Density Field Dynamics: A Complete Unified Theory

Density Field Dynamics (DFD) is a scalar refractive-index theory of gravity defined by the postulate that space is flat and time absolute, permeated by a scalar field ψ(x,t) establishing an optical refractive index n = exp(ψ). Light propagates according to the eikonal of the optical metric ds̃² = −c²dt²/n² + dx², while matter responds to the effective potential Φ = −c²ψ/2. The optical scalar sector ψ governs clock rates, refraction and quasi-static dynamics; a transverse-traceless radiative sector carries gravitational waves on the same metric as light (c_T = c_γ exactly). DFD reproduces the classic weak-field tests of general relativity (γ = β = 1 exactly; a worst-case effective preferred-frame parameter ≲ 4×10⁻⁸ in the solar system; Mercury, Shapiro delay, frame dragging and binary-pulsar decay as in GR), gravitational waves at speed c with two tensor polarizations, and MOND-like galactic phenomenology with μ(x) = x/(1+x) (the weak-response form of DFD's exponential law, a theorem from S³ composition) and a₀ = 2√α cH₀ (derived; 1.1966×10⁻¹⁰ m/s² on bound-matter clocks).

v5.0 is the completed two-volume release: the main volume (433 pp: axioms, theorems with proofs, derived predictions, falsifiers, a table of principal corrections and a list of open review items), the Extended Derivations companion (77 pp), and the complete LaTeX source, from which both volumes rebuild.

Principal results (each traces to a numbered result in the book; every input of the graded predictions is listed in one place, App. FK):

(1) The Hubble tension, read through one stated postulate: matter and the expanding universe keep clocks offset by one constant factor λ, set when matter first binds (App. ZS). On bound-matter clocks the G derivation gives H₀ = 72.09 km/s/Mpc with no parameter (seven Cepheid-free local measurements give 71.87 ± 0.96), and the early clock reads H₀/λ; a forward Boltzmann run leaves the CMB and BAO fit unchanged. The postulate's form is derived; it adds that the gap is constant, and its size is the one measured input, whose derivation is open. A stated same-era rule, λ = (1 + √α)^(3/4), predicts H₀_early = 67.79 km/s/Mpc (+3.0σ from the CMB-anchored 67.52), and the costs are printed, including a 12.92 Gyr laboratory-clock age of the universe.

(2) Dark sector and CMB: the early-clock CMB fit uses four continuous calibrations against ΛCDM's six (fair Δχ² = +3.2 for three fewer effective parameters, two fewer with the ω_b coefficient counted). χ, the Chern–Simons transgression mode of the microsector, is a derived cold, collisionless component with m_χ = 32.005 eV and Ω_χh² = 0.1193 (−0.6σ), conditional on the flux-period identification and stated conventions; χ does not couple to light. On the measured clock the CMB peak ratio is 2.20 (Planck 2.21) and the third-peak height is H₃/H₂ = 0.977, H₃/H₁ = 0.444 (within 0.6σ); the acoustic scale gives 100θ* = 1.04110 and ℓ₁ ≈ 220.4 with no global ψ-lensing map. Clusters and the Bullet Cluster need χ: under the μ-law alone sixteen clusters fall short (relaxed 1.57 ± 0.08, merging 1.99 ± 0.16), and the shortfall is the derived χ at 0.84 ± 0.12 of the cosmic mix (an estimate, with a hydrostatic bias b = 0.21 for the relaxed clusters).

(3) Gravity completion: Newton's law is an exact zero-parameter identity of the quantized ψ sector, with a Kohn-null laboratory discriminator; in the rest-mass sector DFD's gravity is general relativity's written in absolute time (static stars obey TOV, black holes have Schwarzschild's and Kerr's horizons (Kerr beyond first order in the spin argued), two-body dynamics is GR's through second post-Newtonian order); the action completion of the scale-additive field equation is Cassini-exact and momentum-conserving.

(4) Fine-structure constant and electroweak sector: the closed form gives α⁻¹ = 137.03599985, 4.9 ppb from CODATA 2022 (32 times its uncertainty); the integers alone give 137.03307 (21 ppm). The step identifying its hypercharge-trace coefficient with 1/e² is not derived, and the book calls the result a closed form, not a derivation. sin²θ_W = 3/13 = 0.2308 (bare angle, 0.23%); v = M_P α⁸ √(2π) = 246.09 GeV (exponent derived, prefactor fitted); the conjectured Higgs quartic 1/8 gives m_H = 124.6 GeV, 0.40% low.

(5) Flavor and CP: nine charged-fermion mass exponents derived (1.42% leading-order mean error; seven prefactors data-selected, labeled); Cabibbo λ = 31α = 0.2262 (1.8σ); TM1 solar mixing sin²θ₁₂ = 0.3184 (given the stated conjecture sin²θ₁₃ = 3α); Gatto–Sartori–Tonin closure m_s/m_d = 1/(7α) = 19.58. Strong CP: θ̄ = 0 at tree level, with θ_YM = 0 fixed by the spectral action, loop corrections bounded (≲ 10⁻¹⁶), no axion. Baryogenesis: the α⁴ power is derived; the printed mechanism overshoots Planck's η_B three to five times, so ω_b enters the CMB fit at its conventional value.

(6) Clocks, channel-resolved: in the core theory co-located clocks stay in step (the clock-null theorem); the cavity–atom geometric cancellation is derived, and four independent data streams support it, including JILA's 205-day silicon-cavity/Sr record (arXiv:2608.00910). The extended non-metric channel allows species-dependent drifts; its sharpest number is a perihelion-locked annual modulation of the Th-229 nuclear clock, about 350 Hz half-amplitude at α_s(M_Z) (0.9–1.5 kHz at the nuclear-scale α_s; minimal DFD: zero).

(7) Galaxies and the published a₀(z) result: SPARC radial-acceleration residuals below 5%, with n_opt = 1.15 ± 0.12 across the full 175-galaxy SPARC sample (standard MOND's n = 2 lies outside its 95% interval); baryonic Tully–Fisher slope exact; a₀(z) = 2√α cH(z), published in MNRAS (doi:10.1093/mnras/stag1485) and stated as contested, since its exclusion of a frozen a₀ rests on the published bin errors, and massive discs at z ≈ 2, with molecular gas counted, do not show the rise.

Decided since v4.0 and printed as such: the supernova-lensing sign (DES detected ordinary lensing at 6.0σ, against the sign of the optical-distance dressing, which is retired; the core metric is consistent), the ISW amplitude (A_ISW = 1.00; retired as a discriminator), and the Oort-cloud energy budget, which excludes every printed reading of the external-field-regime boost and leaves DFD predicting no wide-binary boost near the Sun. Retired as DFD results: the electromagnetic threshold extension, the solar-corona factor Γ = 4 (DFD predicts the standard coronal ratio) and the conjectured electric–magnetic split value κ = α/4.

Falsifiers (near-term): the Th-229 annual modulation (about 350 Hz; surviving window from about 26 Hz to the kHz level); H₀_early = 67.79 km/s/Mpc against the next DESI BAO release; the a₀(z) rise against JWST-era rotation curves; the H-maser/Sr local-position-invariance coefficient (predicted equal to Cs/Sr's under App. T's family model); a Kennedy–Thorndike signal (DFD core: null); proton decay (null, if baryon number is violated only by the electroweak anomaly); a detected spatial curvature (DFD requires k = 0); the CKM apex γ = 66.31°.

Every claim is tier-labelled (theorem / derived / conjectured / empirical) with explicit falsifiers; the confrontation matrix lists 78 claims (26 theorem, 47 derived, 3 conjectured, 2 empirical; 45 validated, 8 pending, 23 open, 2 contested). Independent verification is invited, and discrepancy reports are welcome.

What's New in v5.0

Change histories for earlier versions (v2.0–v4.0) are preserved in the descriptions of the corresponding version records in this DOI chain.