We derive 227 experimentally measured constants of nature — spanning particle physics, cosmology, nuclear structure, atomic spectroscopy, hadron masses, Higgs decays, and astrophysics — from a single question ("Exists?") and a single scale (M_Pl). No parameters are fitted. The framework identifies reality as a CP¹ sigma model at coupling g²=4 and topological angle θ=π, tiled on the sphere S² by the complete graph K₄. This geometry forces the concealment cost ε = 1/π², from which every Standard Model coupling, mixing angle, and mass ratio follows by algebraic operations on the tetrahedron. The full mass hierarchy descends via m(N) = M_Pl·e^(−Nπ). Of the 227 predictions, 226 can be scored against current measurements: 180 fall within 1%, 105 within 0.1%, with a median deviation of 0.13%. Five testable predictions for unmeasured or poorly constrained quantities are given, including neutrino masses, the dark energy equation of state, and the tensor-to-scalar ratio. A binary pattern algebra on the Z₂×Z₂ tile group identifies the three fermion generations with three K₄ faces, recovers the gauge group SU(3)×SU(2)×U(1) from graph invariants, and governs all flavour-changing transitions through XOR composition — with the W boson as the void-tile carrier. Companion Python code (bccf_builder.py) reproduces every formula as a self-contained, queryable existence matrix of 271 nodes and 747 edges across 27 derivation steps.