Temporal Phase Synchronization Theory (TPST): Cosmological, Electroweak and Particle-Mass Constants from S3 Phase Synchronization -- A Parameter-Free Framework

Abstract

One Acceleration Scale for the Dark Sector: Galaxy Rotation Curves, a 1/24 Dark-Matter Quota, and a Parameter-Free Dark-Energy Law (TSFT working paper, draft v5) We present a chain of results in which a single acceleration scale, a_0 = c K_univ = 1.17e-10 m/s2, anchored in galaxy rotation curves, fixes with no additional free parameters: (i) the radial-acceleration relation of 129 SPARC galaxies (scatter 0.071 dex, equal to MOND with a fitted scale; transition scale within 3% of the empirical value); (ii) the dark-matter and dark-energy fractions through a quantized quota b = 1/24, giving Omega_DM/Omega_b = 5.22 at +0.1 sigma of the DESI DR2 + CMB reference; (iii) a thawing dark-energy law, 1 + w(z) = (2/3) K_univ / H(z), whose present value w_0 = -0.883 falls at -0.67 sigma of the DESI DR2 marginal constraint, out of sample; (iv) cluster truncation radii, r_t = sqrt(G M / a_0), that place the baryon fraction of massive clusters at +0.8 sigma of observations, dissolving the residual-mass problem that has historically ruled out modified-dynamics proposals. The chain survives Big Bang nucleosynthesis by 31 orders of magnitude and reproduces the CMB temperature spectrum by structural identity, at the registered cost of H0 = 65.4 km/s/Mpc under the thawing branch. The underlying framework is a medium of local temporal phases with nematic order, synchronizing under a Lohe-type dynamics whose continuum limit is the harmonic-map flow into S3. Covariantized, it lands in the khronometric family with fixed weight ratios (lambda/beta = 1/3, no parameter) and passes the GW170817 bound by construction; linear growth is that of General Relativity by an invisibility theorem. The paper is self-contained: the capture theorem behind a_0 = c K_univ and the counting behind b = 1/24 are derived in full in the appendices. Methodology: every number was derived blind, frozen as a constant in version-controlled code with an executable test (~550 tests) before confrontation, and confronted exactly once. Named, dated falsifiers are declared: DESI DR3 evidence for phantom crossing, a SH0ES-high resolution of the Hubble tension, or stacked-lensing splashback profiles departing from the predicted mass trend would each break identified links of the chain. Note on this version (v5): this working paper supersedes the particle-physics and electromagnetic claims of previous versions (alpha_EM, hbar, m_H, sin2 theta_W, the fermion mass spectrum, CKM angles). A systematic audit and blind reconstruction of the framework found that those derivations do not survive re-derivation under the present protocol; they are withdrawn pending reconstruction and are deliberately excluded from the present chain. The dark-sector chain presented here is the audited, test-frozen core of the programme. Supplementary material: full thesis in Catalan (TSFT_AnalisisCritic.pdf).