Space-Matter Continuum (SMaC): A Unified Theory Eliminating Dark Matter and Dark Energy

10.5281/zenodo.18451603

We present the Space-Matter Continuum (SMaC) theory, a complete framework
that unifies gravity, time, and the large-scale structure of the Universe. Based
on the empirical discovery that galactic sizes follow R ∝ ρ−0.501±0.011 across 175
SPARC galaxies (R2 = 0.907), we derive fundamental equations where gravita-
tional strength Geff and time flow rate dτ /dt both depend on local continuum
density ρ. Remarkably, two independently measured dimensionless parameters—
Π = V 2 flatReff/(GMbar) from galaxy dynamics and α from β ∝ Σα scaling—yield
identical values: Π = 1.332 ± 0.012 and α = 1.332 ± 0.018, both consistent with
the mathematical constant 4/3. This identity Π = α = 4/3 leads to ρDM ∝ ρ11/6
bar, explaining galactic rotation curves without dark matter particles. Laboratory pre-
dictions include measurable G variations (∆G/G ≈ 10−11 in lead) and time flow
differences (∆τ ≈ 16 s/year in dense media). SMaC resolves both dark matter and
dark energy with zero free parameters, restoring unity to fundamental physics.