Operational Quantum-Probe Boundaries inside a Schwarzschild Black Hole

Central result : The reconstructed finite-profile curvature response peaks outside the mean-area bounce, whereas local quantum-clock decoherence occurs only in the immediate bounce region. Across the tested minimal and Weyl reconstructions, a_response/a_bounce ≈ 1.10 ± 0.03 and a_time/a_bounce ≈ 1.00 ± 0.01. Abstract: We develop an operational test-probe extension of a relationally quantized Schwarzschild interior and compare three scales using one finite-resolution protocol: the radius at which a smeared curvature sensor is maximally responsive, the radius at which a local quantum clock reaches a coherence-loss threshold, and the mean-area bounce radius. The background quantum geometry is the Kantowski–Sachs minisuperspace model with physical constraint C_H = p_b + α²/p_a ≈ 0 and relational clock b. A comoving finite probe carries an internal clock and a curvature sensor. Proper time is treated operationally through a finite-profile kernel rather than identified with the relational clock. For Gaussian physical states we obtain an analytic bounce radius and a direct momentum-space evaluation of local proper-time fluctuations. The curvature channel is reconstructed in two controlled ways: an Eq.-(133)-compatible minimal smeared form and a full finite-profile Weyl seed followed by relational group averaging. The corrected Weyl distribution calculation fixes the clock-sector delta-derivative signs and yields convergent responses. Across the tested states and ordering prescriptions, the curvature-response peak lies approximately 7–13% outside the mean-area bounce, whereas the clock-coherence threshold lies within about 1% of it. The robust qualitative ordering is a_response > a_time ≃ a_bounce. We give domain and closability conditions, numerical convergence audits, branch-preserving and branch-inclusive protocols, and a claim-by-claim separation from prior work on relational black-hole interiors, finite-size detectors, and quantum clocks.