Optimal Strategies in the All-Heads Coin Game

VibeMathed recorded: Optimal Strategies in the All-Heads Coin Game. Consult the linked registry entry for the original report and scope.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Apr 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-verified. Publication: preprint. AI contribution: ai-co-developed. Editorial metadata: CC BY 4.0; linked content retains its own rights.

Canonical aliases: Optimal Strategies in the All-Heads Coin Game · All-heads coin game

Confidence: Not scored

Registry verification: lean verified · preprint · partial

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Attribution

VibeMathed
registry · event recorded by

Peter Pfaffelhuber
human · human collaborator

Claude Opus 4.6 / 4.7 / 4.8
model · ai model contributor · Anthropic

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Optimal Strategies in the All-Heads Coin Game

specialist registry · passed

Every numbered result, including the perturbation analysis, is formally verified in Lean 4 with Mathlib: no `sorry`, no custom axioms (only propext, Classical.choice, Quot.sound), no `native_decide`/`unsafe`. Trust surface is two files (`CoinsLean/Challenge.lean`, `CoinsLean/CoinsLean/Defs.lean`), independently checkable via the Lean comparator on the public repository; manuscript↔Lean map in Appendix A. arXiv preprint (v2, June 2026), not peer-reviewed. Status set to partially resolved (2026-08-02): p = 1/2 and p > 1/2 are fully resolved, but for p < 1/2 the paper gives only a first-order expansion in δ = 1/2 − p near 1/2, leaving the range of validity δ₀(n) open and the numerically observed local maxima outside its reach. Verification tier unchanged: the Lean checks what the paper claims, and the paper does not claim the full small-p regime.

Source ↗

Lean formalization + full transcript:

lean artifact · passed

lean-proof link supplied by the VibeMathed registry.

Source ↗

Optimal Strategies in the All-Heads Coin Game

preprint · pending

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

Source ↗

Artifacts and verifiers

Lean formalization + full transcript:

lean artifact · passed

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

This event attributed to Peter Pfaffelhuber

This event attributed to Claude Opus 4.6 / 4.7 / 4.8

Lean formalization + full transcript: evidence for this event

Optimal Strategies in the All-Heads Coin Game parent of this event

Optimal Strategies in the All-Heads Coin Game evidence for this event

Registry resolution: partial. Reported result type: proved. The registry record and named primary source provide the statement and scope. parent of this event

VibeMathed record: Optimal Strategies in the All-Heads Coin Game evidence for this event

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