CPT-Coherence / Mirror-Mind Theory: A Parent-Boundary Framework for Onto-Physical Entanglement, Coherence-Depth Selection, and Flux-Null Physical Law

CPT-Coherence, also called Mirror-Mind Theory, is formulated as a parent-boundary theory of physical realization. The theory begins from a coherence-depth parent system rather than from an isolated four-dimensional arena. Its fundamental data are a parent Hilbert space ℋ6, a closed semibounded parent action 𝒜6, a self-adjoint parent operator 𝒦6, a boundary trace system γ∂, an antiunitary CPT reflection ΘCPT, a signed boundary Green form 𝒲∂, and a selected reducing branch projector 𝒫ours. Observable physical law is the branch-local reduction of this parent datum through trace quotient, passive Schur compression, flux-null boundary selection, reflection-positive reconstruction, and stable observable descent. The central principle is Onto-Physical Entanglement: physical being is not separable from the admissibility structure by which a state, record, field, or law remains coherent under repeated transformation. The coherence-depth coordinate τ is therefore not a second physical time and not an additional macroscopic spatial direction. It is the internal structural coordinate along which spectral relaxation, branch identity, boundary transport, hidden-sector response, and physical viability are organized. In this sense, particles are not merely eigenstates of a branch Hamiltonian; they are trace-visible, reflection-positive, flux-null bound states of a parent boundary system. The mathematical spine of the framework is the descent chain: 𝒜6 → 𝒦6 → γ∂, MQ, 𝒲∂, 𝒡∂ → 𝒫ours → 𝒯ours → 𝓥∂ → 𝒪phys Once the parent form and its domain are fixed, the trace-access metric, Green form, signed flux grading, reducing branch restriction, and boundary impedance are generated objects rather than independent phenomenological insertions. Hidden-sector effects enter through passive Schur compression, producing visible-sector stiffness, mass-readout, mixing, and transport structures from a common boundary response. Within the three-generation charged-lepton aperture, cyclic branch monodromy decomposes the generation-amplitude space as ℝ3gen = 1 ⊕ 2, with longitudinal and transverse projectors P1 and P2. The parent boundary aperture induces the Koide signature ΣK = P1 - P2. For the generation-amplitude vector xℓ = (√me, √mμ, √mτ)T, the branch flux-null condition xℓTΣKxℓ = 0 is exactly equivalent to: Qℓ = (me + mμ + mτ) / (√me + √mμ + √mτ)2 = 2/3 Thus the charged-lepton Koide relation appears as the null-cone invariant of a balanced monodromy aperture, not as a numerical fit. The same parent-boundary grammar also organizes branch probability, gauge structure, conservative gravitational emergence, ultraviolet/infrared control, and flavor transport. Branch probabilities are normalized trace-access weights over flux-viable record sectors. Gauge fields arise as aperture-frame stabilizer connections preserving the trace and flux structures. Conservative Einstein dynamics is recovered on branches whose τ-exchange current vanishes. Fourth-order coherence-depth stability supplies elliptic ultraviolet control without invoking real-time higher-derivative ghosts, while the associated boundary impedance carries the high-frequency scaling ||N∂(λ)|| = C|λ|3/4(1 + o(1)) for a fourth-order coherence-depth parent. The result is a unified operator-boundary framework in which ontology, measurement, mass hierarchy, gauge transport, and gravitational projection are treated as coordinated consequences of parent coherence, branch selection, trace visibility, Schur response, and flux-null viability. Keywords: CPT-Coherence; Mirror-Mind Theory; Onto-Physical Entanglement; coherence depth; parent operator; boundary triples; Schur complement; flux-null states; Koide relation; branch selection; trace quotient; CPT reflection; Born rule; gauge stabilizer; Einstein branch; ultraviolet regularization.