vvsandClaude Opus 5
b677283afc
S-ablation of A' (server): A' with each of the nine similarity functions in the step - tent 4443 on the paper protocol (13032 over 855 problems), the nearest other function e^-|z| 4988 (+12%; +9% over six corpora), quadratic ones 18410-18422 (+315%); ranking as the contraction law predicts; guarantee held with every S. The audit of section 7 rerun on the regenerated sweeps (APS unchanged: triple by shape -493 with the tent, +250 with 1/sqrt(1+z^2); defect -283 vs +215). Text: abstract and section 3 no longer call the similarity scaffolding - the tent making the step Newton's is a property of the similarity chosen; a paragraph in section 7 on the audit; Table 9a; new 8.6 'What is known, and what is new' - Lagouanelle (the order estimate of 7.1 / 10.5), Rall and Hansen-Patrick (8.1), the log-log slope / COC / ACOC (8.2, formula 6), Schroeder and Traub (the split 7 = false position on sign(f)|f|^(1/m)), Brent's acceptance condition (half), Dekker/Brent (tolerance step); what we found no counterpart for is the decision layer by similarity and analogy and the step set by a similarity whose form is decisive. References 13-19. verify_article: Table 9a, the percentages and the audit numbers added; server 446 OK, 0 BAD; regression x2 1226 passed, 0 failed. 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 | -106 -493 | +194 -122 | -315 -283 | -10 +2515 | -310
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1-sqrt|z| +16 | +226 -47 | -17 -186 | -65 +195 | -34 +18 | -206
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1-|z|^1/3 +3 | +188 -36 | +131 -776 | -359 +215 | +8 +208 | -58
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1/(1+|z|) +165 | -24 +126 | +361 -118 | -354 +8 | -8 +3825 | -407
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(1+|z|)^-2 +29 | -100 -255 | +175 +29 | -235 +204 | -111 +49 | -641
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e^-|z| +64 | -145 -227 | +276 +30 | -404 -2 | -2 +3194 | -473
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1/(1+z^2) +2 | +1 +11 | +275 -9 | -300 +14 | -146 +18 | -825
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e^-z^2 +1 | -3 -224 | +321 -8 | -294 +14 | -77 +10 | -767
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1/sqrt(1+z^2) +0 | +14 +250 | +192 -12 | -264 -10 | -107 +4 | -778
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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 -145 .. +226 (over 9 functions)
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triple by shape APS -493 .. +250 CHA -17 .. +361 (over 9 functions)
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far end by dissimilarity APS -776 .. +30 CHA -404 .. -65 (over 9 functions)
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decision 'defect' APS -283 .. +215 CHA -146 .. +8 (over 9 functions)
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decision 'simpair' (uses S) APS +4 .. +3825 CHA -825 .. -58 (over 9 functions)
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