Abstract and publication identity

We give a complete-current theorem chain from weak quantum continuity to deterministic reference-compatible histories. A continuous spacetime wave, finite action and logarithmic variation, local positive-tube Sobolev regularity, and separate physical-boundary control imply all-times node avoidance and deterministic disintegration. Uniqueness holds among path laws with one finite marginal-domination constant, rather than among all ordinary differential equation solutions at exceptional points. Every original absolutely continuous configuration law is transported by reweighting the same reference paths once. We prove weak whole-path approximation from strong density and current convergence, and a quantitative logarithmic stability estimate that retains the probability of leaving the common positive tube. Singular-domain applications include radial jumps with finite spin and quantum sources, bare Coulomb interactions, and a Coulomb electron with a retained oscillator source. Their common-form and tangent-domain hypotheses are explicit; the high-dimensional product embedding retains its weak error exponent. A separate signed-source theorem bounds endpoint and crossing errors when a comparison current is not exactly conservative. Exact examples demonstrate failures caused by contracted hidden currents, singular entrances, and a nonlocal current with divergent nodal action. These conditional mathematical results provide flow and history interfaces without selecting an original Born ensemble or establishing a complete physical record apparatus.