Manuscript Em03-D@1 · Em03-D-v1.tex · section · 450d878a

Access and effort

A worked packet family and the apparatus resource ledger › Access and effort · lines 1759–1856

{}1.13

Resource	Declared quantity and boundary
Resource	Declared quantity and boundary
Geometry and angular access	The right Schwarzschild exterior; the full angular sphere. The interaction is not pointlike and is not a restricted angular-patch detector.
Coupling support	A compact subset of $∣ t ∣ \leq T, ∣ x ∣ \leq 2 R + T$ , times $S^{2}$ . Its inner radius is strictly greater than the horizon radius for every finite $R$ .
Spatial accuracy	The explicit spectral or ordinary derivative tails $Δ_{R}, D_{p} (R), D_{q} (R)$ . Increasing $R$ enlarges access toward both radiation ends.
Coupling amplitude and derivatives	$λ = ϵ ρ$ . For every fixed derivative order, $∥ \partial^{γ} λ ∥_{\infty} = ϵ ∥ \partial^{γ} ρ ∥_{\infty}$ in the stated dimensionless coordinates. Physical values require the displayed length conversion.
Probe species	One additional real massless scalar on the same exterior. The use of the constant free solution is specific to this declared mass choice.
Probe initial data	Compact Cauchy data equal to the constant solution on the causal predecessor of the coupling zone. The initial support and subsequent processing support grow with the coupling zone.
Processing test	The compact future test $g / ϵ$ . Its test seminorms grow as $ϵ^{- 1}$ for fixed $R, T$ .
Probe covariance	The independent reference Unruh covariance, followed by the exact finite-plane squeeze (eq:squeeze). The residual variance is bounded by $N_{R} ϵ^{2}$ .
Conjugate preparation effort	The squeezing magnitude is $2 lo g (1/ ϵ)$ . A canonically conjugate variance is at least $1/ (4 N_{R} ϵ^{2})$ . No bounded-effort limit is claimed.
Final measurement	The two effects $O_{ϵ}, I - O_{ϵ}$ . Their probabilities are well defined and complete. A laboratory implementation of the final probe POVM is a separate obligation.
Clock	Normalized asymptotic Killing time. A static proper-time implementation at radius $r_{0}$ must convert by $d τ_{proper} = F (r_{0}) d t$ .
Energy and preparation work	No evaluated cooling work, squeezing energy, or optimal reset cost is supplied. Hadamard regularity is not a bound on preparation resources.
Repeated trials	Fresh independent system and probe preparations are additional assumptions if independent-trial statistics are used.

In dimensionless tortoise coordinates, $r (- X) - 1 \sim e^{- X - 1}$ as $X \to \infty$ . Thus the inner-shell access can approach the horizon exponentially in the coordinate support parameter. The construction must not be described as maintaining a fixed proper distance from the horizon.