System Manifold Engine: A 5-Dimensional Warped Brane-World Grand Unified Theorem Deriving the Standard Model Gauge Group, the Speed of Light, and the Higgs Localization Scale from a Single Geometric Ground State

We present the System Manifold Engine (SME), a 4+1 dimensional warped brane-world framework in which the observable universe occupies the n=0 brane of a 5-dimensional Anti-de Sitter bulk. The central result is the 0/3 Ground State Theorem: the energy functional V(γ) = V₀(1 − cos γ) over K unit vectors possesses a unique rigid minimum at K=3 (equilateral configuration, E=4.5V₀) with a positive-definite Hessian after fixing global rotations, while K=2 is non-rigid and K≥4 are higher-energy local minima. This sealed geometric result forces three independent consequences without additional postulates: (1) D_flat = 3 spatial dimensions on the brane, (2) N_g = 3 fermion generations, and (3) the Standard Model gauge group SU(3)×SU(2)×U(1) as the eigenvalue structure of the 3×3 circulant conductance matrix of the K=3 junction network. The speed of light emerges as a derived boundary condition c₀ = c_eff(n=0) of the impedance profile Z_eff(n) = (c₀/ℓ_Pl)·cosh(n/L), where the warp factor A(n) = −ln(cosh(n/L)) is sealed from the 5D Einstein equations. The bulk screening length L is analytically determined from two measured quantities alone: L = M_Pl²/(m_H³·e^79.8), with two geometric primitives (M_Pl and L) and standard electroweak inputs. The claim of "zero free parameters" has been revised to accurately reflect one empirical import (sin^2(theta_W) to fix eps/w) plus standard SM couplings for RGE running. [...] The framework classifies all compact objects via a two-parameter valve-state taxonomy (Ψ, Ω), identifies black holes and white holes as the two valve states of a single multi-connected throat geometry, derives magnetars as clogged-port configurations, and produces 14 falsifiable predictions targeting PLATO, Hyper-Kamiokande, LIGO O5, ALMA, Euclid, FCC-hh, Fermi-LAT, HERA, ngEHT, NICER, JWST, and VLT. We present this framework including its open items and kill criteria without reservation, inviting adversarial engagement from the community.