Controls K1/K2: code and two PREREG amendments, committed before the full run.
simroot/pure.py: flatlagmempt / flatbandmempt / flatflagmempt - A' with only the flat detector swapped (Lagouanelle without declining outside (0,1), with memory; Chandrupatla's band; none). A' itself is untouched: bit-identical to the compiled simbracket on all 868 problems (x2). sweep_controls.py: K2 through sweep_fourth's harness, K1 with the oracle order m*. Amendment 1: m* <= 0 is undefined (aps.15.22-30, C0.04 crashed the first full attempt). Amendment 2 (after the smokes; only corpus-level K1 sums and corpus-4 K2 sums were seen): each side's slope rounded to 0.01, m* defined only when both sides show a zero (jumps C0.03, aps.15.21), group 'multiple/fractional' = m* >= 2 or m* <= 2/3, the branches of section 8.1 (simple roots measured at 0.99999 fell under the registered 'm* < 1'). tests/test_article_numbers.py: the verifier test runs on Linux only (the paper's numbers are a Linux run; libm's last digit differs elsewhere, e.g. 4461 vs 4462). Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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Claude Opus 5
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"""PREREG_controls_2026-09-22: the controls, as registered (commit 77312be).
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K2 (point 6): A' with only the flat detector swapped - Lagouanelle with memory (K2L),
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Chandrupatla's band (K2P), no detector (K2F) - on the six corpora of section 9, harness of
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sweep_fourth.py (same problems, seeding, charging, uniform criterion).
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K1 (point 5): library Chandrupatla and Brent on g = sign(f)|f|^(1/m*), m* the true order read at
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the known root, on the four corpora whose roots are known.
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python -u sweep_controls.py run -> sweep_controls.json, then the report
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python -u sweep_controls.py --smoke K2 on corpus 4 and K1 on all four corpora, no file
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python -u sweep_controls.py --report
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"""
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from __future__ import annotations
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import json
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import math
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import random
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import sys
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from collections import defaultdict
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from multiprocessing import Pool
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import sweep_fourth
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from corpus_roots_jl import solved
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from sweep_full import MAXFEV, XTOL
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from sweep_oos import sign_p
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TAIL = "+half+close+sub"
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K2 = {"K2L": "contra+flatlagmempt" + TAIL, "K2P": "contra+flatbandmempt" + TAIL,
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"K2F": "contra+flatflagmempt" + TAIL}
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for _k, _pre in K2.items():
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sweep_fourth.CONFIGS[_k] = sweep_fourth.spec(_pre)
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SETS = ("APS", "CHA", "NEW", "RJL", "APP", "D")
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K1_SETS = ("APS", "CHA", "NEW", "D")
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def m_star(f, r):
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"""The order at the known root: slope of ln|f| against ln|x - r|, both sides averaged,
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h = 1e-5 max(1, |r|) (registered). 1 when undefined."""
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# amendment 2 of the PREREG (after the smokes, before any full result): each side's slope
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# is rounded to 0.01 and m* is defined only when BOTH sides show a zero (slope > 0) -
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# a jump (C0.03), a flat side (aps.15.21-30) or a pole-like side (C0.04) is undefined
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h = 1e-5 * max(1.0, abs(r))
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vals = []
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for s in (1.0, -1.0):
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try:
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f1, f2 = abs(f(r + s * h)), abs(f(r + s * 2 * h))
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m = (math.log(f2) - math.log(f1)) / math.log(2.0)
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except (ValueError, OverflowError, ZeroDivisionError):
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return 1.0
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if not math.isfinite(m) or round(m, 2) <= 0.0:
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return 1.0
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vals.append(round(m, 2))
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return (vals[0] + vals[1]) / 2.0
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def nonsimple(m):
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"""The group 'multiple/fractional': the branches of section 8.1 where a tangent step loses to
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a halving, m >= 2 or m <= 2/3 (amendment 2)."""
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return m >= 2.0 or m <= 2.0 / 3.0
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def k1_problems(which):
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from corpus_fourth import build as b4
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from corpus_new import build as b1
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from sweep_full import load_problems
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out = []
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if which in ("APS", "CHA"):
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out = [(pid, f, a, b, r) for s, pid, f, a, b, r in load_problems() if s == which]
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elif which == "NEW":
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out = [(pid, f, a, b, r) for _c, pid, f, a, b, r in b1()[0]]
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else:
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out = [(pid, f, a, b, r) for _c, pid, f, a, b, r in b4()[0]]
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return out
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def k1_job(which):
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import scipy.optimize._tstutils as T
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from simroot.baselines import brent_scipy, chandrupatla_lib
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res = {"chandrupatla_g": {}, "brent_g": {}, "mstar": {}}
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for pid, f, a, b, r in k1_problems(which):
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T._f6_cache.clear()
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random.seed(20260921)
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m = m_star(f, r)
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res["mstar"][pid] = m
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inv = 1.0 / m
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def g(x, _f=f, _i=inv):
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v = _f(x)
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return 0.0 if v == 0 else math.copysign(abs(v) ** _i, v)
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for name, meth in (("chandrupatla_g", chandrupatla_lib), ("brent_g", brent_scipy)):
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T._f6_cache.clear()
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random.seed(20260921)
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try:
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x, n, conv = meth(g, a, b, XTOL, MAXFEV)
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x = float(x)
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except Exception:
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x, n, conv = float("nan"), MAXFEV, False
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ok = bool(conv and solved(f, x))
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over = ok and int(n) > 2 * math.ceil(math.log2(abs(b - a) / XTOL)) + 4
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res[name][pid] = [int(n), ok, bool(over)]
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return which, res
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def k2_job(j):
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name, which = j
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return name, which, sweep_fourth.evaluate((name, which))[1]
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def cost(v):
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return v[0] if v[1] else MAXFEV
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def h2h(a, b, keep=None):
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ps = [p for p in a if keep is None or keep(p)]
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w = sum(cost(a[p]) < cost(b[p]) for p in ps)
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l = sum(cost(a[p]) > cost(b[p]) for p in ps)
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return w, len(ps) - w - l, l
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def tot(r, keep=None):
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return sum(cost(v) for p, v in r.items() if keep is None or keep(p))
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def reference():
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seen = json.load(open("sweep_fourth_seen.json", encoding="utf8"))
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four = json.load(open("sweep_fourth_fourth.json", encoding="utf8"))
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ref = {}
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for k in ("Aprime", "chandrupatla"):
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ref[k] = dict(seen[k])
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ref[k].update(four[k])
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return ref
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def report(R):
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ref = reference()
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ap = ref["Aprime"]
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print("C2 - six corpora, A' against each detector (total; A' w/t/l, p); violations in ()")
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for k in K2:
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line = [f" {k}:"]
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for s in SETS:
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w, t, l = h2h(ap[s], R["K2"][k][s])
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line.append(f"{s} {tot(R['K2'][k][s])}({sum(v[2] for v in R['K2'][k][s].values())})"
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f" {w}/{t}/{l}")
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allk = sum(tot(R["K2"][k][s]) for s in SETS)
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print(" ".join(line) + f" | all {allk} vs A' {sum(tot(ap[s]) for s in SETS)}")
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print("\nC1 - corpus 4 (decisive): A' total, control total, A' w/t/l, p -> verdict")
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passed = {}
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for k in K2:
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a, c = ap["D"], R["K2"][k]["D"]
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w, t, l = h2h(a, c)
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passed[k] = tot(a) < tot(c) and w > l and sign_p(w, l) < 0.05
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print(f" {k}: A' {tot(a)} {k} {tot(c)} {w}/{t}/{l} p={sign_p(w, l):.2g} -> "
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+ ("PASSED" if passed[k] else "NOT passed"))
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print(" C1 overall: " + ("PASSED for every control" if all(passed.values())
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else "NOT passed for " + ", ".join(k for k in K2 if not passed[k])))
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print("\nC4 - violations of the 2x bound, all K2 variants, six corpora:",
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sum(v[2] for k in K2 for s in SETS for v in R["K2"][k][s].values()))
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best = min(K2, key=lambda k: tot(R["K2"][k]["D"]))
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print(f"\nC5 - corpus 4 by class, A' against the best control ({best}): totals, w/t/l")
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for cls in ("D1", "D2", "D3", "D4", "D5", "D6"):
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keep = lambda p, c=cls: p.startswith(c) # noqa: E731
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w, t, l = h2h(ap["D"], R["K2"][best]["D"], keep)
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print(f" {cls}: A' {tot(ap['D'], keep)} {best} {tot(R['K2'][best]['D'], keep)} {w}/{t}/{l}")
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print("\nC3 - K1: transform with the true order (m* >= 2 or m* <= 2/3 = 'multiple/fractional')")
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for s in K1_SETS:
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k1 = R["K1"][s]
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mult = lambda p, _m=k1["mstar"]: nonsimple(_m[p]) # noqa: E731
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rest = lambda p, _m=k1["mstar"]: not nonsimple(_m[p]) # noqa: E731
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for title, keep in (("multiple/fractional", mult), ("rest", rest)):
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n = sum(1 for p in k1["mstar"] if keep(p))
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if n == 0:
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continue
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w, t, l = h2h({p: v for p, v in ap[s].items() if keep(p)}, k1["chandrupatla_g"])
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print(f" {s:<4} {title:<20} n={n:3d} A' {tot(ap[s], keep):5d} "
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f"Chandrupatla(g) {tot(k1['chandrupatla_g'], keep):5d} "
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f"Brent(g) {tot(k1['brent_g'], keep):5d} "
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f"Chandrupatla(f) {tot(ref['chandrupatla'][s], keep):5d} "
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f"A' vs Ch(g) {w}/{t}/{l} p={sign_p(w, l):.2g}")
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fam = defaultdict(list)
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for s in K1_SETS:
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for p, m in R["K1"][s]["mstar"].items():
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if nonsimple(m):
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fam[s].append(round(m, 2))
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print(" m* on the multiple/fractional problems (first 8 per corpus):",
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{s: v[:8] for s, v in fam.items()})
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def main():
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smoke = "--smoke" in sys.argv
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if "--report" not in sys.argv:
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k2_jobs = [(k, "fourth") for k in K2] + ([] if smoke else [(k, "seen") for k in K2])
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k1_sets = K1_SETS # the oracle must meet every corpus, also in the smoke
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with Pool(min(6, len(k2_jobs) + len(k1_sets))) as pool:
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k2 = pool.map_async(k2_job, k2_jobs)
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k1 = pool.map_async(k1_job, k1_sets)
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k2, k1 = k2.get(), k1.get()
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R = {"K2": {}, "K1": {}}
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for name, _which, res in k2:
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R["K2"].setdefault(name, {}).update(res)
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for which, res in k1:
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R["K1"][which] = res
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if smoke:
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ap = reference()["Aprime"]
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for k in K2:
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a, c = ap["D"], R["K2"][k]["D"]
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print(f"smoke {k}: corpus 4 total {tot(c)} (A' {tot(a)}), A' w/t/l {h2h(a, c)}, "
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f"violations {sum(v[2] for v in c.values())}")
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for s in K1_SETS:
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k1c = R["K1"][s]
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print(f"smoke K1 {s}: Chandrupatla(g) {tot(k1c['chandrupatla_g'])} Brent(g) "
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f"{tot(k1c['brent_g'])} m* range {min(k1c['mstar'].values()):.3g}.."
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f"{max(k1c['mstar'].values()):.3g}")
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print("controls smoke done")
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return
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with open("sweep_controls.json", "w", encoding="utf8") as fh:
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json.dump(R, fh)
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with open("sweep_controls.json", encoding="utf8") as fh:
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R = json.load(fh)
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report(R)
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print("controls done")
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if __name__ == "__main__":
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main()
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