Paper 32: Recasting Quantum Mechanics Without Imaginary Numbers From Real Overlaps to Finite Timing Continua: Peak, Shoulder, Baseline

We recast single-qubit/spin-½ kinematics in a fully real-valued framework on the 3-sphere S3≅SU(2)S^3\cong\mathrm{SU}(2)S3≅SU(2), replacing complex amplitudes with a real overlap C(Δ)=cos⁡(Δ/2)\mathcal{C}(\Delta)=\cos(\Delta/2)C(Δ)=cos(Δ/2) and Born probabilities P=∣C∣2P=|\mathcal{C}|^2P=∣C∣2. The baseline measurement-sphere mode ψcoh=3/(4π) sin⁡θcos⁡ϕ\psi_{\mathrm{coh}}=\sqrt{3/(4\pi)}\,\sin\theta\cos\phiψcoh=3/(4π)sinθcosϕ is selected non-circularly from OhO_hOh symmetry with infinitesimal rail pinning, yielding ρcoh=ψcoh2\rho_{\mathrm{coh}}=\psi_{\mathrm{coh}}^2ρcoh=ψcoh2. Collapse is modeled as a thresholded loss of angular compatibility (λ=π\lambda=\piλ=π) with causal strain diffusion on the shell. We validate the timing layer on the official Weihs archive (bluesine series), remapped to seven runs with C&V present on both sides and decoded via u32le (C) and ASCII (V). A single-pass coincidence counter with acceptance half-windows W∈{3,5,7}W\in\{3,5,7\}W∈{3,5,7} ns and offset scans exhibits a sharp peak at 0 ns, symmetric shoulders at ±10 ns, and a flat baseline for |offset|≥100 ns. Aggregated parities decrease monotonically with window—E=0.665651E=0.665651E=0.665651 (3 ns), 0.5754170.5754170.575417 (5 ns), 0.4972600.4972600.497260 (7 ns)—consistent with broader windows admitting more near-coincident events. The model is operationally no-signalling, and all artifacts (manifests, summaries, scans, metrics, figures) are published for audit. Net: geometry for phase, overlap for statistics, threshold for collapse—backed by a finite timing continuum (peak–shoulder–baseline).