A' code frozen BEFORE the corpus-4 run (PREREG_close_sub): close (borrowed Dekker/Brent tolerance step, only after a kept promise) and sub (overshoot branch m <= 2/3; the shallow memory is not cleared by the exit - amendment documented). Development on the five seen corpora (uniform sign-change criterion): A' below A everywhere; vs Chandrupatla APS 103/31, CHA 31/10, new-1 109/65, Roots.jl 44/20 p=0.004, applied 48/32 p=0.09 with total 1382 vs 1380. Tests: 1223 passed (full), 358 (gate files).
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
This commit is contained in:
Claude Opus 5
+44
-3
@@ -764,19 +764,21 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
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# category variables below then carry the same string the old tests compared.
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if "+" in prestep:
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parts = prestep.split("+")
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cats = ({"defect"}, {"contra"}, {"exp"}, {"half"}, {"flatanalog", "flatanalogmem", "flatanalogpt",
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cats = ({"defect"}, {"contra"}, {"exp"}, {"half"}, {"close"}, {"sub"},
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{"flatanalog", "flatanalogmem", "flatanalogpt",
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"flatanalogmempt"})
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if (len(parts) != len(set(parts)) or any(not any(p in c for c in cats) for p in parts)
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or any(sum(p in c for p in parts) > 1 for c in cats)):
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raise ValueError(f"unknown composite prestep {prestep!r}")
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if "exp" in parts and not any(p.startswith("flatanalog") for p in parts):
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if (("exp" in parts or "sub" in parts)
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and not any(p.startswith("flatanalog") for p in parts)):
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# the translation limit changes how the analogy reads its order; without the
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# flat regime there is no analogy to read (PREREG_flat_exp_limit)
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raise ValueError("prestep component 'exp' needs a flatanalog* component")
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elif prestep not in ("none", "progress", "slope", "band", "defect", "simpair", "flat",
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"flat2", "flatcreep", "flatstick", "flatstickmid", "flatstickexit",
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"flatjudge", "flatanalog", "flatanalogmem", "contra",
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"flatanalogpt", "flatanalogmempt", "half"):
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"flatanalogpt", "flatanalogmempt", "half", "close"):
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raise ValueError(f"unknown prestep {prestep!r}")
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parts = prestep.split("+")
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pre_dec = next((p for p in parts if p in ("band", "defect", "simpair")), "none")
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@@ -788,6 +790,8 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
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pre_contra = "contra" in parts
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pre_exp = "exp" in parts # PREREG_flat_exp_limit: translation similarity, m = inf
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pre_half = "half" in parts # PREREG_half_contra: the half promised vs the bracket
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pre_close = "close" in parts # PREREG_close_sub: the tolerance step (borrowed)
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pre_sub = "sub" in parts # PREREG_close_sub: the overshoot branch, m <= 2/3
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if pre_dec != "none" and scale not in (
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"derived3", "derived3_cap", "derived3_m", "bracket", "far"):
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# the decision reads a TRIPLE; under the two-point scale there is no third point
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@@ -847,6 +851,8 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
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analogy_seen = False # flatanalogmem: the run has been judged analogous to its past
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analogy_m = math.inf # flatanalog*pt: the order read from the latest analogous pair
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regime_target = None # flatanalog*pt: the point the regime step aimed at
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shallow_seen = False # sub: the run has been judged analogous with m <= 2/3
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shallow_m = math.inf # sub: the order of that pair
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if stats is not None:
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stats['forced'] = 0
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stats['pre_refused'] = 0
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@@ -1079,15 +1085,32 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
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and fx / f_prev >= 0.25)
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m_pair = _analogy_order(cur, configs, translation=pre_exp)
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steep = m_pair is not None and m_pair >= 2.0
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# PREREG_close_sub 2026-09-21 (sub): the tangent step loses to a halving
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# when |1 - 1/m| > 1/2 - for m > 2 (undershoot, the branch above) AND
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# for m < 2/3 (overshoot). The overshoot shows as an unkept promise WITH
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# a sign change; the pair's order says which branch it is.
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shallow = (pre_sub and m_pair is not None
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and 0.0 < m_pair <= 2.0 / 3.0)
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flag_over = (pre_sub and sticky_m is None and last_model
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and f_prev != 0.0 and fx / f_prev <= -0.25)
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if flat_mem:
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if steep:
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analogy_seen = True
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analogy_m = m_pair
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if shallow:
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shallow_seen = True
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shallow_m = m_pair
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enter = flag and analogy_seen
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if not enter and flag_over and shallow_seen:
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enter = True
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analogy_m = shallow_m
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else:
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enter = flag and steep
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if enter:
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analogy_m = m_pair
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elif flag_over and shallow:
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enter = True
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analogy_m = m_pair
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if enter:
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sticky_m = math.inf
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if stats is not None:
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@@ -1207,6 +1230,19 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
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reach = abs(far - x)
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step = (longer if abs(longer) <= reach
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else math.copysign(reach, step))
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if (pre_close and abs(step) < 0.5 * xtol and last_model
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and f_prev != 0.0 and abs(fx / f_prev) < 0.25):
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# Only a CREDIBLE promise is closed on: the model's previous step
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# kept its own promise (|f| fell below the flag's 1/4). Measured in
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# development on x^19: at the start, a slope dominated by f(100) =
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# 1e38 promises the root at x = -10, and closing on that promise
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# replaced the midpoint by near-duplicate points (23 -> 32).
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# PREREG_close_sub 2026-09-21 (close) - BORROWED: Dekker (1969) and
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# Brent (1973) step at least the tolerance. A model promising the
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# root closer than xtol/2 is taken at its word one step further: the
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# new point lands past the root and the bracket closes to the
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# tolerance, instead of being halved down from the far end.
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step = math.copysign(0.5 * xtol, far - x)
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model_target = x + step # the model's own proposal
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if stats is not None and "trace" in stats:
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# DIAGNOSTIC HOOK, behaviour-neutral: records the state each
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@@ -1272,6 +1308,11 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived",
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# flatanalogmem: "linear" refutes "flat" - the remembered analogy is
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# cleared and must be established anew (PREREG_flat_analogy_mem)
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analogy_seen = False
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# NOT shallow_seen (PREREG_close_sub, amendment): the exit judgment - f nearer
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# the line than 0 - tells a flat root from a simple one; at a root of order
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# m < 1 f is far from 0 on both sides, the exit fires falsely, and keeping the
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# shallow memory lets the regime resume at the next overshoot (development:
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# sqrt|x| sgn 19 with it, 65 without)
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if stats is not None:
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stats['stick_exits'] = stats.get('stick_exits', 0) + 1
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if prestep == "flatjudge":
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