Detector-Facing Constraints on Black-Hole Record-Relay Ringdown Signatures: H1 Injection-Recovery Sensitivity Bounds, Quadrature Phase Closure, and the Spin-Precision Gate

This paper addresses the detector-facing problem left open by the Record-Relay black-hole framework. Paper 24 derived the closed record-relay ringdown coordinates, including the delayed onset, the Kerr-mode-relative frequency target, the delayed dual-decay waveform, and the Page-transition width structure. The present paper asks a different question: if those coordinates are mathematically fixed, what can real gravitational-wave strain data say about the possible existence and amplitude of a delayed relay burst? The paper builds a detector-facing constraint framework by placing the Paper 24 record-relay coordinates onto real public H1 gravitational-wave strain. It does not claim that a record-relay burst has been detected. Instead, it tests whether a delayed secondary burst at the predicted time-frequency coordinate would already be visible in the current H1 catalogue, and if not, what amplitude regime is excluded by injection-recovery calibration. Three main results anchor the paper. First, the current H1 phase-marginalized stack shows no statistically significant delayed relay excess at the predicted coordinates. The real stack is consistent with the empirical time-slide background. Second, injection-recovery converts this null result into a detector-facing sensitivity bound. The frozen analysis snapshot excludes strong delayed-burst amplitudes, and a live re-harvest reproduces the same null conclusion and the same exclusion of the strong-amplitude interpretation, though with a weaker numerical threshold. Third, the paper shows that the next decisive test cannot simply be another power stack, because coherent stacking is limited by event-by-event remnant-spin precision. The quantitative layer is intentionally constrained. The analysis uses one hundred usable high-signal, in-band H1 events selected from a larger working candidate set. The final statistic is not the earlier exploratory band-pass statistic, but a repaired PSD-whitened matched-filter quadrature statistic evaluated against empirical time-slide backgrounds. The robust result is therefore not a release-independent posterior upper limit, but the exclusion of strong-amplitude delayed bursts within the declared H1-only template family and normalization. The paper also addresses the phase problem that prevents efficient coherent stacking. A phase-marginalized power stack is robust because it does not assume the unknown relay phase, but it becomes inefficient at weaker amplitudes. A coherent stack would be more sensitive, but only if the event-to-event relay phase can be predicted in advance. The paper develops a conditional horizon-stress bridge: for a finite, sharp, force-dominated stretched-horizon stress pulse, metric continuity selects a force-type source rather than a displacement-type source, producing a quadrature Green-function response. This closes the intrinsic phase only under the stated source condition; it is not a claim of detection and not yet a full Kerr-source theorem. The framework then separates the remaining phase contributions. The radial projection phase is shown, within compact near-horizon source-profile families, to be mainly controlled by source location rather than arbitrary profile shape, and to be absorbed into the same remnant-spin dependence under a common stretched-horizon-thickness premise. The propagation phase, however, is physical and large. It cannot be removed by simply redefining each event’s time coordinate without losing the common clock needed for coherent stacking, nor can it be measured directly before the relay burst is individually detectable. The conclusion is that the detector-facing record-relay problem has three layers: a closed coordinate layer, a current amplitude-constraint layer, and a future coherent-search layer. Paper 24 supplies the closed time-frequency coordinate. Paper 25 places that coordinate on real H1 strain and rules out the strong-amplitude detector-facing interpretation. The remaining low-amplitude regime is not dismissed, but deferred to a spin-resolved coherent search requiring substantially sharper remnant-spin information, plausibly in the Einstein Telescope and Cosmic Explorer era. The paper therefore reframes the black-hole record-relay signature from a qualitative late-burst idea into a falsifiable detector-facing program. It provides a real-strain null result, an injection-recovery amplitude constraint, a protected statistical pipeline, a conditional quadrature phase bridge, a radial-projection reduction, and a spin-precision gate for future coherent tests. It explicitly does not claim discovery, empirical confirmation of Paper 24, or a formal Bayesian posterior upper limit. Keywords: black-hole information, record-relay, gravitational waves, ringdown, quasinormal modes, GWTC, H1 strain, matched filtering, injection recovery, time-slide background, phase-marginalized stacking, coherent stacking, quadrature phase, horizon stress, Kerr perturbations, spin precision, Einstein Telescope, Cosmic Explorer.