vvsandClaude Opus 5
0a62f7babb
Title: 'Root Finding by Similarity and Analogy: A Bracketing Method with a Data-Selected Decision Layer'. Abstract 246 words. Main text 10.4k words (was 17.4k): search reports moved to Appendices A (old 6-7), B (wall-clock), C (negative results); revision history removed; pronouns for Chandrupatla's method fixed; tables numbered in order. New: Algorithm 2 (complete A'), the decision layer counted honestly in 6.5, Code and data availability, Appendix D (30 pre-registrations against the first commit of their own results, read from git by check_prereg_order.py: 25 before, 4 same commit, 1 decided on the smoke; A' frozen at8027d7fbetween corpus 4's definition657df10and its results6d2531e). Literature: Bus & Dekker 1975, Fernandez-Diaz & Menendez-Perez 2023 (two dimensionless parameters; SFRFm on sign(f)|f|^(1/m) with known multiplicity - the nearest precursor of the split), Cordero-Neta-Torregrosa 2021; Illinois and Ridders cited. verify_article: explicit check that every head-to-head row sums to its set. check_new_numbers.py: no number new to the text except headings, references, hashes. Server: verify 527 OK / 0 BAD, regression x2 1232 passed, PDF 30 pages, 0 errors, 0 undefined, 0 overfull. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
15 lines
2.0 KiB
Python
15 lines
2.0 KiB
Python
"""The abstract within 250 words (revision): same claims and numbers, fewer words.
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python -u apply_abstract_250.py
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"""
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PATH = "article/sim_numerics.md"
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NEW = """We replace bisection's midpoint rule by a similarity rule — the step grows with how dissimilar $f(x)$ is to the target 0, under a similarity $S$ with $S(0)=1$ — and derive its contraction factor in closed form. The derivation fixes a base rule before any benchmark is consulted: with the tent similarity and a three-point divided-difference scale it is a Newton step of Muller's order 1.839, clipped to the bracket and projected onto a budget of twice bisection whose multiplier is its one numerical constant. On the 154 problems of Alefeld, Potra and Shi it is level with TOMS 748 and 1.5% behind Chandrupatla's method; on wide brackets it is clearly behind. The gap is a decision, when to give the model up, and we take it by analogy: at a flat root the dimensionless configuration of the last three points recurs under zoom, at a simple root it tends to a line, and the analogous pair gives the order that says whether and where to split. This decision layer, about ten discrete rules selected on two development sets, gives the method A′. On 240 problems fixed before its code was frozen it needs 3656 evaluations against 5717 for Chandrupatla, 5535 for ModAB and 4488 with Lagouanelle's multiplicity estimate in place of the analogy; the lead lies in multiple and fractional roots, present in two of the six families. With the multiplicity known, the classical transformation $\\operatorname{sign}(f)|f|^{1/m}$ is 2.4 to 6.8 times cheaper on multiple roots."""
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src = open(PATH, encoding="utf8").read()
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head, rest = src.split("## Abstract\n\n", 1)
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old, tail = rest.split("\n\n---\n", 1)
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assert "Bisection places its next iterate" in old
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print("old", len(old.split()), "new", len(NEW.split()))
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assert len(NEW.split()) <= 250
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open(PATH, "w", encoding="utf8").write(head + "## Abstract\n\n" + NEW + "\n\n---\n" + tail)
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print("abstract replaced")
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