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Article: the similarity in the step is earned, not scaffolding; literature in place.

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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>
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2026-09-21 21:22:41 +01:00
co-authored by Claude Opus 5
parent 667f243f54
commit b677283afc
12 changed files with 417 additions and 27 deletions
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results_verify_article.txt
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@@ -439,6 +439,43 @@ Section 9 (out-of-sample corpora):
OK Roots.jl, variant carried: totals got (1464, 1566) want (1464, 1566)
OK Roots.jl, variant carried: per problem got (38, 10, 30) want (38, 10, 30)
OK applied, variant carried: totals got (1580, 1382) want (1580, 1382)
Table 9a and section 7: the similarity in the step (fresh audit run):
OK Table 9a ratio APS+CHA got 4443 want 4443
OK Table 9a ratio six corpora got 13032 want 13032
OK Table 9a ratio guarantee got 0 want 0
OK Table 9a exp_abs APS+CHA got 4988 want 4988
OK Table 9a exp_abs six corpora got 14142 want 14142
OK Table 9a exp_abs guarantee got 0 want 0
OK Table 9a rational APS+CHA got 5486 want 5486
OK Table 9a rational six corpora got 14843 want 14843
OK Table 9a rational guarantee got 0 want 0
OK Table 9a ratio_soft APS+CHA got 8360 want 8360
OK Table 9a ratio_soft six corpora got 28500 want 28500
OK Table 9a ratio_soft guarantee got 0 want 0
OK Table 9a sqrt APS+CHA got 12718 want 12718
OK Table 9a sqrt six corpora got 45552 want 45552
OK Table 9a sqrt guarantee got 0 want 0
OK Table 9a cbrt APS+CHA got 17207 want 17207
OK Table 9a cbrt six corpora got 63031 want 63031
OK Table 9a cbrt guarantee got 0 want 0
OK Table 9a exp_sq APS+CHA got 18410 want 18410
OK Table 9a exp_sq six corpora got 67701 want 67701
OK Table 9a exp_sq guarantee got 0 want 0
OK Table 9a cosine APS+CHA got 18412 want 18412
OK Table 9a cosine six corpora got 67854 want 67854
OK Table 9a cosine guarantee got 0 want 0
OK Table 9a rat_sq APS+CHA got 18422 want 18422
OK Table 9a rat_sq six corpora got 67394 want 67394
OK Table 9a rat_sq guarantee got 0 want 0
OK nearest other S costs more, protocol % got 12 want 12
OK worst S costs more, protocol % got 315 want 315
OK nearest other S costs more, six corpora % got 9 want 9
OK quadratic S: four to five times got (4, 5) want (4, 5)
OK audit: shape gain with the tent (APS) got -493 want -493
OK audit: shape gain with 1/sqrt(1+z^2) (APS) got 250 want 250
OK audit: defect gain with the tent (APS) got -283 want -283
OK audit: defect gain with 1-|z|^1/3 (APS) got 215 want 215
OK sign test p for 103:31 got '3e-10' want '3e-10'
OK sign test p for 31:10 got '0.001' want '0.001'
OK sign test p for 108:65 got '0.001' want '0.001'