Structural Escape via Tame Congruence Theory: A Roadmap Toward Park's Conjecture under FRB
Abstract
We present a proof-theoretic and structural roadmap toward Park's conjecture in locally finite varieties: finite residual bound (FRB) should force finite basability (FB) for varieties generated by finite algebras. The framework is organized around a non-vacuous Escape Property EP(g), which transfers the existence of finite critical countermodels for bounded equational fragments into the existence of large finite subdirectly irreducible (SI) algebras inside the variety. The key structural input is a typed dichotomy based on Tame Congruence Theory (TCT) and commutator theory, together with verifiable amplification criteria in both non-abelian and abelian TCT types. This paper is intended as a self-contained and logically non-circular consolidation of the roadmap deposited at [1], with explicit interfaces for the remaining open non-vacuity component.
Fields of Study & Subjects
Advanced Algebra and Logic
Advanced Topology and Set Theory
semigroups and automata theory
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 15 January 2026
- Language
- EN
- Document type
- Preprint