Deterministic Resolution of the Quantum Measurement Problem, Symplectic Liouville Derivation of Born's Rule and Double-Slit Holonomy via Sub-Femtosecond Kuramoto Phase Synchronization

Standalone Research Paper in Quantum Foundations, Mathematical Physics and Nonlinear Dynamical Systems(10 Pages, 6 Sections, 3 Figures, 2 Synthesis Tables, Complete Mathematical Proofs). ABSTRACTSince John von Neumann's 1932 axiomatization, standard quantum mechanics has relied on two dynamically incompatible postulates. Continuous, deterministic, unitary Schroedinger evolution for isolated systems versus discontinuous, stochastic, instantaneous wave-function collapse (tau_collapse = 0) upon measurement. Building upon a Born-Oppenheimer timescale separation epsilon = tau_int / tau_ext << 1 between fast internal compact fiber phase modes and slow four-dimensional spacetime coordinates, we formulate a deterministic nonlinear dynamical resolution of the quantum measurement problem. Maintaining strict epistemic transparency, we separate deductively proven mathematical theorems (Tier A) from constructive physical model postulates (Tier B). Nonlinear Kuramoto Measurement Bifurcation (Section 2):We model the interaction between a quantum superposition state and a macroscopic detector as a coupled Kuramoto phase network with Lorentzian environmental frequency dispersion gamma > 0, proving via self-consistency and Ott-Antonsen reduction that the exact critical coupling threshold K_c = 2 gamma separates unitary wave propagation (K_meas <= 2 gamma => r = 0) from deterministic pointer-state phase locking (K_meas > 2 gamma => r = sqrt(1 - 2 gamma / K_meas) > 0). Finite Sub-Femtosecond Collapse Duration and Critical Slowing-Down (Section 3):Integrating the nonlinear relative-phase equation analytically, we prove that state reduction occurs over a strictly positive, finite sub-femtosecond relaxation time tau_sync = (hbar / (r E_meas)) ln|tan(delta_alpha_0 / 2) / tan(delta_alpha* / 2)| (approx. 0.66 fs for E_meas = 1 eV), replacing von Neumann's instantaneous projection axiom and exhibiting critical slowing-down tau_sync proportional to (kappa_meas - 1)^(-1/2) near the critical threshold kappa_meas = K_meas / (2 gamma) -> 1+. Symplectic Liouville Basin Proof of Born's Rule (Section 4):Using canonical Darboux action-angle coordinates (I_k = |c_k|^2, theta_k) on complex projective Hilbert space CP^(M-1) equipped with the Kaehler-Fubini-Study symplectic form omega_FS = sum dI_k ^ dtheta_k, we prove via Liouville's theorem that under uniform ergodic sampling of the fast internal fiber phase theta_0 in [0, 2 pi), the normalized symplectic basin volume of the k-th pointer attractor equals Born's probability rule P(k) = |c_k|^2 without fundamental stochastic axioms. Double-Slit Holonomy, Quantum Eraser, and Attosecond Metrology Benchmarks (Sections 5 & 6):We derive the exact Englert-Greenberger-Yasin double-slit duality circle V^2 + D_path^2 = 1 (with threshold visibility kink V = kappa_which^(-1/2) for kappa_which > 1) and resolve the Scully-Druehl delayed-choice quantum eraser via bipartite phase-correlation sorting (I(x | D_+) + I(x | D_-) = I_0(x)) without retrocausality, formulating three quantitative falsifiability tests for XUV attosecond pump-probe metrology, circuit QED, and matter-wave interferometry. Note: This paper develops and expands the quantum-foundational architecture introduced in the author's foundational monograph: Theory of Perspectival Dimensionality (TPD), Illustrated English Edition 2.0, Zenodo Permanent Archive, DOI: 10.5281/zenodo.23902867 (Foundational German Edition: DOI: 10.5281/zenodo.23770569) and complements the cellular Kuramoto synchronization paper (DOI: 10.5281/zenodo.23920048).