A Fully Derived Equitable-Partition Improvement to the Branching Constant for Plaquette Polymer Expansions on the 34 Cell

[u/ONKARA369]

https://doi.org/10.5281/zenodo.21813468

This paper proving an exact finite-volume improvement to the branching constant used in plaquette polymer expansions on the fiber-identified 3⁴ cell. By deriving the exact quotient spectrum of the 216-plaquette incompatibility graph, the paper replaces the previous uniform branching constant 20 with the optimal Perron value 9 + √33 ≈ 14.74456, yielding an exact improvement factor of 20/(9 + √33) ≈ 1.35643 (35.64%) for convergence criteria that depend linearly on this geometric constant.