Quantum phenomenology from a classical integer automaton: an emergent Schrödinger sector, exact exchange statistics, CHSH violation without randomness, foliation-independent Bell statistics, a selection-rule theorem for ensemble entanglement, a stimulated parametric pair channel with a capacity wall, a surviving isotropy no-go, two engine-measured forced rationals, and obstruction theorems for dynamic geometry

Q: What does this research mean for the field?

A single bit-exactly reversible, integer-valued lattice automaton can deterministically reproduce a broad range of quantum phenomenology—including an emergent Schrödinger sector, exact exchange statistics, and CHSH violation—and yields a falsifiable prediction for quadratically Planck-suppressed photon dispersion. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

Daniel Marko

doi:10.5281/zenodo.22239348

September 2, 2026Open Access

Quantum phenomenology from a classical integer automaton: an emergent Schrödinger sector, exact exchange statistics, CHSH violation without randomness, foliation-independent Bell statistics, a selection-rule theorem for ensemble entanglement, a stimulated parametric pair channel with a capacity wall, a surviving isotropy no-go, two engine-measured forced rationals, and obstruction theorems for dynamic geometry

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Key Points

To determine whether quantum phenomenology and dynamic spacetime geometry can emerge deterministically from a bit-reversible, integer-valued classical cellular automaton.
Constructed a bit-exactly reversible, integer-valued lattice automaton governed by discrete microstate permutations rather than numerical integration.
Implemented pre-registered computational experiments measuring wave interference, Bell-type CHSH inequality correlations across reference foliations, and clock-rate geometric back-reactions.
Formulated constructive proofs and obstruction theorems evaluating two-particle Hamiltonian derivation, entanglement capacity, and static geometric field sourcing.
The automaton produced deterministic single-object double-slit interference (p < 10⁻⁴) and a CHSH correlation of S = 2.79 that remained foliation-order-independent (|ΔS| < 0.005, S > 2).
A formal selection rule proved autonomous U(1)-equivariant dynamics factorize to Schmidt rank 1, while a stimulated parametric pair channel saturated at K ≤ 1.12.
Local clocks slowed by 30% near matter matching the predicted metric lapse within 1.3%, and the engine-measured photon dispersion coefficient matched the exact rational 187/7680 to within 0.20% (ξiso = 0.024299 ± 0.00011).

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Implication

Computational modeling demonstrates emergent quantum behavior in a reversible integer automaton, indicating that key quantum phenomena can arise deterministically without fundamental randomness.

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Daniel Marko (2026) studied this question.

synapsesocial.com/papers/6a9935c7636c6408cfa7e3a5 https://doi.org/10.5281/zenodo.22239348

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