D2d-C2 — Companion to D2d, Volume 2: Quantum Mechanics I Born Rule · Pauli Exclusion · Canonical Commutation · Spectral Measure
Year: 2026
Type: preprint
Abstract: D2d-C2 covers the quantum-mechanical sector of the Triniton discrete corpus. Results established: (I) the discrete state space H = ℓ²(S/≡), the spectral decomposition of Ũ_step on the finite graph S-4, and the spectral data of H_T on S-4; (II) the Born rule via rationality axioms R1, R3 — conditional derivation with Gleason compatibility check on S-4; (III) the discrete Pauli exclusion principle R15 from PE différencié — formal, unconditional; (IV) the discrete canonical commutation relation R16 [X_μ, P_ν]_disc =iℏ_T δ_μν · (T_μ + T_μ†)/2, equivalently iℏ_T δ_μν cos(k_μ r_min) in Fourier representation — formal, established on the kinematic lattice space ℓ²(ℤ⁴); (V) the spectral measure for explicitly constructed ILC observables with purely discrete spectrum. Zero free parameters. Zero ad hoc adjustments.
Author: Diniz Pinto, Fabio
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211873383
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