P: Particle Genesis — The Standard Model from the Causal Lattice

P establishes the particle sector of the Network Emergent Architecture (N.E.A.)framework. Starting from the single logical primitive of at least one decidablestatement, and proceeding through the finite-bandwidth constraint B=1 and theuniqueness of spatial dimension d=3, the paper derives the emergence of theStandard Model gauge and fermion structure from the discrete causal graph. The central derivation chain is: logical primitive -> B=1 -> d=3 -> C8/K4 -> diamond lattice -> quantum walk -> Dirac fermion -> A4/2T/S4 -> color triplet, weak doublet, generation triplet -> gauge group SU(3)xSU(2)xU(1) -> flavor breaking -> mass chains, CKM, PMNS, CP. The color triplet is traced to the A4 symmetry of the K4 tetrahedron; the weakdoublet to the binary tetrahedral group 2T; the generation triplet to the S4symmetry of the C8 cube. The K4 cycle space is mapped explicitly to the su(3)root system, closing the arithmetic layer of OP-3. Dirac fermions emerge fromdefect quantum walks on the diamond lattice with the Clifford algebra verifiedto machine precision. The paper reports the topological mass chains for charged leptons and quarks,the complete CKM matrix, and a topological candidate for the CP-violating phase,arctan(5/2), with a deviation of 0.87% from experiment. It also demonstrates thedynamical emergence of the color triplet and weak doublet from defect boundstates with degeneracy verified to 1e-15. Logical status is explicitly graded. The CP phase, the mass-chain factorassignment, and the flavor-breaking pattern are recorded as candidates orphenomenological Ansätze rather than first-principles derivations. Open problemsinclude the strict derivation of inter-generational mass ratios, the completeneutrino sector, and the propagator reduction of the defect bound states. All code and Lean 4 proofs are publicly available athttps://github.com/hzhangy/Particle.