A quantum many-body framework for emergent spacetime and gauge fields from self-organised criticality " version 2"

We propose a framework in which spacetime geometry, gauge fields, and chiral fermions are conjectured to emerge from a quantum many-body system that is driven to the edge of chaos by a homeostatic thermostat. The dynamics is governed by a non-linear Lindblad master equation with state-dependent feedback. In a solvable Brownian-circuit limit, a Lyapunov functional drives the system to the maximal chaos bound λ_L = 2πT/ħ. The steady-state Quantum Fisher Information Metric yields, in a two-qubit model, an AdS₂ geometry. A boundary-driven XX chain yields a strictly negative temporal metric component, supporting Lorentzian signature emergence. A multi-layer tensor network with bond dimensions (3,2,1) and a boundary orbifold T²/Z₃ is conjectured to reproduce the Standard Model gauge group SU(3)_C × SU(2)_L × U(1)_Y and three generations of 16 chiral Weyl fermions. The framework leads to tentative predictions for a Z′ boson (2.4–4.8 TeV), a vector leptoquark U₁ (4.3–8.6 TeV), and topological dark matter (12.4 TeV). We report extensive numerical investigations. First, an entropy-based thermostat robustly converges to a target entanglement entropy for up to 8 qubits with errors below 10⁻². Second, a direct scrambling-rate (OTOC) feedback based on the SYK model fails to converge in the tested finite-size regime. Third, the SYK model is shown to be theoretically promising: in the large-N conformal limit it saturates the MSS bound λ_L = 2π/β, but exact diagonalisation up to N=16 yields operational growth rates that are two orders of magnitude smaller and do not scale with N. Fourth, an SYK-inspired effective thermostat converges to the MSS bound with high precision. Fifth, a self-organising global-scan feedback on a spin chain drives the system to the point of maximal short-time entanglement growth. Sixth, in the solvable Brownian-circuit limit, a two-sided feedback loop drives the Lyapunov exponent to the MSS bound from both above and below. Seventh, a kicked-top model with spin j=10 and a bisection feedback loop drives the quantum commutator growth rate to the MSS bound with error 0.0013. Eighth, we verify the entanglement preconditions for emergent gravity: the XX chain ground state is a c = 1 conformal field theory with logarithmic block entropy; the entanglement first law δS_A = δ⟨K_A⟩ holds to first order in two independent settings; and a tree tensor network satisfies the Ryu–Takayanagi formula S(A) = log(D) × boundary(A) exactly. We emphasise that many results remain conjectural and require further investigation.