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.