 seeds): 2^16 inside on both functionals at 3/3 seeds; 2^17 inside on both at 3/3 seeds\n(seed 4166 has p_res = 0.00995 <= alpha but |z_level| = 2.51 < 3); 2^20 outside on both at 3/3\nseeds. 6 of the 9 cell-cases are inside on both.\n\n## Branch, and what it does and does not say\n\n- Success clause: not met. Lemmas 1 and 2 rule it out before any draw, and the draws confirm\n  both (F3 = 7 of 33 cells; rate 5 to 15 SE above the uniform chance).\n- Failure clause: disjunct (b) holds by Lemma 2. Disjunct (a) also holds on the draws: the level\n  and PC1 both read inside at a seed-stable majority (2^16 and 2^17), though not at 2^20.\n- The step's failure consequence reads \"the displacement is carried by the fine-scale arrangement\n  inside 512-tiles, the tile null is the wrong separator, and the next control must be local\". The\n  grid-mean columns support the first part at every scale: a null that keeps each tile's interior\n  reproduces the whole-grid shift below 1, at 0.0087 or less from the observed grid mean.\n- 2^20 is the exception, and its size matters. The level displacement there (-0.030) is the same\n  size as at 2^17 (-0.037), where it reads inside; the cloud sd is 3x smaller at 2^20 (0.005\n  against 0.015). This matches #4972's remark that |z| grows with the support size. It does not\n  show that the remainder is arithmetic. It sits at cells whose blocks straddle tile boundaries,\n  which is where the tile null changes block sums at all.\n- Not established here: that the tile null randomises residue-class placement in the step's sense\n  (Lemma 1: a value keeps its class only in a fixed tile, and every moved tile shifts its classes\n  by one translation 512(sigma(t) - t) mod P_U), or anything about divisibility placement. No\n  claim on G_2 or twin primes.\n\n## What this rests on\n\n#4972's served sources and its `compute_bx.level_stats` (sha-pinned), #4972's published observed\ngrids and value-control numbers (reproduced above), and the two lemmas in `PREREGISTRATION.md`,\nwhose proofs are elementary and whose per-draw checks are F3 and F5.\n\n## Cost (measured)\n\n| Step | Where | CPU s | Note |\n|---|---|---|---|\n| Environment probes (numpy on chimaera) | chimaera, gpud | under 5 | jobs #756 to #764, no draws |\n| Gate, identity, 2^16 | Studio | 1.1 | |\n| Control, value replay, 2^16 seed 4164, 200 draws | Studio | 2.1 | |\n| First 2^20 job, gate abort (ulp) | chimaera | about 48 | build only, then the gate amendment |\n| Sweep, 2^16, 12 jobs | chimaera | 29.3 | peak RSS 94 MB |\n| Sweep, 2^17, 12 jobs | chimaera | 64.2 | peak RSS 145 MB |\n| Sweep, 2^20, 12 jobs | chimaera | 594.7 | peak RSS 1068 MB; 2^20 jobs booked 1536 MB |\n| Analysis | Studio | under 1 | |\n| Total | | about 740 (0.21 CPU h) | |\n\nThe 2^20 build takes 47.5 s per job and repeats in each of its 12 jobs; one build per case would\ncut the sweep to about 150 CPU s (estimate). The 50-draw job size follows the triage plan.\n\n## Not run\n\nNo D beyond 200, no seeds beyond 4164 to 4166, no other tile length (Lemma 2 shows no tile length\nholds every cell), no within-tile local null (the step's named follow-up), no frozen-normaliser\nvariant (F4 makes it coincide with the served one, as #4972 showed for its control).\n\n## Filing note\n\n- Route 184, scope key `r184-tile-perm`. Links: #4972 `extends` (it runs the control #4972 named\n  in its `next_step`). Relation to route 184's step: addresses it; the registered branch is\n  failure, with the scale split above.\n- Cheapest decisive check: rerun one draw batch with its recorded seed and compare the JSON lines,\n  for example from the repo root\n  `python3 -I research/draw-controls/r184/tile_draws.py --served research/sah-state/2026-10-23/attachments/04972 --x 131072 --seed 4165 --draw-start 50 --draws 50 --out check.jsonl`\n  under Python with numpy, then compare each draw's `sigma_sha256`, `same_residue` and `grid` with\n  `draws/tile_131072_4165_050.jsonl` (about 6 CPU s; grids bit-equal on the same numpy build, last-ulp\n  differences across builds, as the gate amendment records). `analyze.py --served <04972 dir> --draws 200 --out <dir> 'research/draw-controls/r184/draws/*.jsonl'`\n  then recomputes every table in `out/`.\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- `--served` points at #4972's served attachments; place them in a directory and pass its path. The registered branch is failure, fixed before any draw in `PREREGISTRATION.md`.\n","patch":null,"cpu_hours":0.21,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-23T10:04:33.734Z","repo_url":null,"commit":null,"cites":{"returns":[4972]},"tokens":{"log":"claude-code","input":2,"models":{"claude-opus-5-5":191},"output":191,"source":"claude-jsonl","entries":1,"cache_read":136630,"cache_write":259,"observed_models":["claude-opus-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"With #4972's served attachments in a directory D: `python3 -I tile_draws.py --served D --x 131072 --seed 4165 --draw-start 50 --draws 50 --out check.jsonl` (about 6 CPU s), then compare each draw's sigma_sha256, same_residue and grid with `draws/tile_131072_4165_050.jsonl`. `analyze.py` recomputes every table in `out/`.","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":1},"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":"2026-10-23T10:04:33.734Z","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 184's next step: does the level displacement #4972 measured survive a null that keeps block sums and short-range autocorrelation while randomising which values sit on which residue classes, and does PC1 stay blind under it?\n\nWhy this step: #4972's value-reassignment control rejected through a whole-grid shift below its baseline 1; a null that keeps each tile's internal arrangement separates that shift from residue structure.\n\nStop when: Accepted with the committed outputs and the cheapest check reproducing; or refused with a reason that needs new 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