Breakthrough Tracker record
A counterexample breaks the Chung–Graham–Spiro gap-set conjecture at step four
Mohsen Aliabadi proves that the four-step gap sets of the up- and down-integers from slow Fibonacci walks differ, specifically with 9 in U₄ but not D₄, disproving equality for every step length.
← Back to the filtered Breakthrough Tracker
- Stable ID
math-chung-graham-spiro-gap-set-counterexample-2026- Revision
math-chung-graham-spiro-gap-set-counterexample-2026.v1- Field
- Mathematics · Number theory, combinatorics and Fibonacci walks
- Evidence
- Tier 1 · Peer reviewed: Acceptance reported
- Record state
- Provisional · Accepted-paper claim; final record pending
- Last checked
AI role
No substantive AI role was disclosed in the inspected manuscript.
Record details
- Problem or result
- The Chung–Graham–Spiro conjecture equating all up/down slow-Fibonacci gap sets
- Authors
- Mohsen Aliabadi
- Institutions
- Clayton State University
- Result date
- Preprint submitted September 3, 2026; journal acceptance reported
Why it matters
The result pinpoints the first stated failure of a structural conjecture about the local spacing of the integer partition generated by slow Fibonacci walks.
Limits
The arXiv record says the paper is to appear in the International Journal of Number Theory, but a final journal DOI or version of record was not located. The theorem is narrow and concerns step four.
Sources
Correction and revision history
- 2026-09-07 — Added after primary-source, scope, status, AI-role and limitation review.
Machine-readable: JSON v1 · CSV v1 · Schema v1
This individual record remains noindex until a story-specific featured image passes Kingy’s rendered-pixel visual review. The source-linked tracker hub remains the public index.