A Work-Unit Formalization of the MGAP4D 4D Mass-Gap Architecture and the Internal 33/20 Gap Theorem

This preprint presents the MGAP4D proof architecture for a four-dimensional mass-gap formalization and records the internal normalized 33/20 gap theorem. The central statement is formulated inside the MGAP4D Hilbert–operator framework: after removing the vacuum line, the excited Hamiltonian Hexc has spectral lower bound 33/20, the value 33/20 is realized by a nonzero excited state, and the resulting excited-sector mass gap is exactly 33/20 in MGAP4D internal normalized units. The paper also describes the accompanying Lean-oriented closure-priority and work-unit execution bundle. The formal archive is organized into seven work units: construction of the vacuum functional, projection onto vacuum/excited sectors, reducing decomposition and spectral union, analytic lower-bound transfer, unbounded zero-form kernel route, atom persistence and exact-gap extraction, and final audit gating. The accompanying review packet records source-hygiene statistics with sorry = 0, admit = 0, axiom = 0, and constant = 0 for the generated Lean source archive. Scope note: this release states the MGAP4D internal theorem and its proof architecture. Public mathematical certification remains review-gated pending independent replay, exact external API binding verification, and reviewer audit.