vvsandClaude Opus 5
0ec7142baf
(2) Valeri: 'similarity should solve the flat-family problem'. The similarity of two successive contraction ratios, min/max(rho_n, rho_n-1), was pre-declared as the detector; it FAILS and is inverted - AUC 0.28-0.42 flat against the rest, and 'the contraction did not speed up' fires more on APS (37.6%) than on the flat families (28.2%). The rho sequence shows why: on x^m the method runs a period-4 cycle - two Newton undershoots at exactly (1-1/m)^m (0.328 for m=5, 0.346 for m=9), one crossing, one nearly empty step (rho ~ 1) - so successive ratios are dissimilar, not constant. The safeguard is not the cause: the steps are as proposed. Candidate detectors suggested by the cycle are new hypotheses, not built. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
25 lines
866 B
Plaintext
25 lines
866 B
Plaintext
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== proposed (projection)
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group states rho_n >= rho_(n-1)
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APS 1429 37.6%
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CHA fun1 83 28.9%
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CHA flat fun3-6 1763 28.2%
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CHA other 237 25.3%
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AUC of S, flat states against:
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APS 0.422
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CHA fun1 0.409
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CHA other 0.386
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== reading (3), as for m>=2
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group states rho_n >= rho_(n-1)
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APS 990 27.5%
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CHA fun1 36 27.8%
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CHA flat fun3-6 659 31.3%
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CHA other 204 16.7%
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AUC of S, flat states against:
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APS 0.284
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CHA fun1 0.345
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CHA other 0.229
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bar to beat (three-point order estimate, m >= 2): 0.2% canonical, 5.8% flat
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