The Emergence of Time from Conserved Continuity

The completed Chronoflux Atlas recovers physical time from conserved continuity. Time is not introduced as an external coordinate, nor identified with any arbitrary parameter used to label a sequence of states. It emerges when the conserved current is admitted as non-vanishing, positive and future-directed timelike. Those conditions select an orientation, generate a chronological order, and define an invariant temporal one-form whose integral gives physical duration along everyadmitted history. I prove that the resulting duration is positive on future-directed causal curves, additive under concatenation and invariant under reparametrisation. The exact frame-current decomposition then separates temporal grouping from spatial drift. Drift changes the relation between frame duration and current proper duration, but cannot erase the current’s temporal orientation while the time like condition remains satisfied. Conservation gives the transport identity between temporal density and expansion, so the product of density and material volume is preserved. Where the Frobenius condition closes, the temporal one-form integrates to a local time function and a foliation by simultaneity surfaces. Where vorticity obstructs such a foliation, invariant duration along the flow remains well defined, assuch, while one global simultaneity convention does not. A compact parent current reduces exactly to the four-dimensional temporal current on local product charts, with the global transport-bundle topology retained as the genuine open boundary. Physical clocks then read the recovered duration through a calibrated phase map. They do not create time. The result closes time as conserved physical order and temporal measure within the admitted Chronoflux branch. Keywords: physical time; temporal current; conserved continuity; proper duration; time orientation;Frobenius theorem; temporal transport; clock map; Chronoflux Atlas