Abstract

We construct a finite operational realization of Page–Wootters clock conditioning using destructive Enter on a named clock register. The complete output consists of a classical clock code and the surviving system; the measured clock names are consumed. An explicit channel identity proves equality of the Born record law and the unnormalized conditional system states with their Page–Wootters counterparts, including arbitrary untouched references. Under a separately stated covariance condition for the clock basis, stationarity of the joint preparation implies unitary relational evolution at the calibrated readings. An exact finite spectral construction establishes that these hypotheses are jointly inhabited.

The probability and update formulas have two distinct justifications: they follow algebraically from the specified instrument, and, when the full Enter characterization hypotheses are satisfied, they are the measurement semantics selected by the previously established operational characterization. We do not rederive that characterization from abbreviated axiom names.

We also give a typed hybrid propagator, complete-channel stability bounds, and refinement independence within an explicitly matched class. The philosophy of Enter is expressed as an interface discipline: a destructive record is not a surviving clock, a decoder, a thermodynamic ledger, or a spacetime geometry. The construction realizes relational extraction, not clock-free quantum gravity, a dynamical causal cone, or spacetime emergence.