Theory of Generated Space — Emergent quantum mechanics from the TGP substrate: measurement, Born rule, superposition, entanglement, spin-statistics, and decoherence from a single soliton ODE

Preprint and supporting numerical material for the TGP emergent-quantum-mechanics paper, a companion to the TGP core paper (Zenodo DOI: 10. 5281/zenodo. 19670324). Starting from the substrate-field framework fixed by the core paper, we show that quantum mechanics is not fundamental but emergent: measurement, the Born rule, superposition, Bell-type entanglement, spin 1/2, spin-statistics, and decoherence all follow from the self-referential dynamics of the substrate field Φ. Key structural results: (i) ℏ = π·χ·Aₜail derived from the scaling symmetry of the soliton ODE, with A (α) =A₀/√α fitted exponent −0. 49999 to R²=0. 9999999955; (ii) ℏ (Φ) =ℏ₀√ (Φ₀/Φ) a position-dependent Planck constant, testable shift Δℏ/ℏ≈−3. 5×10⁻¹⁰ near Earth; (iii) Δx·Δp ≥ ℏ from three independent derivations (oscillation period + Nyquist, Fisher information + Cramér-Rao, energy minimisation) ; (iv) Born rule from measurement asymmetry — detector back-reaction ~ Aₚart^2. 028 with R²=0. 99995, CV=2. 3%; (v) CHSH = 2√2 exactly (Tsirelson bound) from a substrate phasor on the topological singlet π₃ (S³) =ℤ, with E (a, b) =−cos (a−b) to 3. 3×10⁻¹⁶, no-signaling verified; (vi) spin 1/2 from hedgehog-vielbein winding B=1 universal across g₀∈0. 3, 0. 95, analytic B=2∫₀¹ sin² (πu) du=1; (vii) Fermi-Dirac vs Bose-Einstein statistics from exchange phase (−1) B, anyons in 2D from π₁ (config) =ℤ; (viii) decoherence from three converging channels (ℏ (Φ) damping, non-linear mode mixing, environmental back-reaction) plus quantum Darwinism as geometric tail imprint on the substrate. The repository contains the paper source, compiled PDF, and the seven numerical folders that are directly cited: qmfoundations/, qmₘeasurement/, qmₛuperposition/, qmₑntanglement/, qmₛpin/, qmₛtatistics/, qmdecoherence/.