What was already known
Unrestricted Eden predicted that a dimension maximum on such an attractor occurs at an equilibrium or periodic orbit.
AI involvement
Colbrook reports that Codex found the counterexample after an earlier attempted proof. He checked the argument and formulation; ChatGPT 6 assisted later Lean verification.
Codex supplied the counterexample in a human-led project, establishing a central model construction; proof and formalization had human oversight.
Importance
Refutes the unrestricted conjecture with an explicit dynamical system.
Limitations
The construction does not address stronger transitivity or typical-attractor variants. The formal theorem covers the stated ODE and dimension comparison, while the historical interpretation of Eden’s conjecture is external to Lean.
Technical verification
The author reports checking the argument and the formalization documents a complete kernel-checked theorem tied to the paper. These are source-reported, not locally reproduced.
Independent checking
complete Lean proof, statement comparison and axiom audit
- Checker
- Lean kernel via Colbrook formalization
- Scope
- paper Theorem 1.1 and Palomar main theorem, including ODE/flow and dimension maxima
- Basis
- Reported by the linked checker
author’s explicit proof/formulation check and adoption
- Checker
- Matthew J. Colbrook
- Scope
- original counterexample proof and problem formulation
- Basis
- Reported by the linked checker
Human understanding
Colbrook’s paper and reading guide explain the radial dynamics, aperiodic maximizing torus and dimension comparison.
Correction and publication history
Refutes the unrestricted conjecture with an explicit dynamical system.
Read this published revision