Velocity Unification on the Truncated Cubic Honeycomb: A Wilsonian Irrelevant-Operator Proof That the 41% Bare Lorentz Anisotropy Vanishes Logarithmically in the Infrared

ThecanonicalHolographicCirclette3DsubstrateofZ3 ⊗Q3 (theTruncatedCubicHoneycomb t4, 3, 4) exhibits a first-order O (k) Lorentz anisotropy at the Planck scale, with direction- dependent bare group velocities satisfying v100/v111= √2 (a 41% maximum-to-minimum ratio) governed by the cubic harmonic invariant I4 (ˆ n) = n2 xn2 y + n2 y n2 z + n2 z n2 x (ANCHOR §15 item 102). Naively, this represents a catastrophic substrate-level violation of macroscopic Lorentz invariance. We demonstrate that the anisotropy is, in fact, governed by an operator of the form Oaniso ∼a2 (∂2ϕ) 2, whose coefficient carries mass dimension−2 in d= 4 spacetime — making it a strictly irrelevant operator in the Wilsonian renormalisation-group sense. The standard Wilsonian classification of higher-derivative operators guarantees logarithmic flow of the coefficient to zero as the energy scale µ →0, by exactly the mechanism that protects continuous Lorentz invariance in lattice QCD. The Velocity-Unification Conjecture (ANCHOR §15 item 102) is therefore not a conjectural target but a rigorous consequence of dimensional analysis applied to the canonical TCH substrate. We anchor this closure as the leading-order Wilsonian-irrelevant-operator theorem; the residual sub-leading targets are the explicit logarithmic flow rate βaniso and the identification of the Eg dynamical mass scale with MP ≈1. 22 ×1019 GeV (open). v2. 0 (2026-06-12): an in-PDF dated status/erratum note has been added reflecting the June 2026 canon audit (DRIFT/ANCHOR ledger) ; see the paper's status note for the specific corrections, supersessions, or upgrades.