The Double-Edged Sword: Deriving Dark Energy and Dark Matter as Projection Artifacts of Time Emergence

Description / Abstract: The concordance cosmological model (ΛCDM) requires 95% of the universe to be composed of unknown substances: 68% dark energy and 27% dark matter. This paper demonstrates that both requirements arise from a single assumption — that time is fully expressed everywhere and at every epoch — and that the consequences of removing this assumption are sufficient to explain both inventions. Dark energy is the clock error. Using 1,580 Type Ia supernovae from Pantheon+ (z > 0.01), a time emergence function τ(z) with steepness β = ln(δ) = 1.5410 derived from Feigenbaum's universal constant matches ΛCDM to within 6.4% in χ²/dof with zero free cosmological parameters. Seven CMB acoustic peak positions are reproduced to 1.35% RMS, matching ΛCDM's 1.40%. The cosmological constant Λ is the projection of time emergence onto a flat-time coordinate system. Dark matter is the ruler error. Using 175 galaxies from the SPARC database, the Radial Acceleration Relation (RAR) is shown to be a ruler correction: the spatial metric within gravitationally coupled systems is distorted by the τ gradient across the gravitational potential. The RAR exponent is not universal — it depends on galactic coupling topology, with a statistically significant monotonic trend across morphological classes (Kruskal-Wallis p = 0.005). The ground-state exponent is logδ(2) = ln(2)/ln(δ) = 0.4499, derived from the Feigenbaum constant: one period-doubling step. Low surface brightness galaxies converge to within 0.001 of this value. The standard RAR exponent p = 0.5 is not fundamental — it is the sample-averaged mean of a topology-dependent complexity spectrum. Same constant. Same law. Clock and ruler. Both corrections trace to the Feigenbaum architecture confirmed in 50,000 Gaia DR3 stars at p = 10⁻³¹⁰. Keywords: dark energy, dark matter, time emergence, Feigenbaum constant, cosmological constant, radial acceleration relation, SPARC, Pantheon+, Type Ia supernovae, CMB, rotation curves, Universal Cascade Law, nonlinear dynamics, galactic morphology, coupling topology, ΛCDM Additional Notes: Extends and refines the Twin Dragons analysis with two new results: (1) the ground-state RAR exponent logδ(2) derived from the Feigenbaum constant, and (2) the discovery that RAR scatter encodes galactic coupling topology. All analysis code available at github.com/lucian-png/resonance-theory-code. CMB peak heights remain an open calculation, acknowledged honestly.