The Middle Stair of Parallel Chip-Firing
Ji, Li and Wang conjectured in 2024 that every parallel chip-firing game on a finite connected graph whose chip count lies strictly between $2|E|-|V|$ and $2|E|$ has period exactly 2, generalizing the middle rung of Levine's devil's staircase from complete graphs to all graphs. Known before only for trees, cycles, complete and complete bipartite graphs.
Exact FrontierDelta
Scope and record
Occurred: Aug 4, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: expert-verified. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.
Canonical aliases: The Middle Stair of Parallel Chip-Firing · Chip-firing middle stair
Confidence: Not scored
Registry verification: expert verified · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Nathan Lannan
human · human collaborator
Daniel Wang
human · human collaborator
GPT-5.6 Sol
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Daniel Wang
This event attributed to Nathan Lannan
This event attributed to GPT-5.6 Sol