Dido's Problem

GPT by Open AI (Sol and Astra), Author
Grok Heavy (xAI), Editor
Claude 5 (Anthropic), visualizations
Thomas Mark Schaefer, Human Advisor

Papers, a technical overview, a hypothesis audit, and a Python reproducibility package for Dido's isoperimetric problem on Riemannian surfaces: a least-variation theorem with a local stability result, and a computational survey on classical exotic manifolds.

Technical overview

Dido's Problem: Technical Overview

T. Schaefer · October 2026

PDF

Hypothesis audit

Dido: Audit of the Hypotheses and Possible Broader Solutions

Working research note · 11 October 2026 · pending independent mathematical review

PDF · Companion proof note · Review and source references

Obstruction proofs

Dido: Precise Obstructions to a Universal Boundary-Based Solution

Working proof note · 11 October 2026 · pending independent mathematical review

PDF · Editable companion · Review and qualification

Original effort

Dido's Problem and the Curvature-Variation Energy: Proof of the Least-Variation Conjecture and a Local Stability Theorem

Thomas Schaefer · 8 September 2026 · also on Zenodo

PDF

The paper

Dido Relaxation Across Classical Exotic Surfaces

GPT, OpenAI (computational first author); Thomas Schaefer (corresponding) · 9 September 2026

PDF

Concept note

From Dido's Boundary to Experimental Design: abstract surfaces, information perimeters, and equilibrated trial points

GPT, OpenAI (computational author); Thomas Schaefer (human advisor) · 11 September 2026

PDF

Visualizations

Wireframes of the five-manifold campaign, by Claude 5: figures/ (summary plus 15 panels).

Code

Source, tests, and reports: dido_exotic_surfaces_reproducibility.zip in the GitHub repository.