The RHEA-Λ Reversible Gate Family: A Multi-Radix Binary-Ternary-Pentary Cell for Hamiltonian Symbolic Computation in the RHEA-UCM Framework

This paper introduces the RHEA-Λ family of reversible multi-radix logic gates developed
for the RHEA-UCM (Recursive Homeostatic Evolutionary Algorithm – Universal Cell Model)
symbolic computation framework. A single physical gate topology supports binary, ternary, and
pentary modes, with a 3-bit glyph/entropy register enabling local symbolic memory and internal
phase evolution. In higher-radix modes the transitions form strictly bijective, triangular maps
over Z3 ×Z3 ×Z5 and Z
3
5
, providing discrete Hamiltonian, measure-preserving dynamics aligned
with the RHEA-UCM entropy model. Binary mode retains CMOS drop-in compatibility for hybrid reversible– irreversible scheduling under the Lorenz entropy controller. A full mathematical
specification, inverse mappings, commutative diagrams, truth tables, and verification code are
provided.