Abstract

We solve an effective exterior-source model consisting of two temporally ordered couplings of a degenerate qubit to the massless s-wave scalar field on Schwarzschild. The first coupling uses the source observable $Z$, and the second uses $X$. Both source profiles are smooth, compact, strictly exterior, and have full angular-shell support. The initial scalar field is the independently specified Unruh state.

The exact radiation channel is evaluated on every source matrix unit. Its outgoing packet restrictions are normal channels with explicit interference terms, rather than independently assigned displaced Gaussian outputs. We also calculate the retained-source channel and construct a complete complementary channel in a fixed purified field representation.

A phase-matched one-packet comparison model admits an explicit mathematical decoder. Its worst-case referenced recovery error approaches zero when the first displacement grows and the second decreases with their symplectic pairing fixed. Filtered compact bulk approximations realize this comparison with ordered exterior profiles and a source-input half-diamond error bound. Consequently, finite compact parameters exist for which an identified outgoing scalar packet has a provably entangled reference-output state. This is a sufficient transmission regime, not a classification of every parameter choice.

At every finite first-pulse coefficient, the retained source has nonzero input distinguishability. We derive a corresponding nonzero recovery lower bound, while keeping Bell fidelity, worst-case entanglement fidelity, and half-diamond distance distinct. Complete environmental leakage bounds retain unselected radiation, future-horizon degrees of freedom, and background purification.

We prove a new common second-moment bound for the interference-bearing outputs and use it for local bounded-Weyl probability certificates. Coherent local packet access is not assumed or constructed. Causal support, finite signed excess radiative energy, interference energy, switching work, and resource growth are treated separately.

The interactions are effective exterior source laws, not a microscopic gravitational derivation. No black-hole interior information escape or evaporation theorem is established.