vvsandClaude Opus 5 b677283afc Article: the similarity in the step is earned, not scaffolding; literature in place. ...

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>

2026-09-21 21:22:41 +01:00

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new_sections_8_9.md

Article (canonical .md), step 1: 42 stale numbers brought to the regenerated server sweeps (Tables 3-7, 5.3, 7.1-7.4, section 10), statements that no longer hold rephrased ((2)+(3) not worse than either alone on the wide-bracket set; the best constant-free configuration is no longer defect); the rule of section 3 renamed the base rule; new Section 8 (the flat regime recognised by analogy: the flag, the analogy with its own past, the translation limit, the split from the order, five more readings, the proposed method A', Tables 8-9) and Section 9 (out-of-sample evidence on four more corpora, Tables 10-11); negative results and conclusion renumbered 10-11. Abstract, introduction, conclusion and verify_article still to update.

2026-09-21 20:44:31 +01:00

sim_numerics.md

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

2026-09-21 21:22:41 +01:00

sim_numerics.pdf

Slot 2, the decision place: Chandrupatla's own acceptance band, put inside our step rule as an instrument, does NOT close the gap - CHA 3066 (project) / 2899 (credit) against his 2423, while APS doubles 2806 -> 5432, and the band is not idle (63.6% refusals). The fifth independent test of one conclusion: the remaining gap is the ORDER of the model the step is built on, not the place the similarity is read in. By the declared stop rule (M1 and M2 both false) the 'where is the similarity read' line is closed: all four places measured.

2026-09-21 06:58:59 +01:00

sim_numerics.tex

The new sections move into the canonical text, article/sim_numerics.md (Valeri's decision): section 7 'Where the similarity is read' with 7.1 per-place similarity, 7.2 the decision place, 7.3 the fun7 scoring artefact, 7.4 the gap decomposition; negative results 8-11 appended so items 1-7 keep their numbers; abstract paragraph; Future work rewritten (the refuted log transform removed); item 6 now says aps.13.00 is a scoring artefact, not a method failure. Translated into the .md's revised names: code 'ratio' = the tent max(0,1-|z|), code 'rational' = the ratio similarity 1/(1+|z|); the proposed method stays the .md's (tent, 3-point, projection).

2026-09-21 07:48:55 +01:00