Exact Lorentz Invariance from Holographic Projection: Explicit RT Verification and the Boundary Origin of Bulk Symmetry in the Selection-Stitch Model

A persistent objection to discrete spacetime models is the apparent incompatibil- ity between lattice regularity and Lorentz invariance. Previous approaches attempt to recover Lorentz symmetry approximately through statistical averaging, achiev- ing suppression factors that are astronomically small but never identically zero [3]. We demonstrate that this approach fundamentally misidentifies the problem. In the Selection-Stitch Model (SSM) [4], the 3D FCC bulk lattice is not a foundational background—it is an emergent holographic projection of a 2D boundary network. In this paper, we explicitly verify that the SSM’s Stitch-Lift construction satisfies the exact Ryu-Takayanagi (RT) relation [6]. By defining the Stitch operator as a maxi- mally entangled Bell pair projector [4], we derive the exact boundary entanglement entropy SA = ncut ln 2. We then construct the emergent minimal bulk surface γA and geometrically derive Newton’s constant as GN = 2/3L2/(4 ln 2) [8]. Having established the exactness of this holographic map, we prove that: (1) The fundamen- tal 2D hexagonal boundary possesses exact continuous rotational symmetry SO(2). (2) The holographic map preserves this continuous symmetry exactly. (3) The emer- gent 3D bulk inherits exact SO(3) spatial isotropy [5]. (4) In 3+1 dimensions, exact SO(3) uniquely implies SO(3,1) Poincar´e invariance for dimension-4 operators. Ul- timately, the apparent discreteness of the 3D lattice is merely an artifact of the bulk coordinate description. This definitively closes the principal foundational gap in the SSM.