Frustration Found, Length Not
Year: 2026
Type: preprint
Abstract: Granular Entropic Physics (GEP) models spacetime as a bipartite tetrahedral network at the Planck scale. A recurring conjecture is that geometric frustration of the network vacuum generates an emergent mesoscopic correlation length ℓ*. We test this in a minimal, fully reproducible toy model on the bipartite diamond lattice, with site states valued in a finite group and a matching energy. Result I. We construct a minimal Q₈ holonomy-forcing proxy (generators i, j, k, 1 on the four bond directions) in which every local chair hexagon carries the central holonomy W_chair = −1, shown explicitly as i·j⁻¹·k·i⁻¹·j·k⁻¹ = −1 — the discrete analogue of the W = −1 holonomy of the continuous SU(2) theory. This proxy is genuinely frustrated, with an observed seed-stable annealed energy density around E/edge ≈ −0.82. The Abelian V₄ control is, for the tested assignment, unfrustrated (E/edge → −1). The proxy is explicitly not claimed to be the unique or fully symmetric GEP vacuum assignment; its fourth bond direction is the identity. The previously circulated value −7/8 is a local motif estimate and is retired as a lattice energy density. Result II. Using a pre-specified battery of falsification filters — multi-seed stability, finite-size scaling, a convention-free observable, a plateau/null guard, and a parallel-tempering second-moment spin-glass length ξ_SG — we find no robust mesoscopic length. Every length-like signal is convention-dependent and dies under multi-seed or finite-size scaling; every convention-free probe is silent. Conclusion. In this minimal discrete proxy, holonomic frustration is not sufficient to generate a robust mesoscopic correlation length. The result is a deliberately bounded negative that separates the existence of frustration from the existence of a length scale, and contracts the GEP hypothesis space. Limits. A minimal proxy with one trivial bond direction; Q₈ is a discrete proxy for SU(2); the energy floor is an annealing floor, not a proven minimum; the known-signal arm of detection validation is only partially established, so the negative is strong but not closure-level. Here z = 4 is a carrier of frustration, not a proven selection optimum.
Author: Sekanina, Štěpán
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166644111
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