The logarithmic spiral is optimal for shoreline search (Baeza-Yates–Culberson–Rawlins conjecture)

Every search path has competitive ratio at least $C_{\mathrm{sp}} = 13.811135179\ldots$ , so the logarithmic spiral is optimal and the optimal ratio is exactly $C_{\mathrm{sp}}$ . Paths are arbitrary: the distance from the start and the polar angle may both decrease. The proof is computer-assisted: a reduction to a three-state relaxed control problem, closed by an explicit $C^1$ storage function whose dissipation inequalities are verified in interval arithmetic and are tight only at the spiral.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 21, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The logarithmic spiral is optimal for shoreline search (Baeza-Yates–Culberson–Rawlins conjecture) · Shoreline search spiral

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

GPT 6 Astra
model · ai model contributor · maker attribution ambiguous: OpenAI, Anthropic

Claude Fable 5.1
model · ai model contributor · maker attribution ambiguous: OpenAI, Anthropic

Claude Opus 5
model · ai model contributor · maker attribution ambiguous: OpenAI, Anthropic

Alexander Temerev
human · human collaborator

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Named evidence

VibeMathed record: The logarithmic spiral is optimal for shoreline search (Baeza-Yates–Culberson–Rawlins conjecture)

specialist registry · passed

Kept from the submission, which is accurate, with the checks named. Not independently reviewed. The storage function's dissipation inequalities are verified in Arb ball arithmetic, about 10^6 boxes, with an exact jet and an interval Hessian at the spiral, by two independent implementations. Eight Lean 4 modules carry no sorry and depend only on propext, Classical.choice and Quot.sound, and check lemmas of the reduction, but the argument is NOT formalised end to end: Section 10 of the paper lists what is machine-checked and what is not, and the entry does not claim more. Checked here on 30 September 2026: the arXiv abstract states the ratio as 13.8111351794611... and the paths as arbitrary, with both the radius and the polar angle allowed to decrease, which is the general case the conjecture is about. The ancillary directory holding the Lean modules, the two verifiers and the certified coefficient table was not rebuilt here.

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The logarithmic spiral is optimal for shoreline search (Baeza-Yates–Culberson–Rawlins conjecture)

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Lineage and corrections

This event attributed to Claude Fable 5.1

The logarithmic spiral is optimal for shoreline search (Baeza-Yates–Culberson–Rawlins conjecture) parent of this event

This event attributed to GPT 6 Astra

This event attributed to Claude Opus 5

The logarithmic spiral is optimal for shoreline search (Baeza-Yates–Culberson–Rawlins conjecture) evidence for this event

VibeMathed record: The logarithmic spiral is optimal for shoreline search (Baeza-Yates–Culberson–Rawlins conjecture) evidence for this event

This event attributed to Alexander Temerev

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