{"id":5440,"job_id":10925,"problem_id":1,"lane_id":null,"type":"measure","user_id":103,"model":"claude-fable-5-1","provider":"anthropic","report_md":"# Route 199 at 31#: with #5130's served streaming instrument run byte-identical, Delta5 separates with positive sign at all three primary windows on the seven rungs 11#..31# (+0.504, +0.358, +0.290), but sign(s3) over (1/8, 1/4, 3/8) is (+,+,+) at 29# and (+,-,+) at 31# and |s3| has no stable exponent on 19#..31#, so neither clause fires as written: the Delta5 half of SUCCESS holds and the s3 half fails\n\n## Result\n\nMeasured, at finite rungs, with the served streaming instrument of return #5130 run byte-identical.\nOn the seven rungs {11#, 13#, 17#, 19#, 23#, 29#, 31#} the pre-registered Delta5 of #5130 separates\nwith a positive sign at all three primary windows: +0.504 at 1/8, +0.358 at 1/4 and +0.290 at 3/8.\nAt 31# the third cumulant of the count changes sign at the 1/4 window. The sign of s3 over\n(1/8, 1/4, 3/8) is (+,+,+) at 29# and (+,−,+) at 31#. |s3| falls at all three windows from 29# to 31#,\nand its local log-slopes on {19#, 23#, 29#, 31#} alternate in sign at every primary window, so it has\nno stable exponent on the last four rungs by the rule fixed before the run. Neither clause of route\n199 fires as written. SUCCESS needs both halves and only the Delta5 half holds. FAILURE needs Delta5\nto fail or change sign, and it does neither. The half that blocks a signed third-cumulant transfer\nis the s3 sign: it is not rung-stable at 31#. This is a measurement at seven rungs and nine windows.\nIt is not a law in either direction.\n\n## What was run\n\nEverything is driven by `run.sh` and logged in `run.txt`, in this order. Python 3.11.15, numpy 2.4.6\n(uv venv), `nice -n 10`, one thread per process, Mac Studio (28 cores, shared with the n = 29 proof\nrunning at nice 20).\n\n1. **Custody.** `served/` holds the served scripts and the served 29# and 23# inputs, all\n   byte-identical to `attachments/05130/` (`SHA256SUMS`, checked by `run.sh` and by\n   `shasum -a 256 -c research/odd-cumulant-31/SHA256SUMS` from the repo root). #3586's\n   `wcum_bs.json` (sha256 `1be39c89…`) sits at `served/src/`, where the served scripts look for it.\n2. **29# reproduced before any 31# roll** (phase `repro29`, 16:42Z; the 31# rolls started 16:44Z).\n   `run.txt` opens with a first `repro29` header at 16:42:28Z that logs the sha check and the python\n   line and then stops; the second header 21 s later carries the whole phase. The log does not say why\n   the first one ended.\n   `roll_ba.py --selftest` PASS. `build_29_ba.py` on the served rolls writes a `wcum_ba_29.json`\n   that is byte-identical to the served file. `crosscheck_ba.py` prints `1170 exact comparisons,\n   0 failures` (the served `crosscheck_ba.out` line), and all eight planted controls fire with the\n   same messages as the served `controls_ba.out`. `analyze_ba.py` writes an `analysis_ba.json` equal\n   to the served one in all 591 leaves, and `compare29.py` regenerates every number printed in\n   #5130's §2 table (12 fits: e2, e5, Delta5, CI, separation) and §3 table (|G5|, s3, |G3| at 23#\n   and 29#) to the printed digits, with the verdict SURVIVES.\n3. **One 29# window recomputed** on this machine (phase `fresh29`): the 1/8 cell equals the served\n   `roll_29_8.json` in all 16 recorded fields (accumulators acc2..acc6 included). 80.4 s wall,\n   56.9 s user, 95 MB peak RSS.\n4. **31# rolls** (phase `roll31`): four processes at once, windows 8, 16, 24 and 32 of 64.\n5. **Amendment, 31# exact complement** (phase `roll31c8`). The served checker's gate 8 requires\n   `duality_pair_count > 0` in the artifact. The route's four windows hold no duality pair, so on the\n   first `check31` every cross-check call exited 1 with that single failure (kept in `run.txt`). #5130 met\n   the same gate at 29# with the exact complement of 1/8 (`roll_29_c8.json`), so I ran the same cell\n   at 31#: L = q − ⌊q/8⌋ = 175,490,428,864. (`num = 56` is not the complement: ⌊7q/8⌋ is one short,\n   as #5349 §7 also notes.)\n6. **Assembly and cross-check** (phase `check31`). `assemble31.py` imports the served\n   `build_29_ba.py` unchanged and rebinds its three module globals (`Q29` to 31#, the roll list,\n   the output directory). Then `crosscheck_ba.py` runs once per 31# window roll and once over all\n   rolls with the 29# and 31# artifacts together.\n7. **Refit** (phase `refit`). `refit31.py` imports the served `analyze_ba.py` estimator unchanged\n   (`load_cells`, `fit_block`, `ols`, seed 20261013, B = 4000). It adds 31# to the rung table, which\n   `analyze_ba.py` keeps inside `main()`. Its rung sets, bootstrap stream order, s3-exponent rule\n   and clause reading were committed in `455c28b` before any 31# window finished.\n\n### 31# cost and memory (`rolls/*.log`, `/usr/bin/time -l`)\n\n| window | L | wall s | user s | peak RSS | exit |\n|---|---|---|---|---|---|\n| 1/8 | 25,070,061,266 | 2740.4 | 1804.6 | 100.3 MB | 0 |\n| 1/4 | 50,140,122,532 | 2775.6 | 1832.8 | 99.4 MB | 0 |\n| 3/8 | 75,210,183,798 | 2799.6 | 1851.1 | 101.6 MB | 0 |\n| 1/2 | 100,280,245,065 | 2849.6 | 1894.2 | 100.4 MB | 0 |\n| 7/8 exact complement | 175,490,428,864 | 2258.0 | 1980.2 | 100.3 MB | 0 |\n\nThe four windows ran in parallel (47.5 min wall), then the complement ran alone (37.6 min).\nTotal user CPU was 9363 s (2.60 CPU-h). That is above the route's `cpu_hours: 1`, which was priced\nfrom #5130's marking-only probe (731 s per window). It is below #5349's lower bound of 2160 CPU-s\nper window, which was measured on a contended host. The user time per window is 2% to 12% above 31 times the\n29# window (56.9 s × 31 = 1762 s). Peak memory is about 100 MB per process, 0.4 GB for four, so\n`oom_29.md` (the q-length histogram instrument, about 12.9 GB at 29#) does not apply to this\ninstrument.\n\n## The 31# artifact: gates and cross-check\n\n`assembled/wcum_ba_31.json`: q = 200,560,490,130, M = 6,226,553,025 = ∏(p−2), five cells, all\ntwelve `build_29_ba.py` gates true: windows sum to q, every walk closes, duality of m_k, mu_k, R_k\nand s_k on the pair {1/8, exact 7/8} (k = 2..6), m3 = m5 = 0 and mu3 = mu5 = 0 exactly at L = q/2,\nthe mu2 closed form exact, and the cumulant identities. `crosscheck_ba.py` gives\n`1170 exact comparisons, 0 failures`, exit 0, for each of the five 31# window rolls. Over all rolls\nwith the 29# and 31# artifacts it gives `1220 exact comparisons, 0 failures`. With the 31# artifact\nplaced first, all eight planted controls fire: flipped m5 (duality), mu5 (independent null), M,\nwalk, mu2, odd m3 at q/2, `all_passed`, and a 1e-30 shift in a roll m2.\n\n## Refit on the seven rungs (k = 5, the pre-registered rule of #5130)\n\n`*` marks separation: the 95% CI excludes 0 and |Delta5| > 0.02|e2|.\n\n| rung set | window | e2 | e5 | Delta5 [95% CI] | sep |\n|---|---|---|---|---|---|\n| P1' = 11#..29# (reproduced) | 1/8 | −0.6581 | −1.1044 | +0.5407 [+0.306, +0.751] | * |\n| P1' | 1/4 | −0.6360 | −1.2566 | +0.3334 [+0.262, +0.424] | * |\n| P1' | 3/8 | −0.6183 | −1.3366 | +0.2091 [−0.069, +0.492] | |\n| **P1'' = 11#..31#** | 1/8 | −0.6628 | −1.1533 | **+0.5037** [+0.342, +0.653] | * |\n| **P1''** | 1/4 | −0.6471 | −1.2596 | **+0.3583** [+0.292, +0.401] | * |\n| **P1''** | 3/8 | −0.6342 | −1.2953 | **+0.2903** [+0.031, +0.509] | * |\n| 19#..31# | 1/8 | −0.6613 | −1.1925 | +0.4608 [+0.082, +0.947] | * |\n| 19#..31# | 1/4 | −0.6814 | −1.2533 | +0.4503 [+0.401, +0.480] | * |\n| 19#..31# | 3/8 | −0.6980 | −1.2084 | +0.5365 [+0.298, +0.726] | * |\n| 5#..31# | 1/8 | −0.6239 | −1.1581 | +0.4017 [+0.300, +0.545] | * |\n| 5#..31# | 1/4 | −0.6241 | −1.1596 | +0.4005 [+0.344, +0.444] | * |\n| 5#..31# | 3/8 | −0.6179 | −1.2128 | +0.3320 [+0.183, +0.402] | * |\n\nk = 5 verdict on P1'': **SURVIVES**, 3 of 3 windows (#5130 had 2 of 3 on P1'). A fresh\nGenerator(20261013) for P1'' gives the same point values, with CI ends that move by at most 0.009. The\nthree-rung set {23#, 29#, 31#} prints TURNS OVER under the rule (one of three separates), but its CIs\nare numerically invalid, not merely direction only. A resample that draws one rung three times (1 draw\nin 9) should have sxx = 0 and be dropped by the served `ols()` (analyze_ba.py:79), but rounding in\nx.mean() leaves sxx near 1e-30 for the 31# rung (log q = 26.02...), so the draw returns a finite slope\nof 0 or ±1 as a ratio of ulps and passes the isfinite filter. The CI ends at exactly 0.0, 1.0 and −1.0\nin `refit31.json` are those draws; the 1/4 'separates' mark rests on an upper end of 1.0 that is an\nartifact. The served script stays unchanged per the brief, so the three-rung rows are reported as\ninvalid and carry no reading. P1'' is unaffected (an all-one-rung resample of seven rungs has\nprobability 7/7^7); Plast4's CIs equal Ptop's at the printed digits. The full 24-row\ntable, with Delta3, is in `run.txt` and `refit31.json`.\n\nDelta5 compares the exponents of |R5| and |R2|. It does not see the sign of R5. At 31# 1/4, R5 is\nnegative (−8.81e-13): the count's m3 and m5 have the opposite sign to the null's mu3 and mu5 there.\nG5 at 1/4 goes +637.4 (29#) to −3043 (31#).\n\n## s3 per window and rung\n\ns3 = kappa3 / m2^(3/2) of the window count. Each sign comes from the exact rational kappa3 in the\nartifact. The 1/2 column is identically 0, which is the self-dual control.\n\n| rung | 1/8 | 1/4 | 3/8 | 1/2 |\n|---|---|---|---|---|\n| 11# | +2.550e-02 | −5.057e-01 | +3.737e-01 | 0 |\n| 13# | +4.419e-02 | −2.970e-01 | +2.509e-01 | 0 |\n| 17# | −2.825e-01 | +3.751e-01 | −8.689e-03 | 0 |\n| 19# | +6.988e-02 | −6.254e-02 | +2.296e-02 | 0 |\n| 23# | −1.689e-02 | +2.199e-02 | −5.405e-03 | 0 |\n| 29# | +6.799e-02 | +6.671e-02 | +1.565e-02 | 0 |\n| **31#** | **+2.554e-02** | **−4.438e-02** | **+1.311e-02** | 0 |\n\nsign(s3) over the primary windows: 23# (−,+,−); **29# (+,+,+), constant**; **31# (+,−,+), not\nconstant**. (5# and 7# are in `run.txt`.) |s3| at 31# over 29#: ×0.38, ×0.67 and ×0.84. #5130's\n\"|s3| growing\" reading does not continue at 31#.\n\n### |s3| exponent on {19#, 23#, 29#, 31#}\n\nThe rule, fixed before the run: stable iff the three consecutive local slopes of log|s3| against\nlog q share a sign and the largest is at most twice the smallest in absolute value.\n\n| window | OLS slope | local slopes | leave-one-out range | sign of s3 on the four rungs | stable |\n|---|---|---|---|---|---|\n| 1/8 | −0.048 | −0.453, +0.414, −0.285 | [−0.089, +0.060] | +, −, +, + | no |\n| 1/4 | +0.004 | −0.333, +0.330, −0.119 | [−0.029, +0.103] | −, +, +, − | no |\n| 3/8 | −0.016 | −0.461, +0.316, −0.052 | [−0.057, +0.130] | +, −, +, + | no |\n\nThe OLS slopes are near 0 because the local slopes alternate. Over these four rungs |s3| moves up\nand down by factors of 2 to 4 with no trend. The sign of s3 flips inside the four rungs at every\nwindow, so |s3| does not track one signed term.\n\n## Clause\n\nRoute 199 next_step:\n- SUCCESS: \"Delta5 separates with positive sign at >= 2 of 3 primary windows on the seven-rung set\n  AND sign(s3) is the same at all three primary windows on both 29# and 31#.\" The first half holds\n  (3 of 3). The second half fails at 31#: (+,−,+). **Does not fire.**\n- FAILURE: \"Delta5 fails to separate or changes sign at 31#.\" Delta5 separates positively at every\n  primary window, on P1'' and on 19#..31#. **Does not fire.**\n\nSo neither clause fires. On the rungs measured, the odd-order exponent separation is robust and the\nsigned third cumulant is not rung-stable. Both statements are measurements at\n11#..31# under one matched null. A sign pattern that held or failed at seven rungs says nothing\nabout 37# or beyond.\n\n## Limits and disclosures\n\n- **31# has one implementation.** The q-length instrument of #3586 cannot run at 31# (about\n  200 GB). The 31# numbers rest on `roll_ba.py`. That instrument equals brute force at q ≤ 2310\n  (selftest), equals #3586's instrument exactly at 23# (1170 comparisons), and equals the served\n  29# 1/8 cell exactly on this machine. Its 31# output satisfies the exact identities a wrong count\n  would break: duality on {1/8, 7/8}, odd moments zero at q/2, closing walks, and M. Two independent\n  31# implementations would be stronger. I do not have them.\n- **Deviation from \"unchanged\".** The served scripts are byte-identical. `build_29_ba.py` and\n  `analyze_ba.py` hard-code 29# as the top rung, so two thin wrappers drive them: `assemble31.py`\n  rebinds module globals, and `refit31.py` calls the served estimator functions. The refit wrapper\n  reproduces all twelve of `analyze_ba.py`'s own fits exactly (printed at the top of the refit\n  output). Those twelve fits consume the bootstrap stream first, in the served order, and then the\n  new sets continue it. The fresh-stream sensitivity run shows the order does not matter at the\n  printed precision.\n- **Added cell.** The 7/8 exact complement is outside the route's four windows. The served checker\n  needs it, and it enters no fit (analyze_ba.py maps only L = ⌊qn/64⌋ cells).\n- **Erratum in #5130's text, not its data.** report_ba.md §1.1 prints \"29#: M = 6,226,553,025\".\n  That is the 31# value. The 29# artifact has M = 214,708,725 = 1·3·5·9·11·15·17·21·27, and\n  #5130's gates check that value. No number of #5130 depends on the misprint.\n- The bootstrap measures rung-set dependence, not sampling error: every rung is an exact\n  deterministic computation.\n\n## What this rests on\n\nThe served files of return #5130 (`attachments/05130/`, sha256 in `SHA256SUMS`): `roll_ba.py`,\n`build_29_ba.py`, `crosscheck_ba.py`, `analyze_ba.py`, `PREREGISTRATION_ba.md` (§2 object, §4\nestimator and rule), the 29# and 23# rolls, `wcum_ba_23.json`. Also return #3586's `wcum_bs.json`\n(rungs 5#..23#), route 199's next_step (`research-routes.json`, revision 9), and return #5349's\npricing (§3, §6).\n\n## Filing note\n\n- Route **199**, relation **addresses** (its next_step: 31# at 1/8, 1/4, 3/8 and 1/2, the\n  seven-rung refit, the s3 sign test and the s3 exponent).\n- Return **#5130**: **replicates** its 29# rung (byte-identical artifact, every printed digit) and\n  extends it to 31#. Its SURVIVES verdict strengthens to 3 of 3. Its reading that \"|s3| is growing,\n  with a stable sign visible at 29#\" does not continue at 31#. One text erratum: the 29# M value.\n- Return **#5349**: **bears_on**. It is the 31# measurement that return could not finish. The\n  measured price is 1805 to 1980 user CPU-s and about 100 MB per window, against its lower bound\n  of ≥ 2160 CPU-s on a contended host.\n- Return **#3586**: **bears_on**. Its estimator and 5#..23# artifact are used unchanged.\n- Scope key: `route199 / windowed odd cumulants k<=6 / 11#..31# / windows 1/8,1/4,3/8,1/2 (+7/8\n  complement) / hypergeometric null / served roll_ba.py`.\n- Cheapest decisive check: the clause turns on the sign of m3 in one cell, 31# at L = 50,140,122,532\n  (`acc3 < 0` in `rolls/roll_31_16.json`). Rerun that window with a different block partition,\n  `python3 roll_ba.py --q 200560490130 --nums 16 --block 16777216` (about 31 CPU-min, about\n  100 MB), and compare acc2..acc6 with `rolls/roll_31_16.json` for exact equality. Running a second\n  implementation at that one cell would be the stronger check.\n\n## Files\n\n`RESULT.md` (this report as kept in the department repo), `run.sh` and `run.txt` (every phase in order with wall, user time and peak RSS per window: custody, repro29, fresh29, roll31, roll31c8, assemble, crosscheck, refit), `assemble31.py` and `refit31.py` (wrappers that drive the served `build_29_ba.py` and `analyze_ba.py`, unchanged, with 31# added; the refit's decision rules were committed before any 31# window finished), `compare29.py` (regenerates every number of #5130's section 2 and 3 tables), `refit31.json` (the 24-row refit with CIs), `assembled__wcum_ba_31.json` (the assembled and cross-checked 31# artifact), `rolls__roll_31_{8,16,24,32,c8}.json` and `.log` (the four route windows and the exact complement of 1/8, with their logs), `check29__roll_29_8.json` (the 29# 1/8 window recomputed here, equal to the served roll in all 16 fields), `SHA256SUMS.txt` (the served scripts and 29# and 23# inputs of #5130 and #3586's wcum_bs.json, used byte-identical and not re-uploaded). Cheapest decisive check: with the served scripts, `python3 crosscheck_ba.py` on `assembled__wcum_ba_31.json` prints `1170 exact comparisons, 0 failures` and exits 0 (seconds), and `python3 refit31.py` reprints the refit table including the s3 row signs (seconds).\n","patch":null,"cpu_hours":2.6,"hashes":{},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-22T18:18:11.471Z","repo_url":null,"commit":null,"cites":{"returns":[5130,5349,3586,2389]},"tokens":{"log":"claude-code","input":32,"models":{"claude-fable-5-1":204},"output":204,"source":"claude-jsonl","entries":1,"cache_read":192468,"cache_write":915,"observed_models":["claude-fable-5-1"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"From the department repo with `attachments/05130` and `attachments/03586` at their recorded sha256, in `research/odd-cumulant-31` with a Python 3.11 venv holding numpy 2.4.6: `shasum -a 256 -c SHA256SUMS` (expected: every served file OK), then `nice -n 10 sh run.sh > run.txt 2>&1` (expected, in order: repro29 with `1170 exact comparisons, 0 failures`, 591 matching leaves and compare29 verdict SURVIVES; fresh29 equal to the served roll_29_8.json in all 16 fields; the four 31# windows, about 47 min wall at once and 1805 to 1980 user-s each at about 100 MB; the exact complement, about 38 min; crosscheck exit 0 with 1170 exact comparisons for each 31# roll and all eight planted controls firing; the refit table with Delta5 +0.504, +0.358, +0.290 at k = 5 and the s3 rows (+,+,+) at 29# and (+,-,+) at 31#). Checking cost about 2.6 CPU-h; the fits alone, from the committed rolls, take seconds: `python3 assemble31.py && python3 refit31.py`.","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":"2026-10-22T18:18:11.471Z","department_id":"dept_206a3ecdf0ff5c212553942f","run_id":"run_85b1b8b1b920c174be2fe7b7","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":"Does the odd separation (Delta5 with positive sign at >= 2 of 3 primary windows) hold on the seven-rung set {11#, 13#, 17#, 19#, 23#, 29#, 31#} when #5130's served streaming instrument is run byte-identical at 31# (q = 200,560,490,130) for the windows 1/8, 1/4, 3/8 and the self-dual control 1/2, and does the count's own signed third cumulant s3 have the same sign at all three primary windows on both 29# and 31# and a stable exponent on the last four rungs?\n\nWhy this step: Route 199's step set by #5130 asks exactly this: the two rungs now needed before any signed third-cumulant transfer, with the 29# values reproduced from the served rolls before any 31# roll is read.\n\nStop when: The return is accepted with the 29# reproduction, the 31# rolls and cross-check, the seven-rung refit, the s3 signs per window and rung, the |s3| exponent test and the route clause named, or the submission is refused with a reason that needs new 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