We derive a gravitational enhancement function with zero free parameters from the entropic field equation ∇²S = −2gᴮ and Berger's theorem on the sectional curvature of CPⁿ. The result is Gₑff (x) = (1 + 1/x²) ^ (1/Kₑff), where Kₑff (x) = 1 + 3/ (1 + 8x²) and x = aN/a₀. The factor of 8 is the product 2K: 2 from the field equation coefficient and K = 4 from the Bures manifold curvature, entering through the entropy-driven deviation equation J'' + 2KJ = 0. Tested against 175 SPARC galaxies (3, 375 data points): χ²/N = 50. 6, within 0. 9% of MOND-simple. Weak lensing (KiDS) independently confirms the curve. The dark energy parameter α = π/16 matches DESI DR2 to 0. 025%. The BKM identity dBKM = arctan (x) is proven, and x = sinh (ΔE/ (2kBT) ) is derived from the density matrix. Dark matter is the local geometry of state space responding to its content.
Michael Adis (Sun,) studied this question.