Organizational Compaction and Early Black-Hole Formation: Covariant Methods, a Reduced Thermal Example and Critical Formation Tests

This research working master develops a factor-by-factor deduction framework for testing whether organizational compaction can mediate between microscopic interactions and early black-hole formation within the proposed Organized Field Theory (OFT) and its conditional VGM response programme. The central comparison holds total initial energy fixed while varying admitted organizational correlations. Observer-defined polar and axial orientation moments, covariant field and metric variations, electromagnetic and organizational vector sources, anisotropic stresses, enthalpy, entropy production, transport and cosmic expansion are treated as distinct but coupled modules. The mathematical results include a dependency-preserving functional pullback identity, exact elimination of an auxiliary quadratic response yielding a derived toy proxy and a reduced quartic correction, and a conditional critical-boundary displacement theorem under smoothness and transversality assumptions. An executed one-variable thermal relaxation example is compared with its analytic solution, auxiliary-polynomial Newton checks and time step refinement. The parent descriptor kappa = K[g,q] remains distinct from the algebraically derived toy proxy, which has no independent dynamics. A dependency graph identifies the unresolved parent-to-physical-source matching and the subsequent constraint-compatible nonlinear evolution and future-trapping tests. The manuscript provides conditional deductions, explicit admission and rejection criteria, and a specified computational programme; it does not derive the microscopic OFT map, demonstrate an OFT black hole, or report observational confirmation.