The Three-Layer Chiral Minkowski Cellular Automaton: A Unified Discrete Spacetime Model from First Principles

We derive physical observables from the three-layer Chiral Minkowski CA (CMCA) substrate: Rule 110 (right-moving chiral layer), Rule 124 (left-moving chiral layer), and a shared inner Rule 110 tau_c clock (timelike layer). Four principal results follow. (1) Lorentz invariance as observer effect: the CA lattice has a preferred frame at the Planck scale, but PSC Presentation Invariance forces all D-selected observables to be Lorentz-equivariant on the Phi_MDL continuum substrate; machine-certified in Lean 4 with zero sorry (one axiom: d2_universal). Lattice residual epsilon_0(7) = pi^2/147 approximately 6.71%, vanishing as M^{-2} in the continuum limit; at LHC energies delta_LV approximately 8.8e-32, far below existing bounds. (2) Electroweak scale: the Weinberg angle sin^2(theta_W) = 3/13 + lambda^3/(2*cH) approximately 0.231207 (PDG: 0.2312, 0.24 sigma), Lean-certified. Absolute scale gives M_Z = 91.91 GeV (+0.80%) and M_W = 80.61 GeV (+0.30%). (3) Born rule: P(k) = |phi_k|^2 follows from canonical Z7-KG kink quantization via Z7 superselection; certified with zero custom physics axioms (zero sorry). (4) Quantum interference: double-slit fringe pattern reproduced with correlation 0.998. The CMCA is the unique Level-1 GTE discrete model selected by MDL minimality (K_CA = 19 bits).

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-27
DOI
https://doi.org/10.5281/zenodo.20417573
Primary Topic
Quantum Chromodynamics and Particle Interactions
Type
preprint
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preprint

The Three-Layer Chiral Minkowski Cellular Automaton: A Unified Discrete Spacetime Model from First Principles

Nova Spivack
Zenodo (CERN European Organization for Nuclear Research)
Quantum Chromodynamics and Particle Interactions
preprint

The Three-Layer Chiral Minkowski Cellular Automaton: A Unified Discrete Spacetime Model from First Principles

Nova Spivack
preprint en

Abstract

We derive physical observables from the three-layer Chiral Minkowski CA (CMCA) substrate: Rule 110 (right-moving chiral layer), Rule 124 (left-moving chiral layer), and a shared inner Rule 110 tau_c clock (timelike layer). Four principal results follow. (1) Lorentz invariance as observer effect: the CA lattice has a preferred frame at the Planck scale, but PSC Presentation Invariance forces all D-selected observables to be Lorentz-equivariant on the Phi_MDL continuum substrate; machine-certified in Lean 4 with zero sorry (one axiom: d2_universal). Lattice residual epsilon_0(7) = pi^2/147 approximately 6.71%, vanishing as M^{-2} in the continuum limit; at LHC energies delta_LV approximately 8.8e-32, far below existing bounds. (2) Electroweak scale: the Weinberg angle sin^2(theta_W) = 3/13 + lambda^3/(2*cH) approximately 0.231207 (PDG: 0.2312, 0.24 sigma), Lean-certified. Absolute scale gives M_Z = 91.91 GeV (+0.80%) and M_W = 80.61 GeV (+0.30%). (3) Born rule: P(k) = |phi_k|^2 follows from canonical Z7-KG kink quantization via Z7 superselection; certified with zero custom physics axioms (zero sorry). (4) Quantum interference: double-slit fringe pattern reproduced with correlation 0.998. The CMCA is the unique Level-1 GTE discrete model selected by MDL minimality (K_CA = 19 bits).

Zenodo (CERN European Organization for Nuclear Research)
Quantum Chromodynamics and Particle Interactions
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