Pseudovolumes II: Exact Arithmetic Tensor Networks, Fibonacci Topological Phase, and Structural Results across Five Domains

We extend the pseudovolume framework through three new constructions and five
independent structural validations spanning quasicrystal physics, geometric
coding theory, holographic coding, topological phases, and structural
bioinformatics.

The construction produces a 131-point icosahedral quasicrystal via projection
of the integer lattice Z^4 onto the parallel subspace via an explicit
A5-equivariant lifting matrix. Exact arithmetic is carried by the quadratic
field Q(phi) = {a + b*phi : a,b in Q} (phi = (1+sqrt(5))/2), which closes
under G-metric inner products. Building on this, we construct the QPhiPEPS: a
projected entangled pair state whose physical indices are the 131 quasicrystal
sites and whose virtual bond indices lie in Q(phi)^4. The bond contraction
theorem establishes that every G-metric contraction of adjacent bond vectors is
a pure rational, so the MERA coarse-graining hierarchy terminates in Q.

Five structural validations confirm connections to independent scientific
domains: (1) Quasicrystal/icosahedral materials: A5 symmetry of the 131-point
sample verified algebraically and via golden-ratio pair-correlation spacing.
(2) Geometric coding theory: the ring F2[x]/(x^6-1) contains a [6,2,4]
constant-weight code; three MDS codes are identified. (3) Holographic coding:
all four bulk parameters are exactly recoverable from boundary observables; the
MERA circuit is the explicit bulk encoding map. (4) Tensor networks/topological
phases: QPhiPEPS realizes the Fibonacci string-net model on the 131-site
quasicrystal with bond dimension chi=2, quantum dimension d_tau=phi; the
topological phase is non-abelian and universal for topological quantum
computation. (5) Structural bioinformatics: A5 acting on the twenty standard
amino acids produces exactly two orbits of size 10.