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·A_tail derived from the scaling symmetry of the soliton ODE, with A(α)=A_0/√α fitted exponent −0.49999 to R²=0.9999999955; (ii) ℏ(Φ)=ℏ_0√(Φ_0/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 <ΔA_det²> ~ A_part2.028 with R²=0.99995, CV=2.3%; (v) CHSH = 2√2 exactly (Tsirelson bound) from a substrate phasor on the topological singlet π_3(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 g_0∈[0.3,0.95], analytic B=2∫_0^1 sin²(πu)du=1; (vii) Fermi-Dirac vs Bose-Einstein statistics from exchange phase (−1)^B, anyons in 2D from π_1(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: qm_foundations/, qm_measurement/, qm_superposition/, qm_entanglement/, qm_spin/, qm_statistics/, qm_decoherence/.