Pseudovolumes: Computation and Extension, Part II

R Quincy Robinson

Published Jun 30, 2026• 0 citations

Abstract

We develop the computational structure of the pseudovolume tensor of Part Iin two sections. Single-site machinery establishes exact-arithmetic foundations. Thepseudovolume's five simplex vertices, lying in the integer lattice H_Z := Z^4,are projected onto the A5-invariant parallel subspace V_par ≅ R^3 to produce a131-point icosahedral quasicrystal; its A5 symmetry is verified algebraically(Procrustes error ~10^{-16}) and via golden-ratio pair-correlation spacing.Exact arithmetic is carried by the quadratic field Q(phi) = {a + b*phi : a,b inQ}, which closes under the G-metric inner products of H. The QPhiPEPS is aprojected entangled pair state on the 131 quasicrystal sites with Q(phi)-valuedvirtual bond indices and bond dimension chi = 2. The bond contraction theoremestablishes that every G-metric contraction of adjacent bond vectors is a purerational, so the MERA coarse-graining hierarchy terminates in Q. Additionalresults: the ring F_2[x]/(x^6-1) contains a [6,2,4] constant-weight code(W(z) = 1 + 3z^4); all four bulk parameters are exactly recoverable fromboundary observables with a 45:1 compression ratio. H4 multi-site extension lifts the single-site machinery to a multi-sitearchitecture. The subgroup index [2I:2T] = 5 — the unique algebraic origin ofevery occurrence of five in the model — forces a 5-site network with H4 asglobal symmetry group. The A5-equivariant inter-site bond maps force a GHZground state whose entanglement entropy equals log|M(b)| uniformly across allbipartitions. This identifies the invariant Phi(b) = log|M(b)| exactly: it issimultaneously the unnamed spectral invariant of Part I, the entanglemententropy of the 5-site network, and the contextuality measure of the local PVM.The Zimba-Penrose parallel is thereby promoted from analogy to structure. A120-cell tiling extends the network to 600 sites, introducing a qualitativelydistinct inter-cell bond algebra (intra-cell: 16 of 60 A5 elements; inter-cell:12 of 60, equal to |A4|) at each coarsening level. A robustness theorem givesthe exact ground-state fidelity threshold p*(m) = 1 - m^{-5} = 1 -exp(-5*Phi(b)) for preferred bases under independent depolarizing noise. This is Part II of a two-part work. Part I (Foundation, Construction, andProperties) is deposited at https://doi.org/10.5281/zenodo.21038657.

DOI: 10.5281/zenodo.21051912

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