Ternary Lattice

This document assembles the mathematical framework for a spatially extended ternary primitive: the single-site three-level tile (states |+1, |0, |-1) coupled by species-preserving tunneling on a lattice and immersed in an Ohmic environment.

It derives the:

• Lattice Hamiltonian and momentum-space block.

• Band structure and effective second-order couplings.

• Caldeira–Leggett bath dressing, including coherence and transport diagnostics.

• Entropy production and the construction of a Pareto frontier trading coherence, transport, and erasure cost.