Theory Space Elimination via the Sherlock Holmes Method: Why Only Two Theories Survive All Observational Constraints

We apply the Balaban method of exhaustive enumeration with constraint elimination to the problem of gravity and dark matter theories. Any complete theory must specify four components: gravitational mechanism (5 options), dark matter model (5 options), cosmological model (4 options), and propagation model (4 options), yielding 400 distinct theory combinations. We systematically apply observational constraints from GW170817 (|v_GW/c − 1| < 4 × 10⁻¹⁶), binary pulsar orbital decay (0.2% agreement with quadrupole formula), galaxy rotation curves (SPARC, 175 galaxies), the Bullet Cluster (mass-baryon separation), CMB acoustic peaks (r_d = 147 Mpc), EHT black hole shadows (52 μas), perihelion precession (42.98 arcsec/century), frame-dragging (Gravity Probe B), and the radial acceleration relation (0.13 dex scatter). After applying all nine constraints, only two theories survive: (1) General Relativity with ΛCDM, and (2) the Lattice Field Medium (LFM). Both pass every observational test. However, LFM has fewer free parameters (3 vs 6), requires no undetected particles, and derives the acceleration scale a₀ = cH₀/(2π) rather than treating it as a coincidence. Following Sherlock Holmes: "When you have eliminated the impossible, whatever remains, however improbable, must be the truth."