From 15b94242e05e5d8c914fdade40d1d5be7d0c3bc5 Mon Sep 17 00:00:00 2001 From: Valeri Sitnikov Date: Mon, 21 Sep 2026 01:17:25 +0100 Subject: [PATCH] Valeri's second point measured: the similarity function belongs to the PLACE it is read in, not to the method. False position's three-century stall is a similarity read at order one on an approach of order m: with sigma = |f(far)| the residual ratio is (e/E)^m, so raising it to the measured 1/m recovers the distance ratio exactly. Paired inside each cell, the correction is cheaper in 7 of 7 safeguards for S = 1/(1+z) - the one function that makes that place exact inverse interpolation - and in only 29 of 60 cells over all nine functions, i.e. a coin. It does NOT beat Chandrupatla (2884 against 2683 and 2423), it HARMS the slope reading (2806 -> 2854), and it does not cure false position: 127/154 and 10676 become 128/154 and 10043, where Illinois buys 153/154 and 7045 with one constant. Estimator bias measured and stated: a pure cube reads 2.830, not 3 Also fixes a real regression from cc2c499: the derived3_cap branch was inserted in front of the derived3_m note and swallowed its division, so derived3_m silently became derived3 (2806 against 2806) and a refutation recorded in the paper stopped being reproducible. The full pin caught it; a cheap pin now guards it too. And \label{sec:method} never existed while the table on page 7 referenced it. Co-Authored-By: Claude Opus 5 --- FINDINGS_similarity_per_slot.md | 68 ++++++++++++ PREREG_similarity_per_slot_2026-09-21.md | 83 +++++++++++++++ analyze_order.py | 106 +++++++++++++++++++ article/sim_numerics.pdf | Bin 398341 -> 404201 bytes article/sim_numerics.tex | 73 +++++++++++++ results_sweep_order.txt | 115 ++++++++++++++++++++ run_order_sweep.sh | 5 + simroot/pure.py | 71 +++++++++++-- sweep_full.py | 46 +++++++- sweep_order.json | 1 + sweep_order_smoke.json | 1 + tests/test_similarity_per_slot.py | 127 +++++++++++++++++++++++ verify_article.py | 71 +++++++++++++ 13 files changed, 756 insertions(+), 11 deletions(-) create mode 100644 FINDINGS_similarity_per_slot.md create mode 100644 PREREG_similarity_per_slot_2026-09-21.md create mode 100644 analyze_order.py create mode 100644 results_sweep_order.txt create mode 100644 run_order_sweep.sh create mode 100644 sweep_order.json create mode 100644 sweep_order_smoke.json create mode 100644 tests/test_similarity_per_slot.py diff --git a/FINDINGS_similarity_per_slot.md b/FINDINGS_similarity_per_slot.md new file mode 100644 index 0000000..4a91e13 --- /dev/null +++ b/FINDINGS_similarity_per_slot.md @@ -0,0 +1,68 @@ +# FINDINGS — функция похожести ПО МЕСТУ (слот 1) + +Пред-регистрация: `PREREG_similarity_per_slot_2026-09-21.md`. Сетка: 252 конфигурации × 199 задач, +сервер 161, `sweep_order.json`, лог `results_sweep_order.txt`. Якорь достоверности: +`pure.ratio.derived3` воспроизводит опубликованное **2806** бит-в-бит. + +## Вердикты + +| # | предсказание | вердикт | +|---|---|---| +| **L1** | показатель улучшает чтение по дальнему концу | **ВЕРНА — но только при соответствующей функции похожести** | +| **L2** | CHA < 2683 | **ЛОЖНА** — лучшее 2884 | +| **L3** | APS не хуже точки отсчёта | **ЛОЖНА в чтении по наклону** — 2806 → 2854 | +| **L4** | гарантия цела | **ВЕРНА** — 0 нарушений из 108 ячеек семейства гарантии | +| **L5** | шаг не выходит за скобку | **ВЕРНА** — закреплено тестом, с документированным насыщением до ровно 1.0 при `z ≳ 1/eps` | + +## Главное: место определяет функцию + +`far` + `rational` — единственное сочетание, в котором чтение по дальнему концу **есть** точная +обратная интерполяция. Там показатель выигрывает **7 из 7** предохранителей: + +| предохранитель | APS none → order | CHA none → order | +|---|---|---| +| both | 4522 → **3675** | 3387 → **3216** | +| bracket | 4606 → **3542** | 3571 → **3303** | +| credit | 5190 → **4686** | 3013 → **2884** | +| project | 6932 → **6364** | 4794 → **4559** | +| safe | 5987 → **5229** | 4108 → **3923** | +| step | 6435 → **5551** | 4257 → **4022** | +| none | 10676 → **10043** | 8265 → **7794** | + +По всем девяти функциям похожести — **29 из 60 ячеек**, то есть неотличимо от монеты. Вывод, который +это позволяет сделать: **показатель порядка не универсальное улучшение, а согласование функции +похожести с местом, где она читается.** Там, где функция месту не соответствует, измеренный порядок +не помогает и не мешает систематически. + +## Чего НЕ получилось, прямо + +1. **Chandrupatla не побит.** 2884 против 2683 (наше лучшее) и 2423 (его). Пятая попытка против + одной и той же измеренной причины. +2. **Стойло false position беспараметрически не вылечено.** Незащищённый: 127/154 и 10676 → 128/154 + и 10043 (−6%, +1 задача). Illinois с константой ½: 153/154 и 7045. Показатель снимает шестую + часть разрыва, а не разрыв. ⚠️ Наши 10676 и опубликованные 10560 — **не один алгоритм**: наш + метод стартует из середины скобки, классический false position — с конца. +3. **В чтении по наклону показатель вредит** на APS (2806 → 2854) и теряет задачи на CHA. + +## Измеренная граница оценки порядка + +Трёхточечная оценка читает **чистый куб как 2.830, а не 3** — смещение −5.7%, направленное к +единице, то есть к неисправленному чтению. Парабола через три точки несёт только вторую разность, +поэтому порядок кубики недооценивается даже в идеальном бесшумном случае. Закреплено тестом +`test_local_order_reads_a_cube_low_by_a_fixed_bias`; в статье должно стоять как смещение, а не как +точность. + +## Найденный по ходу баг (не в новом коде) + +Коммит `cc2c499` вставил ветку `derived3_cap` прямо перед примечанием `derived3_m` и **проглотил его +делитель**: `derived3_m` молча стал псевдонимом `derived3` (2806 против 2806), и опровержение, +записанное в статью, перестало воспроизводиться. Поймал полный пин +`test_m_loses_on_the_full_benchmark` — ровно то, для чего он и стоит. Исправлено; добавлен дешёвый +пин `test_derived3_m_actually_divides_by_the_order`. + +## Что остаётся неисследованным + +Слот 2 пред-регистрации: **место решения предохранителя**. Полоса приёма Чандрупатлы +(`1−√(1−ξ) < φ < √ξ`) — это другая функция похожести в другом месте: похожесть конфигурации на +линейную, читаемая не для длины шага, а для выбора «модель или деление». У нас в этом месте похожести +нет вовсе. Гонять отдельной сеткой. diff --git a/PREREG_similarity_per_slot_2026-09-21.md b/PREREG_similarity_per_slot_2026-09-21.md new file mode 100644 index 0000000..d565162 --- /dev/null +++ b/PREREG_similarity_per_slot_2026-09-21.md @@ -0,0 +1,83 @@ +# PREREG — функция похожести ПО МЕСТУ, а не одна на метод + +Составлено до прогона. Основание — два замечания Валерия 2026-09-21, идущие подряд: + +1. «просто функция похожести подобрана неверно» — про провал `derived3_cap`; +2. «в принципе функция похожести может быть разной в разных местах… В какой-то статье + упоминалось, что функция похожести может подбираться по домену. В нашем случае это не домен, + а **место параметра**». + +## 1. Что было не так в четырёх предыдущих попытках + +Все четыре (`cbrt`, логарифм, `derived3_m`, `derived3_cap`) меняли **масштаб** `σ`, оставляя +**одну** функцию `S` на весь метод. Измеренная причина разрыва при этом ни разу не была затронута: +недолёт **линейной модели**, 0.93 против 2.26 половинений на пробу. + +## 2. Прочитанное до прогона (корпус экономит замер) + +`article/sim_numerics.tex`, Предложение 4: чтение похожести **по концам скобки** с рациональной +похожестью `S = 1/(1+z)` **тождественно false position** — 127/154, 10560 оценок. То есть слот +«масштаб = значение на дальнем конце» **уже закрыт при `m = 1`**. Гипотеза ниже — ровно про то, +почему он закрыт: стойло false position трёхвековой давности есть чтение похожести **на порядке 1** +там, где подход имеет порядок `m`. + +## 3. Слот 1 — длина шага: показатель = ИЗМЕРЕННЫЙ порядок + +Для `f ≈ K·e^m` (`e = |x − r|`) отношение остатков безразмерно и не требует наклона: + + z = |f(x)| / |f(far)| = (e/E)^m ⇒ z^(1/m) = e/E + +а доля шага до дальнего конца при обратной интерполяции есть `t/(1+t)`, `t = z^(1/m)`. При `m = 1` +это **в точности false position** (Предложение 4), при `m > 1` — обратная интерполяция **порядка m**, +которая для чистой степени попадает в корень **за один шаг**. Показатель `1/m` **не выбирается**: +`m = 1/(1 − f·f''/f'²)` считается `_local_order` по трём уже сделанным оценкам и равен 1, когда +степенная модель не применима. + +**Почему это не повторение `derived3_m`.** Там `m` стоял **делителем масштаба** в чтении по наклону, +где, как доказано в docstring, показатель схлопывается в множитель. Здесь `m` стоит **показателем над +безразмерным отношением**, и схлопывания нет. Плюс структурное свойство: `t/(1+t) < 1` всегда, то +есть шаг **никогда не выходит за скобку** — ложное `m > 1` (27.9% шагов на APS) ограничено дальним +концом, а не проецируется предохранителем. + +**Режимы:** новая шкала `scale="far"` (σ = |f| на том конце, к которому шаг) и новый ключ +`exponent="none"|"order"`. По умолчанию `"none"` — опубликованное поведение бит-в-бит. + +### Сетка (контроль внутри самой сетки) + +Внутри каждой тройки (`S`, шкала, предохранитель) меняется **ровно одно** — показатель. Если +`order` не бьёт `none` в паре `far`+`rational`, гипотеза мертва без толкований. + +## 4. Слот 2 — решение предохранителя (объявляется здесь, гоняется ПОСЛЕ слота 1) + +Чандрупатла выигрывает не шагом, а **полосой приёма**: `1−√(1−ξ) < φ < √ξ`. В наших терминах это +**другая функция похожести в другом месте** — похожесть конфигурации на линейную (`|φ − ξ|`), +читаемая не для длины шага, а для решения «модель или деление». Сейчас у нас в этом месте похожести +нет вовсе: знаковый гейт и проекция. Гоняется **отдельной сеткой после слота 1**, чтобы не смешать +два изменения. + +## 5. Точка отсчёта и цели + +| величина | текущее | цель | +|---|---|---| +| APS-154 | 2726 (лучшее 2527) | **≤ 2527** | +| CHA-45 по-наборно | 2683 | **< 2683** (Chandrupatla 2423) | +| два набора | 5511 | **< 5511** | +| решено | 193/199 | ≥ 193 | +| гарантия `over2x` | 0 | **0** | + +## 6. Предсказания и фальсификаторы + +| # | Предсказание | ФАЛЬСИФИКАТОР → вывод | +|---|---|---| +| **L1** | `exponent="order"` улучшает `far`-чтение против `none` в той же тройке | не улучшает → порядок как показатель над отношением остатков не лечит стойло false position; слот 1 закрыт | +| **L2** | лучшая конфигурация слота 1 даёт CHA < 2683 | не даёт → измеренная причина не устраняется и местом похожести тоже | +| **L3** | APS не хуже 2726 | хуже → снова обмен «широкие за счёт узких», пятый раз | +| **L4** | гарантия цела (`over2x = 0`) | нарушена → немедленное закрытие | +| **L5** | шаг ни разу не выходит за скобку в режиме `far` (проекция предохранителя не срабатывает) | срабатывает → вывод `t/(1+t) < 1` неверно реализован, это баг, а не результат | + +**Правило остановки:** L1 ложна ⇒ слот 1 закрывается, слот 2 гоняется всё равно (это другое место). +L1 верна, L2 ложна ⇒ улучшение записывается как есть, без заявки на Chandrupatla. L4 ложна ⇒ стоп. + +🔴 **Запрет на подбор:** «своя `S` в каждом месте» не даёт права перебрать меню `S` и объявить +победителя. Показатель в слоте 1 **измеряется** (`_local_order`), а не выбирается. Любой выбор `S` +из списка остаётся тем же изъяном, что жёсткая константа, и отчёт обязан называть его выбором. diff --git a/analyze_order.py b/analyze_order.py new file mode 100644 index 0000000..34d2b2c --- /dev/null +++ b/analyze_order.py @@ -0,0 +1,106 @@ +"""Verdicts L1-L5 for PREREG 2026-09-21 slot 1, read off sweep_order.json. + +Nothing here selects a winner by hunting: L1 is a PAIRED comparison inside each +(similarity, guard) cell, which is the only comparison the pre-registration licenses. + + python -u analyze_order.py +""" +from __future__ import annotations + +import json +import math + +REF = {"APS_base": 2806, "APS_best": 2527, "CHA_best": 2683, "BOTH_best": 5511, + "falsepos": (127, 10560), "illinois": (153, 7045), "bisect": (153, 7530)} + + +def load(): + with open("sweep_order.json", encoding="utf8") as fh: + return json.load(fh) + + +def key(r): + s = r["spec"] + return (s[1], s[2], s[3], s[8] if len(s) > 8 else "none") + + +def main(): + res = load() + by = {key(r): r for r in res} + + print("L1 PAIRED: does the measured order improve the FAR reading? " + "(the only licensed comparison)") + print(f"{'similarity':<11} {'guard':<9} {'APS none':>9} {'APS ord':>8} " + f"{'CHA none':>9} {'CHA ord':>8} {'solved n/o':>12}") + wins = losses = 0 + for (sim, sc, gu, ex) in sorted(by): + if sc != "far" or ex != "none": + continue + a, b = by[(sim, sc, gu, "none")], by.get((sim, sc, gu, "order")) + if b is None: + continue + d = (a["APS"]["total"] + a["CHA"]["total"]) - (b["APS"]["total"] + b["CHA"]["total"]) + wins += d > 0 + losses += d < 0 + print(f"{sim:<11} {gu:<9} {a['APS']['total']:9d} {b['APS']['total']:8d} " + f"{a['CHA']['total']:9d} {b['CHA']['total']:8d} " + f"{a['APS']['solved']}+{a['CHA']['solved']}/" + f"{b['APS']['solved']}+{b['CHA']['solved']:>2}") + print(f" -> order cheaper in {wins} of {wins + losses} far cells\n") + + print("L1b same pairing on the DERIVED3 reading") + for (sim, sc, gu, ex) in sorted(by): + if sc != "derived3" or ex != "none" or gu not in ("safe", "project", "none"): + continue + a, b = by[(sim, sc, gu, "none")], by.get((sim, sc, gu, "order")) + if b is None: + continue + print(f"{sim:<11} {gu:<9} {a['APS']['total']:9d} {b['APS']['total']:8d} " + f"{a['CHA']['total']:9d} {b['CHA']['total']:8d} " + f"{a['APS']['solved']}+{a['CHA']['solved']}/" + f"{b['APS']['solved']}+{b['CHA']['solved']:>2}") + + print("\nL2/L3 best cells in the grid, by the paper's per-set rule " + "(solved first, then cost)") + for setname, target in (("APS", REF["APS_best"]), ("CHA", REF["CHA_best"])): + rows = sorted(res, key=lambda r: (r[setname]["n"] - r[setname]["solved"], + r[setname]["total"])) + for r in rows[:3]: + s = r["spec"] + print(f" {setname} {r['label']:<38} {r[setname]['solved']}/" + f"{r[setname]['n']} {r[setname]['total']:6d} " + f"over2x={r[setname]['over']} " + f"(target {target}) exponent={s[8] if len(s) > 8 else 'none'}") + + print("\nL4 guarantee: cells with over2x > 0 (any set)") + bad = [r["label"] for r in res if r["APS"]["over"] or r["CHA"]["over"]] + print(f" {len(bad)} of {len(res)}" + (f": {bad[:6]}" if bad else " -> intact")) + + print("\nFALSE POSITION, unguarded: is the measured order the parameter-free Illinois?") + print(f" {'cell':<34} {'solved':>7} {'APS fev':>9}") + print(f" {'false position (paper)':<34} {REF['falsepos'][0]}/154 " + f"{REF['falsepos'][1]:9d}") + print(f" {'Illinois (constant 1/2)':<34} {REF['illinois'][0]}/154 " + f"{REF['illinois'][1]:9d}") + for ex in ("none", "order"): + r = by.get(("rational", "far", "none", ex)) + if r: + print(f" {'far+rational, guard=none, ' + ex:<34} " + f"{r['APS']['solved']}/154 {r['APS']['total']:9d}") + for ex in ("none", "order"): + r = by.get(("rational", "far", "safe", ex)) + if r: + print(f" {'far+rational, guard=safe, ' + ex:<34} " + f"{r['APS']['solved']}/154 {r['APS']['total']:9d}") + + print("\nBOTH SETS, best order cell against the reference 5511") + rows = [r for r in res if len(r["spec"]) > 8 and r["spec"][8] == "order"] + rows.sort(key=lambda r: (398 - r["APS"]["solved"] - r["CHA"]["solved"], + r["APS"]["total"] + r["CHA"]["total"])) + for r in rows[:3]: + print(f" {r['label']:<38} {r['APS']['solved'] + r['CHA']['solved']}/199 " + f"{r['APS']['total'] + r['CHA']['total']:6d} (reference {REF['BOTH_best']})") + + +if __name__ == "__main__": + main() diff --git a/article/sim_numerics.pdf b/article/sim_numerics.pdf index 0210fda04e0fd3f8412d3bafa041358a9f5b7b5d..459b6a261227840d7d7751066209ee7feb591e46 100644 GIT binary patch delta 158027 zcmV)EK)}C+s2J(h7!f5LTHB7>MiPD3SM*~7 zY+7AieO(v<5_`QHV6zBp1ADROL8GCa*~pSt;`s9Sdx|6RB9aovBN&)rQ)IFG^r@;- z&6Y?Rm6(;4PFz+N z-I$oATO!=XEwXCzZh9=OP% z#ZZLn9ypkT0y@h8?13cOr~;u4b{4E+nNPqBDFlT-X3QaAXeZE(Vow1xL5slzS};*X z*ayxk!ahb!I4aKMW;k`m;j=(aR^iVv=t+Rc0D;CCqmq9?3z$S6Qvg^3c9(<=Fz0d* zn!NJ(G$Rn~txO!_dQM`Kz&FX2tbD-S3I6ag;i-Ecu#yHm5u6bWfjtWc8V}kqSu$ou z*5Sl~Z;v*CXZR*qw&DPsU}gk|1h(>U#tAqg2?J+jKs@aPI6M}DmyywNGBhI+`owXF zj%cDh1tNdp7Muu^-c}(LIg9f^sW=z*(Iv6P6_4>`4j#0VGhmtGj1VI+z+ohQNMM*i 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zH5So-k?L6&v$H}!yE0+)yq41+w|Sgtk!Q>B)|gIPo}TsznAqcPD3qnyZhp}t zn`y2QspIb5&cqYImW-_%PrV&!l%Y%((RUQDdN4s|-<4TDT@TtQN@MXhjXf}Y#P7Yti8fKwcEhE^z=odHQHj%5CX3QP!Af~ z@*`IVPC5yIYeBJ_tTTMCkS>y#1$wRi_{ZGR?%&#ZdL!@Ae+hcGHBSb(^n3|Dzp`O} z+2(MrxME6%7Vc4JV_WfW;*4WS#S6DJ@8|2tmM~+Bj+v8;iUu2J4vRaaXI0lH*!7=4 zd=@?RPJArzEixE?oe6LKSf6tK8tjm?#eJCo%FBwjtfp|Ai9+I-TKPwJ&ov8+Ygxkh z;(t4cMtkkDY*_?Vewmi_+AO!3+)Tfa`!N4C&E KxVDiF^Zx*G>k{bz diff --git a/article/sim_numerics.tex b/article/sim_numerics.tex index c7b6acb..6138979 100644 --- a/article/sim_numerics.tex +++ b/article/sim_numerics.tex @@ -213,6 +213,7 @@ the evaluations. \end{corollary} \section{The method} +\label{sec:method} Corollaries~\ref{cor:chosen}--\ref{cor:derived} fix every choice in the method before any benchmark is consulted. We record them here as a prediction, and @@ -563,6 +564,66 @@ The readings do not compose. Taken together, (2) and (3) give $2884$ and $2859$ --- worse than either alone. Two selections that are each an improvement interfere, which is a reason to measure composition rather than assume it. +\subsection{The similarity function belongs to the place, not to the method} +\label{sec:perplace} + +Everything above varies \emph{where} the similarity is read while keeping one +function $S$ for the whole method. That is itself an assumption, and it is +measurable. Proposition~\ref{prop:falsi} says the two-point normalisation is +false position; what it does not say is \emph{why} false position stalls. Write +$|f|\sim K e^m$ near the current point, $e=|x-r|$. Then the residual ratio +against the far end needs no slope at all, +\begin{equation} +\label{eq:orderz} +z \;=\; \frac{|f(x)|}{|f(x_{\mathrm{far}})|} \;=\; \Bigl(\frac{e}{E}\Bigr)^{m}, +\qquad\text{so}\qquad z^{1/m} \;=\; \frac{e}{E}, +\end{equation} +and under $S=1/(1+z)$ the step fraction is $z/(1+z)$, which is exactly inverse +linear interpolation. False position therefore reads a dimensionless ratio +\emph{at order one} on an approach of order $m$: its three-century-old stall is +a mismatch between the similarity function and the place it is read in. The +exponent $1/m$ is not a constant --- $m=1/(1-ff''/f'^2)$ comes from three +evaluations already paid for, and is $1$ whenever the power model does not +apply. + +Measured over the $252$ cells of the grid, the correction behaves exactly as +that reading predicts and not at all as a universal improvement. Paired inside +each (function, safeguard) cell of the far reading it is cheaper in $29$ of +$60$ cells --- indistinguishable from a coin. But in the one pairing where the +far reading \emph{is} exact inverse interpolation, $S=1/(1+z)$, it is cheaper +in all seven safeguards: + +\begin{table}[h] +\centering +\begin{tabular}{lrrrr} +\toprule +safeguard & APS $m{=}1$ & APS measured $m$ & CHA $m{=}1$ & CHA measured $m$\\ +\midrule +both & 4522 & \textbf{3675} & 3387 & \textbf{3216}\\ +bracket & 4606 & \textbf{3542} & 3571 & \textbf{3303}\\ +credit & 5190 & \textbf{4686} & 3013 & \textbf{2884}\\ +project & 6932 & \textbf{6364} & 4794 & \textbf{4559}\\ +safe & 5987 & \textbf{5229} & 4108 & \textbf{3923}\\ +step & 6435 & \textbf{5551} & 4257 & \textbf{4022}\\ +none & 10676 & \textbf{10043} & 8265 & \textbf{7794}\\ +\bottomrule +\end{tabular} +\caption{The measured order in the step place, on the far reading. Cheaper in +$7$ of $7$ safeguards for the similarity that matches the place, and in $29$ of +$60$ cells over all nine functions.} +\end{table} + +Two limits must be stated with it. The estimator is \emph{biased low}: on a +pure cube, with no noise at all, it returns $2.830$ rather than $3$, because a +parabola through three points carries only the second difference. The bias is +towards $m=1$, that is towards the uncorrected reading, which is the harmless +direction, but it is a bias. And the correction does not rescue the bracket +reading as a method: the best cell it reaches on the wide-bracket set is +$2884$, against $2683$ for reading~(3) above and $2423$ for Chandrupatla. In +the \emph{slope} reading the same exponent is harmful, $2806\to2854$, which is +the same statement read from the other side --- a function that does not belong +to a place does not become right by being applied there. + \subsection{Six problems of the two sets are scored unsolved for every method} \label{sec:fun7} @@ -693,6 +754,18 @@ $3288$ on the canonical set against $2726$, and $3111$ on the wide-bracket set against $2683$. Its apparent extra solves ($194$ instead of $193$) are two \texttt{fun7} problems where it lands inside the flat zero region close enough to satisfy the harness --- the artefact of \S\ref{sec:fun7}, not a capability. +\item \textbf{Reading the similarity at the measured order does not cure false +position.} Since false position's stall is a similarity read at order one +(\S\ref{sec:perplace}), the obvious hope is that reading it at the measured +order is the parameter-free version of the classical fix. It is not. Unguarded, +the correction takes the bracket reading from $127/154$ and $10676$ to $128/154$ +and $10043$ --- one problem and six per cent --- where Illinois, at the price of +one constant (halve the stale ordinate), reaches $153/154$ and $7045$. A sixth +of the gap is not the gap. The correction is real and it is in the right place; +it is simply much smaller than a constant that was chosen for exactly this +failure. \emph{Our} $10676$ and the $10560$ of Table~\ref{tab:aps} are not +the same algorithm --- our iterate starts at the midpoint of the bracket, plain +false position at an end --- and the two must not be differenced. \item \textbf{A logarithmic change of variable does not buy the wide brackets.} Working in $u=\operatorname{sign}(x-c)\log(1+|x-c|/\varepsilon_x)$ makes the step multiplicative, which is the right diagnosis of the flat families --- CHA diff --git a/results_sweep_order.txt b/results_sweep_order.txt new file mode 100644 index 0000000..fd840d7 --- /dev/null +++ b/results_sweep_order.txt @@ -0,0 +1,115 @@ +sweep: 252 configurations x 199 problems (FULL) + 10/252 done, 0s elapsed + 20/252 done, 0s elapsed +/home/valeri/sim-numerics/simroot/pure.py:116: RuntimeWarning: overflow encountered in scalar multiply + "cosine": lambda z: 1.0 / math.sqrt(1.0 + z * z), + 30/252 done, 1s elapsed +/home/valeri/sim-numerics/simroot/pure.py:116: RuntimeWarning: overflow encountered in scalar multiply + "cosine": lambda z: 1.0 / math.sqrt(1.0 + z * z), +/home/valeri/sim-numerics/simroot/pure.py:116: RuntimeWarning: overflow encountered in scalar multiply + "cosine": lambda z: 1.0 / math.sqrt(1.0 + z * z), +/home/valeri/sim-numerics/simroot/pure.py:116: RuntimeWarning: overflow encountered in scalar multiply + "cosine": lambda z: 1.0 / math.sqrt(1.0 + z * z), + 40/252 done, 1s elapsed + 50/252 done, 1s elapsed + 60/252 done, 1s elapsed + 70/252 done, 2s elapsed +/home/valeri/sim-numerics/simroot/pure.py:115: RuntimeWarning: overflow encountered in scalar multiply + "exp_sq": lambda z: math.exp(-z * z), + 80/252 done, 2s elapsed + 90/252 done, 2s elapsed + 100/252 done, 2s elapsed + 110/252 done, 2s elapsed +/home/valeri/sim-numerics/simroot/pure.py:114: RuntimeWarning: overflow encountered in scalar multiply + "rat_sq": lambda z: 1.0 / (1.0 + z * z), +/home/valeri/sim-numerics/simroot/pure.py:114: RuntimeWarning: overflow encountered in scalar multiply + "rat_sq": lambda z: 1.0 / (1.0 + z * z), + 120/252 done, 3s elapsed +/home/valeri/sim-numerics/simroot/pure.py:114: RuntimeWarning: overflow encountered in scalar multiply + "rat_sq": lambda z: 1.0 / (1.0 + z * z), + 130/252 done, 3s elapsed + 140/252 done, 3s elapsed + 150/252 done, 3s elapsed + 160/252 done, 3s elapsed +/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power + "ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2, +/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power + "ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2, +/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power + "ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2, +/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power + "ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2, + 170/252 done, 4s elapsed +/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power + "ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2, +/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power + "ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2, +/home/valeri/sim-numerics/simroot/pure.py:110: RuntimeWarning: overflow encountered in scalar power + "ratio_soft": lambda z: 1.0 / (1.0 + abs(z)) ** 2, + 180/252 done, 4s elapsed + 190/252 done, 4s elapsed + 200/252 done, 4s elapsed + 210/252 done, 4s elapsed + 220/252 done, 4s elapsed + 230/252 done, 4s elapsed + 240/252 done, 5s elapsed + 250/252 done, 5s elapsed + 252/252 done, 5s elapsed +wrote sweep_order.json (5s total) +==================================================================================== +APS: 154 problems (top 20 of 252) +==================================================================================== +configuration solved total fev over 2x +------------------------------------------------------------------------------------ +pure.ratio.derived3.none 153/154 2806 0 +pure.ratio.derived3.project 153/154 2806 0 +pure+ord.ratio.derived3.none 153/154 2854 0 +pure+ord.ratio.derived3.project 153/154 2854 0 +pure+ord.ratio.derived3.step 153/154 3000 0 +pure+ord.ratio.derived3.safe 153/154 3000 0 +pure.ratio.derived3.step 153/154 3036 0 +pure.ratio.derived3.safe 153/154 3036 0 +pure+ord.exp_abs.derived3.project 153/154 3227 0 +pure+ord.exp_abs.derived3.none 153/154 3227 0 +pure.exp_abs.derived3.none 153/154 3264 0 +pure.exp_abs.derived3.project 153/154 3264 0 +pure+ord.exp_abs.derived3.step 153/154 3308 0 +pure+ord.exp_abs.derived3.safe 153/154 3308 0 +pure.exp_abs.derived3.step 153/154 3312 0 +pure.exp_abs.derived3.safe 153/154 3312 0 +pure.rational.derived3.none 153/154 3356 0 +pure.rational.derived3.project 153/154 3356 0 +pure.rational.derived3.step 153/154 3420 0 +pure.rational.derived3.safe 153/154 3420 0 + +==================================================================================== +CHA: 45 problems (top 20 of 252) +==================================================================================== +configuration solved total fev over 2x +------------------------------------------------------------------------------------ +pure.sqrt.far.project 41/45 4516 0 +pure+ord.rational.far.credit 40/45 2884 0 +pure+ord.ratio.derived3.credit 40/45 2994 0 +pure.rational.far.credit 40/45 3013 0 +pure.cbrt.derived3.credit 40/45 3016 0 +pure.ratio.derived3.credit 40/45 3020 0 +pure+ord.cbrt.derived3.credit 40/45 3029 0 +pure.exp_abs.far.credit 40/45 3034 0 +pure+ord.exp_abs.far.credit 40/45 3035 0 +pure+ord.ratio_soft.derived3.credit 40/45 3039 0 +pure.exp_abs.derived3.credit 40/45 3049 0 +pure.ratio_soft.derived3.credit 40/45 3054 0 +pure+ord.exp_abs.derived3.credit 40/45 3067 0 +pure.sqrt.far.credit 40/45 3094 0 +pure+ord.sqrt.far.credit 40/45 3096 0 +pure.ratio.far.credit 40/45 3113 0 +pure.cbrt.far.credit 40/45 3127 0 +pure+ord.rat_sq.far.credit 40/45 3128 0 +pure.rat_sq.far.credit 40/45 3129 0 +pure+ord.cbrt.far.credit 40/45 3130 0 + +==================================================================================== +THE STAGE-0C LAW ACROSS THE GRID +==================================================================================== + scale=derived3 slope c=1 (linear) mean total 6910 mean solved 192.2/199 + scale=derived3 slope c=0 (quadratic) mean total 22334 mean solved 192.8/199 diff --git a/run_order_sweep.sh b/run_order_sweep.sh new file mode 100644 index 0000000..b382c3b --- /dev/null +++ b/run_order_sweep.sh @@ -0,0 +1,5 @@ +#!/bin/bash +# Frozen runner for PREREG 2026-09-21 slot 1 (the similarity read BY PLACE). +# Frozen on purpose: editing a .sh while it runs has broken a run before. +cd "$HOME/sim-numerics" || exit 1 +exec ~/torchenv/bin/python -u sweep_full.py --order diff --git a/simroot/pure.py b/simroot/pure.py index dcae4c6..0538aa4 100644 --- a/simroot/pure.py +++ b/simroot/pure.py @@ -124,6 +124,38 @@ SPACES = ("x", "log") POINT_RULES = ("recent", "shape") DIRECTIONS = ("distance", "dissimilar") +EXPONENTS = ("none", "order") + + +def _read_z(resid, sc, exponent, m): + """The normalised residual the similarity function is applied to. + + Valeri, 2026-09-21: "the similarity function may simply be the wrong one", and then + "the similarity function can differ in different PLACES - not by domain, by the place + of the parameter". This is the step-length place, and here the reading is fixed by + what f looks like locally rather than chosen. + + For |f| ~ K.e^m the residual ratio against the far end is dimensionless and needs no + slope at all: z = |f(x)|/|f(far)| = (e/E)^m, so z^(1/m) = e/E recovers the DISTANCE + ratio exactly. Under S = 1/(1+z) the step fraction is z/(1+z), which at m = 1 is + false position (Proposition 4 in the paper: 127/154, 10560 evaluations) - and false + position's three-century-old stall is precisely a similarity read at order 1 on an + order-m approach. Reading it at the MEASURED order turns the same formula into + order-m inverse interpolation, exact in one step for a pure power. + + m comes from _local_order, i.e. from three evaluations already paid for, and is 1 + whenever the power model does not apply, so nothing here is selected. + """ + z = resid / sc + if exponent == "order" and m is not None and m > 1.0 and z > 0.0: + try: + z = z ** (1.0 / m) + except (OverflowError, ValueError): + return resid / sc + if not math.isfinite(z): + return resid / sc + return z + def _shape_defect(x, fx, u, fu, v, fv): """|phi - xi| for the triple, or None when it is degenerate. @@ -455,7 +487,7 @@ def _local_order(x2, f2, x1, f1, x0, f0): def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", guard="step", stats=None, budget_factor=2.0, budget_extra=None, endowment=1.0, space="x", prestep="none", - points="recent", direction="distance"): + points="recent", direction="distance", exponent="none"): """The pure similarity root finder. similarity : key into PURE_SIMS @@ -505,8 +537,16 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", if similarity not in PURE_SIMS: raise ValueError(f"unknown similarity {similarity!r}") if scale not in ("derived", "derived3", "derived_rho", "derived3_rho", - "derived3_m", "derived3_cap", "start", "bracket"): + "derived3_m", "derived3_cap", "start", "bracket", "far"): raise ValueError(f"unknown scale {scale!r}") + if exponent not in EXPONENTS: + raise ValueError(f"unknown exponent {exponent!r}") + if exponent == "order" and scale not in ("derived3", "derived3_cap", "bracket", "far"): + # the order is read from a three-point divided difference; under the two-point + # scale there is no second difference to read it from, and computing one from + # elsewhere would hide that (PREREG 2026-09-21, slot 1) + raise ValueError("exponent='order' requires scale in " + "{'derived3', 'derived3_cap', 'bracket', 'far'}") if space not in SPACES: raise ValueError(f"unknown space {space!r}") if prestep not in ("none", "progress", "slope"): @@ -604,6 +644,11 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", else: slope = _slope3(x, fx, x_prev, f_prev, x_prev2, f_prev2) sc = abs(slope) * abs(far - x) + if scale == "derived3_m": + # REFUTED as an improvement; kept so the refutation stays + # REPRODUCIBLE, which is the whole point of keeping it. The long + # note is at the end of the derived3_cap branch below. + sc /= _local_order(x, fx, x_prev, f_prev, x_prev2, f_prev2) elif scale == "derived3_cap": # Valeri, 2026-09-21: "if the similarity formed the step, the step would be # large far from the target and small near it". It does not, and the reason @@ -617,7 +662,12 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", # order) returns. A min over what is in hand - no constant, no threshold. slope = _slope3(x, fx, x_prev, f_prev, x_prev2, f_prev2) sc = min(abs(slope) * abs(far - x), max(abs(FA), abs(FB))) - if scale == "derived3_m": + # NOTE on scale="derived3_m" (the live code is in the derived3 branch + # above). On 2026-09-21 the derived3_cap branch was inserted directly + # in front of this note and swallowed the division with it, so + # derived3_m silently became derived3 - 2806 against 2806 - and the + # refutation stopped being reproducible. test_m_loses_on_the_full + # _benchmark caught it, which is what that pin is for. # REFUTED as an improvement - kept for reproducibility. # The DERIVATION holds: dropping the linearity # assumption from the contraction law does produce the @@ -646,10 +696,14 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", # rho it is read from the CURVATURE, which stays # meaningful as |f| goes to zero, and it returns to 1 # at a simple root, leaving the endgame untouched. - sc /= _local_order(x, fx, x_prev, f_prev, - x_prev2, f_prev2) elif scale == "start": sc = start_scale + elif scale == "far": + # the value at the end the step AIMS AT, already computed. With + # S = 1/(1+z) this is false position exactly (Proposition 4), which + # is why it is the honest control for the order exponent: the pair + # (far, none) against (far, order) differs in one thing only. + sc = abs(FB) if far == B else abs(FA) else: sc = max(abs(FA), abs(FB)) if scale.endswith("_rho"): @@ -696,6 +750,9 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", if sc == 0.0 or not math.isfinite(sc): x_new = 0.5 * (A + B) else: + m_loc = (_local_order(x, fx, x_prev, f_prev, x_prev2, f_prev2) + if exponent == "order" else None) + z_now = _read_z(abs(fx), sc, exponent, m_loc) step = None if prestep == "slope": # PRE-STEP GATE ON SHAPE (PREREG 2026-09-21). The step trusts the @@ -720,7 +777,7 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", # less than bisection would remove, spend the same single # evaluation on the midpoint instead. Two lengths already in hand # are compared; there is no threshold and no new constant. - cand = (1.0 - S(abs(fx) / sc)) * (far - x) + cand = (1.0 - S(z_now)) * (far - x) half = 0.5 * (A + B) - x if abs(cand) < abs(half): step = half @@ -734,7 +791,7 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", c_near = A if abs(FA) <= abs(FB) else B step = _log_space_step(S, x, fx, far, slope, c_near, xtol) if step is None: - step = (1.0 - S(abs(fx) / sc)) * (far - x) + step = (1.0 - S(z_now)) * (far - x) if sg.reject_step(step): x_new = 0.5 * (A + B) step = x_new - x diff --git a/sweep_full.py b/sweep_full.py index de779b7..fb637c3 100644 --- a/sweep_full.py +++ b/sweep_full.py @@ -113,11 +113,12 @@ def make_method(spec): prestep = spec[5] if len(spec) > 5 else "none" points = spec[6] if len(spec) > 6 else "recent" direction = spec[7] if len(spec) > 7 else "distance" + exponent = spec[8] if len(spec) > 8 else "none" def m(f, a, b, xtol, maxfev): return pure_root(f, a, b, xtol, maxfev, similarity=sim, scale=scale, guard=guard, space=space, prestep=prestep, - points=points, direction=direction) + points=points, direction=direction, exponent=exponent) return m @@ -131,6 +132,11 @@ def label(spec): tag = f"{tag}+shape" if len(spec) > 7 and spec[7] != "distance": tag = f"{tag}+dissim" + if len(spec) > 8 and spec[8] != "none": + # the exponent must be visible in the label: (far, none) is false position and + # (far, order) is the hypothesis, and a results file that cannot tell them apart + # is worthless + tag = f"{tag}+ord" if len(spec) > 5 and spec[5] != "none": # name the gate by WHICH gate it is: "progress" is a measured negative and must # never be confused with "slope" in a results file @@ -198,6 +204,35 @@ def build_grid_log(smoke): for sim in sims for sc in ("derived", "derived3") for gu in guards] +def _preflight_order_mode(): + """Fail LOUDLY if the per-place reading is not actually deployed. + + Same lesson as _preflight_log_mode: `evaluate` swallows every exception and charges + MAXFEV, so a stale simroot/pure.py on the server reports a sweep of zeros instead of + an error. Checks BOTH new things — the far scale and the order exponent.""" + for sc, ex in (("far", "none"), ("far", "order"), ("derived3", "order")): + x, _n, ok = pure_root(lambda t: t - 1.0, 0.0, 3.0, 1e-10, 100, + similarity="rational", scale=sc, guard="credit", + exponent=ex) + if not (ok and abs(x - 1.0) < 1e-8): + raise SystemExit(f"order-mode preflight FAILED for scale={sc} exponent={ex}: " + "refusing to run a sweep that would report zeros") + + +def build_grid_order(smoke): + """Slot 1 of PREREG 2026-09-21: the similarity function read BY PLACE. + + The exponent is the only thing that moves inside each (similarity, scale, guard) + triple, so (far, none) — which is false position exactly, Proposition 4 — is the + control for (far, order). Baselines are not recomputed; they are in sweep_full.json.""" + _preflight_order_mode() + sims = ["rational", "ratio"] if smoke else sorted(PURE_SIMS) + guards = ("credit", "safe") if smoke else GUARD_MODES + return [("pure", sim, sc, gu, "x", "none", "recent", "distance", ex) + for sim in sims for sc in ("far", "derived3") + for ex in ("none", "order") for gu in guards] + + def build_grid_cap(smoke): """Scale as a SELECTION between the two computed ones (PREREG 2026-09-21): identical to the slope+dissimilar configuration except scale = derived3_cap, so one thing changes.""" @@ -274,10 +309,12 @@ def main(): gatemode = "--gate" in sys.argv # the pre-step gate grid, likewise slopemode = "--slope" in sys.argv # the slope-stability gate grid capmode = "--cap" in sys.argv # scale selected between the two computed ones + ordermode = "--order" in sys.argv # slot 1: the similarity read BY PLACE combomode = "--combo" in sys.argv # modes A and B together pointsmode = "--points" in sys.argv # mode A: triple by shape dirmode = "--direction" in sys.argv # mode B: far end by dissimilarity - specs = (build_grid_cap(smoke) if capmode else + specs = (build_grid_order(smoke) if ordermode else + build_grid_cap(smoke) if capmode else build_grid_combo(smoke) if combomode else build_grid_points(smoke) if pointsmode else build_grid_direction(smoke) if dirmode else @@ -299,8 +336,9 @@ def main(): # the published sweep_full.json is what verify_article.py checks the paper # against, so the log grid never writes into it - if capmode or combomode or pointsmode or dirmode: - base = ("sweep_cap" if capmode else + if ordermode or capmode or combomode or pointsmode or dirmode: + base = ("sweep_order" if ordermode else + "sweep_cap" if capmode else "sweep_combo" if combomode else "sweep_points" if pointsmode else "sweep_direction") out = f"{base}_smoke.json" if smoke else f"{base}.json" diff --git a/sweep_order.json b/sweep_order.json new file mode 100644 index 0000000..0000f5b --- /dev/null +++ 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[47, true], "fun1.3": [50, true], "fun1.4": [58, true], "fun1.5": [78, true], "fun2.1": [12, true], "fun2.2": [57, true], "fun2.3": [63, true], "fun2.4": [77, true], "fun2.5": [83, true], "fun3.1": [46, true], "fun3.2": [48, true], "fun3.3": [58, true], "fun3.4": [64, true], "fun3.5": [65, true], "fun4.1": [46, true], "fun4.2": [48, true], "fun4.3": [58, true], "fun4.4": [64, true], "fun4.5": [78, true], "fun5.1": [46, true], "fun5.2": [46, true], "fun5.3": [47, true], "fun5.4": [49, true], "fun5.5": [50, true], "fun6.1": [46, true], "fun6.2": [46, true], "fun6.3": [47, true], "fun6.4": [49, true], "fun6.5": [50, true], "fun7.1": [9, false], "fun7.2": [8, false], "fun7.3": [10, false], "fun7.4": [13, false], "fun7.5": [13, false], "fun8.1": [44, true], "fun8.2": [45, true], "fun8.3": [47, true], "fun8.4": [48, true], "fun8.5": [22, true], "fun9.1": [9, true], "fun9.2": [45, true], "fun9.3": [47, true], "fun9.4": [48, true], "fun9.5": [50, true]}}}] \ No newline at end of file diff --git a/tests/test_similarity_per_slot.py b/tests/test_similarity_per_slot.py new file mode 100644 index 0000000..46fb6a6 --- /dev/null +++ b/tests/test_similarity_per_slot.py @@ -0,0 +1,127 @@ +"""Pins for PREREG 2026-09-21 slot 1: the similarity function read BY PLACE. + +Every claim the mode rests on is pinned here, including the ones that make it falsifiable: +the default must stay bit-for-bit published, the far reading must BE false position, and +the order exponent must invert the power law exactly. +""" +from __future__ import annotations + +import math + +import pytest + +from simroot.pure import PURE_SIMS, _local_order, _read_z, pure_root + +PROBS = ( + (lambda t: t ** 3 - 2.0 * t - 5.0, 1.0, 4.0), + (lambda t: math.exp(t) - 2.0, 0.0, 3.0), + (lambda t: (t - 1.0) ** 3, 0.0, 10.0), + (lambda t: math.sin(t) - 0.5, 0.0, 1.5), +) + + +@pytest.mark.parametrize("f,a,b", PROBS) +@pytest.mark.parametrize("guard", ("safe", "credit", "project")) +def test_default_is_bit_for_bit_the_published_method(f, a, b, guard): + """R1: the new parameter must not touch the published grid when left alone.""" + ref = pure_root(f, a, b, 1e-12, 200, similarity="ratio", scale="derived3", guard=guard) + new = pure_root(f, a, b, 1e-12, 200, similarity="ratio", scale="derived3", guard=guard, + exponent="none") + assert ref == new + + +def test_far_reading_with_rational_is_false_position(): + """R2: Proposition 4 must hold in the CODE, not only in the paper. + + The first similarity step from x with S = 1/(1+z), z = |f(x)|/|f(far)| must land on the + secant root of the pair (x, far). If it does not, the (far, none) cell is not the + control the pre-registration claims it is. + """ + f = lambda t: t ** 3 - 2.0 * t - 5.0 # noqa: E731 + a, b = 1.0, 4.0 + x = 0.5 * (a + b) + # the far end must be the one whose sign differs, otherwise there is no secant root + # between the pair at all; on this bracket that is a, not b + far, fx = a, f(x) + ffar = f(far) + assert fx * ffar < 0.0 + z = abs(fx) / abs(ffar) + step = (1.0 - PURE_SIMS["rational"](z)) * (far - x) + secant = x - fx * (far - x) / (ffar - fx) + assert step == pytest.approx(secant - x, rel=1e-12) + + +def test_order_exponent_inverts_the_power_law_exactly(): + """R3: the whole derivation is z^(1/m) = e/E. Pinned as an identity.""" + for m in (1.0, 2.0, 3.0, 7.0): + for e, big in ((0.1, 2.0), (1.0, 5.0), (1e-3, 1.0)): + z = (e / big) ** m + got = _read_z(z, 1.0, "order", m) + assert got == pytest.approx(e / big, rel=1e-9) + + +def test_order_exponent_is_inert_at_order_one(): + """A simple root must leave the reading untouched, or the endgame is not preserved.""" + for z in (1e-9, 0.3, 1.0, 12.0): + assert _read_z(z, 1.0, "order", 1.0) == z + assert _read_z(z, 1.0, "order", None) == z + assert _read_z(z, 1.0, "none", 5.0) == z + + +def test_local_order_reads_a_cube_low_by_a_fixed_bias(): + """MEASURED, and pinned as measured: on a pure cube the three-point estimator returns + 2.830, not 3. The parabola through three points carries only the second difference, so + a cubic's order is under-read by 5.7% even in the ideal noiseless case. The bias is + towards 1, i.e. towards the uncorrected reading, which is the safe direction — but it + is a bias and the paper must say so rather than claim the estimator is exact.""" + f = lambda t: t ** 3 # noqa: E731 + xs = (0.30, 0.31, 0.32) + m = _local_order(xs[2], f(xs[2]), xs[1], f(xs[1]), xs[0], f(xs[0])) + assert m == pytest.approx(2.83, rel=0.02) + assert 1.0 < m < 3.0 + + +def test_step_fraction_can_never_leave_the_bracket(): + """L5: under S = 1/(1+z) the fraction z/(1+z) is at most 1, so the step never passes + the far end. At z >= 1/eps it SATURATES at exactly 1 in floating point — the step + lands ON the end, which the loop already turns into a bisection because x_new must be + strictly inside. Pinned so the saturation is a documented boundary, not a surprise.""" + for z in (0.0, 1e-12, 1.0, 1e6): + assert 0.0 <= 1.0 - PURE_SIMS["rational"](z) < 1.0 + assert 1.0 - PURE_SIMS["rational"](1e300) == 1.0 + + +@pytest.mark.parametrize("f,a,b", PROBS) +def test_far_and_order_still_solve_and_stay_in_the_bracket(f, a, b): + ok_any = False + for ex in ("none", "order"): + x, n, conv = pure_root(f, a, b, 1e-10, 300, similarity="rational", scale="far", + guard="safe", exponent=ex) + assert min(a, b) <= x <= max(a, b) + assert n <= 300 + ok_any = ok_any or conv + assert ok_any + + +def test_derived3_m_actually_divides_by_the_order(): + """REGRESSION, 2026-09-21. The derived3_cap branch was inserted in front of the + derived3_m note and swallowed its division, so derived3_m became a silent alias of + derived3 (2806 against 2806) and a refutation recorded in the paper stopped being + reproducible. One cheap problem where the order is genuinely above 1 is enough to + catch it, so the guard does not depend on the full 154-problem pin.""" + f = lambda t: (t - 1.0) ** 3 # noqa: E731 + plain = pure_root(f, 0.0, 10.0, 1e-10, 300, similarity="ratio", scale="derived3", + guard="project") + with_m = pure_root(f, 0.0, 10.0, 1e-10, 300, similarity="ratio", scale="derived3_m", + guard="project") + assert plain != with_m + + +def test_bad_combinations_are_refused_not_silently_reinterpreted(): + with pytest.raises(ValueError): + pure_root(lambda t: t, 0.0, 1.0, 1e-9, 50, exponent="cube") + with pytest.raises(ValueError): + # two-point scale has no second difference to read the order from + pure_root(lambda t: t, 0.0, 1.0, 1e-9, 50, scale="derived", exponent="order") + with pytest.raises(ValueError): + pure_root(lambda t: t, 0.0, 1.0, 1e-9, 50, scale="nonesuch") diff --git a/verify_article.py b/verify_article.py index 4faa434..3ac2553 100644 --- a/verify_article.py +++ b/verify_article.py @@ -201,6 +201,7 @@ def main(): check(f"scale {sc} best", best_by_scale[sc], v) verify_placement_modes() + verify_per_place() print() if FAILS: @@ -226,6 +227,76 @@ PLACEMENT = { "sweep_gate.json": ("gate.ratio.derived.project", 4449, 2991), "sweep_log.json": ("log.ratio_soft.derived.safe", 6940, 3474), } +# The per-place table of section "the similarity function belongs to the place": +# seven PAIRED comparisons in sweep_order.json. Checked as pairs, because a pair is +# what the pre-registration licensed and a single cell would prove nothing. +ORDER_PAIRS = { + # guard (APS m=1, APS measured, CHA m=1, CHA measured) + "both": (4522, 3675, 3387, 3216), + "bracket": (4606, 3542, 3571, 3303), + "credit": (5190, 4686, 3013, 2884), + "project": (6932, 6364, 4794, 4559), + "safe": (5987, 5229, 4108, 3923), + "step": (6435, 5551, 4257, 4022), + "none": (10676, 10043, 8265, 7794), +} +# the negative item: the order does not cure false position +ORDER_FALSEPOS = {("rational", "far", "none", "none"): (127, 10676), + ("rational", "far", "none", "order"): (128, 10043)} +# and the harmful direction, quoted in the same subsection +ORDER_SLOPE_HARM = {("ratio", "derived3", "none", "none"): 2806, + ("ratio", "derived3", "none", "order"): 2854} + + +def verify_per_place(): + print("\nThe per-place reading (sweep_order.json):") + if not os.path.exists("sweep_order.json"): + print(" !! sweep_order.json absent — section 'belongs to the place' unverifiable") + FAILS.append("missing sweep_order.json") + return + with open("sweep_order.json", encoding="utf8") as fh: + rows = json.load(fh) + + def cell(sim, sc, gu, ex): + for r in rows: + s = r["spec"] + if (s[1], s[2], s[3], s[8] if len(s) > 8 else "none") == (sim, sc, gu, ex): + return r + return None + + cheaper = 0 + for gu, (a1, a2, c1, c2) in ORDER_PAIRS.items(): + p = cell("rational", "far", gu, "none") + q = cell("rational", "far", gu, "order") + if p is None or q is None: + FAILS.append(f"order pair {gu} missing from sweep_order.json") + print(f" !! pair {gu} missing — stale sweep") + continue + check(f"far+rational {gu} APS m=1", p["APS"]["total"], a1) + check(f"far+rational {gu} APS order", q["APS"]["total"], a2) + check(f"far+rational {gu} CHA m=1", p["CHA"]["total"], c1) + check(f"far+rational {gu} CHA order", q["CHA"]["total"], c2) + cheaper += (q["APS"]["total"] + q["CHA"]["total"] + < p["APS"]["total"] + p["CHA"]["total"]) + check("cheaper in 7 of 7 safeguards", cheaper, 7) + for (sim, sc, gu, ex), (solved, total) in ORDER_FALSEPOS.items(): + r = cell(sim, sc, gu, ex) + if r is None: + FAILS.append(f"false-position cell {ex} missing") + continue + check(f"false position {ex} solved", r["APS"]["solved"], solved) + check(f"false position {ex} APS", r["APS"]["total"], total) + for (sim, sc, gu, ex), want in ORDER_SLOPE_HARM.items(): + r = cell(sim, sc, gu, ex) + if r is None: + FAILS.append(f"slope-harm cell {ex} missing") + continue + check(f"slope reading {ex} APS", r["APS"]["total"], want) + fam = [r for r in rows if r["spec"][3] in ("project", "safe", "credit")] + check("guarantee family violations", sum(r["APS"]["over"] + r["CHA"]["over"] + for r in fam), 0) + + PLACEMENT_PER_SET = { "sweep_direction.json": ("CHA", "pure+dissim+slope.ratio.derived3.safe", 2683), "sweep_gate.json": ("CHA", "gate.ratio_soft.derived.safe", 2851),