A Mathematical Curiosity — VI Bulk-Boundary Correspondence in Rank-3 Discrete Lattices

Isomorphic Mapping of 6-bit Information Structures on Finite Semigroups We investigate the information-theoretic properties of the M=576 finite algebraic structure. We demonstrate that the associated Fock space representation (Dimension 64) provides a canonical framework for organizing 6-bit information density. This document establishes the structural isomorphism between the algebraic monoid and natural coding systems: 1. Capacity: The system naturally addresses a state space of 2^6 = 64 distinct elements, isomorphic to the standard codon table capacity. 2. Structured Degeneracy: The spectral decomposition of the Charge operator partitions the information space into fixed classes (1, 6, 15, 20, 15, 6, 1), offering a model for synonymous coding and degeneracy matching the 20 central states. 3. Stability: The interplay between idempotence and nilpotence provides a mechanism for intrinsic error correction and state selection within the code. This work proposes M_ext as an algebraic basis for biological information theory and error-correcting codes.