Advanced Vibe Mathematics: A Case Study

How one 6.5-hour AI session produced four articles, three genuine results, two identical 19m31s thinking blocks, and one honest reckoning with an open problem

This document reconstructs a single ChatGPT session (8:35 PM to ∼3:05 AM, March 13–14, 2026) that began with a Gemini-generated speculative paper on exponential period decompositions, passed through compactification theory, collided with an irrelevant globalization semiring, nearly collapsed in mutual frustration, pivoted to primary sources in q-rational geometry, and ultimately produced four standalone articles, including the derivation of the exact Springborn span law

L_z = ((V_x − V_z)(V_z − V_y)) / (u_∞ − V_z), u_∞ = 1 / (1 − q).

Two of the extended thinking blocks lasted exactly 19 minutes and 31 seconds. The first produced a rigorous analysis of the (1 − q)² obstruction; the second produced a 17-page article. Both the user’s contributions (including genuine derailments) and ChatGPT’s (including genuine evasion of computation) are reconstructed from the full chat export and raw thinking traces.

Primary reference. Jouteur–Paris–Romaskevich–Thomas, Plane geometry of q-rationals and Springborn operations, arXiv:2603.04295, 2026.