Standard Model Structure From Stencil Geometry

Standard Model Structure from Stencil Geometry develops a structural classification of Standard Model free parameters within the CAELIX framework. The central claim is that these parameters do not all belong to the same ontological tier. Parameters determined by stencil topology, particle content and interaction combinatorics are treated as geometric. Parameters determined by runtime propagation burden are treated as computational. This separation is the organising principle of the paper. Using a balanced-ternary lattice with state space −1, 0, +1, a 7-voxel identity stencil and a 5-voxel propagation stencil, the paper constructs candidate derivations for nine non-mass Standard Model parameters from a small set of countable structural integers. These include: • the weak mixing angle sin²θW • the strong coupling constant αₛ • the strong CP angle θQCD • the three CKM mixing angles • the three PMNS mixing angles Within the balanced-ternary sign-symmetric substrate picture, θQCD is forced to zero by exact sign symmetry of the underlying alphabet. Mass parameters are excluded from the geometric derivation on physical grounds. In the CAELIX picture, mass is not a label attached to a particle but the computational cost of propagating that particle’s stencil through the lattice. Mass therefore belongs to the computational tier, not the geometric one. A small boundary class is also identified. This includes the fine structure constant and the Higgs vacuum expectation value, both treated as structurally important but not derived within the present geometric treatment. The paper does not claim a completed proof of all Standard Model parameters. It claims that a single balanced-ternary stencil framework provides a unified route for separating geometric parameters from computational ones, and for deriving the geometric class from countable lattice structure.