Transposition is Nearly Optimal for IID List Update

Precise statement

In the list update problem, is the simple transposition rule optimal under IID requests? The question traces to Rivest's 1976 study of self-organizing lists. The paper proves transposition is within a small constant factor of the optimal online algorithm under any IID distribution.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5 Pro

"The AI generated the idea that the inequality might hold, and hypothesized, based on experiments with small n, that coefficients of the corresponding polynomial appear to be nonnegative. Although the AI was unable to prove these statements... these suggestions were essential for motivating the proof approach pursued in this paper."

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

No verification note supplied.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-03-10

   arXiv

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.