Rigidity, Descents, and Cone Walks in Pattern-Avoiding Canon Permutations

This preprint proves four conjectures on pattern avoidance in canon permutations, gives all twelve counting formulas for the 64 subsets of three-letter forbidden permutations at fixed alphabet size three, and determines principal descent factorizations. It also solves the intermediate repeated-endpoint enumeration by multichain and cone-walk methods and enumerates general alternating orbits by Davenport-Schinzel skeleton order polynomials. A Lean 4 formalization of the principal results is in progress; the present version does not claim completed formal verification. Subsequent development has been reorganized into two focused articles. The combinatorial continuation is 10.5281/zenodo.22091632, and the focused analytic cone-walk companion is 10.5281/zenodo.22091634. Version 1 remains the original unified preprint and priority record for the results stated here.