Logical and sign repairs

The Hamiltonian and displacement signs agree. The printed interaction $H_I=g{Z}_S{\Phi }_F$ gives $W(-sg{k}_F)$, not $W(sg{k}_F)$. The conditional characteristic phase and packet amplitude use that sign consistently.

Time ordering has a proved domain and phase. The central phase is derived from chronological Weyl products. No bounded-generator theorem is applied to an unbounded field.

The initial field is independent of the message. Every source-dependent displacement follows from the specified interaction, not from an alternative initial radiation state.

The scalar channel is normal only after restriction. The field state functional is defined first. The finite-mode trace-class densities are then constructed explicitly. No global physical radiation density is assumed.

Tracing the source removes its off-diagonal blocks. This is why the accessible radiation channel is measure-and-prepare. A visible classical signal is not unknown-qubit recovery.

Cosine and sine witnesses serve different tasks. The cosine expectation is even in the source sign. The sine witness supplies the nonzero sign-sensitive certificate.

Equal source-label counts are not equal radiation states. Parity proves equality of the whole selected joint number law, while the sine effect proves a state difference. The common displaced law can still differ from the Hawking baseline.

The selected packet is not the entire signal. Unselected outgoing modes, the future horizon, and the retained source are not replaced by vacuum or omitted from interpretation.

The retained source is not the full complement. No environmental decoupling distance is inferred without the unselected field and a specified background purification.

Local probe access is a probability construction. It is not a coherent field-to-memory channel or an instrument comparison retaining quantum outputs.

The local scheme is after source switching. A future measurement time slice is explicitly chosen. The scattering endpoint is not used to signal into the physical past.

Growing access and squeezing are priced. Arbitrary mathematical accuracy is not a fixed-shell, bounded-effort, or fixed-hardware theorem.

Excess energy is not a difference of infinities. The positive rank-one two-point change defines the finite energy. A nonmonochromatic packet is not assigned an exact single frequency.

Switching work is not source mass loss. The source is degenerate and the drive is prescribed. No black-hole evaporation dynamics follows from this ledger.

The source is exterior. No interior communication, gravitational origin, or resolution of the black-hole information problem is inferred.