The Geometry of the Standard Model: Deriving the Higgs Mass, Lagrangians, and Gravity Echoes from Lattice Saturation

We propose that the Standard Model Lagrangian is the continuum limit of a discrete vacuum

geometry, specifically the "Saturation-Stitch" vacuum [1,2]. Using the Selection-Stitch Model

(SSM), we derive the fundamental sectors of particle physics from the properties of a saturated

Cuboctahedral Lattice (K = 12).

1. The Lagrangian Sector: We derive the Klein-Gordon (Scalar), Dirac (Spinor), and

Yang-Mills (Gauge) Lagrangians as the elastic limits of lattice tension, topological braiding,

and stitch preservation. Crucially, we show that the Non-Bipartite Topology of the simplicial

lattice naturally resolves the "Fermion Doubling Problem," allowing chiral fermions to exist

without spurious mirrors [3].

2. The Higgs Sector: UsingtheratioofSurface(108)toVolume(1728)states, wecalculate

a geometric coupling λ≈0.125, predicting a Higgs mass of 123.11 GeV. We explicitly derive the

factor of 2 from the bi-directional topological flux across shared lattice interfaces.

3. The Gravity Sector: We interpret the Event Horizon as a "Phase Boundary" where

the lattice melts. As established in our renormalization framework [2], this breakdown of con-

nectivity slows gravitational waves to the fundamental lattice speed (v≈c/4). We apply this to

the recent LIGO detection GW250114, predicting a prompt echo delay of ∆t ≈2.7 ms, which

matches the observed "221 mode" window.