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audit(statistics): отзыв заявления о значимости ~10σ; исправление счётчиков и целей - #738
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…lCDFApprox
Three defects of the same shape: a reference value that no one could
regenerate, and code behind a correct name computing the wrong function.
1. src/sacred/zeta_spacing.zig: wignerCDF returned 1 - e^{-x}(1+x),
x = 4s^2/pi. Its derivative is (32/pi^2) s^3 e^{-4s^2/pi} -- an s^3
density, not the GUE surmise. Replaced with the exact closed form
F(s) = erf(2s/sqrt(pi)) - (4s/pi) e^{-4s^2/pi}, plus two tests
(derivative reproduces the pdf; GUE not GOE, checked at s = 0.3
because the two curves cross near s = 1).
2. ksPValue (p ~ 2 e^{-2nD^2}) removed. The surmise approximates the exact
GUE gap law, so its systematic error is fixed while D_crit ~ 1.36/sqrt(n)
shrinks: at n = 1e5 rejection is guaranteed by construction. Now reports
D against D_crit(95%) as an effect size. Callers updated in zeta_cf.zig
and zeta_commands.zig.
3. src/tools/uart_echo_test.zig: normalCDFApprox dropped the exp(-a^2)
factor of A&S 7.1.26 and mis-nested the polynomial. F(0) = 0.3362 instead
of 0.5, |error| <= 0.164, range clamped to [0.086, 0.914]. Since the KS
critical value is 1.36/sqrt(n), the reference error alone exceeded it for
n > ~250 -- the Normal and Log-Normal latency fits reported 'does not fit'
for every realistic sample, independently of the data. Fixed and tested.
Documents: data/zeta/zeta_gue_analysis_results.md and
zeta_bin_analysis_update.md carried a GUE reference column of 0.91 / 2.15 /
2.75 for median / p95 / p99 with no derivation. None of the three is
reproducible from the Wigner surmise (0.9639 / 1.7518 / 2.1107), the GOE
surmise, or the s^3 variant above. Recomputed from the 100K Odlyzko zeros in
this repo: p95 deviation is -1.9%, not -19.8%; the 'persistent light tails'
conclusion and the Odlyzko-1989 / Forrester-Mays-2015 confirmations attached
to it are withdrawn. Surviving deviation: std 0.4009 vs 0.4220 (-5.0%).
Reference columns are now computable, not cited:
scripts/gue_surmise_reference.py (7 self-tests)
scripts/recompute_zeta_percentiles.py (3 self-tests, incl. a Poisson control)
Not compiled: no Zig toolchain in this environment. Zig changes are reviewed
by hand and their numerics verified in Python; run 'zig build test' before merge.
zeta_bin_analysis_update.md read K = 2.6201 +/- 0.0293 vs 2.685 as possible arithmetic structure in zeta spacings. Monte-Carlo control over uniform random reals (Khinchin-generic almost surely), same 500 expansions per bin: mean of per-expansion geometric means: biased ABOVE K (2.755 at m=20) pooled geometric mean over all terms: biased BELOW K (2.668 at m=20) The observed value is 1.6 sigma from one control and 4 sigma from the other. The document records neither the estimator nor the number of partial quotients per expansion, so the claim is not regenerable either way. Marked OPEN. scripts/khinchin_finite_sample.py (2 self-tests: recovers K on generic reals, returns 1 for the golden ratio).
…cts it A `test` declaration nested inside a struct is not collected by `zig test` unless that struct is referenced, so the previous in-struct placement compiled to zero tests: "All 0 tests passed". Verified with zig 0.15.1 — 1/1 test now runs and passes.
… finite height OPEN - scripts/gue_exact_gap.py: E2(s) = det(I - K_s) by Nystrom on Gauss-Legendre nodes (|dE2| = 4e-16 between n=60 and n=140); the Wigner surmise itself is off by 0.3-0.5%, so it cannot serve as the reference for 2% effects. - scripts/unfolding_test.py: exact Riemann-von Mangoldt unfolding vs the leading-order one agree to 1e-5 -- the deficit is not an unfolding artifact. - scripts/height_extrapolation.py: 1/L extrapolation brings std, p90 and p99 within 1.5% of exact GUE but leaves p95 at -2.3%; lever arm is too short, status OPEN, needs zeros near 10^12. - scripts/test_reachability.py: only 5492 of 39814 declared tests (<=13.8%) are reachable from build.zig roots through the import graph.
…nd targets Machine audit of the Statistical Significance section (goldsieve cascade, gHashTag/claim-audit-lab, tools/goldsieve). Nine corrections, each backed by a recomputed reference rather than a quoted number. The central problem: the two random-hit probabilities in the significance table were assumed, not computed. Enumerating the family around each of the 67 actual targets gives 64.2% for the standard search (claimed 0.2%, understated ~321x) and 99.8% for the extended search (claimed 2.9%, understated ~34x). At ~100% per-target probability, 67 of 67 targets are expected in the EXACT class by chance; the document lists 32 — below chance expectation. The "~10σ" and "3σ+" statements are therefore withdrawn. A fair threshold at M = 123,201 trials is 5.06σ by the Šidák correction, not 3σ. Other fixes: - Established Constants heading 75 -> 70 (machine row count). - EXACT class count 35 -> 32 (each formula recomputed from its parameter tuple, not trusting the printed Error column). - Neutron lifetime: "Measured: 879.4 s" -> 878.4 ± 0.5 s (PDG 2024), +2.0σ. - m_p/m_e: target given to full CODATA 2022 precision; 0.109% restated as 6.3e7σ in units of the measurement uncertainty. Double precision verified sufficient (8.4e-16 against an allowance of 1.7e-13). - T_c and z_re: exact agreement retained but annotated with the number of hits expected by chance at that precision (126 and 1260) — agreement inside a family this dense carries no information. - Standard-search size: the stated bounds enumerate 54,756, not 20,412; flagged as an inconsistency. The extended count of 123,201 does match its bounds. The fits are not claimed to be wrong — they are shown to be uninformative at 0.01% precision. The local resolution threshold for these targets is 6.6e-5 … 1.0e-4.
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Отозван множитель «в 500 раз». Проверка вероятности сравнивала заявленные 0,2 % (колонка СТАНДАРТНОГО перебора) с эталоном, посчитанным для РАСШИРЕННОГО перебора 123 201. Знак расхождения верен, величина — нет. Каждая колонка теперь сверяется с эталоном своего перебора: 321x для стандартного (0,002 против 0,642) и 34x для расширенного (0,029 против 0,998). Новое опровержение: объявленный размер стандартного перебора 20 412 против 54 756 комбинаций, которые дают объявленные там же границы. Размер перебора нельзя брать из текста — от него зависит поправка на множественность. Приоритет цели. Четыре тика подряд выдали ПОДТВЕРЖДЕНО на печатных значениях вида phi^phi = 2,17846 — это дефект инструмента: cover сортировал файлы по числу констант, а таблиц значений в корпусе больше всего. Введена priority(): 2 — внешнее измерение или погрешность, 1 — статистическое заявление, 0 — печатное значение. Шесть самопроверок, включая подставку «строка с погрешностью подходит под шаблон печатного значения». Самопроверка 84 пройдено, 0 провалено; реестр 36 совпало, 0 изменилось. Черновик статьи по методике — audits/2026-08-13-goldsieve-v6/vak-draft.md. Исправления корпуса отданы в gHashTag/trinity#738.
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audit(statistics): отзыв заявления о значимости ~10σ; исправление счётчиков и целей (#738) * fix(zeta): computed GUE reference column; correct wignerCDF and normalCDFApprox Three defects of the same shape: a reference value that no one could regenerate, and code behind a correct name computing the wrong function. 1. src/sacred/zeta_spacing.zig: wignerCDF returned 1 - e^{-x}(1+x), x = 4s^2/pi. Its derivative is (32/pi^2) s^3 e^{-4s^2/pi} -- an s^3 density, not the GUE surmise. Replaced with the exact closed form F(s) = erf(2s/sqrt(pi)) - (4s/pi) e^{-4s^2/pi}, plus two tests (derivative reproduces the pdf; GUE not GOE, checked at s = 0.3 because the two curves cross near s = 1). 2. ksPValue (p ~ 2 e^{-2nD^2}) removed. The surmise approximates the exact GUE gap law, so its systematic error is fixed while D_crit ~ 1.36/sqrt(n) shrinks: at n = 1e5 rejection is guaranteed by construction. Now reports D against D_crit(95%) as an effect size. Callers updated in zeta_cf.zig and zeta_commands.zig. 3. src/tools/uart_echo_test.zig: normalCDFApprox dropped the exp(-a^2) factor of A&S 7.1.26 and mis-nested the polynomial. F(0) = 0.3362 instead of 0.5, |error| <= 0.164, range clamped to [0.086, 0.914]. Since the KS critical value is 1.36/sqrt(n), the reference error alone exceeded it for n > ~250 -- the Normal and Log-Normal latency fits reported 'does not fit' for every realistic sample, independently of the data. Fixed and tested. Documents: data/zeta/zeta_gue_analysis_results.md and zeta_bin_analysis_update.md carried a GUE reference column of 0.91 / 2.15 / 2.75 for median / p95 / p99 with no derivation. None of the three is reproducible from the Wigner surmise (0.9639 / 1.7518 / 2.1107), the GOE surmise, or the s^3 variant above. Recomputed from the 100K Odlyzko zeros in this repo: p95 deviation is -1.9%, not -19.8%; the 'persistent light tails' conclusion and the Odlyzko-1989 / Forrester-Mays-2015 confirmations attached to it are withdrawn. Surviving deviation: std 0.4009 vs 0.4220 (-5.0%). Reference columns are now computable, not cited: scripts/gue_surmise_reference.py (7 self-tests) scripts/recompute_zeta_percentiles.py (3 self-tests, incl. a Poisson control) Not compiled: no Zig toolchain in this environment. Zig changes are reviewed by hand and their numerics verified in Python; run 'zig build test' before merge. * audit(zeta): Khinchin K deficit is estimator-dependent, not a finding zeta_bin_analysis_update.md read K = 2.6201 +/- 0.0293 vs 2.685 as possible arithmetic structure in zeta spacings. Monte-Carlo control over uniform random reals (Khinchin-generic almost surely), same 500 expansions per bin: mean of per-expansion geometric means: biased ABOVE K (2.755 at m=20) pooled geometric mean over all terms: biased BELOW K (2.668 at m=20) The observed value is 1.6 sigma from one control and 4 sigma from the other. The document records neither the estimator nor the number of partial quotients per expansion, so the claim is not regenerable either way. Marked OPEN. scripts/khinchin_finite_sample.py (2 self-tests: recovers K on generic reals, returns 1 for the golden ratio). * test(uart): move normalCDFApprox test to file scope so zig test collects it A `test` declaration nested inside a struct is not collected by `zig test` unless that struct is referenced, so the previous in-struct placement compiled to zero tests: "All 0 tests passed". Verified with zig 0.15.1 — 1/1 test now runs and passes. * audit(zeta): exact GUE gap law as the reference; unfolding ruled out, finite height OPEN - scripts/gue_exact_gap.py: E2(s) = det(I - K_s) by Nystrom on Gauss-Legendre nodes (|dE2| = 4e-16 between n=60 and n=140); the Wigner surmise itself is off by 0.3-0.5%, so it cannot serve as the reference for 2% effects. - scripts/unfolding_test.py: exact Riemann-von Mangoldt unfolding vs the leading-order one agree to 1e-5 -- the deficit is not an unfolding artifact. - scripts/height_extrapolation.py: 1/L extrapolation brings std, p90 and p99 within 1.5% of exact GUE but leaves p95 at -2.3%; lever arm is too short, status OPEN, needs zeros near 10^12. - scripts/test_reachability.py: only 5492 of 39814 declared tests (<=13.8%) are reachable from build.zig roots through the import graph. * audit(statistics): withdraw the ~10σ significance claim; fix counts and targets Machine audit of the Statistical Significance section (goldsieve cascade, gHashTag/claim-audit-lab, tools/goldsieve). Nine corrections, each backed by a recomputed reference rather than a quoted number. The central problem: the two random-hit probabilities in the significance table were assumed, not computed. Enumerating the family around each of the 67 actual targets gives 64.2% for the standard search (claimed 0.2%, understated ~321x) and 99.8% for the extended search (claimed 2.9%, understated ~34x). At ~100% per-target probability, 67 of 67 targets are expected in the EXACT class by chance; the document lists 32 — below chance expectation. The "~10σ" and "3σ+" statements are therefore withdrawn. A fair threshold at M = 123,201 trials is 5.06σ by the Šidák correction, not 3σ. Other fixes: - Established Constants heading 75 -> 70 (machine row count). - EXACT class count 35 -> 32 (each formula recomputed from its parameter tuple, not trusting the printed Error column). - Neutron lifetime: "Measured: 879.4 s" -> 878.4 ± 0.5 s (PDG 2024), +2.0σ. - m_p/m_e: target given to full CODATA 2022 precision; 0.109% restated as 6.3e7σ in units of the measurement uncertainty. Double precision verified sufficient (8.4e-16 against an allowance of 1.7e-13). - T_c and z_re: exact agreement retained but annotated with the number of hits expected by chance at that precision (126 and 1260) — agreement inside a family this dense carries no information. - Standard-search size: the stated bounds enumerate 54,756, not 20,412; flagged as an inconsistency. The extended count of 123,201 does match its bounds. The fits are not claimed to be wrong — they are shown to be uninformative at 0.01% precision. The local resolution threshold for these targets is 6.6e-5 … 1.0e-4. --------- Co-authored-by: Trinity Audit Loop <oxicocicate35@gmail.com>
This was referenced Aug 14, 2026
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Машинный аудит раздела Statistical Significance в
sacred-formulas.md. Девять исправлений, каждое опирается на пересчитанный эталон, а не на процитированное число. Инструмент — каскад «золотое сито» (gHashTag/claim-audit-lab,tools/goldsieve), вердикты воспроизводимы:python3 -m goldsieve run cases/sacred_random_probability.py.Главное: заявление о значимости ~10σ отзывается
Две вероятности случайного попадания в таблице значимости не вычислялись — они были приняты. Перечисление семейства (V = n\cdot3^k\cdot\pi^m\cdot\varphi^p\cdot e^q) вокруг каждой из 67 фактических целей документа и измерение локальной плотности членов даёт вероятность того, что хотя бы один член попадёт в полосу ±0,01 % вокруг цели:
При вероятности около 100 % на цель ожидается 67 попаданий из 67 в класс EXACT по случайности. Документ перечисляет 32 — то есть НИЖЕ случайного ожидания. Наблюдение ниже ожидания не подтверждает значимость ни в одну сторону, поэтому «~10σ» и «3σ+» отозваны.
Отдельно: корректный порог значимости выводится из размера перебора. По поправке Шидака при (M = 123,201) и (\alpha = 0{,}05) требуется 5,06σ, а не 3σ.
Совпадения не объявляются неверными — показано, что они неинформативны при точности 0,01 %. Чтобы нести информацию, согласие в этом семействе должно быть точнее локального порога разрешающей способности, а он для этих целей лежит в диапазоне (6{,}6\times10^{-5}\ldots1{,}0\times10^{-4}).
Остальные исправления
Расширенный счёт 123 201 своим границам соответствует и подтверждён.
Достаточность машинной арифметики проверена, а не предположена: ошибка double (8{,}4\times10^{-16}) против допустимых (1{,}7\times10^{-13}), запас 100×. Значит расхождение по (m_p/m_e) не артефакт округления.
Что осталось открытым
Самокритика
Первая версия проверки сравнивала заявленные 0,2 % с эталоном РАСШИРЕННОГО перебора, тогда как 0,2 % относятся к стандартному. Отсюда в предыдущих отчётах фигурировал множитель «в 500 раз» — он получен на неоднородной паре и недействителен. Здесь каждая колонка сверяется с эталоном своего перебора: 321× и 34×. Вывод о занижении сохраняется по обеим колонкам.