Modal Triplet Theory and Nonrelativistic Quantum Mechanics: A Coherent-Sector Reconstruction and the Born-Source Boundary

This paper asks what Modal Triplet Theory (MTT) presently establishes about nonrelativistic quantum mechanics. We separate four questions that are often conflated: whether MTT can encode a quantum model, whether a coherent sector reconstructs its Hilbert-space dynamics, whether one selected MTT source emits the required operators and instruments, and whether the probability law is derived for every apparatus. A complete quantum-mechanical record is defined, including the complex Hilbert space, state cone, operator algebra, self-adjoint Hamiltonian and domain, unitary evolution, clock convention, composition rule, effects, instruments, and source certificates. The main theorem is conditional: if one selected upper MTT state emits this record and the evaluation diagram commutes, then MTT reconstructs the corresponding quantum theory on the declared domain. Projection alone does not create a complex structure, noncommutative observable algebra, self-adjoint Hamiltonian, tensor product, or probability law. We give sufficient closed-form and reducing-subspace conditions for an exact coherent-sector Hamiltonian, and we show why reproducing an arbitrarily supplied Schrodinger potential is an expressiveness result rather than a prediction. Time is treated as an evolution or clock parameter; the valid Mandelstam–Tamm relation replaces the former unsupported universal self-adjoint time operator. Gleason- and Busch-type theorems characterize probability assignments after Hilbert/effect structure and additivity are assumed; they do not source those assignments. A stronger positive result is available on one selected domain: the canonical q=79 binary one-anchor recorder gives an exact stopped output measure and second-moment Born descent on its commuting Fock output algebra, with no fitted probability or additional classical noise. General apparatus contexts, finite-bandwidth and non-Markov control, pre-quantum probability semantics, and objective single-history selection remain open. The result is therefore a rigorous coherent-sector reconstruction with one exact selected measurement domain, not a complete first-principles derivation of all quantum mechanics.