A Lorentz Shield for Discrete Space: Bulk Propagation with Lattice Sampling on the Tetrahedral–Octahedral Honeycomb

Discrete models of space face a well-known obstruction: a lattice defines a preferred frame and preferred directions, and Collins et al. showed that radiative corrections carry Planck-scale Lorentz violation into low-energy physics without the expected suppression. We propose a mechanism intended to keep space discrete at the Planck scale while making this violation unobservable below the Planck energy, except for one suppressed residue. It rests on three postulates. (P1) Quanta propagate in a continuous bulk with one extra spatial dimension, not along the lattice. (P2) The three-dimensional brane, structured as the tetrahedral–octahedral honeycomb (TOT), is only the set of interaction points: a quantum appears on the brane as samples of a continuous field at the centres of the triangular faces (apertures). (P3) Geometric universality: every field couples to the lattice only through the same apertures. Established (geometry). Face centres are fixed points of the TOT subdivision, never reached by vertices or edges at any level; a TOT cell holds eight apertures with minimum spacing one third of the edge; the aperture sets of successive levels are nested. Conditional results. If the brane dynamics is the exact sampling of a band-limited bulk field, restricted to modes even in W and, below the Planck energy, constant across a Planck-scale W, lattice dispersion is absent below the band limit; the evolution operator that would realise this is not yet constructed. If universality survives quantum corrections, dimension-4 Lorentz violation reduces to a common metric that a choice of coordinates removes; this loop stability is not proven. If the dynamics is CPT-symmetric and the lattice background is invariant under time reversal, the CPT-odd dimension-5 photon operators behind linear dispersion and vacuum birefringence are forbidden to all orders; CPT-even dimension-5 operators of the fermion sector are not covered by this argument. Under the same conditions, Bell's dynamical argument hides the preferred frame. Predictions (hypotheses to be tested). No linear energy-dependent photon delay, no first-order vacuum birefringence, and a quadratic delay with an octahedral (ℓ = 4) dependence on direction. The note states a mechanism with conditional results and a four-step calculation programme; it is not a completed derivation.