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January 17, 2026Open Access

Structural Escape via Tame Congruence Theory: A Roadmap Toward Park's Conjecture under FRB

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Authors

JHJoaquim Reizi Higuchi

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Overview

The paper demonstrates a structural proof roadmap toward Park's conjecture, suggesting FRB implies FB in finite algebras.

Key Points

  • The aim is to establish that finite residual bound leads to finite basability for locally finite varieties.
  • Developed a proof-theoretic framework for Park's conjecture.
  • Introduced an Escape Property that connects finite countermodels to subdirectly irreducible algebras.
  • Applied Tame Congruence Theory and commutator theory for structural analysis.
  • Provided a clear roadmap for finite basability in locally finite varieties.
  • Demonstrated the existence of large finite algebras using the Escape Property.
  • Outlined verifiable amplification criteria for both non-abelian and abelian theories.

Cite This Study

Joaquim Reizi Higuchi (2026) studied this question.

synapsesocial.com/papers/696b26b2d2a12237a9349ed9https://doi.org/10.5281/zenodo.18255628
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