161 lines
6.9 KiB
Python
161 lines
6.9 KiB
Python
"""Pins for PREREG_flat_regime_2026-09-21.md: the flat gate (prestep='flat')."""
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from __future__ import annotations
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import math
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import pytest
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from simroot.pure import pure_root
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XTOL, MAXFEV = 1e-12, 200
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PROBS = (
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(lambda t: t ** 3 - 2.0 * t - 5.0, 1.0, 4.0),
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(lambda t: math.exp(t) - 2.0, 0.0, 3.0),
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(lambda t: 6.0 * (t - 2.0) ** 5, 0.0, 10.0),
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(lambda t: t ** 19, -10.0, 100.0),
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)
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@pytest.mark.parametrize("f,a,b", PROBS)
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@pytest.mark.parametrize("guard", ("project", "credit", "safe"))
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def test_the_default_is_untouched(f, a, b, guard):
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ref = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", guard=guard)
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off = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", guard=guard,
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prestep="none")
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assert ref == off
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@pytest.mark.parametrize("f,a,b", PROBS)
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@pytest.mark.parametrize("guard", ("project", "credit"))
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@pytest.mark.parametrize("ext", ("none", "pattern"))
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def test_the_guarantee_holds_with_the_gate(f, a, b, guard, ext):
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x, n, ok = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
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guard=guard, prestep="flat", extrapolate=ext)
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assert ok and min(a, b) <= x <= max(a, b)
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half = math.ceil(math.log2(abs(b - a) / XTOL))
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assert n <= (2 * half + 3 if guard == "project" else half + 4), n
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@pytest.mark.parametrize("f,a,b", PROBS)
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@pytest.mark.parametrize("guard", ("project", "credit"))
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@pytest.mark.parametrize("ext", ("none", "pattern"))
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def test_the_guarantee_holds_with_the_twice_gate(f, a, b, guard, ext):
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x, n, ok = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
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guard=guard, prestep="flat2", extrapolate=ext)
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assert ok and min(a, b) <= x <= max(a, b)
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half = math.ceil(math.log2(abs(b - a) / XTOL))
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assert n <= (2 * half + 3 if guard == "project" else half + 4), n
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def test_the_twice_gate_is_silent_where_the_model_is_exact_and_fires_on_a_power():
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st = {}
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pure_root(lambda t: 3.0 * t - 1.0, -2.0, 5.0, XTOL, MAXFEV, similarity="ratio",
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scale="derived3", guard="project", prestep="flat2", stats=st)
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assert st["pre_refused"] == 0
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st = {}
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pure_root(lambda t: t ** 9, -1.0, 2.0, XTOL, MAXFEV, similarity="ratio",
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scale="derived3", guard="project", prestep="flat2", stats=st)
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assert st["pre_refused"] > 0
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@pytest.mark.parametrize("f,a,b", PROBS)
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@pytest.mark.parametrize("guard", ("project", "credit"))
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@pytest.mark.parametrize("ext", ("none", "pattern"))
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def test_the_guarantee_holds_with_the_creep_gate(f, a, b, guard, ext):
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x, n, ok = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
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guard=guard, prestep="flatcreep", extrapolate=ext)
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assert ok and min(a, b) <= x <= max(a, b)
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half = math.ceil(math.log2(abs(b - a) / XTOL))
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assert n <= (2 * half + 3 if guard == "project" else half + 4), n
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def test_the_creep_gate_is_silent_on_a_line_fires_on_a_power_and_spares_a_simple_root():
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"""Measured before pinning: silent where the model is exact, fires on x^9, and does
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NOT fire on x^3 - 2x - 5 over [1, 4], where the single flag fired once."""
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runs = {}
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for name, f, a, b in (("line", lambda t: 3.0 * t - 1.0, -2.0, 5.0),
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("x9", lambda t: t ** 9, -1.0, 2.0),
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("cubic", lambda t: t ** 3 - 2.0 * t - 5.0, 1.0, 4.0)):
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st = {}
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pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
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guard="project", prestep="flatcreep", stats=st)
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runs[name] = st["pre_refused"]
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assert runs["line"] == 0 and runs["x9"] > 0 and runs["cubic"] == 0, runs
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def test_the_gate_never_fires_where_the_model_is_exact():
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"""On a straight line the model's step lands on the root: r = 0, never >= 1/4."""
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st = {}
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pure_root(lambda t: 3.0 * t - 1.0, -2.0, 5.0, XTOL, MAXFEV, similarity="ratio",
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scale="derived3", guard="project", prestep="flat", stats=st)
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assert st["pre_refused"] == 0
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def test_the_gate_fires_on_a_pure_power():
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"""On x^9 the tangent step leaves (8/9)^9 = 0.35 of |f| on the same side."""
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st = {}
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pure_root(lambda t: t ** 9, -1.0, 2.0, XTOL, MAXFEV, similarity="ratio",
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scale="derived3", guard="project", prestep="flat", stats=st)
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assert st["pre_refused"] > 0
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# ---- PREREG_flat_stick_2026-09-21: the sticky flat regime and its midpoint ablation ----
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from simroot.pure import _order_from_promise, _order_split # noqa: E402
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@pytest.mark.parametrize("m", (2.0, 3.0, 5.0, 9.0, 19.0, 100.0))
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def test_the_order_is_read_back_from_its_own_promise(m):
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r = (1.0 - 1.0 / m) ** m
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assert _order_from_promise(r) == pytest.approx(m, rel=1e-9)
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def test_no_finite_order_at_or_above_one_over_e_gives_the_midpoint():
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assert math.isinf(_order_from_promise(math.exp(-1.0)))
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assert math.isinf(_order_from_promise(0.9))
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assert _order_split(-1.0, -3.0, 2.0, 5.0, math.inf) == 0.5
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@pytest.mark.parametrize("m", (1, 3, 5, 9))
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def test_the_split_lands_on_the_root_of_an_exact_power(m):
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f = lambda t: (t - 0.3) ** m # noqa: E731
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assert _order_split(-1.0, f(-1.0), 2.0, f(2.0), float(m)) == pytest.approx(0.3, abs=1e-12)
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def test_the_split_does_not_overflow_on_extreme_ends():
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x = _order_split(0.0, -1e-300, 1.0, 1e300, 2.0)
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assert 0.0 <= x < 1e-100
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x = _order_split(0.0, -1e300, 1.0, 1e-300, 2.0)
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assert 1.0 - x < 1e-100 and x <= 1.0
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@pytest.mark.parametrize("f,a,b", PROBS)
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@pytest.mark.parametrize("guard", ("project", "credit"))
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@pytest.mark.parametrize("ext", ("none", "pattern"))
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@pytest.mark.parametrize("gate", ("flatstick", "flatstickmid"))
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def test_the_guarantee_holds_with_the_sticky_regime(f, a, b, guard, ext, gate):
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x, n, ok = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
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guard=guard, prestep=gate, extrapolate=ext)
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assert ok and min(a, b) <= x <= max(a, b)
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half = math.ceil(math.log2(abs(b - a) / XTOL))
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assert n <= (2 * half + 3 if guard == "project" else half + 4), n
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@pytest.mark.parametrize("gate", ("flatstick", "flatstickmid"))
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def test_the_sticky_regime_is_silent_on_a_line_and_holds_on_a_power(gate):
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st = {}
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pure_root(lambda t: 3.0 * t - 1.0, -2.0, 5.0, XTOL, MAXFEV, similarity="ratio",
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scale="derived3", guard="project", prestep=gate, stats=st)
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assert st["pre_refused"] == 0
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st = {}
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_x, n, _ok = pure_root(lambda t: t ** 9, -1.0, 2.0, XTOL, MAXFEV, similarity="ratio",
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scale="derived3", guard="project", prestep=gate, stats=st)
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# once entered, every later non-forced step is a split: many, not one
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assert st["pre_refused"] >= 3, st
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def test_an_infinite_end_gives_the_midpoint_not_nan():
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"""Audit bug 2026-09-21: an infinite |f| made lq nan, and the nan step reached the
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safeguard before the loop checked finiteness."""
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assert _order_split(0.0, -math.inf, 2.0, 1.0, 3.0) == 1.0
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assert _order_split(0.0, -math.inf, 2.0, math.inf, 3.0) == 1.0
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