BH-VP1: GWTC-3 Tests-of-GR Posterior Diagnostic Gates in CHC

BH-VP1 is a bounded public posterior-comparison diagnostic for CHC-BH1/BH2. Its purpose is to test whether official public LVK/GWTC-3 Tests-of-GR posterior products can be read back as compact-object diagnostic surfaces. The diagnostic comparison does not re-run LVK inference, replace waveform pipelines, reinterpret the LVK likelihood, or infer a microscopic black-hole theorem. It also does not claim a GR violation from diagnostic stress rows.

The admissible interpretation is: quote BH-VP1 uses official public Tests-of-GR posterior diagnostic boards for IMR consistency, ringdown, parametrized deviations, and spin-induced quadrupole tests, with bounded CHC compact-object interpretation. quote

The forbidden readings are: compact-object theorem; black-hole interior closure; quantum-gravity solution; EHT/LVK pipeline replacement; return-kernel theorem closure; or microscopic entropy theorem.

The primary public source is the LVK GWTC-3 Tests of General Relativity posterior release. The public posterior products cover IMR consistency, Lorentz-invariance violation, parametrized tests of GR, an updated ringdown test, and spin-induced quadrupole moment tests [citation]. The LIGO DCC release for P2100456 and GWOSC public records identify the relevant Tests-of-GR source families, event metadata, and parameter-estimation products used for this diagnostic reading [citation]. The published GWTC-3 Tests-of-GR paper reports the corresponding GR-test suite and summarizes the standard interpretation that no evidence for deviations from GR was found [citation].

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The VP1 companion record uses the following gate sequence.

- BH-R0: public-source identification. Required official public posterior source surfaces must be identifiable and tied to the declared diagnostic comparison. - BH-R1: posterior source summary. Public archive/HDF5 readability and parameter maps are recorded. - BH-R2: IMR consistency diagnostic board. IMR posterior coordinates are read back under the declared diagnostic rule. - BH-R3: ringdown diagnostic board. Updated ringdown posterior coordinates are read back under the declared diagnostic rule. - BH-R4: supporting parametrized and spin-induced quadrupole boards. Parametrized deformation and spin-quadrupole posterior surfaces are recorded as diagnostic/supporting boards. - BH-R5: interpretation boundary. All outputs remain diagnostic-only and non-claim boundaries are enforced.

The companion source summary identifies the public-source surfaces listed below and the source state summarized in Table reference. Multi-GB posterior surfaces remain external to the manuscript body; the companion statement identifies the public source metadata needed to interpret the bounded diagnostic. center 1.10

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The diagnostic board labels are listed in Table reference. The IMR board passes the declared IMR consistency diagnostic. The updated ringdown, parametrized, and spin-induced quadrupole boards return diagnostic stress labels. These stress labels identify posterior-comparison sensitivity under the declared rule; they are not interpreted as GR-violation claims.

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The spin-induced quadrupole diagnostic board contains 20 rows, of which 9 are diagnostic-stress rows under the declared diagnostic convention. The comparison treats dQuadMonS as a deviation parameter with GR reference value zero. This convention is only a diagnostic comparison rule and not an LVK reanalysis.

The final companion-record classification is

\boxed{\texttt{BH-VP1-TGR-DIAGNOSTIC-PARTIAL}}.

The label is assigned because the public archive source gate passed, the IMR board received an assigned pass label, the updated ringdown and spin-induced quadrupole boards received assigned diagnostic labels, the parametrized board is present as a supporting stress surface, and the non-claim boundary is explicitly preserved.

This result extends BH-VP0's compact diagnostic surface by adding official GWTC-3 Tests-of-GR posterior products. It does not change BH1/BH2 into theorem-level compact-object papers.

The GWTC-4.0 Tests-of-GR literature includes the O4a overview/general-test, parameterized-test, and remnant-test papers [citation], together with public data-product surfaces for those studies [citation]. This BH--VP1 record nevertheless remains a GWTC-3 posterior-comparison diagnostic record, because its imported object is the official GWTC-3 Tests-of-GR posterior surface. The cited GWTC-4.0 parameter-estimation public release supplies parameter-estimation posterior samples and a catalog PE surface, not a replacement for the declared GWTC-3 TGR v2 posterior diagnostic analysis [citation]. The GWTC-4.0 source summaries do not supply an adopted BH--VP1 object ledger or replace the stated GWTC-3 analysis. Importing the GWTC-4 TGR data products would require a separate object ledger and classification boundary; their availability alone establishes neither waveform-consistency closure, ringdown-residual closure, a GR-violation claim, nor a compact-object theorem for BH1/BH2.

The compact-target extension separates smooth black-hole solutions into winding sectors, but it does not create a generic deviation from general relativity. Zero-winding configurations retain the local canonical scalar equations, while a nonzero winding branch must solve the coupled regularity and boundary-value problem and carry its gradient-energy cost. A posterior deformation parameter without that solution is not a prediction of target topology.

For a declared nonzero branch, the same finite parameter vector must control inspiral, merger, ringdown, and remnant summaries. The joint sensitivity matrix then determines the refittable directions, and its left null space supplies overidentifying posterior residuals. Mode-specific deformation coefficients that raise the response to full rank remove this content and define a broader phenomenological test rather than confirmation of the CHC branch.

The closure test for the GWTC-3 strong-field diagnostics is applied to a dimensionless observable vector $y\in\mathbb R^m$TeXy\in\mathbb R^m formed from fixed reference scales and the declared basket of inspiral, merger, ringdown, and propagation residuals. Let $a$TeXa range over the independent constitutive inputs comprising waveform family, phase branch, source population, and detector calibration.

proposition: Functional saturation, finite closure, and sector admissibility. Suppose the unrestricted prediction map $F:a\mapsto y$TeXF:a\mapsto y is continuously differentiable on a Banach space of constitutive inputs. If $D_aF$TeXD_aF is surjective and has a bounded right inverse at the calibration point, the unrestricted family is locally open in observable space and supplies no nonzero local equality restriction on $y$TeXy. Suppose instead that a single microscopic closure replaces $a$TeXa by finite parameters $\theta\in\mathbb R^p$TeX\theta\in\mathbb R^p, with profiled nuisance coordinates $\eta\in\mathbb R^q$TeX\eta\in\mathbb R^q. If

J=D_\eta F_{\rm cl}D_\theta F_{\rm cl},
 \qquad \operatorname{rank}J=r<m,

then there are $m-r$TeXm-r independent first-order restrictions

w^{\mathsf T}\delta y=0,
 \qquad w\in\ker J^{\mathsf T}.

If the rank is constant locally, these restrictions are tangent to a compatibility manifold of codimension $m-r$TeXm-r. For this sector, the finite closure is admissible only if a nonzero winding branch is admitted only after a regular strong-field solution fixes one joint waveform deformation across events.

proof. Split surjectivity gives a bounded right inverse $R$TeXR with $D_aF\,R=I_m$TeXD_aF\,R=I_m. The Banach-space submersion theorem then makes $F$TeXF locally onto a neighborhood of the calibrated observable vector. Any smooth equality holding throughout that image must therefore vanish on an open set and contributes no model-specific local restriction. Under finite closure, the attainable first-order variations are exactly the column space of $J$TeXJ. Its orthogonal complement is $\ker J^{\mathsf T}$TeX\ker J^{\mathsf T}, whose dimension is $m-r$TeXm-r by rank--nullity, which proves reference. The constant-rank theorem supplies the stated local manifold. The sector condition is necessary because an event-wise phase correction can absorb waveform residuals without testing a field equation. Failure of that condition therefore rejects the proposed microscopic closure before parameter estimation can be counted as evidence for it.

BH-VP1 supplies a bounded public diagnostic record for CHC-BH1/BH2. The public record identifies the official GWTC-3 Tests-of-GR posterior surfaces, assigns IMR, ringdown, parametrized, and spin-quadrupole diagnostic labels, and returns . The assigned status is a companion diagnostic source basis only. It is not an LVK/EHT pipeline replacement, not a GR-violation claim, not a compact-object theorem, and not a quantum-gravity solution.

Data and code availability..

This companion manuscript uses public gravitational-wave catalog and test-summary materials as described in the text. No proprietary observational data are introduced. Cited public references and companion statements, where provided, are identified by the companion source summaries cited in the text.

Funding and competing interests..

No external funding was received for this work. The author declares no competing interests.