From e4769be9a3487cea5055e00b9a0ec6d96fbf20d8 Mon Sep 17 00:00:00 2001 From: Valeri Sitnikov Date: Sun, 20 Sep 2026 23:27:43 +0100 Subject: [PATCH] =?UTF-8?q?slope-stability=20gate:=20the=20PROJECT'S=20OWN?= =?UTF-8?q?=20target=20is=20met=20for=20the=20first=20time=20=E2=80=94=205?= =?UTF-8?q?922=20<=206026=20over=20both=20sets=20at=20193/199=20with=20the?= =?UTF-8?q?=20guarantee=20intact=20(slope.ratio.derived3.project:=20APS=20?= =?UTF-8?q?2848=20+=20CHA=203074),=20CHA=20improves=204516=20->=202903=20(?= =?UTF-8?q?x1.56),=20repairs=2077.5%=20->=2055.3%.=20Honest=20cost:=20APS?= =?UTF-8?q?=202806=20->=202848,=20which=20moves=20us=20from=201st=20to=203?= =?UTF-8?q?rd=20on=20the=20canonical=20set=20(chandrupatla=202785,=20toms7?= =?UTF-8?q?48=202820),=20so=20my=20stricter=20S1=20fails=20while=20the=20p?= =?UTF-8?q?roject=20target=20passes=20=E2=80=94=20a=20positioning=20decisi?= =?UTF-8?q?on,=20recorded=20not=20resolved.=20Refusal=20CURRENCY=20is=20wh?= =?UTF-8?q?at=20decides:=20bracket=20progress=204449=20vs=20model=20shape?= =?UTF-8?q?=202848,=20a=201601-evaluation=20difference=20for=20the=20same?= =?UTF-8?q?=20'refuse=20before=20the=20step'=20idea?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-Authored-By: Claude Opus 5 --- FINDINGS_slope_gate.md | 51 ++++++++++++++++++ PREREG_slope_gate_2026-09-21.md | 71 ++++++++++++++++++++++++ explain_chandrupatla.py | 2 +- results_sweep_slope.txt | 76 ++++++++++++++++++++++++++ simroot/pure.py | 26 ++++++++- sweep_full.py | 24 ++++++++- sweep_slope.json | 1 + sweep_slope_smoke.json | 1 + tests/test_prestep_gate.py | 4 +- tests/test_slope_gate.py | 95 +++++++++++++++++++++++++++++++++ 10 files changed, 345 insertions(+), 6 deletions(-) create mode 100644 FINDINGS_slope_gate.md create mode 100644 PREREG_slope_gate_2026-09-21.md create mode 100644 results_sweep_slope.txt create mode 100644 sweep_slope.json create mode 100644 sweep_slope_smoke.json create mode 100644 tests/test_slope_gate.py diff --git a/FINDINGS_slope_gate.md b/FINDINGS_slope_gate.md new file mode 100644 index 0000000..7318bef --- /dev/null +++ b/FINDINGS_slope_gate.md @@ -0,0 +1,51 @@ +# Findings — гейт на устойчивости наклона (`PREREG_slope_gate_2026-09-21.md`) + +Числа с Linux. Свип в своём `sweep_slope.json`; `sweep_full.json` не тронут (git-статус чист). +Признак отказа: два последовательных знака локального наклона различны ⇒ деление пополам. Сравнивается +**знак**, ни одной константы (закреплено тестом T2). + +## 1. Результат + +| проверка | цель | измерено | вердикт | +|---|---|---|---| +| **S1** APS-154 не дорожает | ≤2806 | **2848** (+1.5 %, 42 вызова) | 🔴 FAIL | +| **S2** CHA-45 дешевеет против 4516 | <4516 | **2903** (×1.56) | 🟢 PASS | +| **S3** ремонты сторожа падают против 77.5 % | <77.5 % | **55.3 %** | 🟢 PASS | +| **S4** гарантия `2⌈log₂(w/xtol)⌉+3` | `over2x=0` | 0 во всех конфигурациях | 🟢 PASS | +| **S5** качество пробы растёт | >1.422 | **1.432** | 🔴 в пределах шума | +| **цель ПРОЕКТА** (из `NEXT_PAPER_logarithmic.md`, записана до сессии): два набора | <6026 при 193/199 и целой гарантии | **5922** одной конфигурацией `slope.ratio.derived3.project` (APS 2848 + CHA 3074) | 🟢 **PASS** | + +Сравнение с базлайнами по двум наборам: Chandrupatla **5208**, ITP-oracle **5871**, наши **5922** — +цель проекта взята, базлайны не побиты. + +## 2. 🔴 Цена названа точно + +На APS-154: Chandrupatla 2785, TOMS 748 2820, **наши опубликованные 2806 (1-е место)**, Brent 2889. +С гейтом наши **2848** ⇒ **третье место вместо первого** на каноническом наборе. То есть трейд не +«+1.5 %», а **потеря заголовка статьи** в обмен на уход двух наборов под 6026 и ×1.56 на широких +скобках. + +## 3. Развилка (решение Валерия, не моё) + +Мой `S1` строже цели, которую проект поставил себе сам: + +- по **S1** («ни копейки на каноническом наборе») режим **не принимается**; +- по **цели проекта** («побить 6026 на двух наборах при 193/199 и целой гарантии») режим + **принимается**: 5922. + +Оба критерия записаны заранее, и они не совпадают. Это выбор позиционирования: держать «1-е место на +APS при нуле настроечных констант» или взять «5922 < 6026 при целой гарантии» ценой третьего места. + +## 4. Что установлено независимо от развилки + +- **Признак отказа решает.** Прогресс скобки — неверная валюта (APS 4449), форма модели — верная + (APS 2848). Разница между двумя гейтами: **1601 вызов** на APS при одинаковой идее «отказывайся до + шага, бесплатно». +- **Перевод Chandrupatla на язык похожести оказался рабочим рецептом, а не только описанием:** его + гейт читает форму конфигурации до шага; наш аналог для нашего шага — устойчивость наклона; и именно + он дал первое за линию попадание в цель проекта. +- **Ремонты — следствие, а не причина:** они упали 77.5 % → 55.3 %, но качество пробы почти не + изменилось (1.422 → 1.432). Значит выигрыш пришёл не от «меньше ремонтов», а от того, что отказ + случается **в нужных местах**; счётчик ремонтов — индикатор, а не цель. +- 🔴 **Не повторять:** гейт по прогрессу скобки (`FINDINGS_prestep_gate.md`), логарифмическая замена + (`FINDINGS_logarithmic.md`), `cbrt` по набору и три детектора режима (`NEXT_PAPER_logarithmic.md`). diff --git a/PREREG_slope_gate_2026-09-21.md b/PREREG_slope_gate_2026-09-21.md new file mode 100644 index 0000000..9df7859 --- /dev/null +++ b/PREREG_slope_gate_2026-09-21.md @@ -0,0 +1,71 @@ +# PREREG — гейт на УСТОЙЧИВОСТИ НАКЛОНА (форма, а не прогресс) + +Составлено до реализации. Основание — два измерения этой линии: + +1. `FINDINGS_prestep_gate.md`: гейт по **прогрессу скобки** обваливает ремонты (77.5 % → 15.9 %) и + впервые берёт цель ITP на CHA (**2851 ≤ 2857**), но APS дорожает 2806 → **4449**, потому что + прогресс скобки — **неверная валюта отказа**: секущий шаг обрушивает ошибку, почти не двигая + скобку (в проекте это уже измерено: **150 против 86**). +2. `FINDINGS_logarithmic.md` §3: Chandrupatla отказывает не по прогрессу, а по **форме конфигурации** + (`ξ`, `φ` — безразмерные отношения; полоса есть окрестность линейного случая), и его отказ стоит + **ноль** вызовов. + +**Гипотеза:** нужный признак отказа — не «сколько обещает шаг», а «установилась ли модель, которой +шаг доверяет». Наш шаг доверяет **локальному наклону**, значит вопрос доверия — **устойчивость +наклона**. + +--- + +## 1. Признак, выведенный для НАШЕГО шага (и без единой константы) + +Метод оценивает наклон на каждом шаге (`derived` — по двум последним точкам, `derived3` — по трём). +Две последовательные оценки `slope_prev` и `slope` дают безразмерное сравнение. Объявленный признак +отказа — **несогласие знака**: + +> если `slope_prev` и `slope` оба не нули и **их знаки различны**, локальная модель не установилась +> (функция локально даже не монотонна в одном направлении) ⇒ шаг заменяется делением пополам. + +Почему это беспараметрично: сравнивается **знак**, а не величина; порога нет, множителя нет, +сравнения с выбранным числом нет. Почему это форма, а не прогресс: признак читается из конфигурации +данных (две оценки наклона), а не из обещанной длины шага. + +**Почему ожидается инертность на каноническом наборе** (то, чего не хватило прошлой попытке): у +простого корня гладкой функции знак наклона устойчив, значит гейт молчит и APS не дорожает. Срабатывать +он должен в плоских областях широких скобок, где оценки наклона мелкие и болтаются. + +**Чего НЕ делаем:** не вводим порог на отношение величин наклонов (`|s1|/|s2| < k` — это константа +`k`); не переносим полосу `1−√(1−ξ) < φ < √ξ` (выведена для обратной квадратичной интерполяции). + +**Режим:** `prestep="slope"`; `"none"` остаётся по умолчанию и побитово прежним; `"progress"` остаётся +в коде как **измеренный отрицательный результат**, помеченный в докстринге. + +## 2. Предсказания и фальсификаторы + +| # | Предсказание | ФАЛЬСИФИКАТОР → вывод | +|---|---|---| +| **S1** | APS-154 **не дорожает**: по-наборный лучший ≤ **2806** | >2806 → шестая попытка тем же трейдом; признак «форма» тоже не спасает, линия закрывается | +| **S2** | CHA-45 дешевеет против x-пространства: по-наборный лучший < **4516** | не дешевеет → гейт инертен всюду, гипотеза о наклоне неверна | +| **S3** | доля ремонтов сторожем падает против 77.5 % | не падает → гейт не бьёт в механизм | +| **S4** | гарантия `2⌈log₂(w/xtol)⌉+3` цела: `over2x = 0` | нарушена → закрытие немедленно | +| **S5** | качество пробы на CHA растёт против 1.422 | не растёт → отказ не улучшает пробу, только переставляет расходы | + +**Правило остановки:** S1 или S4 ложны ⇒ режим не принимается. S1 верна и S2 верна ⇒ **это первый +режим линии, который берёт широкие скобки, не продавая узкие**, и тогда следующий шаг — свип по всей +сетке и проверка, попадает ли лучшая конфигурация в цель <6026 на двух наборах. + +## 3. Протокол и гейты реализации + +Протокол статьи: 154 APS + 45 CHA, цена — вызовы `f`, провал = полный бюджет, граница `2×` на каждом +решённом прогоне, конфигурация фиксируется выводом до рейтинга, числа только с **Linux**, свип пишется +в свой `sweep_slope.json`. + +| # | Условие реализации | Проверка тестом | +|---|---|---| +| **T1** | `prestep="none"` побитово как раньше | равенство кортежей возврата на наборе задач и сторожей | +| **T2** | в гейте нет ни одной константы | греп по коду гейта (без комментариев): допустимы только `0.0` и `0.5` | +| **T3** | гейт инертен там, где знак наклона устойчив | на гладкой монотонной задаче число вызовов совпадает с `prestep="none"` | +| **T4** | гейт срабатывает там, где знак наклона меняется | на задаче с немонотонностью `stats['pre_refused'] ≥ 1` | +| **T5** | отказ не добавляет вызова | `pre_refused ≤ nfev − 2` | + +**Дисциплина:** аудит после правки и до запуска; смоук ×2 локально; свип на сервере с замороженной +копией; числа немедленно. diff --git a/explain_chandrupatla.py b/explain_chandrupatla.py index 959e783..e75a662 100644 --- a/explain_chandrupatla.py +++ b/explain_chandrupatla.py @@ -149,4 +149,4 @@ def main(prestep="none"): if __name__ == "__main__": import sys - main("progress" if "--gate" in sys.argv else "none") + main("slope" if "--slope" in sys.argv else "progress" if "--gate" in sys.argv else "none") diff --git a/results_sweep_slope.txt b/results_sweep_slope.txt new file mode 100644 index 0000000..e518500 --- /dev/null +++ b/results_sweep_slope.txt @@ -0,0 +1,76 @@ +sweep: 126 configurations x 199 problems (FULL) + 10/126 done, 1s elapsed + 20/126 done, 1s elapsed + 30/126 done, 1s elapsed + 40/126 done, 1s elapsed + 50/126 done, 2s elapsed + 60/126 done, 2s elapsed + 70/126 done, 2s elapsed + 80/126 done, 2s elapsed + 90/126 done, 2s elapsed + 100/126 done, 2s elapsed + 110/126 done, 3s elapsed + 120/126 done, 3s elapsed + 126/126 done, 3s elapsed + +wrote sweep_slope.json (4s total) + +==================================================================================== +APS: 154 problems (top 20 of 126) +==================================================================================== +configuration solved total fev over 2x +------------------------------------------------------------------------------------ +slope.ratio.derived3.none 153/154 2848 0 +slope.ratio.derived3.project 153/154 2848 0 +slope.ratio.derived3.step 153/154 3020 0 +slope.ratio.derived3.safe 153/154 3020 0 +slope.ratio.derived.step 153/154 3105 0 +slope.ratio.derived.safe 153/154 3105 0 +slope.ratio.derived.none 153/154 3131 0 +slope.ratio.derived.project 153/154 3131 0 +slope.exp_abs.derived3.step 153/154 3322 0 +slope.exp_abs.derived3.safe 153/154 3322 0 +slope.exp_abs.derived.project 153/154 3326 0 +slope.exp_abs.derived.none 153/154 3326 0 +slope.exp_abs.derived3.none 153/154 3328 0 +slope.exp_abs.derived3.project 153/154 3328 0 +slope.exp_abs.derived.step 153/154 3358 0 +slope.exp_abs.derived.safe 153/154 3358 0 +slope.rational.derived3.step 153/154 3436 0 +slope.rational.derived3.safe 153/154 3436 0 +slope.ratio.derived3.credit 153/154 3507 0 +slope.rational.derived3.none 153/154 3521 0 + +==================================================================================== +CHA: 45 problems (top 20 of 126) +==================================================================================== +configuration solved total fev over 2x +------------------------------------------------------------------------------------ +slope.ratio.derived3.step 40/45 2903 0 +slope.ratio.derived3.safe 40/45 2903 0 +slope.rational.derived3.step 40/45 2965 0 +slope.rational.derived3.safe 40/45 2965 0 +slope.exp_abs.derived3.step 40/45 2966 0 +slope.exp_abs.derived3.safe 40/45 2966 0 +slope.cbrt.derived.credit 40/45 2995 0 +slope.ratio.derived3.credit 40/45 2997 0 +slope.ratio_soft.derived3.credit 40/45 3055 0 +slope.ratio.derived.credit 40/45 3059 0 +slope.ratio.derived3.project 40/45 3074 0 +slope.ratio.derived3.none 40/45 3075 0 +slope.ratio_soft.derived.credit 40/45 3094 0 +slope.exp_abs.derived3.credit 40/45 3095 0 +slope.cbrt.derived3.credit 40/45 3107 0 +slope.exp_abs.derived.credit 40/45 3113 0 +slope.cosine.derived.credit 40/45 3130 0 +slope.cosine.derived3.credit 40/45 3130 0 +slope.exp_sq.derived.credit 40/45 3130 0 +slope.exp_sq.derived3.credit 40/45 3130 0 + +==================================================================================== +THE STAGE-0C LAW ACROSS THE GRID +==================================================================================== + scale=derived slope c=1 (linear) mean total 6920 mean solved 193.0/199 + scale=derived slope c=0 (quadratic) mean total 22164 mean solved 193.0/199 + scale=derived3 slope c=1 (linear) mean total 6204 mean solved 193.0/199 + scale=derived3 slope c=0 (quadratic) mean total 21698 mean solved 193.0/199 diff --git a/simroot/pure.py b/simroot/pure.py index 468bf59..5198f77 100644 --- a/simroot/pure.py +++ b/simroot/pure.py @@ -467,8 +467,12 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", raise ValueError(f"unknown scale {scale!r}") if space not in SPACES: raise ValueError(f"unknown space {space!r}") - if prestep not in ("none", "progress"): + if prestep not in ("none", "progress", "slope"): raise ValueError(f"unknown prestep {prestep!r}") + if prestep == "slope" and scale not in ("derived", "derived3"): + # there is no slope to judge under a chosen or bracket scale; judging something + # else would hide that, so the call fails instead + raise ValueError("prestep='slope' requires scale in {'derived', 'derived3'}") if space == "log" and scale not in ("derived", "derived3"): # u-space needs a slope; with a chosen or bracket scale there is none to # transform, and computing something anyway would hide that (PREREG §3a). @@ -497,6 +501,8 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", sg.credit = endowment forced = 0 pre_refused = 0 + slope = 0.0 + slope_prev = None if stats is not None: stats['forced'] = 0 stats['pre_refused'] = 0 @@ -596,7 +602,20 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", x_new = 0.5 * (A + B) else: step = None - if prestep == "progress": + if prestep == "slope": + # PRE-STEP GATE ON SHAPE (PREREG 2026-09-21). The step trusts the + # local slope, so the question of trust is whether that slope has + # SETTLED: two consecutive estimates of opposite sign mean the local + # model is not established at all, and the evaluation is better spent + # halving. A SIGN is compared, not a magnitude — no threshold, no + # factor, no constant. Where the slope sign is stable (a simple root + # of a smooth f) the gate is inert, which is exactly what the + # progress gate could not manage: it charged APS 4449 against 2806. + if (slope_prev is not None and slope != 0.0 and slope_prev != 0.0 + and (slope > 0.0) != (slope_prev > 0.0)): + step = 0.5 * (A + B) - x + pre_refused += 1 + if step is None and prestep == "progress": # PRE-STEP GATE (PREREG 2026-09-21). Measured cause of our cost: # the safeguard REPAIRS 77.5% of evaluations after the fact, while # Chandrupatla REFUSES its model on 72% of steps for free and @@ -635,6 +654,9 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", x_new = projected step = x_new - x sg.note_step(step) + # the slope this step trusted, kept so the NEXT step can ask whether it + # has settled (prestep="slope"); only meaningful for the derived scales + slope_prev = slope if not math.isfinite(x_new) or not (min(A, B) < x_new < max(A, B)): x_new = 0.5 * (A + B) diff --git a/sweep_full.py b/sweep_full.py index 5772321..55d3af0 100644 --- a/sweep_full.py +++ b/sweep_full.py @@ -125,7 +125,9 @@ def label(spec): if len(spec) > 4 and spec[4] != "x": tag = spec[4] if len(spec) > 5 and spec[5] != "none": - tag = f"{tag}+gate" if tag != "pure" else "gate" + # name the gate by WHICH gate it is: "progress" is a measured negative and must + # never be confused with "slope" in a results file + tag = f"{tag}+{spec[5]}" if tag != "pure" else spec[5] return f"{tag}.{spec[1]}.{spec[2]}.{spec[3]}" @@ -189,6 +191,15 @@ def build_grid_log(smoke): for sim in sims for sc in ("derived", "derived3") for gu in guards] +def build_grid_slope(smoke): + """The slope-stability gate grid (PREREG 2026-09-21). Only derived scales: there must be + a slope to judge. Baselines are not recomputed — they are in sweep_full.json.""" + sims = ["ratio", "sqrt"] if smoke else sorted(PURE_SIMS) + guards = ("credit", "safe") if smoke else GUARD_MODES + return [("pure", sim, sc, gu, "x", "slope") + for sim in sims for sc in ("derived", "derived3") for gu in guards] + + def build_grid_gate(smoke): """The pre-step gate grid (PREREG 2026-09-21): the published x-space step with the gate switched on. Baselines are not recomputed - they are already in sweep_full.json.""" @@ -219,7 +230,9 @@ def main(): smoke = "--smoke" in sys.argv logmode = "--log" in sys.argv # the u-space grid, written to its OWN file gatemode = "--gate" in sys.argv # the pre-step gate grid, likewise - specs = (build_grid_gate(smoke) if gatemode else + slopemode = "--slope" in sys.argv # the slope-stability gate grid + specs = (build_grid_slope(smoke) if slopemode else + build_grid_gate(smoke) if gatemode else build_grid_log(smoke) if logmode else build_grid(smoke)) t0 = time.time() print(f"sweep: {len(specs)} configurations x 199 problems " @@ -236,6 +249,13 @@ 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 slopemode: + out = "sweep_slope_smoke.json" if smoke else "sweep_slope.json" + with open(out, "w", encoding="utf8") as fh: + json.dump(results, fh) + print(f"\nwrote {out} ({time.time() - t0:.0f}s total)\n", flush=True) + report(results) + return if gatemode: # never into sweep_full.json: that file is what verify_article.py checks the # paper against, and the smoke run of 2026-09-21 did land in sweep_smoke.json diff --git a/sweep_slope.json b/sweep_slope.json new file mode 100644 index 0000000..5970f0b --- /dev/null +++ b/sweep_slope.json @@ -0,0 +1 @@ +[{"label": "slope.cbrt.derived.bracket", "spec": ["pure", "cbrt", "derived", "bracket", "x", "slope"], "APS": {"total": 9928, "solved": 153, "n": 154, "over": 0, "per": {"aps.01.00": [62, true], "aps.02.00": [60, true], "aps.02.01": [63, true], "aps.02.02": [66, true], "aps.02.03": [60, true], "aps.02.04": [62, true], "aps.02.05": [63, true], "aps.02.06": [67, true], "aps.02.07": [68, true], "aps.02.08": [65, true], "aps.02.09": [68, true], "aps.03.00": [66, true], "aps.03.01": [62, true], "aps.03.02": [64, true], "aps.04.00": [67, true], "aps.04.01": [59, true], "aps.04.02": [62, true], "aps.04.03": [64, true], "aps.04.04": [64, true], 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true], "fun5.4": [82, true], "fun5.5": [84, true], "fun6.1": [63, true], "fun6.2": [63, true], "fun6.3": [67, true], "fun6.4": [70, true], "fun6.5": [75, true], "fun7.1": [7, false], "fun7.2": [12, false], "fun7.3": [10, false], "fun7.4": [7, false], "fun7.5": [16, false], "fun8.1": [63, true], "fun8.2": [63, true], "fun8.3": [63, true], "fun8.4": [69, true], "fun8.5": [72, true], "fun9.1": [60, true], "fun9.2": [55, true], "fun9.3": [63, true], "fun9.4": [64, true], "fun9.5": [68, true]}}}] \ No newline at end of file diff --git a/tests/test_prestep_gate.py b/tests/test_prestep_gate.py index 328c7ed..d404023 100644 --- a/tests/test_prestep_gate.py +++ b/tests/test_prestep_gate.py @@ -38,7 +38,9 @@ def test_R1_the_published_path_is_bit_identical_with_the_gate_off(): def test_R2_the_gate_carries_no_chosen_constant(): src = inspect.getsource(P.pure_root) - start = src.index('if prestep == "progress":') + # anchor on the CONDITION, not on a whole line: the line grew a `step is None and` + # prefix when the slope gate was inserted ahead of it, and the exact-line anchor broke + start = src.index('prestep == "progress"') end = src.index('if step is None and space ==', start) # the gate block only body = src[start:end] # comments carry the MEASURED numbers that justify the gate (77.5 %, 2.310 halvings); diff --git a/tests/test_slope_gate.py b/tests/test_slope_gate.py new file mode 100644 index 0000000..8f80773 --- /dev/null +++ b/tests/test_slope_gate.py @@ -0,0 +1,95 @@ +"""Gates T1-T5 for the slope-stability gate (PREREG_slope_gate_2026-09-21.md). + +The progress gate refused on the wrong currency (bracket progress) and charged APS 4449 +against 2806. This gate refuses on the SHAPE of the model instead: two consecutive slope +estimates of opposite sign mean the local model is not established, so the evaluation is +spent halving. A SIGN is compared — no threshold, no factor, no constant. +""" + +from __future__ import annotations + +import inspect +import math +import re + +import pytest + +from simroot import pure as P + +SMOOTH = [ # simple roots, stable slope sign: the gate must be inert + (lambda t: t ** 3 - 2.0 * t - 5.0, 2.0, 3.0), + (lambda t: math.exp(t) - 5.0, 0.0, 3.0), + (lambda t: t ** 2 - 2.0, 0.5, 2.0), + (lambda t: math.cos(t) - t, 0.0, 1.0), +] +# the bracket must straddle zero AND contain a sign change of the SLOPE: f' = 3t^2 - 1 +# vanishes at t = +-0.577, so the local slope estimate flips sign inside (-2, 2). +# (An earlier version used sin(8t)e^-t + 0.05 on (0,1), which does not straddle zero at +# all — f(0) = +0.05, f(1) = +0.41 — and the method rightly refused the call.) +WOBBLY = (lambda t: t ** 3 - t + 0.2, -2.0, 2.0) + + +def test_T1_the_published_path_is_bit_identical_with_the_gate_off(): + for f, a, b in SMOOTH: + for guard in ("credit", "project", "safe", "step"): + base = P.pure_root(f, a, b, 1e-12, 300, similarity="ratio", + scale="derived3", guard=guard) + off = P.pure_root(f, a, b, 1e-12, 300, similarity="ratio", + scale="derived3", guard=guard, prestep="none") + assert base == off, (guard, base, off) + + +def test_T2_the_gate_carries_no_constant(): + src = inspect.getsource(P.pure_root) + start = src.index('if prestep == "slope":') + end = src.index('if step is None and prestep == "progress"', start) + code = "\n".join(line.split("#", 1)[0] for line in src[start:end].splitlines()) + literals = set(re.findall(r"(?" in code and "!=" in code # a SIGN comparison, not a magnitude test + + +def test_T3_the_gate_is_inert_where_the_slope_sign_is_stable(): + """This is what the progress gate could not do — it fired on excellent steps.""" + for f, a, b in SMOOTH: + off = P.pure_root(f, a, b, 1e-12, 300, similarity="ratio", scale="derived3", + guard="credit") + on = P.pure_root(f, a, b, 1e-12, 300, similarity="ratio", scale="derived3", + guard="credit", prestep="slope") + assert on[1] == off[1], (off, on) # identical evaluation count + + +def test_T4_the_gate_fires_where_the_slope_sign_flips(): + f, a, b = WOBBLY + st = {} + x, n, ok = P.pure_root(f, a, b, 1e-10, 300, similarity="ratio", scale="derived3", + guard="credit", prestep="slope", stats=st) + assert ok and abs(f(x)) < 1e-6 + assert st["pre_refused"] >= 1, st + + +def test_T5_a_refusal_costs_no_extra_evaluation(): + f, a, b = WOBBLY + st = {} + _x, n, ok = P.pure_root(f, a, b, 1e-10, 300, similarity="ratio", scale="derived3", + guard="credit", prestep="slope", stats=st) + assert ok + assert st["pre_refused"] <= n - 2, (st, n) + + +def test_the_mode_needs_a_slope_to_judge(): + with pytest.raises(ValueError): + P.pure_root(lambda t: t, -1.0, 1.0, 1e-10, 100, scale="bracket", prestep="slope") + with pytest.raises(ValueError): + P.pure_root(lambda t: t, -1.0, 1.0, 1e-10, 100, prestep="nonsense") + + +def test_both_gates_remain_available_and_distinct(): + """"progress" is kept as a MEASURED NEGATIVE (APS 4449 vs 2806), not deleted.""" + f, a, b = WOBBLY + a1 = P.pure_root(f, a, b, 1e-10, 300, similarity="ratio", scale="derived3", + guard="credit", prestep="progress") + a2 = P.pure_root(f, a, b, 1e-10, 300, similarity="ratio", scale="derived3", + guard="credit", prestep="slope") + assert a1[2] and a2[2] + assert a1 != a2 or a1[1] == a2[1] # they may coincide, but both must run