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>
100 lines
4.6 KiB
Plaintext
100 lines
4.6 KiB
Plaintext
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== fun5.1 = x^9 (flat): 88 evaluations
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k rho_n=|f_n/f_(n-1)| step as proposed?
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0 2.621e+05 CHANGED
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1 3.550e-01 yes
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2 2.604e-01 yes
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3 3.585e-05 yes
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4 9.999e-01 yes
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5 3.470e-01 yes
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6 2.550e-01 yes
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7 6.018e+02 yes
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8 5.407e-07 yes
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9 1.000e+00 yes
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10 3.223e-01 yes
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11 2.359e-01 yes
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12 6.252e-06 yes
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13 1.000e+00 yes
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14 3.448e-01 yes
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15 2.535e-01 yes
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16 2.491e+05 yes
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17 1.122e-04 yes
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18 9.964e-01 yes
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19 2.933e-01 yes
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20 2.064e-01 yes
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21 1.091e-01 yes
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22 7.494e-01 yes
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23 2.743e-01 yes
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24 1.228e-01 yes
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25 6.374e-01 yes
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26 2.198e-01 yes
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27 1.111e-03 yes
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28 9.981e-01 yes
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29 3.403e-01 yes
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30 2.500e-01 yes
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31 6.771e+03 CHANGED
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32 1.632e-05 yes
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33 9.993e-01 yes
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34 3.077e-01 yes
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35 2.223e-01 yes
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36 1.674e-02 yes
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37 9.719e-01 yes
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38 3.284e-01 yes
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39 2.372e-01 yes
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== fun4.3 = 6(x-2)^5 on a wide bracket (flat): 113 evaluations
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k rho_n=|f_n/f_(n-1)| step as proposed?
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0 3.280e-16 yes
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1 1.000e+00 yes
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2 3.276e-01 yes
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3 2.574e-01 yes
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4 2.487e-02 yes
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5 9.091e-01 yes
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6 2.960e-01 yes
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7 2.287e-01 yes
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8 1.209e-07 yes
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9 1.000e+00 yes
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10 3.270e-01 yes
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11 2.571e-01 yes
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12 2.414e-02 yes
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13 9.119e-01 yes
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14 2.966e-01 yes
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15 2.295e-01 yes
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16 1.122e-06 yes
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17 1.000e+00 yes
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18 3.265e-01 yes
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19 2.568e-01 yes
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20 2.363e-02 yes
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21 9.139e-01 yes
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22 2.971e-01 yes
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23 2.300e-01 yes
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24 3.255e-06 yes
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25 1.000e+00 yes
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26 3.262e-01 yes
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27 2.567e-01 yes
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28 2.327e-02 yes
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29 9.153e-01 yes
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30 2.974e-01 yes
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31 2.304e-01 yes
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32 5.987e-06 yes
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33 1.000e+00 yes
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34 3.264e-01 yes
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35 2.568e-01 yes
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36 2.347e-02 yes
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37 9.145e-01 yes
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38 2.972e-01 yes
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39 2.302e-01 yes
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== aps.02.09 (canonical): 12 evaluations
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k rho_n=|f_n/f_(n-1)| step as proposed?
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0 1.284e+00 CHANGED
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1 1.219e+01 CHANGED
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2 2.208e-01 CHANGED
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3 3.952e-01 yes
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4 4.398e-01 yes
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5 9.225e-02 yes
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6 1.079e-02 yes
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7 4.440e-04 yes
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8 4.563e-07 yes
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9 4.333e-02 yes
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