Pandey Parity Conjecture for Generalized Petersen Graphs

Precise statement

For every $n \ge 2k + 1$, is the independence polynomial of $GP(n, k)$ real-rooted if and only if $k$ is even? Exact Sturm counts refute both directions.

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

Demonstrandum multi-agent pipeline

Found by the Demonstrandum multi-agent pipeline; every refutation ships a finite certificate, a mutation-tested checker, and an independent clean-room recomputation.

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

Verification boundary

unreviewed

Exact certificate verified by two independently written checkers; public artifacts repository. Not externally refereed.

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

Timeline

1. 2026-06-12

   Demonstrandum artifacts repository (RESULTS.md)

   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

construction (source-reported)

Source-reported tools: construction.

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.