Abstract

We construct and analyze a specified apparatus-model realization of finite destructive number readout for one outgoing Hawking packet. The stationary field prescription is an explicit predecessor input. Its centered quasifree restriction gives a normal geometric one-mode density, proved here without assuming a density operator for the entire stationary radiation field.

The apparatus consists of a passive temporal-mode capture port, a memory oscillator, a binary register, and a complete readout instrument. A smooth, finitely switched capture interaction has an explicit transfer kernel. A zero-integral temporal-window construction controls packet mismatch and prevents an infrared integrability shortcut. Unselected positive-frequency radiation is not replaced by vacuum: its occupation and correlations enter a reference-stable mode-comparison bound. Vacuum auxiliary ports and independent apparatus preparations are separately declared model data.

Coherent oscillator–register extraction is generated by explicit number-selective swap pulses. Its finite control-domain error is exactly the probability above a second cutoff when the stated global block structure is present. Bounded control perturbations and a distinct support-only certificate are treated separately. A complete noisy readout instrument includes assignment errors, quantum readout errors, spectator coupling, imperfect preparation, and visible failure outcomes.

The resulting transfer and implementation budgets are derived from model parameters and substituted into finite-count, mean-bias, and record–spectator–reference bounds. A constructive tolerance schedule and an apparatus resource ledger are supplied. These are model-level results. A local Schwarzschild-field coupling, a justified laboratory effective model, and experimental implementation remain separate obligations.