Standard model structure and the causal diamond boundary

The origin of the Standard Model's parameter structure remains open. A companion paper addressing large-angle cosmological anomalies treated the observer's causal diamond boundary as a finite recording aperture. This paper investigates the hypothesis that the internal angular geometry of that same boundary constrains the Standard Model's parameter structure. The minimal faithful sampling register of the first three axial angular modes on the boundary sphere S² of an observer's causal diamond is the path graph P₃, whose Laplacian spectrum 0, 1, 3 intertwines exactly with the angular Casimir spectrum 0, 2, 6 only in four spacetime dimensions. Four theorems connect operators on the axial (m=0, ℓ ≤ 2) quotient of S² to operators on the graph, spanning scalar, signed-scalar, vector, and symmetric-tensor representations. Two recording constants, a finite-aperture survival factor g = 1/d = 1/4 (the attenuation per recording step at the boundary) and an endpoint hazard λ = (d−1) / (16π²) = 3/ (16π²) (the one-loop probability that boundary shape fluctuations disrupt a recording event), both originate in the modular Hamiltonian of the causal diamond boundary in the companion paper. Together with the reduced Planck mass and the P₃ algebra, these constants generate closed-form candidate formulae that match charged-lepton mass ratios (0. 10% RMS), the six quark masses (0. 51% RMS), CKM mixing and CP violation (1. 9% RMS), the Higgs boson mass (125. 21 GeV, +0. 09%), and electroweak boson masses (mZ to +0. 03%), with no continuous flavour parameters within the closed-form formulae, after adopting a common empirical matching scale. All algebraic identities and numerical predictions were verified by reproduction scripts included in the data deposit. The framework, whose derivational status varies across sectors, offers several non-adjustable predictions: sin²θ₂₃ = 0. 500 and δCP = −90° (both exact), normal neutrino mass ordering with m₁ = 0, no QCD axion, and |Vᵤb| ≈ ½|Vᵤs||Vcb|. Several of these are testable by forthcoming experiments within the coming decade. This is a preliminary presentation of a new hypothesis regarding Standard Model parameter structure, for community feedback. It does not claim a derivation of the Standard Model. Subsequent versions will be deposited on Zenodo as the framework is evaluated and refined.