A First-Principles Derivation of Physical Time from an Eleven-Dimensional Covariant Master Action

Quantum theory on a prescribed background and general relativity assign fundamentally different roles to time. The former uses an external parameter to describe change, whereas the latter makes temporal duration part of the dynamical spacetime metric. This paper derives a common origin for these structures within an eleven-dimensional-to-four-dimensional information-projection theory. Observable spacetime is treated as a physical readout of a larger information–geometric support, and time is obtained through successive physical transitions rather than inserted as a primitive background variable. The construction begins with the fibration \\(F_x^7\\hookrightarrow E^{11}\\xrightarrow{\\pi}M_4^{\\mathrm{read}}\\). The seven-dimensional internal fibre carries potential-state and compatibility data whose reduction induces effective covariance, memory, boundary response and source terms on the four-dimensional readout domain. Local event formation is governed by a heterogeneous \\(9+1+1\\) structure: a \\(3\\times 3\\) covariance-bearing event field, a coupled event-epoch update and a residual-recovery response. Conditional expectation, open-system projection, spectral activation, free-boundary variation, stochastic reduced dynamics and covariant source functionals express and test this native dynamics in conventional mathematical physics without replacing its generative order. Physical event time arises when state-dependent activation, boundary stabilization and capsule persistence produce distinguishable occurrences whose records carry an asymmetric causal precedence. Recurrent sectors of those persistent objects support relational and dynamical clocks. Pulling the common rendered lapse back to the resulting worldtube gives positive proper duration. Normalized clock geometry nevertheless retains a common positive rescaling orbit. The paper proves that this orbit leaves the relational history, phase geometry, normalized temporal coframe and normalized lapse data unchanged while changing the full proper period. The remaining scale is fixed by a scale-sensitive temporal quantity obtained from the same seven-term parent action. A temporal Noether generator, boundary Hamiltonian or equivalent direct proper-frequency observable intersects the rescaling orbit transversely and determines a locally unique positive period on the declared physical branch. Periodic-orbit and rendered-cell constructions provide independent realizations or consistency checks of that same temporal quantity rather than additional multiplicative normalizations. The resulting duration is then expressed in a replaceable reference-clock chart. In the present SI, the caesium-133 hyperfine transition supplies that chart; it represents an internally determined time in seconds and hertz but is not the dynamical origin of time.