A Conditional Operator Encoding of Wave-Particle Duality in MTT Local Kernels, Spectral Coherence, Instruments, and the Born-Bridge Boundary

This paper gives a conditional operator encoding of wave-particle duality. A positive filtered operator has local and spectral representations; an exhausting sharp-limit family yields a delta kernel, coherent phase transport yields interference, positive Schur multipliers yield valid dephasing channels, and POVMs completed by quantum instruments model outcome probabilities and state updates. These results are mathematically compatible with standard quantum mechanics but do not derive it, because the state, Hamiltonian, effects, instrument, and damping channel are supplied as inputs. A survivor-basin account is an additional MTT interpretation. It reproduces the Born rule only if a state-dependent basin measure satisfies the explicit basin-Born bridge criterion for every admitted state and outcome. A selected common MTT source for all these objects remains open.