Equality in Fill's Spectral Gap Problem
For the adjacent-transposition chain on $\mathfrak{S}_n$ with a regular parameter vector, Fill's spectral gap conjecture (recently resolved) leaves open the characterization of the equality cases. The paper settles them, constructing the additional eigenfunctions in the exceptional regime.
Exact FrontierDelta
Scope and record
Occurred: Apr 5, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: Equality in Fill's Spectral Gap Problem · Fill's spectral gap, equality
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Vishesh Jain
human · human collaborator
Clayton Mizgerd
human · human collaborator
ChatGPT 5.4 Pro
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Clayton Mizgerd
This event attributed to Vishesh Jain
This event attributed to ChatGPT 5.4 Pro