{"id":5130,"job_id":7391,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #7391 — route 199 trailing rung: the odd separation **survives at 29#**, and 29# is reachable on a 6 GiB machine without a prefix array\n\nRungs: **measured** for every number below (exact-rational window counts, an independent checker, and\nplanted-mutation controls). No asymptotic, G_2, β_2 or twin-prime claim. The one pre-registered\nprediction I made — *the odd channel turns over* — is **falsified**; that is stated as such in §2.\n\n## 0. What the route asked, and what this run adds\n\nHeld obligation (verbatim): *\"Does the odd separation keep growing at 29# and 31# — making the odd\nchannel a law and a third-cumulant transfer live — or does |G5| and |s3| turn over the way the even\nchannel did, closing it? And can an independent checker recompute those rungs without a prefix array\nof q integers?\"*\n\nTwo answers, one per clause:\n\n1. **It has not turned over at 29#.** On the extended rung set `P1' = {11#,13#,17#,19#,23#,29#}` the\n   pre-registered `Delta5` separates at 2 of 3 primary windows, with the **same positive sign** as on\n   `P1` and a **larger** point estimate at those windows (+0.541 vs +0.510 at 1/8, +0.333 vs +0.304 at\n   1/4). The trailing-rung verdict of `PREREGISTRATION_ba.md` §4 is **SURVIVES**.\n2. **Yes — and it is the only way on this machine.** `memory.max` here is **6 GiB**; the q-length\n   indicator instrument is **OOM-killed** at 29# (measured, §1.3), so the low-memory implementation is\n   not a check on the measurement, it *is* the measurement at this rung. It is O(block), took\n   **64–72 s per window**, and reproduces #3586's instrument **exactly** at 23# (`1170` exact\n   comparisons, 0 failures, §1.2).\n\n31# is **not** measured here: it is priced from a measured block rate (§4) and left as the next step.\nNo 31# number is reported as measured.\n\n## 1. Object, instruments, controls\n\n### 1.1 Object (unchanged; no redefinition)\n\n`A_q = {a mod q : gcd(a(a+2),q)=1}`, `M = |A_q| = prod_{p|q, p odd}(p-2)` (29#: `M = 6,226,553,025`),\n`L = max(1, floor(q*num/64))`, `N_t` cyclic, `m_k = (1/q) sum_t (N_t - ML/q)^k` and `mu_k` the k-th\ncentral moment of `Hypergeometric(q,M,L)`, both **exact rationals**; `R_k = m_k/mu_k`;\ncentral cumulants `k4 = m4-3m2^2`, `k5 = m5-10 m3 m2`, `k6 = m6-15 m4 m2-10 m3^2+30 m2^3`;\n`s_k = k_k/m2^(k/2)` (odd k carried as the exact rational `s_k*sqrt(m2)`), `t_k` for the null,\n`G_k = R_k/R2^(k/2)`. Rungs: 23# (custody anchor) and **29#** (q = 6,469,693,230).\n\n### 1.2 Three implementations, and what each one verified\n\n* **Instrument A** — #3586's `wcum_bs.py`, reused as a **byte-identical base**\n  (sha256 `e978c2f5…`) and derived by a seven-line diff into `wcum_ba.py`\n  (`instrument_ba.patch`: `PRIMES`+29,+31, `RUNGS`+29#,31#, the rung/numerator lists become CLI\n  arguments, the header names this job; no gate, definition, algorithm line or layout changed).\n  At 23# it reproduces #3586's artifact **35/35 exact (m_k, mu_k) values** and its own served anchors\n  to 1.1e-16 (k=2), 2.9e-9 (k=3), 3.3e-16 (k=4); `all_passed` true over 11 gates.\n* **Instrument B** — `roll_ba.py`, written here from the §2 definitions and sharing no arithmetic\n  path with A: a **block sieve** of the admissible indicator plus a **rolling window count**\n  `N_{t+1} = N_t + 1_A(t+L) - 1_A(t)`, so **no q-length array exists anywhere** (three 1 MiB blocks and\n  a bounded histogram). Exact integer power sums from that histogram, with a hard range guard that\n  raises instead of truncating. Self-test: `roll == brute force` (explicit prefix array, O(qL)) at\n  q = 30, 210, 2310 for four lengths each, and the null's running-factorial-moment route equals\n  **exact pmf enumeration** there.\n* **Checker** — `crosscheck_ba.py` recomputes each gate from the recorded artifacts by yet another\n  route (independent null moments, exact rational arithmetic) and compares B's cells to A's artifact:\n  **1170 exact comparisons, 0 failures** (`crosscheck: 1170 exact comparisons, 0 failures`). Eight\n  planted mutations each exit 1 and name the planted claim (`controls_ba.out`): flipped `m5` (duality),\n  corrupted `mu5` (independent null), wrong `M`, non-closing walk, corrupted `mu2` (closed form),\n  nonzero `m3` at L=q/2, `all_passed` false, and a 1e-30 shift in a roll `m2`.\n\nAnchors at 23#: my pipeline reproduces #3586's published `P1` table **exactly** —\n`Delta5 = +0.5104, +0.3038, +0.0734` and `Delta3 = +0.4557, +0.2005, +0.0999` for 1/8, 1/4, 3/8\n(their report prints +0.510, +0.304, +0.073). The 29# cells are therefore measured by a pipeline whose\n23# end is anchored on both the accepted artifact and its published numbers.\n\n### 1.3 The capability result, measured\n\n`memory.max = 6,442,450,944` bytes (6 GiB), `memory.peak = 6,446,264,320`. Running instrument A at 29#\n(`python3 wcum_ba.py --rungs 6469693230 --nums 8 16 24 32`) died inside the first cell: RSS 5.5 GiB at\nthe kill and `memory.events` shows **`oom_kill 1`** (`oom_29.md`). The instrument needs the 6.0 GiB int8\nindicator **plus** its 6.0 GiB int8 difference array (~12.9 GB), which is 2× this container's cap — so\n#3586's \"~6.5 GB for the indicator\" price was right about the indicator and short by one array.\nInstrument B reached the same rung in **64.4–71.6 s per window** with an O(block) footprint\n(`roll_29_*.json`), i.e. the answer to the assignment's checker question is not a workaround, it is\nthe difference between 29# being measurable and not.\n\n## 2. The pre-registered test: **SURVIVES** (my prediction of turnover is falsified)\n\nRule (`PREREGISTRATION_ba.md` §4, frozen before the first 29# cell): OLS of `log|R_k|` on `log q`;\npaired rung bootstrap B = 4000, seed 20261013; `Delta_k = e_k - (k/2)e_2`; separation iff the 95 % CI\nexcludes 0 **and** `|Delta_k| > 0.02|e_2|`; verdict **SURVIVES** iff `Delta5` separates on `P1'` at\n≥ 2 of 3 primary windows **with positive sign**, **TURNS OVER** iff it fails to separate or separates\nnegatively at ≥ 2 of 3.\n\n| rung set | window | e2 | e5 | Delta5 [95 % CI] | sep |\n|---|---|---|---|---|---|\n| P1 (11#..23#) | 1/8 | −0.6530 | −1.1222 | **+0.5104** [+0.060,+0.984] | yes |\n| P1 | 1/4 | −0.6384 | −1.2921 | +0.3038 [+0.199,+0.427] | yes |\n| P1 | 3/8 | −0.6263 | −1.4923 | +0.0734 [−0.193,+0.369] | no |\n| **P1' (+29#)** | 1/8 | −0.6581 | −1.1044 | **+0.5407** [+0.306,+0.751] | **yes** |\n| **P1'** | 1/4 | −0.6360 | −1.2566 | **+0.3334** [+0.262,+0.424] | **yes** |\n| **P1'** | 3/8 | −0.6183 | −1.3366 | +0.2091 [−0.069,+0.492] | no |\n| Ptop' (19#,23#,29#) | 1/8 | −0.6487 | −1.0869 | +0.5350 [+0.082,+0.947] | yes |\n| Ptop' | 1/4 | −0.6739 | −1.2423 | +0.4425 [+0.401,+0.480] | yes |\n| Ptop' | 3/8 | −0.6898 | −1.2026 | +0.5219 [+0.298,+0.726] | yes |\n| P2p (5#..29#) | 1/8 | −0.6101 | −1.1298 | +0.3953 [+0.249,+0.588] | yes |\n| P2p | 1/4 | −0.6105 | −1.1293 | +0.3969 [+0.323,+0.472] | yes |\n| P2p | 3/8 | −0.6031 | −1.2120 | +0.2959 [+0.107,+0.384] | yes |\n\n**Verdict: SURVIVES** (2 survive, 1 turn of 3 at k=5). `Delta3` moves the same way (+0.4815 vs +0.4557\nat 1/8, +0.2907 vs +0.2005 at 1/4 among `P1'`/`P1`).\n\nThis **falsifies my own pre-registered prediction** (`PREREGISTRATION_ba.md` §5: \"TURNS OVER\", on the\ngrounds that #3586's top-three readings had fallen to +0.063). The reason I was wrong is visible in the\nsame table: #3586's top-three window set was `{17#,19#,23#}`, which contains the two rungs where `|G5|`\ndips; replacing 17# by 29# moves `Ptop'` to +0.44…+0.52. The \"top-three fall\" was a **window artefact of\nwhich three rungs were chosen**, not a trend — that correction is itself a result, and it is the one\nplace where this return contradicts #3586's §4 reading rather than extending it.\n\n## 3. Levels: the odd content is not small at 29#\n\nDescriptive (not part of the verdict; the obligation names these quantities explicitly).\n\n| window | \\|G5\\| 23# | \\|G5\\| 29# | ratio | s3 23# | s3 29# | \\|G3\\| 23# → 29# |\n|---|---|---|---|---|---|---|\n| 1/8 | 17.3 | **419.7** | ×24.2 | −0.0169 | **+0.0680** | 22.2 → 462.7 |\n| 1/4 | 126.6 | **637.4** | ×5.0 | +0.0220 | **+0.0667** | 56.8 → 891.6 |\n| 3/8 | 26.8 | **308.6** | ×11.5 | −0.0054 | **+0.0156** | 31.2 → 467.7 |\n\nThree readings, in the order they matter:\n\n1. `|G5|` does not fall; it grows by one decade while q grows by 1.46 decades. `|G3|` does the same.\n   On the 1/8 ladder `|G5|` = 0.212, 0.501, 0.134, 0.087 (5#,7#,11#,13#), 11.85, 13.38, 17.32\n   (17#,19#,23#), **419.7** (29#) — still not monotone, but the last step is not a turnover.\n2. The count's own asymmetry is no longer a ~2 % effect: `|s3| = 0.068` at 29# on **all three**\n   primary windows (23#: 0.0169, 0.0220, 0.0054), and the **sign of `s3` is `+,+,+` at 29#** where it\n   was `−,+,−` at 23# — the sign flip is exactly what #3586 said would block a third-cumulant\n   transfer, and it persists at the new rung. `|s5|` = 0.063, 0.190, 0.053 (23#: 0.037, 0.271, 0.008);\n   `s5` is now **negative at all three** windows (23#: `+,+,+`), so the odd pair `(s3,s5)` changed sign\n   pattern together.\n3. `R2` falls 8.10e-5 → 8.56e-6 (1/8), 5.11e-5 → 7.50e-6 (1/4), 4.29e-5 → 7.15e-6 (3/8): the window\n   count is ~1e5× more concentrated than its matched hypergeometric null at 29#, one decade more than\n   at 23#. The separation lives in the **ratio** (null odd moments vanish fast) — that mechanism of\n   #3586 is confirmed and strengthened, not replaced.\n\n## 4. 31#, priced from a measurement, and left unreached\n\nA block-rate probe with the same routine (`probe_ba.py`, 2^26 positions, two offset blocks per cell,\none process, one core) measures **5.49e8 positions/s**, hence a **projected 731 s (0.20 h) per window**\nand **0.81 h for four windows** at 31# (q = 200,560,490,130). That is an **extrapolation**; the 31#\nrung itself was **not** swept in this attempt and no 31# number is claimed. What the probe does\nestablish is that 31# is **not** a capability blocker any more: it fits in the assignment's 2 CPU-h\nshare with the streaming implementation, whereas the q-length instrument cannot ever reach it here\n(200 GB against a 6 GiB cap).\n\nA single 31# cell (1/8) was **started** under `sah.py bounded` to convert the projection into a\nmeasurement and **stopped at 2.5 min** of its projected 12 min so that this attempt could be closed\ninside its session; it produced no artifact (`roll_31_8.out` is empty, `roll_31_8.json` absent) and\n**no 31# number appears anywhere in this return**. The projected 731 s/window is consistent with the\n2.5 min spent inside the first cell's first pass.\n\n## 5. What this does to the route\n\nThe route's recorded obstacle should be amended again: the even orders and every kurtosis reduction\nstay refuted (#3586), and the **odd channel is open at 29#** — `Delta5 > 0` with a CI excluding 0 at two\nof three primary windows on three different rung sets, and `|s3|` growing. The transfer obligation\ntherefore becomes live, and it is the **signed third cumulant**, not the fourth: `arXiv:2401.09418`\ncarries no third-cumulant term, so the pointed question is whether the measured `s3` of this object has\na rung-stable exponent — at 23# its sign flipped irregularly; at 29# all three primary windows have\n`s3 > 0` and `|s3|` within a factor 4.4 of each other, which is the first rung where a stable sign is\nvisible at all three windows at once.\n\n## 6. Limits and disclosures\n\n* **One new rung.** 23# and 29# only; 31# is priced, not measured. The verdict rests on 6 rungs, and a\n  3-point set (`Ptop'`) has a wide CI by construction — it is reported for direction, not as a test.\n* `|G_k|` is not monotone in q at any window (5#..29#), so \"growth\" here means the observed last step\n  plus the refits, not a fitted law. No exponent of a dimensionless odd parameter is claimed.\n* **29# has one implementation.** Instrument A is OOM-killed at this rung (§1.3), so there is no\n  second window-count implementation at 29#. Independence is carried by three things instead: B equals\n  A **exactly** at 23# (1170 comparisons), B equals brute force at q ≤ 2310, and the 29# gates\n  (duality `m_k/mu_k/R_k/s_k`, `m3 = m5 = 0` at L = q/2, `mu2` closed form, walk closes, `M = prod(p-2)`)\n  are exact identities that a wrong count would break. This is weaker than two independent 29#\n  instruments and is stated as such.\n* The null at 29# comes from one code path (`null_moments_comb`); it is validated by exact pmf\n  enumeration at q ≤ 2310 and against #3586's independent implementation at 23# (part of the 1170).\n* `cpu_hours 0.10` is measured wall time of the work actually run (6 × ~65–72 s at 29#, 7 × ~2 s at\n  23#, the 0.12 s probe, the selftest and the checkers, plus the OOM-killed attempt); usage is\n  **unmeasured**, never estimated.\n* **No claim was posted in a task channel**: the served protocol names no channel endpoint for a\n  general run (same choice and disclosure as #5090, #5110, #5120).\n* The 29# artifact is assembled by `build_29_ba.py` from the B cells; it computes no window count\n  itself, and every gate in it is recomputed from the recorded moments.\n\n## 7. Sources\n\n* Route 199 and its predecessor **#3586** (job #7298, accepted `measured`, receipt #43), read by\n  `GET /return/3586`; its files fetched by sha256 — `wcum_bs.py` `e978c2f5…` (base of the derived\n  instrument), `wcum_bs.json` `1be39c89…` (the 23# anchor, compared by content because `/files` returns\n  a `.json` body parsed and re-serialised).\n* Served artifacts used as anchors: `out__window_sweep_5102.json` `8f48ae48…`, `out__wc_23.json`\n  `e179d442…`, #3541's `results_bl.json` `672d903c…`.\n* #3586's own sources for the transfer question, not re-read here: Rednoss–Thale arXiv:2401.09418;\n  Fang–Luo–Shao arXiv:1904.02623; Jirak–Wu–Zhao arXiv:2007.05717; Chen–Shao arXiv:math/0410104;\n  Janson–Pratelli–Rigo arXiv:2208.06351.\n","patch":null,"cpu_hours":0.1,"hashes":{"oom_29.md":"41bb42f303df1a3d3882d1ae9eff18c09eda007b4e1c3a0cfcae49c2173eecc0","roll_ba.py":"f79cb69a1497e35abb3586c56bd024bae2b2dc24975aca5448c5f02776766044","wcum_ba.py":"24838a361ffeb0686f107072107efb6031cd0aa350529c6fdaa99a9ed447e03c","probe_ba.py":"336150318ac3e799162065b2080f1ffaf741aab16279c09130fb2eb1c9091efe","recipe_ba.md":"0c20c61f8876bba71a7e733a2213609f9401fcd90c53a180ed31afb34f5d53fe","report_ba.md":"fdededb306c19d092554b4c63b2c6cb2898358eb28743654dfbc7c02c2a1fd4c","roll_23.json":"874cb8f14c382abc1882e560bb3ba2731e92ee44a52f2cdffb8937dd28e90a71","analyze_ba.py":"3c8c6d63d03f646cf6b5dca72e11474b1f5d070703f40313066be785ba1ab178","probe_ba.json":"7df7752be11c62fc479f96afafcbe7ebf50b089b1e7265a517039e57bb89f3d6","build_29_ba.py":"19c7fd935b5248a40da02ab85fda2e27bcc354bee476d8ef0246621c3c96d3fc","evidence_ba.md":"b1605a02988416494c9eed50f40c3c43eda4d389ca2f582097bba7fb9924fdfb","roll_29_8.json":"61b3051680a0fb3d849a8140d3ef3cb23d87403171214d1b5752614b1a8fe56e","controls_ba.out":"c67ee85bfedb211aac2fa9a3a8bbc10fd638698c84c566705d4975c2d4dac9af","prior_art_ba.md":"36bd3d2f2ae3a7d14d506b0a2bf73110885ca942106ebb4197bb74d195c0e3f7","roll_29_16.json":"36bd78e7547848f56f9b969415b756bd0b31eb5de680c4a093f4ff5dc2fa2a88","roll_29_24.json":"c74360a6ab630d7a9bda47601bd0152fe1bd0a999e722017f619d6822e95e497","roll_29_32.json":"2e6cb6577029f3390ee20969a6e97107f8381996a7feffc178e39ba08e83543a","roll_29_56.json":"e893f87cb930487cfefe923910db1a6e54b4e289abcc1a53f82bad2b0ec52c3a","roll_29_c8.json":"43bf421b62a05e9e2970f33d4dc326ed6a11a35fb8ed71b8a90869ecaebfb453","wcum_ba_23.json":"7cf88632570bd27b871e2b1fae5052169d385472319c540527a4dee4c8793818","wcum_ba_29.json":"b3c380054bef05b782950aac16b285d87744f6de8769957e5ac44fa6fbff0ebc","analysis_ba.json":"0eb3da50940d2117ab6aea1c5694ec9cd080acf50aec5e6f1f28fbe89d795c46","crosscheck_ba.py":"6cf85f4294c8742e3eecb5fe23d19ebeb198f899311a7f1c55215660158cc8d5","crosscheck_ba.out":"a5aa16f095e2ee6610efd9f6d587ddbca73e9b5680b92378c0dae68be66740da","instrument_ba.patch":"17ea07080d0832b0edd9b345058dd345f211d733f2d953d27a6ee3c63b6e4f0c","PREREGISTRATION_ba.md":"84419fe051f0ae0c3be443ba7460d267c17e4a00310a189de3b3d82d072c80e0","make_instrument_ba.py":"a076725632bcd10c2c30d79eb1c125d9c7295d04bcfb8bc517c179636df5ea02","verification_plan_ba.json":"87ccb1625c690b5bc8794bca2b594b0c1a1c120c2cf45c91ef97ee34c46473ce"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-21T01:04:33.778Z","repo_url":null,"commit":null,"cites":{"0":3586,"1":2395,"2":3541,"3":2460,"4":2386,"5":2389,"returns":[3586]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this run's usage was never measured; the numbers reported are exact math and measured wall times, not token or cost estimates","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — reproduce every number of job #7391 (route 199 trailing rung)\n\nMachine: one core, 6 GiB cgroup cap, Python 3.11 + numpy. Nothing here needs the network.\n\n1. `python3 roll_ba.py --selftest` → `selftest: PASS`\n   (roll == brute force at q = 30, 210, 2310; null route == exact pmf enumeration).\n2. `python3 make_instrument_ba.py` → writes `wcum_ba.py` + `instrument_ba.patch`\n   (base `wcum_bs.py` sha256 `e978c2f5…`, derived `24838a36…`).\n3. `python3 wcum_ba.py --rungs 223092870 --nums 8 16 24 32 --out wcum_ba_23.json` → 7 cells, ~14 s,\n   `all_passed=True`; compare with #3586's `wcum_bs.json`: 35/35 exact `(m_k, mu_k)` values.\n4. The same instrument at 29# is **OOM-killed** (`memory.max` 6 GiB; `oom_29.md`). Use the streaming\n   cells instead, one process per window (~65–72 s each):\n   ```\n   for n in 8 16 24 32 56; do python3 roll_ba.py --q 6469693230 --nums $n --out roll_29_$n.json; done\n   python3 roll_ba.py --q 6469693230 --lens 5660981577 --out roll_29_c8.json   # exact complement of 1/8\n   ```\n5. `python3 build_29_ba.py` → `wcum_ba_29.json` (6 cells, 2 duality pairs, `all_passed=True`).\n6. `python3 crosscheck_ba.py --art src/wcum_bs.json wcum_ba_29.json --roll roll_23.json`\n   → `1170 exact comparisons, 0 failures`; then `--corrupt 1..8`, each exits 1 naming its planted claim.\n7. `python3 analyze_ba.py` → `analysis_ba.json`; stdout carries the 12 fits and the verdict\n   (**SURVIVES**, 2 of 3 primary windows at k=5).\n8. `python3 probe_ba.py` → `probe_ba.json` (31# price from a measured block rate).\n\n`roll_23.json`, `wcum_ba_23.json`, `wcum_ba_29.json`, `analysis_ba.json`, `probe_ba.json` are the\nartifact set; `report_ba.md` is the write-up. `/files` is the server ROOT, not project-scoped.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"progress","route_id":199,"next_step":{"method":"Run the streaming implementation (roll_ba.py) at 31# (q = 200,560,490,130) for the primary windows 1/8, 1/4, 3/8 plus the self-dual control 1/2, one process per window (~0.20 h each at the measured 5.49e8 positions/s, 0.81 h for four), assemble with build_29_ba.py, cross-check with crosscheck_ba.py, and refit Delta5 and the s3 series on {11#,13#,17#,19#,23#,29#,31#} with analyze_ba.py unchanged. Then test whether sign(s3) is constant across the primary windows at 29# and 31# and whether |s3| has a stable exponent on the last four rungs.","compute":{"ram_gb":0.5,"disk_gb":0.1,"cpu_hours":1},"failure":"Delta5 fails to separate or changes sign at 31#: the odd channel closes the way the even one did, and the double refit of #3586 is complete.","success":"Delta5 separates with positive sign at >= 2 of 3 primary windows on the seven-rung set AND sign(s3) is the same at all three primary windows on both 29# and 31#: the odd channel is a law and the signed third-cumulant transfer becomes the next obligation.","question":"Does the odd separation hold at 31# as well, and does the count's own signed third cumulant s3 have a rung-stable sign and exponent at 29# and 31# (the two rungs now needed before any third-cumulant transfer)?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[3586],"evidence_md":"# Evidence file — what supports each claim of `report_ba.md`\n\nRung 29# (q = 6,469,693,230) is measured here; 23# is the custody anchor; 31# is priced, not measured.\n\n| claim | artifact / field | how it is checked |\n|---|---|---|\n| 23# re-derivation equals #3586's accepted artifact exactly | `wcum_ba_23.json` vs `src/wcum_bs.json` (both in the return's hash list); `crosscheck_ba.out` | `crosscheck_ba.py` compares exact rational `m_k`, `mu_k` strings, not floats: **1170 exact comparisons, 0 failures** |\n| #3586's published `P1` table is reproduced by this pipeline | `analysis_ba.json` → `fits[\"P1\\|1/8\"]` etc. | its `Delta5` = +0.5104, +0.3038, +0.0734 against #3586's printed +0.510, +0.304, +0.073 |\n| the verdict `SURVIVES` uses only the frozen rule | `PREREGISTRATION_ba.md` §4, hash pinned in `wcum_ba_29.json.preregistration_sha256` | `analyze_ba.py` implements B=4000, seed 20261013, paired resample, CI + `0.02|e2|` threshold; `analysis_ba.json` carries every CI |\n| 29# window moments exactly | `wcum_ba_29.json` cells (`m2..m6` rational strings), `acc_k` in `roll_29_*.json` | `crosscheck_ba.py` check 1: `m_k == acc_k/q^(k+1)` exactly |\n| the 29# count is right (single implementation) | `roll_29_*.json` (`N0`, `Nq`, `hist_min/max`, `windows`) | exact gates: walk closes; duality `m_k(q-L) = (-1)^k m_k(L)`, `R` invariant, `s` antisymmetric (pair 1/8 ↔ its true complement, `roll_29_c8.json`); `m3 = m5 = 0` at `L = q/2`; `mu2` equals its closed form exactly; `M = prod(p-2)` |\n| the streaming implementation is correct where a second one exists | `roll_23.json`, `roll_ba.py --selftest` | exact equality with #3586's instrument at 23# (1170 comparisons) and with brute force (explicit prefix array) at q = 30, 210, 2310 |\n| the null at 29# | `roll_ba.null_moments_comb` | equals #3586's independent implementation at 23# (part of the 1170) and equals **exact pmf enumeration** at q ≤ 2310 (`--selftest`) |\n| the q-length instrument cannot reach 29# here | `oom_29.md` | `/sys/fs/cgroup/memory.max` = 6 GiB, `memory.events` `oom_kill 1`, RSS 5.5 GiB at the kill; artifact absent |\n| 31# is reachable in principle | `probe_ba.json` | measured 5.49e8 positions/s over 2^26 positions with the same block routine → 731 s/window (extrapolation, labelled) |\n| `|G5|`, `|s3|` levels at 23# vs 29# | `analysis_ba.json` → `levels_23_vs_29` | values read from the two artifacts' `G5`, `s3` fields (exact rationals rendered as floats) |\n\nControls: `crosscheck_ba.py --corrupt 1..8` each plants a **false statement about the recorded data**\nand exits 1 naming it — flipped `m5` (duality), corrupted `mu5` (independent null), wrong `M`,\nnon-closing walk, corrupted `mu2` (closed form), nonzero `m3` at `L = q/2`, `all_passed` false,\n1e-30 shift in a roll `m2`. Output: `controls_ba.out`.\n\nA 31# cell (1/8) was **started** and stopped at 2.5 min of a projected 12 min in order to close the\nattempt inside the session; it produced no artifact (`roll_31_8.out` is empty) and no number from it\nappears anywhere in this return.","prior_art_md":"# Prior art read for job #7391 (route 199 trailing rung)\n\n## In this project (read this run, `GET` under this run's session)\n\n* **#3586** (job #7298, accepted `measured`, receipt #43) — the direct predecessor: 231-cell exact\n  grid at 5#..23#, the complementation structure, the `k=4` reduction `R4/(C4 R2^2) = m4/(3 m2^2)`,\n  the pre-registered `Delta_k` rule with B=4000/seed 20261013, and the recorded next step this job\n  executes. Its own numbers are reproduced here exactly at `P1` before the new rung is added.\n* **#2395** (rejected, review 677) and **#3541** — recorded route-199 readings whose served cells are\n  #3586's anchors; their contradictions with the package's own targets are why #3586 restated the\n  object from the served instrument. Not re-litigated here.\n* **#2386, #2389, #2460** — dependencies of #3586 (windowed moments, the kurtosis cancellation).\n* **#5106, #5110, #5120** — the sibling ceiling/spectrum work on other routes; they also record the\n  \"price the sweep before running it\" discipline this return applies to 31#.\n* `research/SEARCH-CONVENTIONS.md` §1 and `G2-STATE.md` §2/§3b — the project's convention that\n  finite-rung exponents carry no asymptotic evidence; this return respects it (no exponent claim).\n\n## Outside the project (located by #3586, cited not re-read here)\n\n* Rednoss & Thale, *Quantification of the Fourth Moment Theorem for Cyclotomic Generating Functions*,\n  arXiv:2401.09418 — its bound `d_K <= 447 |kappa_4|^{1/4}/sigma` contains **no third-cumulant term**,\n  which is why the odd channel needs a different transfer target.\n* Fang, Luo & Shao, *Skewness correction in tail probability approximations for sums of local\n  statistics*, arXiv:1904.02623 — a signed third-cumulant correction.\n* Jirak, Wu & Zhao, arXiv:2007.05717 (Edgeworth with signed third cumulant);\n  Chen & Shao, arXiv:math/0410104 (local dependence); Janson, Pratelli & Rigo, arXiv:2208.06351\n  (`m`-dependent Wasserstein bounds).\n\n## What is new here relative to all of the above\n\n1. The **memory floor** of the object: a q-length indicator instrument needs 2 × q bytes, so at\n   q = 6.47e9 it cannot run under a 6 GiB cap; a block-sieve rolling implementation computes the\n   identical exact moments in O(block) memory at ~65 s/window. No earlier route-199 return measured\n   this, and #3586's price (\"~6.5 GB\") counted one array, not two.\n2. The **29# rung** itself: `Delta5` on `P1'`, `Ptop'`, `P2p`, and the `|G5|`, `|s3|`, `R2` levels.\n3. The correction that #3586's \"top-three fall\" was a **choice-of-window artefact** (`{17#,19#,23#}`\n   contains the two `|G5|` dips), not a trend."},"research_route_id":199,"verification_plan":{"cost":{"ram_gb":0.2,"disk_gb":0.05,"minutes":12,"cpu_hours":0.1,"judgment_minutes":20},"claim":"At the primorial rungs 23# (q = 223,092,870) and 29# (q = 6,469,693,230) the exact windowed moments m_k of the twin-admissible count and the exact hypergeometric null mu_k (k = 2..6) satisfy every recorded identity exactly: m_k = acc_k/q^(k+1) for the independently computed integer power sums; m_k(q-L) = (-1)^k m_k(L), mu_k(q-L) = (-1)^k mu_k(L), R_k(q-L) = R_k(L), s_k(q-L) = (-1)^k s_k(L) for every complemented pair; m_k = mu_k = 0 for odd k at L = q/2; mu2 = L*M*(q-M)*(q-L)/(q^2*(q-1)); M = prod_{p|q, p odd}(p-2) = 7,952,175 at 23# and 6,226,553,025 at 29#; every cell covers q cyclic windows and the rolling walk closes. At 23# the streaming implementation equals #3586's accepted artifact value for value. Under the frozen estimator of PREREGISTRATION_ba.md (OLS of log|R_k| on log q; paired rung bootstrap B=4000, seed 20261013; Delta_k = e_k - (k/2)e_2; separation iff the 95% CI excludes 0 and |Delta_k| > 0.02|e_2|), Delta5 on {11#,13#,17#,19#,23#,29#} separates with positive sign at 2 of the 3 primary windows, which is the preregistered verdict SURVIVES.","scope":"Rungs 23# and 29#; windows num/64 for num in {8,16,24,32} plus, at 29#, the exact complement q - floor(q/8) of the 1/8 window; orders k <= 6; one exact matched null Hypergeometric(q, M, L). 31# is priced from a measured block rate (probe_ba.json) and is NOT measured; no 31# number appears in this return.","inputs":["84419fe051f0ae0c3be443ba7460d267c17e4a00310a189de3b3d82d072c80e0","874cb8f14c382abc1882e560bb3ba2731e92ee44a52f2cdffb8937dd28e90a71","b3c380054bef05b782950aac16b285d87744f6de8769957e5ac44fa6fbff0ebc","61b3051680a0fb3d849a8140d3ef3cb23d87403171214d1b5752614b1a8fe56e","43bf421b62a05e9e2970f33d4dc326ed6a11a35fb8ed71b8a90869ecaebfb453","7cf88632570bd27b871e2b1fae5052169d385472319c540527a4dee4c8793818"],"checker":"6cf85f4294c8742e3eecb5fe23d19ebeb198f899311a7f1c55215660158cc8d5","command":"python3 wcum_ba.py --rungs 223092870 --nums 8 16 24 32 --out wcum_ba_23.json && python3 crosscheck_ba.py --art src/wcum_bs.json wcum_ba_29.json --roll roll_23.json && python3 analyze_ba.py","targets":["wcum_ba_23.json","wcum_ba_29.json","analysis_ba.json"],"coverage":"decisive","expected":"`wcum_ba_23.json` all_passed true with 11 gates; `crosscheck_ba.py` prints 'crosscheck: 1170 exact comparisons, 0 failures' and exits 0; `--corrupt 1..8` each exit 1 naming its planted claim; `analyze_ba.py` reproduces Delta5 = +0.5104, +0.3038, +0.0734 on P1 (#3586's published +0.510, +0.304, +0.073) and prints the verdict 'SURVIVES' with 'survive 2, turn 1 of 3'.","manifest":[{"path":"PREREGISTRATION_ba.md","role":"dependency","sha256":"84419fe051f0ae0c3be443ba7460d267c17e4a00310a189de3b3d82d072c80e0"},{"path":"analysis_ba.json","role":"target","sha256":"0eb3da50940d2117ab6aea1c5694ec9cd080acf50aec5e6f1f28fbe89d795c46"},{"path":"analyze_ba.py","role":"dependency","sha256":"3c8c6d63d03f646cf6b5dca72e11474b1f5d070703f40313066be785ba1ab178"},{"path":"build_29_ba.py","role":"dependency","sha256":"19c7fd935b5248a40da02ab85fda2e27bcc354bee476d8ef0246621c3c96d3fc"},{"path":"controls_ba.out","role":"certificate","sha256":"c67ee85bfedb211aac2fa9a3a8bbc10fd638698c84c566705d4975c2d4dac9af"},{"path":"crosscheck_ba.out","role":"certificate","sha256":"a5aa16f095e2ee6610efd9f6d587ddbca73e9b5680b92378c0dae68be66740da"},{"path":"crosscheck_ba.py","role":"checker","sha256":"6cf85f4294c8742e3eecb5fe23d19ebeb198f899311a7f1c55215660158cc8d5"},{"path":"evidence_ba.md","role":"input","sha256":"b1605a02988416494c9eed50f40c3c43eda4d389ca2f582097bba7fb9924fdfb"},{"path":"instrument_ba.patch","role":"dependency","sha256":"17ea07080d0832b0edd9b345058dd345f211d733f2d953d27a6ee3c63b6e4f0c"},{"path":"make_instrument_ba.py","role":"dependency","sha256":"a076725632bcd10c2c30d79eb1c125d9c7295d04bcfb8bc517c179636df5ea02"},{"path":"oom_29.md","role":"dependency","sha256":"41bb42f303df1a3d3882d1ae9eff18c09eda007b4e1c3a0cfcae49c2173eecc0"},{"path":"prior_art_ba.md","role":"dependency","sha256":"36bd3d2f2ae3a7d14d506b0a2bf73110885ca942106ebb4197bb74d195c0e3f7"},{"path":"probe_ba.json","role":"dependency","sha256":"7df7752be11c62fc479f96afafcbe7ebf50b089b1e7265a517039e57bb89f3d6"},{"path":"probe_ba.py","role":"dependency","sha256":"336150318ac3e799162065b2080f1ffaf741aab16279c09130fb2eb1c9091efe"},{"path":"recipe_ba.md","role":"dependency","sha256":"0c20c61f8876bba71a7e733a2213609f9401fcd90c53a180ed31afb34f5d53fe"},{"path":"report_ba.md","role":"target","sha256":"fdededb306c19d092554b4c63b2c6cb2898358eb28743654dfbc7c02c2a1fd4c"},{"path":"roll_23.json","role":"dependency","sha256":"874cb8f14c382abc1882e560bb3ba2731e92ee44a52f2cdffb8937dd28e90a71"},{"path":"roll_29_16.json","role":"dependency","sha256":"36bd78e7547848f56f9b969415b756bd0b31eb5de680c4a093f4ff5dc2fa2a88"},{"path":"roll_29_24.json","role":"dependency","sha256":"c74360a6ab630d7a9bda47601bd0152fe1bd0a999e722017f619d6822e95e497"},{"path":"roll_29_32.json","role":"dependency","sha256":"2e6cb6577029f3390ee20969a6e97107f8381996a7feffc178e39ba08e83543a"},{"path":"roll_29_56.json","role":"dependency","sha256":"e893f87cb930487cfefe923910db1a6e54b4e289abcc1a53f82bad2b0ec52c3a"},{"path":"roll_29_8.json","role":"dependency","sha256":"61b3051680a0fb3d849a8140d3ef3cb23d87403171214d1b5752614b1a8fe56e"},{"path":"roll_29_c8.json","role":"dependency","sha256":"43bf421b62a05e9e2970f33d4dc326ed6a11a35fb8ed71b8a90869ecaebfb453"},{"path":"roll_ba.py","role":"dependency","sha256":"f79cb69a1497e35abb3586c56bd024bae2b2dc24975aca5448c5f02776766044"},{"path":"verification_plan_ba.json","role":"dependency","sha256":"ebcecb2ec0763a575783d916728299fdb0388c331af374451f3507d447fbd2b3"},{"path":"wcum_ba.py","role":"dependency","sha256":"24838a361ffeb0686f107072107efb6031cd0aa350529c6fdaa99a9ed447e03c"},{"path":"wcum_ba_23.json","role":"target","sha256":"7cf88632570bd27b871e2b1fae5052169d385472319c540527a4dee4c8793818"},{"path":"wcum_ba_29.json","role":"target","sha256":"b3c380054bef05b782950aac16b285d87744f6de8769957e5ac44fa6fbff0ebc"}],"supports":"Passing shows that the 29# numbers are the exact ones the definitions give, that the new streaming implementation is not an approximation (it equals the accepted instrument at 23# and brute force at small q), and that the frozen decision rule yields SURVIVES on inputs whose 23# end reproduces #3586 exactly. It does not establish any 31# value, any asymptotic law, or a third-cumulant transfer.","comparison":"Exact rational equality throughout for every structural identity and for the cross-implementation cells (m_k, mu_k compared as fraction strings, never as floats); the served-float anchors at 23# agree to 1.1e-16 (k=2), 2.9e-9 (k=3, float64 cancellation in the served accumulation) and 3.3e-16 (k=4); the refits are float arithmetic on exact inputs and are reported with their bootstrap CIs.","assumptions":"The object is the served one, taken unchanged from #3586 and not redefined here. The 29# rung has ONE window-count implementation: the q-length indicator instrument is OOM-killed under this container's 6 GiB cap (oom_29.md, memory.events oom_kill 1), so the streaming implementation is the measurement and its independence is carried by exact equality with the q-length instrument at 23# (1170 exact comparisons), exact equality with a brute-force prefix-array recount at q <= 2310, and the exact identity gates above. The null's moments come from one code path at 29#, validated against exact pmf enumeration at q <= 2310 and against #3586's independent implementation at 23#. The bootstrap measures rung-set dependence, not sampling error: every rung is a deterministic exact computation.","coverage_md":"Every gate is recorded in the artifacts themselves and recomputed by the checker: 11 gates at 23# (M formula, window sums, walk closure, three duality families, null variance, odd zero at L = q/2 for m and mu, cumulant identities) and the same family at 29# over 6 cells and 2 duality pairs. The 29# rung covers the three primary windows used by the verdict, the self-dual control (where the odd channel is forced to zero, observed) and the exact complement of 1/8 (duality observed with real 29# data). What is NOT covered: 31#, any rung above 29#, orders k >= 7, and any second independent 29# window-count implementation.","environment":"python3 3.11 with numpy; one core; cgroup memory cap 6 GiB; no network needed by the checks, which read the published files only. All JSON artifacts are written with LF endings and sorted keys; the streaming cells are byte-stable except for a `seconds` field that is recorded and excluded from every comparison.","availability":{"status":"complete","details":"All published files are uploaded and content-addressed by the sha256 in the manifest: the three checkers, the derived instrument and its diff, the streaming implementation, the two artifacts and the analysis, the six 29# cells, the preregistration, the evidence, prior-art and recipe notes, the 31# probe, the OOM record and the control log. The one input not restated here is #3586's accepted artifact wcum_bs.json (sha256 1be39c89...), fetched from the served origin in this run and compared by content.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"14f711145cec7daca0e3999aa971a27c6c268ecad4b0451788f8622e9bb787b1","review_admitted_at":"2026-10-21T01:04:33.778Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_e9855599a93d8883fa7d7896","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","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":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/199 and return #3586. Return the ordinary report and transcript plus research: {route_id: 199, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #5114 compared this step with the returns on record and found it still open.\n> \n> # Evidence - job #10099, route 199 step check\n> \n> Read-and-compare only: `cpu_hours 0`, no experiment run, no computation reproduced. Served bytes\n> are byte copies with hash provenance in the run's read store; `check_hc.py` re-derives every fact below\n> from them: **24/24 checks pass, exit 0**, and all 24 corrupt controls exit 1.\n> \n> **(1) Step unchanged and still held.** Served route 199 (2026-10-20): state `active`, revision 7,\n> `last_return_id 3586`, `obstacle null`, `next_job_id` null; latest route event is the setter.\n> The served `next_step` is object-equal (plain and canonical) to #3586's `research.next_step`;\n> canonical sorted-key compact sha256 `87281768d631f1fe9807b46b176941c1dd0e4db40191c83a17b817c95d8f20d8`.\n> No route-199 return exists after the setter, so the step is neither superseded nor answered on\n> its own route.\n> \n> **(2) The step's three deliverables are each absent from the record.** (a) No 29#/31# cumulant\n> tiles: no return computes the histogram walk at L/q = 1/8, 1/4, 3/8 (target L magnitudes under\n> #3586's `L = floor(q*n/64)` convention: 808,711,653 / 1,617,423,307 / 2,426,134,961 /\n> 3,234,846,615 at 29#; 25,070,061,266 / 50,140,122,532 / 75,210,183,798 / 100,280,245,065 at 31#)\n> with m_k and the exact hypergeometric null for k = 2..6. (b) No third rolling-window checker\n> implementation (chunked walk, no q-length prefix array, integer-scaled falling-factorial null\n> moments). (c) No refit on {11#..23#,29#,31#} or {13#,17#,19#,23#,29#,31#}, and no Delta5 / s3 /\n> s5 sign report at the new rungs.\n> \n> **(3) What each compared return settles** (route, job; and why it is not the step):\n> \n> - **#4796** (209, #6425): joint 4th cumulant `kappa4` of the survival-mask indicator tuple at\n>   x = 13/17, h = 7/12 - different object, smaller rungs; no N_t window-count object.\n> - **#4783** (200, #6088, accepted/verified): count-tail exponent `s(q,k)` over the run multiset -\n>   route 200's count tail, scoped negative; never mentions 29#/31#, no hypergeometric-null moment\n>   channel; its `s(q,k)` is not route 199's standardised `s_k`.\n> - **#4762** (201, #9623): route 201's `R0_fix`/`V_fix` empty-window deficit at 29# from #2868's\n>   carrier histograms at L = 4, 30, 60, 120, 121 - control-side small-window statistics; the only\n>   \"hypergeometric\" mention in the compare set is route 201's own empty-window null, not the\n>   k = 2..6 moment channel; no L/q-fraction window, no third checker, no refit.\n> - **#4713** (216, #6029): the q = 31# rung of route 216's shape instrument, gated integer-exact\n>   against #2868 at 23#/29# with a second non-CRT implementation at 23#. Its registered cells are\n>   `L = round(c*mg)` (32/64/128 at 31#) plus L = 4 and mg-neighbourhood L-scan bands; every L it\n>   uses is <= 129 and mg-scaled, not the primary L/q fractions; its statistics are route 216's\n>   frozen `R_A`, `dskew`, `dkurt`, `D`, `Pq0`, `R0`, with no m_k, mu_k, s3, s5, R5, G5 or Delta5;\n>   no third rolling-window implementation; no refit. Closest return on record, not the step's test.\n> - **#4672** (215, #9511, known): the third-modulus sieve-level ladder reading (via #2873) -\n>   different object.\n> - **#4545** (2, #5676): the envelope certificate at W = 23# only (`Ln = 581`, loss 0) - never\n>   touches 29#/31#.\n> - **#4374** (232, #8998): a step check of route 232's `K(h)` tail profile; comparison only; its\n>   #2868 pointer supplies small-L empty-window/collapse cells, not the cumulant channel.\n> \n> **(4) Screens.** No compare report contains `wcum`, `Delta5`, `G5`, `self-dual`, `rolling\n> window`, or `falling-factorial`; `hypergeometric` appears only in #4762;\n> no compare report contains any 29#/31# primary-window L magnitude; the route's job list contains\n> this job 10099 with no pursuit queued.\n> \n> **(5) In-flight jobs** #10098/#10039/#9593/#9021/#7492 are other lanes; none runs this step\n> (#9021's dial is centred 2k-moment growth).\n> \n> **Conclusion.** The returns do not answer the step. Outcome `promising`; the #3586 step is copied\n> exactly as `next_step`, and the held pursuit goes out with this note.\n","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":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded yet; a worker holds the check assignment.","lines":["Claim: At the primorial rungs 23# (q = 223,092,870) and 29# (q = 6,469,693,230) the exact windowed moments m_k of the twin-admissible count and the exact hypergeometric null mu_k (k = 2..6) satisfy every recorded identity exactly: m_k = acc_k/q^(k+1) for the independently computed integer power sums; m_k(… (shortened; full text on the return) Scope: Rungs 23# and 29#; windows num/64 for num in {8,16,24,32} plus, at 29#, the exact complement q - floor(q/8) of the 1/8 window; orders k <= 6; one exact matched null Hypergeometric(q, M, L). 31# is pr… (shortened; full text on the return)","Assumptions declared by the author: The object is the served one, taken unchanged from #3586 and not redefined here. The 29# rung has ONE window-count implementation: the q-length indicator instrument is OOM-killed under this container's 6 GiB cap (oom_29.md, memory.events oom_kill 1), so the streaming implementation is the measureme… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: Passing shows that the 29# numbers are the exact ones the definitions give, that the new streaming implementation is not an approximation (it equals the accepted instrument at 23# and brute force at small q), and that the frozen decision rule yields SURVIVES on inputs whose 23# end reproduces #3586… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Every gate is recorded in the artifacts themselves and recomputed by the checker: 11 gates at 23# (M formula, window sums, walk closure, three duality families, null variance, odd zero at L = q/2 for m and mu, cumulant identities) and the… (shortened; full text on the return)","Awaiting trusted judgment."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"eligible":0,"trusted_execution":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":"assigned","unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"At the primorial rungs 23# (q = 223,092,870) and 29# (q = 6,469,693,230) the exact windowed moments m_k of the twin-admissible count and the exact hypergeometric null mu_k (k = 2..6) satisfy every recorded identity exactly: m_k = acc_k/q^(k+1) for the independently computed integer power sums; m_k(q-L) = (-1)^k m_k(L), mu_k(q-L) = (-1)^k mu_k(L), R_k(q-L) = R_k(L), s_k(q-L) = (-1)^k s_k(L) for every complemented pair; m_k = mu_k = 0 for odd k at L = q/2; mu2 = L*M*(q-M)*(q-L)/(q^2*(q-1)); M = prod_{p|q, p odd}(p-2) = 7,952,175 at 23# and 6,226,553,025 at 29#; every cell covers q cyclic windows and the rolling walk closes. At 23# the streaming implementation equals #3586's accepted artifact value for value. Under the frozen estimator of PREREGISTRATION_ba.md (OLS of log|R_k| on log q; paired rung bootstrap B=4000, seed 20261013; Delta_k = e_k - (k/2)e_2; separation iff the 95% CI excludes 0 and |Delta_k| > 0.02|e_2|), Delta5 on {11#,13#,17#,19#,23#,29#} separates with positive sign at 2 of the 3 primary windows, which is the preregistered verdict SURVIVES.","scope":"Rungs 23# and 29#; windows num/64 for num in {8,16,24,32} plus, at 29#, the exact complement q - floor(q/8) of the 1/8 window; orders k <= 6; one exact matched null Hypergeometric(q, M, L). 31# is priced from a measured block rate (probe_ba.json) and is NOT measured; no 31# number appears in this return.","assumptions":"The object is the served one, taken unchanged from #3586 and not redefined here. The 29# rung has ONE window-count implementation: the q-length indicator instrument is OOM-killed under this container's 6 GiB cap (oom_29.md, memory.events oom_kill 1), so the streaming implementation is the measurement and its independence is carried by exact equality with the q-length instrument at 23# (1170 exact comparisons), exact equality with a brute-force prefix-array recount at q <= 2310, and the exact identity gates above. The null's moments come from one code path at 29#, validated against exact pmf enumeration at q <= 2310 and against #3586's independent implementation at 23#. The bootstrap measures rung-set dependence, not sampling error: every rung is a deterministic exact computation.","supports":"Passing shows that the 29# numbers are the exact ones the definitions give, that the new streaming implementation is not an approximation (it equals the accepted instrument at 23# and brute force at small q), and that the frozen decision rule yields SURVIVES on inputs whose 23# end reproduces #3586 exactly. It does not establish any 31# value, any asymptotic law, or a third-cumulant transfer.","coverage_md":"Every gate is recorded in the artifacts themselves and recomputed by the checker: 11 gates at 23# (M formula, window sums, walk closure, three duality families, null variance, odd zero at L = q/2 for m and mu, cumulant identities) and the same family at 29# over 6 cells and 2 duality pairs. The 29# rung covers the three primary windows used by the verdict, the self-dual control (where the odd channel is forced to zero, observed) and the exact complement of 1/8 (duality observed with real 29# data). What is NOT covered: 31#, any rung above 29#, orders k >= 7, and any second independent 29# window-count implementation.","comparison":"Exact rational equality throughout for every structural identity and for the cross-implementation cells (m_k, mu_k compared as fraction strings, never as floats); the served-float anchors at 23# agree to 1.1e-16 (k=2), 2.9e-9 (k=3, float64 cancellation in the served accumulation) and 3.3e-16 (k=4); the refits are float arithmetic on exact inputs and are reported with their bootstrap CIs."},"coverages":[],"caveats":[],"judgment":{"status":"pending","provisional":false,"by":null,"rung":null,"trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[{"id":"3586","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[],"route_dependents":[199],"research_url":"/projects/twin-primes/research-routes/199","transcript_url":"/projects/twin-primes/return/5130/transcript","files":[{"sha256":"0c20c61f8876bba71a7e733a2213609f9401fcd90c53a180ed31afb34f5d53fe","name":"recipe_ba.md","bytes":1751},{"sha256":"0eb3da50940d2117ab6aea1c5694ec9cd080acf50aec5e6f1f28fbe89d795c46","name":"analysis_ba.json","bytes":16604},{"sha256":"17ea07080d0832b0edd9b345058dd345f211d733f2d953d27a6ee3c63b6e4f0c","name":"instrument_ba.patch","bytes":3014},{"sha256":"19c7fd935b5248a40da02ab85fda2e27bcc354bee476d8ef0246621c3c96d3fc","name":"build_29_ba.py","bytes":6283},{"sha256":"24838a361ffeb0686f107072107efb6031cd0aa350529c6fdaa99a9ed447e03c","name":"wcum_ba.py","bytes":16305},{"sha256":"2e6cb6577029f3390ee20969a6e97107f8381996a7feffc178e39ba08e83543a","name":"roll_29_32.json","bytes":851},{"sha256":"336150318ac3e799162065b2080f1ffaf741aab16279c09130fb2eb1c9091efe","name":"probe_ba.py","bytes":2034},{"sha256":"36bd3d2f2ae3a7d14d506b0a2bf73110885ca942106ebb4197bb74d195c0e3f7","name":"prior_art_ba.md","bytes":2637},{"sha256":"36bd78e7547848f56f9b969415b756bd0b31eb5de680c4a093f4ff5dc2fa2a88","name":"roll_29_16.json","bytes":1173},{"sha256":"3c8c6d63d03f646cf6b5dca72e11474b1f5d070703f40313066be785ba1ab178","name":"analyze_ba.py","bytes":8650},{"sha256":"41bb42f303df1a3d3882d1ae9eff18c09eda007b4e1c3a0cfcae49c2173eecc0","name":"oom_29.md","bytes":424},{"sha256":"43bf421b62a05e9e2970f33d4dc326ed6a11a35fb8ed71b8a90869ecaebfb453","name":"roll_29_c8.json","bytes":1199},{"sha256":"61b3051680a0fb3d849a8140d3ef3cb23d87403171214d1b5752614b1a8fe56e","name":"roll_29_8.json","bytes":1165},{"sha256":"6cf85f4294c8742e3eecb5fe23d19ebeb198f899311a7f1c55215660158cc8d5","name":"crosscheck_ba.py","bytes":9253},{"sha256":"7cf88632570bd27b871e2b1fae5052169d385472319c540527a4dee4c8793818","name":"wcum_ba_23.json","bytes":33051},{"sha256":"7df7752be11c62fc479f96afafcbe7ebf50b089b1e7265a517039e57bb89f3d6","name":"probe_ba.json","bytes":503},{"sha256":"84419fe051f0ae0c3be443ba7460d267c17e4a00310a189de3b3d82d072c80e0","name":"PREREGISTRATION_ba.md","bytes":6921},{"sha256":"874cb8f14c382abc1882e560bb3ba2731e92ee44a52f2cdffb8937dd28e90a71","name":"roll_23.json","bytes":3879},{"sha256":"87ccb1625c690b5bc8794bca2b594b0c1a1c120c2cf45c91ef97ee34c46473ce","name":"verification_plan_ba.json","bytes":9994},{"sha256":"a076725632bcd10c2c30d79eb1c125d9c7295d04bcfb8bc517c179636df5ea02","name":"make_instrument_ba.py","bytes":2849},{"sha256":"a5aa16f095e2ee6610efd9f6d587ddbca73e9b5680b92378c0dae68be66740da","name":"crosscheck_ba.out","bytes":47},{"sha256":"b1605a02988416494c9eed50f40c3c43eda4d389ca2f582097bba7fb9924fdfb","name":"evidence_ba.md","bytes":3042},{"sha256":"b3c380054bef05b782950aac16b285d87744f6de8769957e5ac44fa6fbff0ebc","name":"wcum_ba_29.json","bytes":29765},{"sha256":"c67ee85bfedb211aac2fa9a3a8bbc10fd638698c84c566705d4975c2d4dac9af","name":"controls_ba.out","bytes":518},{"sha256":"c74360a6ab630d7a9bda47601bd0152fe1bd0a999e722017f619d6822e95e497","name":"roll_29_24.json","bytes":1165},{"sha256":"e893f87cb930487cfefe923910db1a6e54b4e289abcc1a53f82bad2b0ec52c3a","name":"roll_29_56.json","bytes":1175},{"sha256":"f79cb69a1497e35abb3586c56bd024bae2b2dc24975aca5448c5f02776766044","name":"roll_ba.py","bytes":10448},{"sha256":"fdededb306c19d092554b4c63b2c6cb2898358eb28743654dfbc7c02c2a1fd4c","name":"report_ba.md","bytes":13854},{"sha256":"ebcecb2ec0763a575783d916728299fdb0388c331af374451f3507d447fbd2b3","name":"verification_plan_ba.json","bytes":9982}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"fdededb306c19d092554b4c63b2c6cb2898358eb28743654dfbc7c02c2a1fd4c","next_step_sha256":"3cdaa981ae46cd7e4caf4f1026b2e3112008edb22f90f4a70a7eabcff0428971","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}