The Quantum Pyramids Conjecture

Precise statement

Englert and Rehacek conjectured which measurement is globally information-optimal for an ensemble of equiangular equiprobable pure states. Their conjecture holds, via the remaining entropy inequalities of Holevo and Utkin.

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

ChatGPT Pro 5.4

The acknowledgement credits the model with calculations used to prove the technical lemmas in the appendix.

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

Verification boundary

unreviewed

Single-author arXiv preprint; not yet peer-reviewed.

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

Timeline

1. 2026-06-12

   arXiv:2606.14698 - Resolving the Edge of a Quantum Pyramid

   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.