D2d-C2 — Companion to D2d, Volume 2: Quantum Mechanics I Born Rule · Pauli Exclusion · Canonical Commutation · Spectral Measure

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-07
DOI
https://doi.org/10.5281/zenodo.22650556
Primary Topic
Quantum Mechanics and Applications
Type
preprint
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D2d-C2 — Companion to D2d, Volume 2: Quantum Mechanics I Born Rule · Pauli Exclusion · Canonical Commutation · Spectral Measure

Fabio Diniz Pinto
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
preprint

D2d-C2 — Companion to D2d, Volume 2: Quantum Mechanics I Born Rule · Pauli Exclusion · Canonical Commutation · Spectral Measure

Fabio Diniz Pinto
preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Quantum Mechanics and Applications
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