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>
20 lines
2.2 KiB
Plaintext
20 lines
2.2 KiB
Plaintext
Gain of each reading (APS | CHA), by the similarity S used in the STEP. Negative = cheaper.
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S in the step slope-sign gate triple by shape far end by dissimilarity decision 'defect' decision 'simpair' (uses S)
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tent 1-|z| +42 | -146 -493 | +205 -122 | -289 -283 | -10 +2515 | -310
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1-sqrt|z| +16 | +167 -47 | +9 -186 | -43 +195 | -27 +18 | -199
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1-|z|^1/3 +3 | +186 -36 | +139 -776 | -368 +215 | +12 +208 | -50
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1/(1+|z|) +165 | -87 +126 | +358 -118 | -327 +8 | -8 +3825 | -432
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(1+|z|)^-2 +29 | -158 -255 | +182 +29 | -217 +204 | -111 +49 | -670
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e^-|z| +64 | -203 -227 | +278 +30 | -382 -2 | -2 +3194 | -503
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1/(1+z^2) +2 | +1 +11 | +273 -9 | -223 +14 | -172 +18 | -853
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e^-z^2 +1 | -3 -224 | +303 -8 | -214 +14 | -179 +10 | -790
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1/sqrt(1+z^2) +0 | +14 +250 | +186 -12 | -211 -10 | -171 +4 | -844
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Does the gain depend on S? Range of the gain over the nine functions:
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slope-sign gate APS +0 .. +165 CHA -203 .. +186 (over 9 functions)
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triple by shape APS -493 .. +250 CHA +9 .. +358 (over 9 functions)
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far end by dissimilarity APS -776 .. +30 CHA -382 .. -43 (over 9 functions)
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decision 'defect' APS -283 .. +215 CHA -179 .. +12 (over 9 functions)
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decision 'simpair' (uses S) APS +4 .. +3825 CHA -853 .. -50 (over 9 functions)
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