BKT-37Y09 Orthogonal Projection, Hidden-Sector Self-Energy, and Cross-Channel Identifiability in Proton-Structure Studies

Orthogonal Projection, Hidden-Sector Self-Energy, and Cross-Channel Identifiability in Proton-Structure Studies This publication develops a mathematical, physical, and statistical framework for testing whether proton-structure data contain a stable dynamical component that cannot be reduced to the parameters, uncertainties, and systematic directions of a complete QCD and Standard Model reference description. The central formal distinction is: r_perp != Q|Psi> != Sigma_Q(E) Here, r_perp is the weighted orthogonal residual in data space, Q|Psi> is a state in a complementary sector of the physical state space, and Sigma_Q(E) is the energy-dependent self-energy through which that sector influences observable dynamics. A nonzero residual is therefore not, by itself, evidence for a hidden sector. The framework combines weighted orthogonal projection, the Feshbach formalism, spectral representation, extended Fisher-Cramer-Rao information, nonlinear model geometry, and cross-channel low-rank tests. A candidate signal must be non-tangential to the full reference model, informationally identifiable, stable outside the training sample, transferable between independent channels without redefining its profile, and globally significant after look-elsewhere calibration. The numerical examples are reproducible synthetic benchmarks used to validate the methodology. They are not measurements of an additional proton sector. The previously tested strong common-direction hypothesis remains unsupported: p_boot = 0.799 Delta_OOS = -0.0106 +/- 0.059 sim = 0.43-0.86 < 0.90 Accordingly, the tested low-rank realization is classified as FAIL, the general latent-sector hypothesis remains INCONCLUSIVE, and its identification with the Metafield is NOT ESTABLISHED. The framework is applicable to combined analyses of elastic form factors, GPDs, DVCS and DDVCS, energy-momentum-tensor observables, lattice QCD, proton-Roper transitions, and forward-proton measurements at Jefferson Lab, the EIC, CERN, and the HL-LHC. This work extends: BKT-37Y06-SYN - doi:10.5281/zenodo.21772449BKT-37Y07 - doi:10.5281/zenodo.21918077BKT-37Y08 - doi:10.5281/zenodo.21982430