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 <noreply@anthropic.com>
This commit is contained in:
Claude Opus 5
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"""Verdicts L1-L5 for PREREG 2026-09-21 slot 1, read off sweep_order.json.
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Nothing here selects a winner by hunting: L1 is a PAIRED comparison inside each
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(similarity, guard) cell, which is the only comparison the pre-registration licenses.
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python -u analyze_order.py
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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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REF = {"APS_base": 2806, "APS_best": 2527, "CHA_best": 2683, "BOTH_best": 5511,
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"falsepos": (127, 10560), "illinois": (153, 7045), "bisect": (153, 7530)}
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def load():
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with open("sweep_order.json", encoding="utf8") as fh:
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return json.load(fh)
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def key(r):
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s = r["spec"]
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return (s[1], s[2], s[3], s[8] if len(s) > 8 else "none")
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def main():
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res = load()
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by = {key(r): r for r in res}
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print("L1 PAIRED: does the measured order improve the FAR reading? "
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"(the only licensed comparison)")
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print(f"{'similarity':<11} {'guard':<9} {'APS none':>9} {'APS ord':>8} "
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f"{'CHA none':>9} {'CHA ord':>8} {'solved n/o':>12}")
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wins = losses = 0
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for (sim, sc, gu, ex) in sorted(by):
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if sc != "far" or ex != "none":
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continue
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a, b = by[(sim, sc, gu, "none")], by.get((sim, sc, gu, "order"))
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if b is None:
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continue
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d = (a["APS"]["total"] + a["CHA"]["total"]) - (b["APS"]["total"] + b["CHA"]["total"])
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wins += d > 0
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losses += d < 0
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print(f"{sim:<11} {gu:<9} {a['APS']['total']:9d} {b['APS']['total']:8d} "
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f"{a['CHA']['total']:9d} {b['CHA']['total']:8d} "
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f"{a['APS']['solved']}+{a['CHA']['solved']}/"
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f"{b['APS']['solved']}+{b['CHA']['solved']:>2}")
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print(f" -> order cheaper in {wins} of {wins + losses} far cells\n")
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print("L1b same pairing on the DERIVED3 reading")
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for (sim, sc, gu, ex) in sorted(by):
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if sc != "derived3" or ex != "none" or gu not in ("safe", "project", "none"):
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continue
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a, b = by[(sim, sc, gu, "none")], by.get((sim, sc, gu, "order"))
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if b is None:
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continue
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print(f"{sim:<11} {gu:<9} {a['APS']['total']:9d} {b['APS']['total']:8d} "
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f"{a['CHA']['total']:9d} {b['CHA']['total']:8d} "
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f"{a['APS']['solved']}+{a['CHA']['solved']}/"
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f"{b['APS']['solved']}+{b['CHA']['solved']:>2}")
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print("\nL2/L3 best cells in the grid, by the paper's per-set rule "
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"(solved first, then cost)")
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for setname, target in (("APS", REF["APS_best"]), ("CHA", REF["CHA_best"])):
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rows = sorted(res, key=lambda r: (r[setname]["n"] - r[setname]["solved"],
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r[setname]["total"]))
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for r in rows[:3]:
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s = r["spec"]
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print(f" {setname} {r['label']:<38} {r[setname]['solved']}/"
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f"{r[setname]['n']} {r[setname]['total']:6d} "
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f"over2x={r[setname]['over']} "
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f"(target {target}) exponent={s[8] if len(s) > 8 else 'none'}")
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print("\nL4 guarantee: cells with over2x > 0 (any set)")
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bad = [r["label"] for r in res if r["APS"]["over"] or r["CHA"]["over"]]
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print(f" {len(bad)} of {len(res)}" + (f": {bad[:6]}" if bad else " -> intact"))
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print("\nFALSE POSITION, unguarded: is the measured order the parameter-free Illinois?")
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print(f" {'cell':<34} {'solved':>7} {'APS fev':>9}")
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print(f" {'false position (paper)':<34} {REF['falsepos'][0]}/154 "
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f"{REF['falsepos'][1]:9d}")
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print(f" {'Illinois (constant 1/2)':<34} {REF['illinois'][0]}/154 "
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f"{REF['illinois'][1]:9d}")
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for ex in ("none", "order"):
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r = by.get(("rational", "far", "none", ex))
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if r:
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print(f" {'far+rational, guard=none, ' + ex:<34} "
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f"{r['APS']['solved']}/154 {r['APS']['total']:9d}")
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for ex in ("none", "order"):
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r = by.get(("rational", "far", "safe", ex))
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if r:
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print(f" {'far+rational, guard=safe, ' + ex:<34} "
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f"{r['APS']['solved']}/154 {r['APS']['total']:9d}")
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print("\nBOTH SETS, best order cell against the reference 5511")
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rows = [r for r in res if len(r["spec"]) > 8 and r["spec"][8] == "order"]
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rows.sort(key=lambda r: (398 - r["APS"]["solved"] - r["CHA"]["solved"],
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r["APS"]["total"] + r["CHA"]["total"]))
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for r in rows[:3]:
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print(f" {r['label']:<38} {r['APS']['solved'] + r['CHA']['solved']}/199 "
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f"{r['APS']['total'] + r['CHA']['total']:6d} (reference {REF['BOTH_best']})")
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if __name__ == "__main__":
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main()
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