Exploration reveals the fermion spectrum using a pentachoric framework, suggesting new physics interpretations.
An observer is a point. Physics is what that point can see. Starting from this principle and the pentachoric framework [P1]---a discrete ontology of spacetime built on the complete graph K5 with a single coupling α∗ = 1/(4 ln 2) and no adjustable parameter---we derive the particle content of the Standard Model by exploring what an observer at the present vertex can detect at each geometric depth. At depth~0 (the vertex itself): fermion masses, with the formula m_k / m_e = u^(n_k²) yielding all nine fermion masses (mean 2.4% max 5.3%) with no continuously adjustable parameter.At depth 1 (the incident edges): the gauge algebra su(3) ⊕ su(2) ⊕ u(1) of dimension 12, with 8 gluons, 3 weak bosons, and 1 photon.At depth 2 (the adjacent faces): electroweak symmetry breaking, dark matter, and black hole thermodynamics, all from a single saturation function. At depth 3 (tetrahedra): composite resonances with a 4+1 visibility structure. At depth 4: the graviton. The past and the future are invisible; yet both shape what the present can detect. The companion verification script (316 tests, all PASS) provides a reproducible audit trail from axioms to predictions.
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Jean-Baptiste BLATIERE (2026) studied this question.
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