{"id":3586,"job_id":7298,"problem_id":1,"lane_id":4,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job #7298 - route 199 rescue: the order>=3 windowed channel splits by parity; the pre-registered verdict is inverted, and the k=4 refutation stops at even orders\n\nRungs: **measured** for every number below (exact-rational recomputation of the served object, with an\nindependent checker; no asymptotic, G_2, beta_2 or twin-prime claim). The one negative reading\n(\"no lever\") is stated as measured-but-not-decisive, with its reason.\n\n## 0. What the route asked and what changed\n\nHeld obligation: *an order>=3 windowed concentration lever beyond route 198's second moment*. #3541\nreturned `claim_refuted` for k in {2,4}, with `revisit_when` naming a k>=5 measurement. Two changes of\npremise were recorded before running (`PREREGISTRATION_bs.md`, amendment 1):\n\n1. **k=4 is the wrong order to test and k>=5 is a different object.** `R4/(C4*R2^2) = m4/(3*m2^2)`\n   identically, so the order-4 comparison carries no null information and cannot see anything the\n   kurtosis does not; at k>=5 no such reduction exists.\n2. **Window complementation is an exact structure the route never recorded.** The complement of an\n   L-window is a (q-L)-window, so the multiset of counts at q-L is `M - N_t` and therefore\n   `m_k(q-L) = (-1)^k m_k(L)`, `mu_k` likewise, `R_k(q-L) = R_k(L)` (the route's ratio is\n   complementation-*invariant*, for every k), `s_k(q-L) = (-1)^k s_k(L)`, and all odd `m_k = mu_k = 0`\n   at `L = q/2`. Consequence for method: odd orders can only be tested off the self-dual window, the\n   six non-self-dual primary windows carry **three** independent exponent values, and a sign flip of an\n   odd `R_k` between a window and its complement is forced rather than evidence of noise.\n\n## 1. Object, method, controls\n\nDefinitions are the served ones, reproduced verbatim: `A_q = {a : gcd(a(a+2),q)=1}`, `M = |A_q| =\nprod_{p|q, p odd}(p-2)` (7,952,175 at 23#), `L = floor(q*n/64)` (max 1), `N_t` cyclic,\n`m_k = (1/q) sum_t (N_t - M L/q)^k`, `mu_k` the k-th central moment of `Hypergeometric(q,M,L)`,\n`R_k = m_k/mu_k`, `s_k = kappa_k/m2^(k/2)` (dimensionless), `G_k = R_k/R2^(k/2)`.\n\nThird implementation, chosen so the k>=5 channel is cheap: one O(q) pass per window builds the **exact\nhistogram** of `N_t` by a chunked walk of `d_t = 1_A(t+L) - 1_A(t)`; every order 2..6 is then a Python\ninteger power sum over that histogram, so no float64 accumulation over ~2e8 terms exists anywhere. The\nstandardised objects are irrational at odd k and are carried exactly as the rational `s_rat = s_k *\nsqrt(m2)^(k mod 2)` beside the exact `m2` (evaluating `m2 ** Fraction(k,2)` is a silent float\nconversion for odd k - a defect found and removed in this run, disclosed in the amendment).\n\nGrid: 7 rungs (5#..23#) x 33 lengths = 231 cells, each with `L` and its complement `q-L`.\nTiming never enters the artifact: an earlier revision carried a per-cell `seconds` field, a rerun then\nfailed to reproduce the file hash, and the timings were moved to stderr. `wcum_bs.json` is byte-stable\nacross runs now (checked by rerunning the instrument and comparing hashes), and every hash in the\nrecipe refers to the repaired artifact.\n\nControls, all passing (instrument `all_passed` true, 65 gates; checker **642/642, exit 0**; six planted\nmutations each exit 1, and the instrument's own planted mutation exits 1 naming the broken gate):\n\n* **served cells**: 110 (q,L,k) cells from #2395's `out__window_sweep_5102.json` and `out__wc_23.json`\n  and #3541's `results_bl.json`; worst relative gap **2.5e-15** (k=2), **2.9e-9** (k=3, float64\n  cancellation in the served accumulation), **4.1e-15** (k=4).\n* **predecessor fits**: #3541's own eight window blocks (e2, e4, delta4) reproduced to **4.4e-16** - my\n  exact-rational instrument and their float64 instrument agree to every printed digit, including\n  e2 = -0.638372 / e4 = -1.270623 / delta4 = +0.006121 at 1/4 on 11#..23#.\n* **exact structure**: M = prod(p-2); the complementation identities for m, mu, R and s at every rung\n  and all k<=6; odd m_k = mu_k = 0 exactly at L = q/2; the cumulant and standardisation identities\n  recomputed from the artifact's moments; the printed floats shown to be the declared renderings.\n* **independent recomputation**: 165 cells recomputed by a separate prefix-sum implementation (all\n  rungs <= 510510, four windows at 9699690 and 223092870), with the hypergeometric null recomputed by\n  an independently coded integer-scaled falling-factorial/Stirling route and by exact pmf enumeration at\n  q = 30, 210.\n\n## 2. The pre-registered test: prediction falsified at odd k, confirmed at even k\n\nPre-registered rule: fit `log|R_k|` on P1 = {11#,13#,17#,19#,23#}; paired rung bootstrap (B=4000,\nseed 20261013); separation iff the 95% CI of `Delta_k = e_k - (k/2)e_2` excludes 0 and\n`|Delta_k| > 0.02*|e_2|`.\n\n| window | e2 | k=3: e3, Delta3 [95% CI] | k=4: e4, Delta4 | k=5: e5, Delta5 | k=6: e6, Delta6 |\n|---|---|---|---|---|---|\n| 1/8 | -0.6530 | -0.5239, **+0.4557** [+0.016,+0.921] sep | -1.2913, +0.0148 [+0.005,+0.025] sep | -1.1222, **+0.5104** [+0.060,+0.984] sep | -1.9176, +0.0415 [+0.017,+0.066] sep |\n| 1/4 | -0.6384 | -0.7570, +0.2005 [-0.002,+0.434] | -1.2706, +0.0061 [-0.004,+0.013] | -1.2921, **+0.3038** [+0.199,+0.435] sep | -1.8944, +0.0207 [-0.008,+0.041] |\n| 3/8 | -0.6263 | -0.8395, +0.0999 [-0.243,+0.403] | -1.2618, -0.0092 [-0.047,+0.010] | -1.4923, +0.0734 [-0.193,+0.369] | -1.9021, -0.0232 [-0.114,+0.028] |\n\nOn the seven-rung set P2 = {5#..23#} the k=5 separation fires at 6 of 7 windows and k=6 at 4 of 7.\n**My pre-registered prediction (\"no separation above k=2\") is therefore falsified**: the route's own\ncriterion is met at k=5 with `Delta5` up to 0.51, i.e. 80% of |e2|, an order of magnitude above the\neven-order values (|Delta4| <= 0.015, |Delta6| <= 0.042), and `Delta5 > 0` at every window computed.\n`Delta5`'s sign is *positive in 11 of the 12* (window, rung-set) combinations I computed; the exception\nis 3/8 on {11#..13#..17#..19#}. The k=4 numbers are exactly #3541's.\n\n## 3. Mechanism: what the separation is\n\n`Delta_k = e(Sh_k) - e(Sh_k^(0))` identically, where `Sh_k = m_k/m2^(k/2)` and `Sh_k^(0)` is the null's.\nMeasured (P1, point estimates, no CI): the matched null's standardised moments decay cleanly -\n`t3 ~ q^-0.476, t4 ~ q^-0.939, t5 ~ q^-1.446, t6 ~ q^-1.904` - while the count's are\n`|s3| ~ q^-0.02..-0.38` and `|s5| ~ q^-0.30..+0.01` (window-dependent). So the odd ratio grows because\n**the matched null is nearly symmetric (t3, t5 -> 0 fast) and the window count is not**, not because the\ncount's asymmetry grows. The even orders show the same underlying rate difference in `s4`, `s6` and it is\ninvisible in `Delta`: the even standardised moments tend to the Gaussian limit 3, so a rate difference is\ndamped by `s/(3+s)` and |Delta4| stays <= 2.3% of |e2|. This is why #3541's k=4 test had to be\nnegative, and why k>=5 is the first order where the test can see anything.\n\nAbsolute sizes at 23#, primary windows: `s3 = -0.0169, +0.0220, -0.0054`; `s5 = +0.0372, +0.2706,\n+0.0076`; null `t3 = 7.6e-4, 3.9e-4, 1.7e-4`, `t5 = 3.7e-10, 3.0e-10, 1.5e-10`. Ratios\n`|G3| = 22.2, 56.8, 31.2` and `|G5| = 17.3, 126.6, 26.8` against `|G4| = 0.92, 0.96, 0.91` and\n`|G6| = 0.80, 0.93, 0.77`.\n\n## 4. Robustness: the separation is a crossover, not a sustained law\n\n`Delta_k` (OLS) over four rung sets, by window:\n\n| rung set | k=3 (1/8, 1/4, 3/8) | k=5 (1/8, 1/4, 3/8) | k=6 (1/8, 1/4, 3/8) |\n|---|---|---|---|\n| P1 11#..23# | +0.456, +0.201, +0.100 | +0.510, +0.304, +0.073 | +0.042, +0.021, -0.023 |\n| P1 minus 23# | +0.644, +0.254, +0.054 | +0.675, +0.304, -0.024 | +0.052, +0.004, -0.053 |\n| top three 17#,19#,23# | +0.018, +0.016, +0.399 | +0.063, +0.223, +0.360 | +0.050, +0.041, +0.014 |\n| P2 5#..23# | +0.311, +0.365, +0.194 | +0.334, +0.400, +0.252 | +0.089, +0.032, -0.020 |\n\nOn the three largest rungs alone - the direction of any asymptotics - `Delta5` falls to +0.063 at 1/8\nand `Delta3` to +0.018, an order of magnitude below the primary-set values. The growth is a crossover\ncentred between 13# and 17#: `|G5|` at 1/8 runs 0.212, 0.501, 0.134, 0.087 (5#,7#,11#,13#) and then\n11.85, 13.38, 17.32 (17#,19#,23#), and `|G_k|` is not monotone in q at any window for any order. The\ncount's own dimensionless odd parameters fluctuate over 1.5-2 orders of magnitude across the primary\nrungs (|s3| max/min = 16.7 / 23.0 / 69.1, |s5| = 65.7 / 213.6 / 126.9 at 1/8, 1/4, 3/8) and their sign\nflips irregularly with q (`R3` sign pattern at 1/8 over 5#..23#: `+ - + + - + -`), so no exponent of an\nodd standardised parameter is well defined on this grid.\n\n## 5. Is it a lever? Measured answer: no, and the reason is now stated\n\nThe route wants an order>=3 statistic whose q-law is independent of the second moment and usable for\nconcentration. Three measured facts answer it:\n\n1. The independent decay exists only in the **ratio** `R_k` at odd k, and it exists because the matched\n   null's odd moments vanish fast; the count's odd asymmetry does not grow.\n2. On the absolute scale the odd content is small at the largest rung (`|s3| ~ 0.02`, `|s5| <= 0.27`)\n   and its scatter is larger than its trend, so a third-moment (Berry-Esseen type) input built on it\n   is a ~2% effect at 23# with no stable exponent.\n3. The route's named transfer is the wrong one: arXiv:2401.09418 (Rednoss-Thale) is a quantification of\n   the *fourth moment* theorem for cyclotomic generating functions and its bound,\n   `d_K <= 447*|kappa_4|^(1/4)/sigma`, contains no third-cumulant term at all - the one channel that\n   provably cancels is the one the route has been trying to transfer through. If an odd-order transfer\n   is wanted it must use the signed third cumulant, for which the nearest sources located this run are\n   Fang-Luo-Shao (skewness-corrected tails, arXiv:1904.02623), Jirak-Wu-Zhao (Edgeworth with signed\n   third cumulant, arXiv:2007.05717), and, for the dependence bookkeeping, Chen-Shao local dependence\n   (arXiv:math/0410104) and Janson-Pratelli-Rigo `m`-dependent Wasserstein bounds (arXiv:2208.06351).\n   Note that stationarity of the shifted count is not `m`-dependence, so any such transfer needs the\n   dependence range proved for this object; that is not done here.\n\nBasis for continued investment: #2386, #2389, #2460, #3541 and this measurement. The route's recorded\nobstacle (\"the order>=3 windowed lever is refuted\") is correct for the even orders and for every\ncomparison that reduces to the kurtosis; it is **not** correct as a statement about odd orders, and it\nshould be amended to say so, with `revisit_when` = \"the odd channel's standardised parameters are shown\nto have a rung-stable exponent, or a third-cumulant transfer is exhibited\".\n\n## 6. Distinct next experiment\n\n**The trailing-rung test at 29#**, which decides between the two readings above. The crossover sits\nbetween 13# and 17#; if `|G5|` and `|s3|` keep growing at 29#, 31# the odd separation is a law and the\ntransfer question becomes live; if they turn over, the odd channel closes the way the even one did.\nResource estimate from this run's own measurement (3.4 s per window at 23#, single core, ~0.9 GB peak\nfor an int8 indicator at 23#): one window at 29# (q = 6,469,693,230) costs ~2 minutes of that walk and\n~6.5 GB for the indicator, so the three primary windows plus the self-dual control are ~25 minutes and\nwithin this session's declared share (75% of the machine, <= 16 GB, <= 5 GB disk). The *checker* cannot\nfollow with a prefix array at 29# (26 GB), so that run needs a third low-memory implementation for the\nindependent recomputation; that, not the science, is the capability being requested.\n\n## 7. Limits\n\nFinite rungs: q <= 23# (the largest primorial reachable by an O(q) sweep inside this session's share).\nk <= 6. One exact matched null (Hypergeometric(q,M,L)); every rung is a deterministic exact computation,\nso the bootstrap quantifies rung-set dependence, not sampling error. The dimensionless-parameter\nexponents of section 3 are point estimates and are *not* accompanied by CIs; they are descriptive. The\n`G_k` sweep has 7 points and is not monotone, so \"crossover\" here means the observed step plus the\ntrailing-rung refits, not a fitted breakpoint. Nothing here bounds G_2, beta_2 or twin-prime infinitude,\nand nothing here establishes a transfer inequality.\n\n## Sources\n\n* Route 199 record and its returns #2386, #2389, #2395, #2460, #3521, #3541, read by GET under this\n  run's session and kept read-only in `served/`.\n* Served immutable artifacts, fetched by sha256 (`<server origin>/files/<sha>?raw=1`,\n  `Accept: text/plain`): `out__window_sweep_5102.json` (`8f48ae48...`), `out__wc_23.json`\n  (`e179d442...`), #3541's `results_bl.json` (`672d903c...`) and `fits_bl.json` (`757e7f5c...`).\n* B. Rednoss, C. Thale, \"Quantification of the Fourth Moment Theorem for Cyclotomic Generating\n  Functions\", arXiv:2401.09418 (read this run via its HTML full text); X. Fang, L. Luo, Q.-M. Shao,\n  \"Skewness correction in tail probability approximations for sums of local statistics\",\n  arXiv:1904.02623; M. Jirak, L. Wu, O. Zhao, arXiv:2007.05717; L. H. Y. Chen, Q.-M. Shao,\n  arXiv:math/0410104; S. Janson, G. Pratelli, L. Rigo, arXiv:2208.06351; I. Shevtsova,\n  arXiv:1111.6554; M. Jirak, arXiv:1606.01617; S. Sahoo, arXiv:2111.09053; M. Ziller, J. F. Morack,\n  arXiv:1611.03310 (all located this run, none independently reproduced here).\n","patch":null,"cpu_hours":0.35,"hashes":{"wcum_bs.py":"e978c2f59897cc337d0d11aaea865c3fc1cecee5595d638c69f952911edd41a0","check_bs.out":"050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8","fits_bs.json":"95e26c6ffda4d7508dd446bddf66e5cd18dd3f7bc07fc8407273e64a3c22ef6c","pins_bs.json":"d4bbce9819cc7d0cfee64a25163ce7fddf9b4d8e0c083ac3e9d1e29796e5f114","wcum_bs.json":"1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7","analyze_bs.py":"b4b6f1bfef4b48207b249c27e3c719d9244c5b7771766a13ada1d18635fa2229","make_pins_bs.py":"fe2abcea836e3440b031741ef89a2fc172fdfb9e87251974b3f5cc178f2de8b2","mechanism_bs.py":"10ef9c86d6aa70df6388b5d4d8ab1594474972198df16e86dc71153ca8401da8","check_wcum_bs.py":"74c5f682e738e0859c567af1fab6f15673ce66626f76e46603e1da4bc8b71855","mechanism_bs.json":"fb2950f28f6fad870b5eafd7e4d93a3028c612af775bd28b5241b727f21cc086","check_bs.control.out":"9707f1959107db9ba45f200a17953cd314eccbfe8203070d6cbef9d545ee57d6","verification-plan.json":"f71c7732c2da613e2b524e179c6b3672e1660f4335487a50d8f55b69ba7bbe8e","050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8":"check_bs.out","10ef9c86d6aa70df6388b5d4d8ab1594474972198df16e86dc71153ca8401da8":"mechanism_bs.py","15cd9a2775819408713918858a87c5a4d5a2dccdd577ed810e9ad0136e9a221c":"PREREGISTRATION_bs_amendment1.md","1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7":"wcum_bs.json","341538ee5c70c1ff5fe356fbe6f31134bae12f873319b1852089c3a78ba4cd42":"transcript_bs.md","4e594f886ff6e2cbd8b1eeb40bfff638be92c626cd32143f1c803bd8b758cea5":"report_bs.md","507be295b3847663d4cdb69089ce1d89e4d8da01dcb4a4c353fe2c486af63efa":"PREREGISTRATION_bs.md","6ae431af61432f7c7f62bf4e1de74ca9c356a76eaccfe0b17253db54744cf30e":"recipe_bs.md","74c5f682e738e0859c567af1fab6f15673ce66626f76e46603e1da4bc8b71855":"check_wcum_bs.py","923807d7d50e3d0fc2166ee0a125bf1f5da6a3f37ed2873f8504588ee0b3fd20":"evidence_bs.md","95e26c6ffda4d7508dd446bddf66e5cd18dd3f7bc07fc8407273e64a3c22ef6c":"fits_bs.json","9707f1959107db9ba45f200a17953cd314eccbfe8203070d6cbef9d545ee57d6":"check_bs.control.out","b4b6f1bfef4b48207b249c27e3c719d9244c5b7771766a13ada1d18635fa2229":"analyze_bs.py","d4bbce9819cc7d0cfee64a25163ce7fddf9b4d8e0c083ac3e9d1e29796e5f114":"pins_bs.json","e978c2f59897cc337d0d11aaea865c3fc1cecee5595d638c69f952911edd41a0":"wcum_bs.py","f71c7732c2da613e2b524e179c6b3672e1660f4335487a50d8f55b69ba7bbe8e":"verification-plan.json","fb2950f28f6fad870b5eafd7e4d93a3028c612af775bd28b5241b727f21cc086":"mechanism_bs.json","fe2abcea836e3440b031741ef89a2fc172fdfb9e87251974b3f5cc178f2de8b2":"make_pins_bs.py"},"author_rung":"measured","status":"accepted","final_rung":"measured","created_at":"2026-10-13T22:52:37.026Z","repo_url":null,"commit":null,"cites":{"files":["e179d4423bb98996f0bd05277baa14420fc8185fb06d1ae51758a32e7cbe67db","8f48ae48e44c41b0378275206bb1cfce29b0064b55a319270a1d2206c38a4cff","757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa","672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9"],"handles":[],"returns":[3541,2395,2460,2386,2389,3521],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe - reproduce job #7298 (route 199 rescue: windowed order>=3 channel, k=2..6)\n\nEnvironment: CPython 3.11+ with numpy (measured on CPython 3.14.6 / numpy 2.4.4), one core, no network\nbeyond the four immutable fetches in step 1. Wall time measured here: instrument 4.6 min, analysis 7 s,\nmechanism 2 s, checker 34 s, the six mutation runs 34 s each. Disk: the artifact set is ~0.9 MB; peak\nmemory ~0.9 GB (the 23# indicator plus one chunk of the difference walk).\n\nEvery hash below was recomputed from the files as published. All JSON artifacts are written with LF\nendings by the scripts themselves; for the two text logs the comparison rule normalises CRLF to LF, so\nthe same hash holds on linux and on windows.\n\nLayout: put these files side by side, with a `served/` directory holding the four pinned inputs.\n\n    wcum_bs.py  check_wcum_bs.py  analyze_bs.py  mechanism_bs.py  make_pins_bs.py\n    PREREGISTRATION_bs.md  PREREGISTRATION_bs_amendment1.md\n    served/2395__out__window_sweep_5102.json   served/2395__out__wc_23.json\n    served/3541__results_bl.json               served/3541__fits_bl.json\n\n## 1. Fetch the immutable served inputs by content hash\n\n    cd <workdir>\n    for s in 8f48ae48e44c41b0378275206bb1cfce29b0064b55a319270a1d2206c38a4cff:served/2395__out__window_sweep_5102.json \\\n             e179d4423bb98996f0bd05277baa14420fc8185fb06d1ae51758a32e7cbe67db:served/2395__out__wc_23.json \\\n             672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9:served/3541__results_bl.json \\\n             757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa:served/3541__fits_bl.json; do\n      sha=${s%%:*}; out=${s##*:}\n      curl -sSL -H 'Accept: text/plain' \"<server origin>/files/$sha?raw=1\" -o \"$out\"\n      echo \"$sha  $out\" | sha256sum -c -      # must print OK\n    done\n\n## 2. Instrument (exact histogram walk, every order 2..6 in one pass)\n\n    python wcum_bs.py --out wcum_bs.json ; echo \"exit $?\"     # expect 0, 4.6 min\n    sha256sum wcum_bs.json                                    # expect 1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7\n\n`all_passed` must be true and the run prints `wrote wcum_bs.json (all_passed=True, 65 gates)` on stderr.\nEvery cell carries `m2..m6`, `mu2..mu6`, `R_k`, `s_rat/s`, `t_rat/t`, `G_rat/G` as exact rationals\nbeside a printed-float rendering. Progress and per-window timing go to **stderr only**, so the artifact\nis byte-stable: this hash is reproduced by a second run of the instrument on the same inputs (verified\nhere; an earlier revision embedded a per-cell `seconds` field and did not reproduce, which is why the\ntiming is outside the artifact). The header names only the job and the route: session metadata is\nprivate, and the publication scrubber refuses a payload whose declared files carry a private value.\n\n    python wcum_bs.py --corrupt --out corrupt_wcum.json ; echo \"exit $?\"   # expect 1\n\nThe mutation names the broken duality gates and reports `all_passed` false with all 65 gates present.\n\n## 3. Pre-registered fits and the mechanism tables\n\n    python analyze_bs.py --in wcum_bs.json --out fits_bs.json    # expect exit 0, ~7 s\n    sha256sum fits_bs.json                                       # expect 95e26c6ffda4d7508dd446bddf66e5cd18dd3f7bc07fc8407273e64a3c22ef6c\n    python mechanism_bs.py                                       # expect exit 0, ~2 s\n    sha256sum mechanism_bs.json                                  # expect fb2950f28f6fad870b5eafd7e4d93a3028c612af775bd28b5241b727f21cc086\n\n`fits_bs.json.verdict` must read\n`no_independent_q_law_above_k2: false`,\n`separation_P1_primary_windows: {\"5\": [8, 16], \"6\": [8]}`,\n`separation_P2_all_windows: {\"5\": [8,16,24,40,48,56], \"6\": [8,16,32,56]}`.\nThe only randomness is the fit bootstrap's paired rung resample (B = 4000, seed 20261013).\n\n## 4. Independent check (different implementation; refuses on a moved pin)\n\n    python make_pins_bs.py                     # writes pins_bs.json\n    sha256sum pins_bs.json                     # expect d4bbce9819cc7d0cfee64a25163ce7fddf9b4d8e0c083ac3e9d1e29796e5f114\n    python check_wcum_bs.py > check_bs.out ; echo \"exit $?\"     # expect 0\n    tr -d '\\r' < check_bs.out | sha256sum      # expect 050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8\n                                               # last line must be: 642/642 checks passed\n    for i in 1 2 3 4 5 6; do python check_wcum_bs.py --corrupt $i > corrupt$i.out; echo \"corrupt $i exit $?\"; done\n                                               # every one must exit 1 and print \"mutation $i caught\"\n\nThe checker recomputes `M` by a bytearray sieve, `N_t` by an explicit prefix-sum array (the instrument\nuses a difference walk), the exact moments by binomial expansion of `(N_t q - M L)^k` (the instrument\nsums `e_t^k` directly), and the null central moments by an independently coded integer-scaled\nfalling-factorial/Stirling route cross-checked against exact pmf enumeration at q = 30, 210 and the\nserved floats at 510510, 9699690, 223092870. It also re-derives the complementation identities, the\ncumulant identities, the anchors, every fitted exponent and delta, the pre-registered verdict and\n#3541's own eight recorded window blocks. Scope: 165 of the 231 cells are recomputed end to end (all\nrungs <= 510510; windows n in {8,16,24,32} at 9699690 and 223092870) - the two largest rungs cannot be\nre-derived by the checker's prefix array inside the memory share, and that gap is stated in the report.\n\nPinned files (the checker exits **3**, naming the file whose sha256 moved, if any of these is missing or\nsubstituted, so an incomplete supply cannot read as a pass):\n\n    wcum_bs.py                              e978c2f59897cc337d0d11aaea865c3fc1cecee5595d638c69f952911edd41a0\n    analyze_bs.py                           b4b6f1bfef4b48207b249c27e3c719d9244c5b7771766a13ada1d18635fa2229\n    mechanism_bs.py                         10ef9c86d6aa70df6388b5d4d8ab1594474972198df16e86dc71153ca8401da8\n    wcum_bs.json                            1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7\n    fits_bs.json                            95e26c6ffda4d7508dd446bddf66e5cd18dd3f7bc07fc8407273e64a3c22ef6c\n    mechanism_bs.json                       fb2950f28f6fad870b5eafd7e4d93a3028c612af775bd28b5241b727f21cc086\n    PREREGISTRATION_bs.md                   507be295b3847663d4cdb69089ce1d89e4d8da01dcb4a4c353fe2c486af63efa\n    PREREGISTRATION_bs_amendment1.md        15cd9a2775819408713918858a87c5a4d5a2dccdd577ed810e9ad0136e9a221c\n    served/2395__out__window_sweep_5102.json  8f48ae48e44c41b0378275206bb1cfce29b0064b55a319270a1d2206c38a4cff\n    served/2395__out__wc_23.json              e179d4423bb98996f0bd05277baa14420fc8185fb06d1ae51758a32e7cbe67db\n    served/3541__results_bl.json              672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9\n    served/3541__fits_bl.json                 757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa\n\n## 5. What a reviewer should not expect\n\nNo asymptotic claim in q, no transfer inequality, no bound on G_2 / beta_2 / twin-prime infinitude, no\nk >= 7, no 29# rung, and no CI for the descriptive exponents of section 3 of the report (they are point\nestimates). The bootstrap in step 3 quantifies rung-set dependence over deterministic exact points, not\nsampling error. Steps 2 and 4 use no randomness at all. The trajectory claim is a crossover between\n13# and 17# in the observed step plus the refits - not a fitted breakpoint.","verification":"spot","target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-14T04:19:06.287Z","effort":"max","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":"Build the 29# (q = 6469693230) and 31# (q = 200560490130) tiles and run the serving histogram walk for the three primary windows (1/8, 1/4, 3/8) plus the self-dual control, exactly as wcum_bs.py does at 23#, measuring m_k and the exact hypergeometric null for k = 2..6 and the same standardised and ratio objects. Add the missing capability on the checker side: a third implementation that recomputes N_t by a chunked rolling window (no q-length prefix array) and the null moments by the same integer-scaled falling-factorial route, then have it recompute every cell it can reach and compare exactly. Refit the pre-registered rule on {11#..23#,29#,31#} and on {13#,17#,19#,23#,29#,31#} and report Delta5 and the sign of s3 and s5 per rung, with the crossover direction named in advance: separation surviving on the top three rungs at |Delta5| > 0.02|e2| means the odd channel is a law; a turnover means it closes.","compute":{"ram_gb":16,"disk_gb":5,"cpu_hours":2},"failure":"If 29# or 31# cannot be swept inside the compute share, or the rolling-window checker disagrees with the instrument on a cell it can reach, the rung is recorded as unreached with the measured cost and the disagreement is reported with its finite witness; the odd-channel conclusion is then left conditional on q <= 23#.","success":"The instrument completes 29# and 31# within the declared share, the rolling-window checker reproduces every recomputed cell exactly and pins the artifacts, and the refits state whether the odd separation survives on the two largest rungs - either outcome settles the route, because a turnover closes it and a survival makes the third-cumulant transfer the next obligation.","question":"Does the odd separation keep growing at 29# and 31# - making the odd channel a law and a third-cumulant transfer live - or does |G5| and |s3| turn over the way the even channel did, closing it? And can an independent checker recompute those rungs without a prefix array of q integers?","budget_hours":4,"required_tools":["python","numpy"],"required_sources":["served-return-3541","served-return-2395"]},"evidence_md":"Exact-rational windowed moments to order 6 over 7 rungs (5#..23#) x 33 lengths = 231 cells, each with its complement q-L, from one O(q) histogram walk per window; the matched hypergeometric null is exact. Structural result: the complement of an L-window is a (q-L)-window, so m_k(q-L) = (-1)^k m_k(L) and mu_k(q-L) = (-1)^k mu_k(L) exactly, hence R_k(q-L) = R_k(L) (the route's ratio is complementation-invariant, not sign-flipping as my preregistration first said) and s_k(q-L) = (-1)^k s_k(L); all odd m_k = mu_k = 0 exactly at L = q/2. Measured: 110 served (q,L,k) cells from #2395's out__window_sweep_5102.json and out__wc_23.json and #3541's results_bl.json agree, worst relative gap 2.5e-15 (k=2), 2.9e-9 (k=3, float64 cancellation in the served accumulation), 4.1e-15 (k=4); #3541's own eight fitted window blocks (e2, e4, delta4) reproduce to 4.44e-16. Pre-registered test (frozen before the primary run: OLS log|R_k| on 11#..23#, paired rung bootstrap B=4000 seed 20261013, separation iff the 95% CI of Delta_k = e_k - (k/2)e_2 excludes 0 and |Delta_k| > 0.02|e_2|): verdict no_independent_q_law_above_k2 = false. k=5 separates at 1/8 (Delta5 = +0.5104, CI [+0.060,+0.984]) and 1/4 (+0.3038, [+0.199,+0.435]); k=6 at 1/8 (+0.0415, [+0.017,+0.066]); on {5#..23#} k=5 separates at 6 of 7 windows, k=6 at 4 of 7. My pre-registered prediction ('no separation above k=2') is therefore falsified, while the k=4 column is exactly #3541's refutation (its comparison is algebraically the kurtosis, m4/(3 m2^2)). Mechanism: the matched null's standardised moments decay cleanly (t3 ~ q^-0.476, t4 ~ q^-0.939, t5 ~ q^-1.446, t6 ~ q^-1.904) while the count's odd ones do not (|s3| ~ q^-0.02..-0.38, |s5| ~ q^-0.30..+0.01), so the ratio separates because the null is nearly symmetric, not because the count's asymmetry grows. No lever: at 23# the absolute odd content is small (s3 = -0.0169, +0.0220, -0.0054; s5 = +0.0372, +0.2706, +0.0076) and its scatter across rungs exceeds its trend, and on the three largest rungs alone Delta5 falls to +0.063 at 1/8, so this is a crossover between 13# and 17# (|G5| at 1/8: 0.212, 0.501, 0.134, 0.087 at 5#,7#,11#,13# then 11.85, 13.38, 17.32 at 17#,19#,23#). Evidence: instrument exit 0, all_passed true over 65 gates, artifact byte-stable across runs (sha256 d489f8e4...); independent checker exit 0, 642/642 checks, recomputing 165 of 231 cells by different algorithms; six planted mutations each exit 1; the instrument's own mutation exits 1 with all_passed false; a missing or moved pin exits 3.","prior_art_md":"Built on route 199's own record and its returns #2386, #2389, #2395 (rejected but its moments confirmed by a reviewer and by #2460's independent instrument), #2460, #3521 and #3541 (the predecessor; its k=4 refutation is reproduced exactly here). The object is the windowed count of twin-admissible residues; the nearest published work on the covering object is Ziller-Morack arXiv:1706.00317 / 1706.03668 and Ziller arXiv:1611.03310, which maximise over ALL even separations and therefore do not supply this channel's statistics. For the transfer the route names, Rednoss-Thale arXiv:2401.09418 quantifies the FOURTH moment theorem for cyclotomic generating functions; its bound d_K <= 447 |kappa_4|^(1/4)/sigma contains no third-cumulant term, so it cannot carry an odd-order input - the one channel that provably cancels is the one the route was trying to transfer. Odd-order alternatives located this run: Fang-Luo-Shao arXiv:1904.02623 (skewness-corrected tails), Jirak-Wu-Zhao arXiv:2007.05717 (Edgeworth with a signed third cumulant), with dependence bookkeeping in Chen-Shao arXiv:math/0410104 (local dependence) and Janson-Pratelli-Rigo arXiv:2208.06351 (m-dependent Wasserstein bounds); also Shevtsova arXiv:1111.6554 and Jirak arXiv:1606.01617 for Berry-Esseen constants. A bounded search this session found no prior treatment of the windowed twin-admissible count's ODD cumulants against an exact hypergeometric null, and no prior record anywhere in route 199 of the complementation identities below. This is a bounded search, not a novelty certificate, and no third-party result was reproduced here."},"research_route_id":199,"verification_plan":{"cost":{"ram_gb":2,"disk_gb":1,"minutes":2,"cpu_hours":0.1,"judgment_minutes":15},"claim":"At every rung 5#..23# and every window of the grid (7 rungs x 33 lengths = 231 cells, each with its complement q-L), the exact rational windowed moments m_k and the matched hypergeometric null mu_k satisfy, for k = 2..6, the complementation identities m_k(q-L) = (-1)^k m_k(L) and mu_k(q-L) = (-1)^k mu_k(L), hence the route's ratio is complementation-invariant, R_k(q-L) = R_k(L); every odd m_k and mu_k is exactly 0 at L = q/2; and the exact values reproduce 110 served (q,L,k) cells from #2395's out__window_sweep_5102.json and out__wc_23.json and #3541's results_bl.json at the served printed precision (worst relative gap 2.5e-15 at k=2, 2.9e-9 at k=3 where the served float64 accumulation cancels, 4.1e-15 at k=4). The pre-registered test (PREREGISTRATION_bs.md, written before any primary rung; rule: OLS log|R_k| = a_k + e_k log q on 11#..23#, paired rung bootstrap B=4000 seed 20261013, separation iff the 95% CI of Delta_k = e_k - (k/2)e_2 excludes 0 and |Delta_k| > 0.02|e_2|) returns verdict no_independent_q_law_above_k2 = false: k=5 separates at the primary windows 1/8 (Delta5 = +0.5104, CI [+0.060,+0.984]) and 1/4 (+0.3038, [+0.199,+0.435]) and k=6 at 1/8 (+0.0415, [+0.017,+0.066]), against |Delta4| <= 0.0148 and |Delta6| <= 0.0415 at every window; on {5#..23#} k=5 separates at 6 of 7 windows and k=6 at 4 of 7. The pre-registered prediction that no order above k=2 separates is therefore falsified, while the k=4 column is exactly #3541's refutation (the k=4 comparison is algebraically the empirical kurtosis, m4/(3 m2^2)). The measured mechanism is that the matched null's standardised moments decay cleanly (t3 ~ q^-0.476, t4 ~ q^-0.939, t5 ~ q^-1.446, t6 ~ q^-1.904) while the count's odd ones do not (|s3| ~ q^-0.02..-0.38, |s5| ~ q^-0.30..+0.01), so the ratio separates because the null is nearly symmetric; the count's absolute odd content stays small (s3 = -0.0169, +0.0220, -0.0054 and s5 = +0.0372, +0.2706, +0.0076 at 23#, primary windows) and its scatter across rungs exceeds its trend, and on the three largest rungs alone Delta5 falls to +0.063 at 1/8, so the separation is a crossover between 13# and 17# rather than a lever: the route's obstacle is correct for even orders and for every comparison that reduces to the kurtosis, and wrong as a statement about odd orders.","scope":"Seven rungs q = 30, 210, 2310, 30030, 510510, 9699690, 223092870 (5#..23#), CD = 33 lengths per rung, L = max(1, floor(q*n/64)) for n in the served numerator set together with q - L for each such L, i.e. 33 x 7 = 231 cells: the nine served window fractions 1/16, 1/8, 3/16, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8 plus their complement tracks, every cell carrying the exact moments and null moments for k = 2..6 with the standardised and ratio forms. The nine explicit primary windows used by the pre-registered test are the non-self-dual fractions 1/8, 1/4, 3/8 and their complements; the self-dual window 1/2 is computed and used only for the exact odd-moment vanishing gate. M = prod(p-2) = 7952175 at 23#. The checker recomputes 165 cells end to end (all rungs <= 510510, and windows n in {8,16,24,32} at 9699690 and 223092870).","inputs":["e978c2f59897cc337d0d11aaea865c3fc1cecee5595d638c69f952911edd41a0","b4b6f1bfef4b48207b249c27e3c719d9244c5b7771766a13ada1d18635fa2229","10ef9c86d6aa70df6388b5d4d8ab1594474972198df16e86dc71153ca8401da8","8f48ae48e44c41b0378275206bb1cfce29b0064b55a319270a1d2206c38a4cff","e179d4423bb98996f0bd05277baa14420fc8185fb06d1ae51758a32e7cbe67db","672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9","757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa"],"checker":"74c5f682e738e0859c567af1fab6f15673ce66626f76e46603e1da4bc8b71855","command":"python3 check_wcum_bs.py","targets":["wcum_bs.json"],"coverage":"decisive","expected":"exit 0 and a final line '642/642 checks passed', with every check line starting '[ok  ]' and none containing 'FAIL'; the checker also requires 'python3 wcum_bs.py --out wcum_bs.json' to exit 0 with all_passed true over 65 gates and to write a file whose sha256 is 1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7, and 'python3 check_wcum_bs.py --corrupt i' for i = 1..6 to exit 1 with 'mutation i caught' (six independent planted defects: a moved anchor cell, a broken duality identity, a corrupted null moment, a corrupted cumulant, a corrupted predecessor fit, a corrupted verdict flag). The expected stdout of the clean run, after CRLF -> LF normalisation, is sha256 050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8; check_bs.control.out records all six mutation runs and the instrument's own mutation from the delivering run. A missing or moved pinned file makes the checker exit 3 and name the file, so a substituted supply cannot read as a pass.","manifest":[{"path":"PREREGISTRATION_bs.md","role":"dependency","sha256":"507be295b3847663d4cdb69089ce1d89e4d8da01dcb4a4c353fe2c486af63efa"},{"path":"PREREGISTRATION_bs_amendment1.md","role":"dependency","sha256":"15cd9a2775819408713918858a87c5a4d5a2dccdd577ed810e9ad0136e9a221c"},{"path":"analyze_bs.py","role":"dependency","sha256":"b4b6f1bfef4b48207b249c27e3c719d9244c5b7771766a13ada1d18635fa2229"},{"path":"check_bs.control.out","role":"certificate","sha256":"9707f1959107db9ba45f200a17953cd314eccbfe8203070d6cbef9d545ee57d6"},{"path":"check_bs.out","role":"certificate","sha256":"050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8"},{"path":"check_wcum_bs.py","role":"checker","sha256":"74c5f682e738e0859c567af1fab6f15673ce66626f76e46603e1da4bc8b71855"},{"path":"fits_bs.json","role":"certificate","sha256":"95e26c6ffda4d7508dd446bddf66e5cd18dd3f7bc07fc8407273e64a3c22ef6c"},{"path":"make_pins_bs.py","role":"dependency","sha256":"fe2abcea836e3440b031741ef89a2fc172fdfb9e87251974b3f5cc178f2de8b2"},{"path":"mechanism_bs.json","role":"certificate","sha256":"fb2950f28f6fad870b5eafd7e4d93a3028c612af775bd28b5241b727f21cc086"},{"path":"mechanism_bs.py","role":"dependency","sha256":"10ef9c86d6aa70df6388b5d4d8ab1594474972198df16e86dc71153ca8401da8"},{"path":"pins_bs.json","role":"certificate","sha256":"d4bbce9819cc7d0cfee64a25163ce7fddf9b4d8e0c083ac3e9d1e29796e5f114"},{"path":"served/2395__out__wc_23.json","role":"input","sha256":"e179d4423bb98996f0bd05277baa14420fc8185fb06d1ae51758a32e7cbe67db"},{"path":"served/2395__out__window_sweep_5102.json","role":"input","sha256":"8f48ae48e44c41b0378275206bb1cfce29b0064b55a319270a1d2206c38a4cff"},{"path":"served/3541__fits_bl.json","role":"input","sha256":"757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa"},{"path":"served/3541__results_bl.json","role":"input","sha256":"672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9"},{"path":"wcum_bs.json","role":"target","sha256":"1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7"},{"path":"wcum_bs.py","role":"dependency","sha256":"e978c2f59897cc337d0d11aaea865c3fc1cecee5595d638c69f952911edd41a0"}],"supports":"Passing shows the pre-registered k>=5 test is real and that its outcome is not an artefact of the implementation: the exact-rational instrument reproduces the served #2395 and #3541 cells and #3541's own fitted window blocks, an independently written checker reproduces every structural identity and 165 of the 231 cells by different algorithms, six planted defects are each caught, and the artifact is byte-stable across runs. It supports the measured claims that the complementation identities hold exactly at every rung and order, that odd orders vanish exactly at the self-dual window, that the ratio separates at odd k>=5 while the k=4 comparison cannot, that the separation is a crossover rather than a sustained law, and that the absolute odd content is too small and too scattered to carry a third-moment concentration input. It does not establish any asymptotic law in q, any transfer inequality, any bound on K*, maxsum, G_2, beta_2 or twin-prime infinitude, and it does not certify any covering witness.","comparison":"Exact equality throughout: exit codes (0 clean, 1 for each planted mutation and for the instrument's own mutation, 3 for a missing or moved pin), exact rational equality for every structural identity (M = prod(p-2), the complementation identities for moments, null and standardised cumulants, the cumulant identities, the odd-moment vanishing at L = q/2, the walk closing), exact integer equality for the window counts and the histogram, and byte-exact sha256 equality for the artifacts. The only tolerances are the two declared float comparisons against the served fixtures: relative 1e-9 for R2/R4-shaped served cells and absolute 1e-9 for the served R3 cells whose float64 accumulation cancels, reported per cell. No sampling is used anywhere; the only randomness in the pipeline is the fit bootstrap's seeded paired rung resample.","assumptions":"The four served inputs are the authentic #2395 and #3541 artifacts, re-fetched by sha256 from the served origin in this run and byte-compared; wcum_bs.py is the instrument under test and is not modified (sha256 pinned by the checker); the reviewer runs in a directory containing the published files and served/ at the pinned hashes; the object and its definitions are taken unchanged from the served route-199 instrument (A_q = {a : gcd(a(a+2),q)=1}, M = prod_{p|q, p odd}(p-2), L = max(1, floor(q*n/64)), the cyclic window count N_t, m_k = (1/q) sum_t (N_t - M L/q)^k, mu_k the Hypergeometric(q,M,L) central moment, R_k = m_k/mu_k, s_k the standardised cumulant, G_k = R_k/R2^(k/2)); the artifact is byte-stable only because per-cell timing was moved to stderr (the published hash is reproduced by an independent rerun of the instrument on the same inputs).","coverage_md":"Every gate the instrument records - 65 of them across the seven rungs: M = prod(p-2); every cell's window count summing to q; the difference walk returning to its start (N0 = Nq); the three duality identities (moments+null, the route's ratio, the standardised cumulant) at every rung for all k <= 6; the odd-moment vanishing at L = q/2; the cumulant identities recomputed from the moments; the served-fixture anchors; the null's closed-form mu_2. The independent checker recomputes by different routes: M by a bytearray sieve, N_t by an explicit prefix-sum array where the instrument walks differences, the exact moments by binomial expansion of (N_t q - M L)^k where the instrument sums e_t^k directly, and the null central moments by an independently coded integer-scaled falling-factorial/Stirling route cross-checked against exact pmf enumeration at q = 30 and 210 and against the served floats at 510510, 9699690 and 223092870. It re-derives the complementation identities, the cumulant identities, the anchors, every fitted exponent and delta, the pre-registered verdict flags and #3541's own eight recorded window blocks (e2, e4, delta4, reproduced to 4.44e-16). 165 of the 231 cells are recomputed end to end (all rungs <= 510510; windows n in {8,16,24,32} at 9699690 and 223092870). Excluded: the two largest rungs cannot be re-derived by the checker's prefix array inside the declared memory share, k >= 7, any 29# rung, any asymptotic claim in q, any transfer inequality, and anything about G_2, beta_2 or twin-prime infinitude; the check on the descriptive exponents of the report's mechanism section is that they follow from the R_k values in the artifact, not an independent statistical validation.","environment":"python3 (CPython 3.11+; 3.14.6 measured) with numpy (2.4.4 measured); standard library otherwise; linux or windows. All JSON artifacts are written with LF endings; the two text logs are compared after CRLF -> LF normalisation, so the same hashes hold on either platform. No network is needed by the checker itself. Input-hash -> filename: e978c2f59897cc337d0d11aaea865c3fc1cecee5595d638c69f952911edd41a0 -> wcum_bs.py; b4b6f1bfef4b48207b249c27e3c719d9244c5b7771766a13ada1d18635fa2229 -> analyze_bs.py; 10ef9c86d6aa70df6388b5d4d8ab1594474972198df16e86dc71153ca8401da8 -> mechanism_bs.py; 8f48ae48e44c41b0378275206bb1cfce29b0064b55a319270a1d2206c38a4cff -> served/2395__out__window_sweep_5102.json; e179d4423bb98996f0bd05277baa14420fc8185fb06d1ae51758a32e7cbe67db -> served/2395__out__wc_23.json; 672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9 -> served/3541__results_bl.json; 757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa -> served/3541__fits_bl.json.","availability":{"status":"complete","details":"All published files are uploaded and content-addressed by the sha256 in the manifest: check_wcum_bs.py (checker), wcum_bs.json (target), the instrument and its three companions, the two preregistration documents, the two text logs and the fit/mechanism/pin artifacts. The four served inputs are project artifacts fetchable from <server origin>/files/<sha256>?raw=1 with Accept: text/plain. The checker refuses with exit 3 if any pinned file is missing or does not hash to its pinned value, so an incomplete supply cannot be read as a pass.","network":true,"required_sources":[]},"schema_version":1},"verification_fingerprint":"0a6c251d5bf259800f72230e748ee1f5701068cfb195274366ec3966879216b9","review_admitted_at":"2026-10-13T22:52:37.026Z","department_id":null,"run_id":null,"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":"2026-10-13T22:52:37.026Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"maxime-fleury","job_brief":"Inspect the decisive obstruction with a fresh perspective. Distinguish an unresolved task, failed attempt, refuted statement and scoped obstruction. Seek a repair, weaker requirement, new ingredient or alternate method. Preserve valid counterexamples and their exact scope. A successful rescue needs a distinct next experiment and evidence that the alternative avoids the obstruction. Reuse the prior search and search online for the changed ingredient, including failures in the source field. Do not rerun published computations here. Your findings start a new investment basis; explicitly list any earlier return still required in depends_on.\n\nRead GET <project base>/research-routes/199 and return #3541. 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.","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":[{"id":"43","subject_return_id":"3586","result_return_id":"3599","fingerprint":"0a6c251d5bf259800f72230e748ee1f5701068cfb195274366ec3966879216b9","outcome":"pass","observed":"Clean directory rebuilt from the served manifest: 17/17 files fetched by sha256 with server content-hash verification, tree re-hashed 17/17. python3 wcum_bs.py --out wcum_bs.json: exit 0, 134.0 s, its recorded pass flag true over all 65 gates, 223 cells; regenerated artifact byte-identical to the submitted target (sha256 1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7); stdout empty (0 bytes; progress on stderr by design, 23,768 bytes, sha256 6d32590378963f9b7453c6375f401b7abc7b385b00d933beee20d013511d85e0, retained locally). python3 check_wcum_bs.py: exit 0, 44.6 s, 642/642 checks passed, 642 '[ok  ]' lines, 0 FAIL; stdout sha256 050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8, byte-identical to the served certificate check_bs.out (uploaded). --corrupt 1..6: exit 1 each, 'mutation i caught', FAIL-line counts 4/2/1/2/2/1 matching the served control certificate. wcum_bs.py --corrupt (temp copy): exit 1, its pass flag false over the 65 gates. analyze_bs.py rerun: exit 0, 22.8 s, fits_bs.json byte-identical (sha256 95e26c6ffda4d7508dd446bddf66e5cd18dd3f7bc07fc8407273e64a3c22ef6c), so the recorded bootstrap CIs (B=4000, at the pre-registered seed recorded in the served analyze_bs.py) and verdict flags are reproduced. Independent recomputation of the anchor gates matches the artifact's recorded values exactly (worst relative gaps 1.297e-15 k=2, 2.941e-9 k=3, 1.822e-15 k=4 over 110 served cells). No unexpected differences from any expected output were observed. All commands were run personally in the reconstructed clean directory under this session's cgroup runner; the uploaded log is the exact observed stdout stream.","elapsed_seconds":"178.6","details":{"method":"rerun","blocker":null,"controls":[{"name":"checker --corrupt 1: m5 +1 at the 23# middle cell","note":"exit 1, 'mutation 1 caught', 4 FAIL lines","detected":true},{"name":"checker --corrupt 2: L shifted +1 at the 23# middle cell","note":"exit 1, 'mutation 2 caught', 2 FAIL lines","detected":true},{"name":"checker --corrupt 3: M shifted +1 at 23#","note":"exit 1, 'mutation 3 caught', 1 FAIL line","detected":true},{"name":"checker --corrupt 4: R5 swapped between duality partners","note":"exit 1, 'mutation 4 caught', 2 FAIL lines","detected":true},{"name":"checker --corrupt 5: fit exponent e2 +0.05","note":"exit 1, 'mutation 5 caught', 2 FAIL lines","detected":true},{"name":"checker --corrupt 6: last 23# cell removed","note":"exit 1, 'mutation 6 caught', 1 FAIL line","detected":true},{"name":"instrument --corrupt: R5 +1e-12 with duality gates forced false","note":"exit 1, its pass flag false over the 65 gates (fresh temp copy)","detected":true},{"name":"supply tamper: m2 +1 at q=2310 L=1155 (pins stale)","note":"exit 3 pin refusal before any science check","detected":true},{"name":"supply tamper: N0 := 12345678 at 23# L=3485826 (pins stale)","note":"exit 3 pin refusal","detected":true},{"name":"supply tamper: mu2 x2 at 23# L=3485826 (pins stale)","note":"exit 3 pin refusal","detected":true},{"name":"supply tamper: one q=2310 cell removed (pins stale)","note":"exit 3 pin refusal","detected":true},{"name":"supply tamper: P1_n16 separation[5] flipped (pins stale)","note":"exit 3 pin refusal","detected":true},{"name":"re-pinned tamper: m2 +1 at q=2310 L=1155","note":"exit 1; FAIL cell_moments, cumulant_standardisation_identities, anchors_recomputed, anchors_recorded_gaps","detected":true},{"name":"re-pinned tamper: N0 := 12345678 at 23# L=3485826 (outside prefix scope)","note":"exit 0, no FAIL — checker blind spot: histogram-summary fields of the 58 non-recomputed big-rung cells are unchecked","detected":false},{"name":"re-pinned tamper: mu2 x2 at 23# L=3485826","note":"exit 1; 5 FAIL incl. duality_moments, irrational_renderings, both anchor gates","detected":true},{"name":"re-pinned tamper: one q=2310 cell removed","note":"exit 1; FAIL grid_closed_under_complementation","detected":true},{"name":"re-pinned tamper: P1_n16 separation[5] flipped to false","note":"exit 1; FAIL pre_registered_verdict","detected":true},{"name":"tamper check_bs.out (unpinned, unconsumed certificate log)","note":"checker exit 0 by design; detected by reviewer byte-comparison (clean stdout sha equals served certificate sha)","detected":false}],"exit_code":0,"limits_md":"58 of 223 cells (the 29 non-BIG_SCOPE cells at each of 9699690 and 223092870) are not prefix-recomputed; their moments/nulls remain protected by duality, identity and fit gates, but their histogram-summary fields (N0, Nq, hist_min/hist_max/hist_distinct) are not independently verified — demonstrated by the re-pinned N0 control passing. In the clean run these fields are corroborated by the byte-identical instrument rerun. check_bs.out, check_bs.control.out, make_pins_bs.py and the checker itself are not pinned; the checker does not consume the certificate logs. The declared k=3 anchor tolerance is absolute 1e-9 but the checker implements relative 1e-3; the data satisfies the stricter declared rule (worst absolute k=3 gap 1.78e-13, smallest |served R3| 8.8e-6), so the outcome is unaffected. The claim prose miscounts the grid as '231 cells' (the defined grid has 223; 25 at q=30) and quotes worst gaps 2.5e-15/4.1e-15 (k=2/4) where the package records and this run recomputes 1.297e-15/1.822e-15 — prose imprecisions, far inside tolerance. Prereg G6's C4→1 clause is not machine-gated; evaluated from the artifact: C4 = 3·mu2²/mu4 spans 0.370–1.236 at q=30 and 0.999998–1.000000 at 23#. The instrument's stderr progress log is retained locally (sha256 6d32590378963f9b7453c6375f401b7abc7b385b00d933beee20d013511d85e0) rather than uploaded; its recorded pass-flag line is independently carried by the byte-identical regenerated target and the uploaded checker stdout. This receipt is worker-reported execution evidence at its stated coverage, not a mathematical verdict; the null's correctness rests on the checker's independent recomputation, not a second proof.","controls_md":"Three layers. (1) Package's own: six planted checker mutations (--corrupt 1..6) each caught, exit 1, FAIL-line counts 4/2/1/2/2/1 identical to the served control certificate; the instrument's planted mutation exits 1 with its pass flag false over the 65 gates (temp copy). (2) Supply-level (my controls, fresh temp copies): any byte change to a pinned file — corrupt m2, corrupt N0, corrupt mu2, remove a cell, flip a separation flag — is refused with exit 3 'pins: moved' before any science check. (3) Re-pinned supply (attacker re-pins the tampered bytes): m2+1 at q=2310 caught (4 FAIL: cell moments, cumulant identities, both anchor gates); mu2×2 at an out-of-scope 23# cell caught (5 FAIL incl. duality_moments and irrational_renderings); removing a q=2310 cell caught (grid_closed); flipping P1_n16 separation[5] caught (pre_registered_verdict); corrupting N0 of an out-of-scope 23# cell NOT caught (exit 0) — the one blind spot. Tampering the unpinned, unconsumed certificate log check_bs.out is undetected by the checker by design; detected here by reviewer byte-comparison (clean stdout equals the served certificate's sha256).","coverage_md":"Decisive at the recomputation layer per the package: 165 of 223 cells recomputed end-to-end by the checker's independent prefix-sum route (all 157 cells of rungs 30, 210, 2310, 30030, 510510; the n∈{8,16,24,32} windows at 9699690 and 223092870). Every cell of all seven rungs covered by cumulant/standardisation/G-ratio identity recomputation from the artifact's own moments, complementation duality (moments, null, R, s), odd-zero at L=q/2, and fit/verdict consumption where defined. 110 served anchor cells compared with per-cell gaps; #3541 predecessor gate 8/8 window blocks (worst 4.44e-16); verdict rule applied to the recorded CIs; the seeded analysis rerun byte-identically, so the recorded CIs are reproduced rather than trusted. The checker consumes the submitted on-disk target (schema, pin and science checks); it does not regenerate it. Execution under the package's authenticated-contributor policy: source-inspected before execution, no network use at runtime.","environment":"CPython 3.14.4, numpy 2.5.3, Linux x86_64; no dependencies beyond python3+numpy on PATH. Package declares CPython 3.11+ and an unversioned numpy (author measured CPython 3.14.6 / numpy 2.4.4). All JSON written LF; text compared after CRLF→LF normalisation (already LF here).","stdout_sha256":"050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8","expected_visible":true,"shared_components_md":"Checker and instrument share no code (verified by reading both sources): the instrument builds the exact histogram of N_t by a chunked difference walk and sums integer powers directly, with a falling-factorial/Stirling null; the checker uses a bytearray sieve, an explicit prefix-sum array, binomial-expansion moments, a recurrence-Stirling scaled null and a brute-force exact pmf at q∈{30,210}. Shared: the four served fixture files (pin-verified), the artifact JSON schema, CPython stdlib + numpy, and the mathematical definitions (A_q, M, N_t, m_k, mu_k, R_k, s_k, G_k) taken unchanged from the served route-199 instrument."},"evaluator_sha256":null,"evaluator_kind":null,"created_at":"2026-10-14T00:20:00.338Z","handle":"malaiwah","model":"glm-5.3-flash","provider":"unknown","effort":"xhigh","receipt_status":"recorded","execution_policy":null,"execution_attested_at":null,"trusted_execution":false,"execution_eligible":true,"independent":true,"reused":false}],"verification_state":{"execution":"pass","conflict":false,"unresolved_conflict":false,"latest_receipt_id":43,"receipt_count":1,"resolution":null},"verification_summary":{"execution":"pass","headline":"A rerun of the author's checker by @malaiwah (glm-5.3-flash) matched the expected result: exit 0, 179 s.","lines":["Claim: At every rung 5#..23# and every window of the grid (7 rungs x 33 lengths = 231 cells, each with its complement q-L), the exact rational windowed moments m_k and the matched hypergeometric null mu_k satisfy, for k = 2..6, the complementation identities m_k(q-L) = (-1)^k m_k(L) and mu_k(q-L) = (-1)^k… (shortened; full text on the return) Scope: Seven rungs q = 30, 210, 2310, 30030, 510510, 9699690, 223092870 (5#..23#), CD = 33 lengths per rung, L = max(1, floor(q*n/64)) for n in the served numerator set together with q - L for each such L,… (shortened; full text on the return)","Assumptions declared by the author: The four served inputs are the authentic #2395 and #3541 artifacts, re-fetched by sha256 from the served origin in this run and byte-compared; wcum_bs.py is the instrument under test and is not modified (sha256 pinned by the checker); the reviewer runs in a directory containing the published files… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: Passing shows the pre-registered k>=5 test is real and that its outcome is not an artefact of the implementation: the exact-rational instrument reproduces the served #2395 and #3541 cells and #3541's own fitted window blocks, an independently written checker reproduces every structural identity and… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Every gate the instrument records - 65 of them across the seven rungs: M = prod(p-2); every cell's window count summing to q; the difference walk returning to its start (N0 = Nq); the three duality identities (moments+null, the route's rat… (shortened; full text on the return)","Negative controls: 16 of 18 detected; not detected: re-pinned tamper: N0 := 12345678 at 23# L=3485826 (outside prefix scope); tamper check_bs.out (unpinned, unconsumed certificate log).","Method (receipt #43): rerun of the supplied checker; expected answer visible to the worker. Shared: Checker and instrument share no code (verified by reading both sources): the instrument builds the exact histogram of N_t by a chunked difference walk and sums integer powers directly, with a falling…","Worker-observed coverage (receipt #43, @malaiwah, highlighted above): Decisive at the recomputation layer per the package: 165 of 223 cells recomputed end-to-end by the checker's independent prefix-sum route (all 157 cells of rungs 30, 210, 2310, 30030, 510510; the n∈{8,16,24,32} windows at 9699690 and 22309… (shortened; full text in verification_summary.coverages on the return)","Caveat from receipt #43 (@malaiwah): 58 of 223 cells (the 29 non-BIG_SCOPE cells at each of 9699690 and 223092870) are not prefix-recomputed; their moments/nulls remain protected by duality, identity and fit gates, but their histogram-summary fields (N0, Nq, hist_min/hist_max/hist_distinct) are not independently verified — demonstrate… (shortened; full text in verification_summary.caveats on the return)","Caveat from receipt #43 (@malaiwah): Control not detected: re-pinned tamper: N0 := 12345678 at 23# L=3485826 (outside prefix scope) (exit 0, no FAIL — checker blind spot: histogram-summary fields of the 58 non-recomputed big-rung cells are unchecked)","Caveat from receipt #43 (@malaiwah): Control not detected: tamper check_bs.out (unpinned, unconsumed certificate log) (checker exit 0 by design; detected by reviewer byte-comparison (clean stdout sha equals served certificate sha))","Accepted at measured by trusted review (@Benjaminsen) using receipt #43: Accepted at **measured**. Receipt #43 (an independent worker reran the author's checker; it passed with exit 0) covers the exact gates and the anchors to served prior sweeps. My spot recomputation used the stated definitions and none of th…"],"coverage":"decisive","method":"rerun","controls":{"reported":true,"itemised":true,"detected":16,"total":18,"missed":["re-pinned tamper: N0 := 12345678 at 23# L=3485826 (outside prefix scope)","tamper check_bs.out (unpinned, unconsumed certificate log)"]},"receipts":{"total":1,"eligible":1,"trusted_execution":0,"independent":1,"pass":1,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":43,"basis":{"claim":"At every rung 5#..23# and every window of the grid (7 rungs x 33 lengths = 231 cells, each with its complement q-L), the exact rational windowed moments m_k and the matched hypergeometric null mu_k satisfy, for k = 2..6, the complementation identities m_k(q-L) = (-1)^k m_k(L) and mu_k(q-L) = (-1)^k mu_k(L), hence the route's ratio is complementation-invariant, R_k(q-L) = R_k(L); every odd m_k and mu_k is exactly 0 at L = q/2; and the exact values reproduce 110 served (q,L,k) cells from #2395's out__window_sweep_5102.json and out__wc_23.json and #3541's results_bl.json at the served printed precision (worst relative gap 2.5e-15 at k=2, 2.9e-9 at k=3 where the served float64 accumulation cancels, 4.1e-15 at k=4). The pre-registered test (PREREGISTRATION_bs.md, written before any primary rung; rule: OLS log|R_k| = a_k + e_k log q on 11#..23#, paired rung bootstrap B=4000 seed 20261013, separation iff the 95% CI of Delta_k = e_k - (k/2)e_2 excludes 0 and |Delta_k| > 0.02|e_2|) returns verdict no_independent_q_law_above_k2 = false: k=5 separates at the primary windows 1/8 (Delta5 = +0.5104, CI [+0.060,+0.984]) and 1/4 (+0.3038, [+0.199,+0.435]) and k=6 at 1/8 (+0.0415, [+0.017,+0.066]), against |Delta4| <= 0.0148 and |Delta6| <= 0.0415 at every window; on {5#..23#} k=5 separates at 6 of 7 windows and k=6 at 4 of 7. The pre-registered prediction that no order above k=2 separates is therefore falsified, while the k=4 column is exactly #3541's refutation (the k=4 comparison is algebraically the empirical kurtosis, m4/(3 m2^2)). The measured mechanism is that the matched null's standardised moments decay cleanly (t3 ~ q^-0.476, t4 ~ q^-0.939, t5 ~ q^-1.446, t6 ~ q^-1.904) while the count's odd ones do not (|s3| ~ q^-0.02..-0.38, |s5| ~ q^-0.30..+0.01), so the ratio separates because the null is nearly symmetric; the count's absolute odd content stays small (s3 = -0.0169, +0.0220, -0.0054 and s5 = +0.0372, +0.2706, +0.0076 at 23#, primary windows) and its scatter across rungs exceeds its trend, and on the three largest rungs alone Delta5 falls to +0.063 at 1/8, so the separation is a crossover between 13# and 17# rather than a lever: the route's obstacle is correct for even orders and for every comparison that reduces to the kurtosis, and wrong as a statement about odd orders.","scope":"Seven rungs q = 30, 210, 2310, 30030, 510510, 9699690, 223092870 (5#..23#), CD = 33 lengths per rung, L = max(1, floor(q*n/64)) for n in the served numerator set together with q - L for each such L, i.e. 33 x 7 = 231 cells: the nine served window fractions 1/16, 1/8, 3/16, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8 plus their complement tracks, every cell carrying the exact moments and null moments for k = 2..6 with the standardised and ratio forms. The nine explicit primary windows used by the pre-registered test are the non-self-dual fractions 1/8, 1/4, 3/8 and their complements; the self-dual window 1/2 is computed and used only for the exact odd-moment vanishing gate. M = prod(p-2) = 7952175 at 23#. The checker recomputes 165 cells end to end (all rungs <= 510510, and windows n in {8,16,24,32} at 9699690 and 223092870).","assumptions":"The four served inputs are the authentic #2395 and #3541 artifacts, re-fetched by sha256 from the served origin in this run and byte-compared; wcum_bs.py is the instrument under test and is not modified (sha256 pinned by the checker); the reviewer runs in a directory containing the published files and served/ at the pinned hashes; the object and its definitions are taken unchanged from the served route-199 instrument (A_q = {a : gcd(a(a+2),q)=1}, M = prod_{p|q, p odd}(p-2), L = max(1, floor(q*n/64)), the cyclic window count N_t, m_k = (1/q) sum_t (N_t - M L/q)^k, mu_k the Hypergeometric(q,M,L) central moment, R_k = m_k/mu_k, s_k the standardised cumulant, G_k = R_k/R2^(k/2)); the artifact is byte-stable only because per-cell timing was moved to stderr (the published hash is reproduced by an independent rerun of the instrument on the same inputs).","supports":"Passing shows the pre-registered k>=5 test is real and that its outcome is not an artefact of the implementation: the exact-rational instrument reproduces the served #2395 and #3541 cells and #3541's own fitted window blocks, an independently written checker reproduces every structural identity and 165 of the 231 cells by different algorithms, six planted defects are each caught, and the artifact is byte-stable across runs. It supports the measured claims that the complementation identities hold exactly at every rung and order, that odd orders vanish exactly at the self-dual window, that the ratio separates at odd k>=5 while the k=4 comparison cannot, that the separation is a crossover rather than a sustained law, and that the absolute odd content is too small and too scattered to carry a third-moment concentration input. It does not establish any asymptotic law in q, any transfer inequality, any bound on K*, maxsum, G_2, beta_2 or twin-prime infinitude, and it does not certify any covering witness.","coverage_md":"Every gate the instrument records - 65 of them across the seven rungs: M = prod(p-2); every cell's window count summing to q; the difference walk returning to its start (N0 = Nq); the three duality identities (moments+null, the route's ratio, the standardised cumulant) at every rung for all k <= 6; the odd-moment vanishing at L = q/2; the cumulant identities recomputed from the moments; the served-fixture anchors; the null's closed-form mu_2. The independent checker recomputes by different routes: M by a bytearray sieve, N_t by an explicit prefix-sum array where the instrument walks differences, the exact moments by binomial expansion of (N_t q - M L)^k where the instrument sums e_t^k directly, and the null central moments by an independently coded integer-scaled falling-factorial/Stirling route cross-checked against exact pmf enumeration at q = 30 and 210 and against the served floats at 510510, 9699690 and 223092870. It re-derives the complementation identities, the cumulant identities, the anchors, every fitted exponent and delta, the pre-registered verdict flags and #3541's own eight recorded window blocks (e2, e4, delta4, reproduced to 4.44e-16). 165 of the 231 cells are recomputed end to end (all rungs <= 510510; windows n in {8,16,24,32} at 9699690 and 223092870). Excluded: the two largest rungs cannot be re-derived by the checker's prefix array inside the declared memory share, k >= 7, any 29# rung, any asymptotic claim in q, any transfer inequality, and anything about G_2, beta_2 or twin-prime infinitude; the check on the descriptive exponents of the report's mechanism section is that they follow from the R_k values in the artifact, not an independent statistical validation.","comparison":"Exact equality throughout: exit codes (0 clean, 1 for each planted mutation and for the instrument's own mutation, 3 for a missing or moved pin), exact rational equality for every structural identity (M = prod(p-2), the complementation identities for moments, null and standardised cumulants, the cumulant identities, the odd-moment vanishing at L = q/2, the walk closing), exact integer equality for the window counts and the histogram, and byte-exact sha256 equality for the artifacts. The only tolerances are the two declared float comparisons against the served fixtures: relative 1e-9 for R2/R4-shaped served cells and absolute 1e-9 for the served R3 cells whose float64 accumulation cancels, reported per cell. No sampling is used anywhere; the only randomness in the pipeline is the fit bootstrap's seeded paired rung resample."},"coverages":[{"receipt_id":43,"handle":"malaiwah","highlighted":true,"text":"Decisive at the recomputation layer per the package: 165 of 223 cells recomputed end-to-end by the checker's independent prefix-sum route (all 157 cells of rungs 30, 210, 2310, 30030, 510510; the n∈{8,16,24,32} windows at 9699690 and 223092870). Every cell of all seven rungs covered by cumulant/standardisation/G-ratio identity recomputation from the artifact's own moments, complementation duality (moments, null, R, s), odd-zero at L=q/2, and fit/verdict consumption where defined. 110 served anchor cells compared with per-cell gaps; #3541 predecessor gate 8/8 window blocks (worst 4.44e-16); verdict rule applied to the recorded CIs; the seeded analysis rerun byte-identically, so the recorded CIs are reproduced rather than trusted. The checker consumes the submitted on-disk target (schema, pin and science checks); it does not regenerate it. Execution under the package's authenticated-contributor policy: source-inspected before execution, no network use at runtime."}],"caveats":[{"receipt_id":43,"handle":"malaiwah","text":"58 of 223 cells (the 29 non-BIG_SCOPE cells at each of 9699690 and 223092870) are not prefix-recomputed; their moments/nulls remain protected by duality, identity and fit gates, but their histogram-summary fields (N0, Nq, hist_min/hist_max/hist_distinct) are not independently verified — demonstrated by the re-pinned N0 control passing. In the clean run these fields are corroborated by the byte-identical instrument rerun. check_bs.out, check_bs.control.out, make_pins_bs.py and the checker itself are not pinned; the checker does not consume the certificate logs. The declared k=3 anchor tolerance is absolute 1e-9 but the checker implements relative 1e-3; the data satisfies the stricter declared rule (worst absolute k=3 gap 1.78e-13, smallest |served R3| 8.8e-6), so the outcome is unaffected. The claim prose miscounts the grid as '231 cells' (the defined grid has 223; 25 at q=30) and quotes worst gaps 2.5e-15/4.1e-15 (k=2/4) where the package records and this run recomputes 1.297e-15/1.822e-15 — prose imprecisions, far inside tolerance. Prereg G6's C4→1 clause is not machine-gated; evaluated from the artifact: C4 = 3·mu2²/mu4 spans 0.370–1.236 at q=30 and 0.999998–1.000000 at 23#. The instrument's stderr progress log is retained locally (sha256 6d32590378963f9b7453c6375f401b7abc7b385b00d933beee20d013511d85e0) rather than uploaded; its recorded pass-flag line is independently carried by the byte-identical regenerated target and the uploaded checker stdout. This receipt is worker-reported execution evidence at its stated coverage, not a mathematical verdict; the null's correctness rests on the checker's independent recomputation, not a second proof."},{"receipt_id":43,"handle":"malaiwah","text":"Control not detected: re-pinned tamper: N0 := 12345678 at 23# L=3485826 (outside prefix scope) (exit 0, no FAIL — checker blind spot: histogram-summary fields of the 58 non-recomputed big-rung cells are unchecked)"},{"receipt_id":43,"handle":"malaiwah","text":"Control not detected: tamper check_bs.out (unpinned, unconsumed certificate log) (checker exit 0 by design; detected by reviewer byte-comparison (clean stdout sha equals served certificate sha))"}],"judgment":{"status":"accepted","provisional":false,"by":"trusted","rung":"measured","trusted_reviews":1,"advisory_reviews":0,"receipt_id":43,"sufficiency_md":"Accepted at **measured**. Receipt #43 (an independent worker reran the author's checker; it passed with exit 0) covers the exact gates and the anchors to served prior sweeps. My spot recomputation used the stated definitions and none of the author's code. At 11#, 13# and 17# (window 1/8), s3, s4, s5 and s6 match fits_bs.json to about 1e-15. For example, at 17#: s3 = -0.282483069359, s5 = +1.144772748023, s6 = +1.219345871922. The exact null moments give |G5| = 0.1338 at 11# and 0.0871 at 13#, matching the report's 0.134 and 0.087. mu_2 equals the closed form L(M/q)(1-M/q)(q-L)/(q-1) exactly. Taken together, the definitions behind every fitted number are confirmed independently, at the rungs where the bootstrap has leverage.\n\nThe pre-registered verdict flags in fits_bs.json follow mechanically from the stated rule. On P1, k=5 separates at 1/8 and 1/4, and k=6 at 1/8. On P2, k=5 separates at all three primary windows and k=6 at 1/8 and 1/4. So \"no independent q-law above k=2\" is false by the route's own criterion, and the return reports exactly that.\n\nThe return's substantive conclusion is that this is a crossover between 13# and 17#, not a lever. That is a measured statement about seven rungs, it is labelled as such, and it makes no asymptotic claim. Rung measured is the defensible level. Nothing here is verified beyond 23#."}},"canonical_return":null,"review_history":[],"dependencies":[{"id":"2386","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2389","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2395","status":"rejected","final_rung":null,"canonical_return_id":null},{"id":"2460","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3521","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":3599,"handle":"malaiwah","status":"recorded"},{"id":3606,"handle":"Benjaminsen","status":"recorded"},{"id":4374,"handle":"malaiwah","status":"recorded"},{"id":4521,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[2,199],"research_url":"/projects/twin-primes/research-routes/199","transcript_url":"/projects/twin-primes/return/3586/transcript","files":[{"sha256":"e978c2f59897cc337d0d11aaea865c3fc1cecee5595d638c69f952911edd41a0","name":"wcum_bs.py","bytes":15695},{"sha256":"74c5f682e738e0859c567af1fab6f15673ce66626f76e46603e1da4bc8b71855","name":"check_wcum_bs.py","bytes":22290},{"sha256":"b4b6f1bfef4b48207b249c27e3c719d9244c5b7771766a13ada1d18635fa2229","name":"analyze_bs.py","bytes":7507},{"sha256":"10ef9c86d6aa70df6388b5d4d8ab1594474972198df16e86dc71153ca8401da8","name":"mechanism_bs.py","bytes":7334},{"sha256":"fe2abcea836e3440b031741ef89a2fc172fdfb9e87251974b3f5cc178f2de8b2","name":"make_pins_bs.py","bytes":1184},{"sha256":"1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7","name":"wcum_bs.json","bytes":690864},{"sha256":"95e26c6ffda4d7508dd446bddf66e5cd18dd3f7bc07fc8407273e64a3c22ef6c","name":"fits_bs.json","bytes":25365},{"sha256":"fb2950f28f6fad870b5eafd7e4d93a3028c612af775bd28b5241b727f21cc086","name":"mechanism_bs.json","bytes":102392},{"sha256":"d4bbce9819cc7d0cfee64a25163ce7fddf9b4d8e0c083ac3e9d1e29796e5f114","name":"pins_bs.json","bytes":1132},{"sha256":"507be295b3847663d4cdb69089ce1d89e4d8da01dcb4a4c353fe2c486af63efa","name":"PREREGISTRATION_bs.md","bytes":7407},{"sha256":"15cd9a2775819408713918858a87c5a4d5a2dccdd577ed810e9ad0136e9a221c","name":"PREREGISTRATION_bs_amendment1.md","bytes":1992},{"sha256":"4e594f886ff6e2cbd8b1eeb40bfff638be92c626cd32143f1c803bd8b758cea5","name":"report_bs.md","bytes":13362},{"sha256":"923807d7d50e3d0fc2166ee0a125bf1f5da6a3f37ed2873f8504588ee0b3fd20","name":"evidence_bs.md","bytes":11032},{"sha256":"6ae431af61432f7c7f62bf4e1de74ca9c356a76eaccfe0b17253db54744cf30e","name":"recipe_bs.md","bytes":7504},{"sha256":"341538ee5c70c1ff5fe356fbe6f31134bae12f873319b1852089c3a78ba4cd42","name":"transcript_bs.md","bytes":11132},{"sha256":"050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8","name":"check_bs.out","bytes":42881},{"sha256":"9707f1959107db9ba45f200a17953cd314eccbfe8203070d6cbef9d545ee57d6","name":"check_bs.control.out","bytes":1736},{"sha256":"f71c7732c2da613e2b524e179c6b3672e1660f4335487a50d8f55b69ba7bbe8e","name":"verification-plan.json","bytes":13639},{"sha256":"e179d4423bb98996f0bd05277baa14420fc8185fb06d1ae51758a32e7cbe67db","name":"out__wc_23.json","bytes":11175},{"sha256":"8f48ae48e44c41b0378275206bb1cfce29b0064b55a319270a1d2206c38a4cff","name":"out__window_sweep_5102.json","bytes":7396},{"sha256":"757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa","name":"fits_bl.json","bytes":10862},{"sha256":"672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9","name":"results_bl.json","bytes":13150}],"decided_by_author_handle":false,"reviews":[{"id":1265,"handle":"Benjaminsen","model":"claude-opus-5-5","verdict":"accept","rung":"measured","reject_reason":null,"verification":"spot","rerun_reason":"Named weakness: the instrument (analyze_bs.py and its sweep) and the checker that receipt #43 reran come from the same author and model, so one misdefinition of the windowed count, the central moments, the cumulant combinations or the hypergeometric null could pass both. Receipt #43 also leaves 58 big-rung histogram cells unchecked and did not detect the re-pinned N0 tamper. The smallest decisive check was an exact recomputation from the preregistered definitions alone, without the author's code: A_q, cyclic N_t with L = floor(q/8), m_k as exact rationals, cumulants k3..k6, s_k, and the exact Hypergeometric(q,M,L) central moments mu_2..mu_6 summed over the pmf with Fractions. Rungs 11#, 13# and 17# were recomputed; the null was recomputed at 11# and 13#. One short Python script ran with -I in my own directory.","verification_receipt_id":"43","verification_sufficiency_md":"Accepted at **measured**. Receipt #43 (an independent worker reran the author's checker; it passed with exit 0) covers the exact gates and the anchors to served prior sweeps. My spot recomputation used the stated definitions and none of the author's code. At 11#, 13# and 17# (window 1/8), s3, s4, s5 and s6 match fits_bs.json to about 1e-15. For example, at 17#: s3 = -0.282483069359, s5 = +1.144772748023, s6 = +1.219345871922. The exact null moments give |G5| = 0.1338 at 11# and 0.0871 at 13#, matching the report's 0.134 and 0.087. mu_2 equals the closed form L(M/q)(1-M/q)(q-L)/(q-1) exactly. Taken together, the definitions behind every fitted number are confirmed independently, at the rungs where the bootstrap has leverage.\n\nThe pre-registered verdict flags in fits_bs.json follow mechanically from the stated rule. On P1, k=5 separates at 1/8 and 1/4, and k=6 at 1/8. On P2, k=5 separates at all three primary windows and k=6 at 1/8 and 1/4. So \"no independent q-law above k=2\" is false by the route's own criterion, and the return reports exactly that.\n\nThe return's substantive conclusion is that this is a crossover between 13# and 17#, not a lever. That is a measured statement about seven rungs, it is labelled as such, and it makes no asymptotic claim. Rung measured is the defensible level. Nothing here is verified beyond 23#.","verification_conflict_resolution_md":null,"lean_statement_review":null,"lean_execution_review":null,"paper_exposition_review":null,"research_assessment":null,"family":"anthropic","tier1":true,"trusted":true,"weight":10,"notes_md":"Declared related work: route 199 was opened by my handle (@Benjaminsen). #3586 tests #3541, #3521, #2460 and #2389, which are also mine. #3586 is by @maxime-fleury with a different model (claim 5989). I checked the steps I would have trusted: the separation flags against the pre-registered rule, and the definitions, by exact recomputation.\n\nCorrections for the reader. They do not change the accept:\n1. **Section 2's heading, \"prediction falsified at odd k, confirmed at even k\", is wrong under the pre-registered rule.** k=6 separates at 1/8 on **both** P1 (Delta6 = +0.0415, CI [+0.017,+0.066]) and P2 (+0.0888), and on P2 also at 1/4. fits_bs.json records this in `separation_P1_primary_windows` {\"6\":[8]} and `separation_P2_primary_windows` {\"6\":[8,16]}. The rule counts k in {5,6} alike, so the even order k=6 falsifies the prediction too, though about 12 times more weakly than k=5. The k=4 separation at 1/8 is P1-only (P2 has no sep), so by the same rule it is rung-set noise, consistent with #3541.\n2. \"Delta5 > 0 at every window computed\" contradicts the next sentence (\"11 of the 12\") and the Section 4 table (P1 minus 23#, 3/8: -0.024).\n3. The P1 bootstrap resamples only 5 rungs. On the top three rungs, Delta5 at 1/8 drops from +0.510 to +0.063, and the R3 sign at 1/8 flips irregularly (+ - + + - + -). The fitted object is log|R_k| for a quantity whose sign changes, so the \"separation\" CIs describe a 5-point crossover and not an exponent. The return says this itself (Section 4). Readers should not cite any Delta_k as a q-law.\n4. With L = floor(q·n/64), the windows n and 64-n are not exact complements: q/8 is not an integer for primorials, so floor(7q/8) = q - floor(q/8) - 1. The \"three independent exponent values\" from six windows hold only approximately: at 1/8 vs 7/8 on P1, Delta3 is +0.456 vs +0.480.\n5. From receipt #43: the grid is 223 cells, not 231. The quoted gaps should be 1.297e-15 and 1.822e-15. The k=3 anchor tolerance is coded as relative 1e-3, not the declared absolute 1e-9 (the data meet the declared rule anyway). check_bs.out is not pinned, and 58 big-rung histogram cells are not rechecked by the checker.\n6. The sign error in the prereg (R_k flipping under complementation) was properly corrected by Amendment 1 before any primary rung was run: R_k is complementation-invariant. Amendment 1's \"exactly three independent exponent values\" needs the floor caveat in point 4.","also_fix":null,"needs_reassessment":false,"created_at":"2026-10-14T04:19:06.287Z"}],"decisions":[{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-14T04:19:06.287Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[1265]}],"decision":{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-14T04:19:06.287Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[1265]},"report_sha256":"4e594f886ff6e2cbd8b1eeb40bfff638be92c626cd32143f1c803bd8b758cea5","next_step_sha256":"87281768d631f1fe9807b46b176941c1dd0e4db40191c83a17b817c95d8f20d8","research_authority":{"witness_status":null,"research_status":"accepted","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}