Vertex-Minimal Paper Tori
A paper torus is an embedded polyhedral torus isometric to a flat torus. Schwartz proves no paper torus with 7 vertices exists and constructs one with 8, settling the minimum-vertex question in the flat-torus embedding tradition of Császár-torus combinatorics and the Lazarus-Tallerie universal triangulation.
Exact FrontierDelta
Scope and record
Occurred: Jul 20, 2025
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-assisted. Imported under CC BY 4.0.
Canonical aliases: Vertex-Minimal Paper Tori · Paper tori
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Richard Evan Schwartz
human · human collaborator
ChatGPT-4o
model · ai model contributor · OpenAI
ChatGPT-5
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Richard Evan Schwartz
This event attributed to ChatGPT-5
This event attributed to ChatGPT-4o