A Geometric Origin of the MOND Acceleration Scale from S³ Field Coherence

Within the Geometric Universe Framework (GUF), the MOND accelerationthreshold a₀ is proposed to arise from the geometry of the three-sphere S³. The S³ manifold has two distinct length scales: the dynamical coherencescale R_H = c/H₀ and the geometric curvature radius R_S³ = √24·R_H (fromΩk = −1/24, established in GUF P3). Field coherence is postulated to trackR_H. The characteristic acceleration of the manifold is c·H₀ (the uniquecombination of c and H₀ with units of acceleration). The MOND threshold iswhere the Yukawa exponential envelope of the cosmic field has decayed by onecoherence length; at r = R_H the envelope contributes exp(−1) = 1/e exactly. With an empirical coefficient κ = 1/2, the result is: a₀ = c · H₀ / (2e) = 1.2038 × 10⁻¹⁰ m/s² Using H₀ = 67.36 ± 0.54 km/s/Mpc (Planck 2018, Aghanim et al. 2020), thismatches five independent empirical determinations of a₀ spanning 1983–2023to within 0.9%, with no numerically tuned coefficients and no gravitationalconstant anywhere in the derivation. The derivation has two rigorous steps (dimensional uniqueness of c·H₀;exp(−1) = 1/e as exact identity), one explicit postulate (field coherencetracks R_H), and three amber steps. The coefficient κ = 1/2 is treated asempirical: two natural integral routes (Yukawa hemisphere average; exact S³scalar Green's function hemisphere average) have been evaluated and do notproduce this factor. The most likely remaining candidate is the two-helicitydegeneracy of the EM field on S³. The exact S³ Green's function is thesingle calculation that would simultaneously resolve the field decay formand constrain the geometric origin of κ. The paper identifies the physical mechanism behind the 40-year empiricalcoincidence a₀ ≈ cH₀: it is a field coherence phase boundary, not anumerical accident. Three falsifiable predictions are given, includinga₀(z) = c·H(z)/(2e) — a redshift dependence testable with JWST. Companion papers: P1 (fine structure constant), P2 (cosmological parameters),P3 (Ωm = 1/π, DOI: 10.5281/zenodo.18688410), Hubble correction(DOI: 10.5281/zenodo.18859435). All part of the Geometric Universe Framework(Zenodo community: geometric-universe-framework).