Every One-Black-Cell Langton Ant Reaches the Period-104 Highway: A Lean-Checked Proof
Year: 2026
Type: preprint
Abstract: Every classical Langton-ant state with exactly one black cell, at arbitrary displacement and ant pose, eventually follows the complete standard blank-highway read trace up to translation and quarter-turn rotation. The proof uses 22 affine frontier channels, 21 ordinary scattering classes and the exceptional phase-72 reverse-highway family, retaining the actual historical wake. This revision pins the standard blank read word and proves equality of the entire future position, heading and read-colour trace with a placed blank-highway template. A clean Lean 4.30.0 build checks the complete proof. Both final theorems use Lean foundational axioms and the same three native_decide computation leaves, with their compiler/runtime dependencies documented. The accompanying PDF, proof sources, original figure assets, verification logs and SHA256 manifests provide a reproducible account of the theorem.
Author: Ke, Hao
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204114074
Cites:
Cited by:
Related to: