Emergent Quantum Mechanics, Gravity and the Standard Model from a Classical Causal Network The three-layer commitment of QSN-G
Year: 2026
Type: article
Abstract: I’ve been working on a programme called QSN-G. The goal is to start with a classical causal network and derive, rather than assume, the target physics. The current version is a three-layer commitment:- A1 (substrate): a finite causal network with commutative local algebras, faithful local states, and a coarse-graining map.- A2 (dynamics): a local reflection-symmetric action with a Gibbs measure, plus H2: no edge joins the future to the past.- P1 (phase): the specified Hamiltonian sits in the massive, locally indistinguishable phase (gap, finite correlation length, local indistinguishability).- C1 (conjecture): the 4D decay-to-area law.- C2 (conjecture): the emergent spectral triple is selected by the CCM axioms with KO-dimension 6 and A_F = ℂ ⊕ ℍ ⊕ M₃(ℂ).No Hilbert space, manifold, gauge group, Standard Model algebra, Einstein–Hilbert action, or Born rule appears in A1, A2, or P1.What is actually proved- Finite-volume QM is a theorem from A1 + A2 via Osterwalder–Schrader reconstruction. The infinite-volume QFT requires a separate thermodynamic-limit argument and is conditional on P1 + the sprinkling interpretation.- Gravity is a theorem conditional on P1 + C1: P1 gives exponential decay via the equivalence circle, C1 gives the area law, and Jacobson’s entanglement equilibrium gives Einstein’s equations with G = 1/(4η).- The Standard Model is a theorem conditional on P1 + C2: CCM is a theorem; C2 is the selection step.- Time is the parameter of the OS unitary group; the continuum is conditional on the sprinkling interpretation.Two concrete results that may be of independent interest1. Reflection symmetry is not reflection positivity. A 7-node graph with a Θ-invariant Gaussian action and a crossing edge gives an explicit functional with∫ Θ(F) F dμ = −7932450 / 229031633 < 0So the standard OS argument needs H2 as an independent hypothesis. The paper gives the exact rational certificate.2. A Lean 4 certificate. 37 theorems in the Part VIII module, checked with #print axioms; they depend only on propext, Classical.choice, and Quot.sound. There is no sorry and no custom axiom. It covers the finite OS core, the Clausius algebra, the 4D null-cone lemma, the anomaly sums, the phase diagram, and the exact counterexample.What I am not claiming- C1 and C2 are open. No 4D proof of the area law; no proof that the QSN produces the CCM triple.- Infinite-volume QM is conditional, not a theorem from A1 + A2 alone.- P1 is a chosen phase, motivated but not derived.- This is not a complete theory of everything; it is a conditional reduction with the gaps named.I’d value criticism on- Is H2 physically natural, or is it an ad hoc fix?- Is the equivalence-circle step applied correctly in 4D?- Is the finite/infinite-volume distinction in the OS section stated correctly?- Does the 4D null-cone lemma actually close the Raychaudhuri step, or is there a hidden factor?- Any obvious no-go theorem I’ve missed.Links- Paper (PDF): https://github.com/nyimbi/qsn/blob/main/05_Workbench/paper/QSN-G_arXiv-1.pdf- Repository: https://github.com/nyimbi/qsn- Lean certificate: https://github.com/nyimbi/qsn/tree/main/05_Workbench/lean_certificate/qsng- Full monograph: https://github.com/nyimbi/qsn/blob/main/05_Workbench/QSN-G_MONOGRAPH.md
Author: Odero, Nyimbi
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225377938