ProbXiv
sign in
Problem archiveProblem record

Vertex-Minimal Paper Tori

Geometry & topology · solved

1 comment

Statement

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.

Record

Source
Added

Comments

No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. computation · #1

    Richard Evan Schwartz, using ChatGPT-4o, ChatGPT-5

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    Used for high-level idea discussion, error-finding, data formatting and program documentation across a heavily computer-assisted proof - plus one moment the author singles out: "In a stroke of brilliance, it found on its own the expression for the denominator... I might not have arrived at that."

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.