The preceding chapter derived physical time as arc length along the base circle τ¹. But arc length is a mathematical construction — it exists at every refinement depth, even at α₁. The fact that physical time exists does not yet explain why it manifests as the familiar parameter that clocks measure and observers experience.

This chapter addresses the gap. Not all refinement depths produce a well-defined temporal readout. At very early depths (n close to 1), the primorial structure is too coarse for the arc-length parameter to be read out by any physical subsystem: there are no clocks, no oscillators, no periodic processes that could register the passage of ticks. At very late depths (n → ∞), the ticks become so short that the temporal readout saturates and freezes.

Temporal ignition depends on spectral purity (Book III, III.T19): a well-defined time direction requires that the eigenvalue spectrum on the boundary is cleanly separated along the critical line, so that the arc-length parameter admits a unique readout at each refinement depth.

Between these two extremes lies the temporal epoch: the range of refinement depths at which proper time is a well-defined, operationally meaningful quantity. The present chapter identifies three epochs (the relevant definition, V.D17), defines the ignition condition that marks the onset of the temporal epoch (the relevant definition, V.D18), constructs the “now” hypersurface Σ_{now} (the relevant definition, V.D19), and proves that the current state of the universe lies well within the temporal epoch (the relevant theorem, V.T10).