CHC-FRC-VP1: Official CHIME/FRB Exposure-Injection Selection-Stress Gates

VP0 establishes a catalog-side CHIME/FRB selection-stress result for FRC. VP1 adds two public selection-control layers: an injection-assisted completeness stress analysis and an exposure-context stress analysis. This analysis reports a declared public-data stress result on the stated CHIME/FRB exposure and injection route. The result may be used in FRC only as declared-window compatibility under visible CHIME/FRB exposure and injection controls.

The CHIME/FRB Open Data catalog tutorial states that Catalog 1 data are available from the official CHIME/FRB website in CSV and FITS formats and gives the Catalog 1 column route, including sky position, exposure columns, SNR, DM, excess-DM proxies, fluence, and exclusion flags [citation]. The First CHIME/FRB Catalog is the Catalog 1 scientific reference used for the public table and the selection-calibration context [citation]. The injection tutorial states that the Catalog 1 injection dataset has two files: a full HDF5 file with five million synthetic FRBs and a pickle/DataFrame file for the subset actually injected into the live CHIME/FRB intensity stream, described as about 85,000 events [citation]. The exposure tutorial gives a Catalog 1 exposure-map route through CHIME/FRB Open Data and points to the exposure data in CANFAR [citation]. The beam-model tutorial describes the Catalog 1 beam model used for analyses and gives the sensitivity-calculation interface [citation]. The injection system paper explains that injections are used to map intrinsic burst properties to expected SNR while accounting for telescope characteristics such as beam model and calibration factors [citation].

The declared VP1 evaluation used the following public data objects: center

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center The larger injection and exposure objects are listed in the companion source summary under the declared official-input objects; their public-source basis is recorded there together with the replay diagnostic summary.

Let $C$TeXC be the official Catalog 1 table and $I$TeXI the official live-injected table. The staged column map is center

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center

For declared fluence quantiles $q\in\{0.5,0.6,0.7,0.8\}$TeXq\in\{0.5,0.6,0.7,0.8\}, define

\epsilon(q)=\frac{\#\{i\in I:F_I(i)\ge Q_q(F_I),\ D_I(i)=1\}}{\#\{i\in I:F_I(i)\ge Q_q(F_I)\}},

where $D_I$TeXD_I is the declared Catalog 1 pipeline detection mask. The primary injection stability score is

S_{\rm inj}=\frac{\operatorname{sd}_{q}\epsilon(q)}{\operatorname{mean}_{q}\epsilon(q)}.

Exposure columns are recorded as exposure-context stress support, not as a reconstructed all-sky selection function.

The declared evaluation returns 84,697 injection rows, 29,641 detected injection rows, and the following efficiency grid: center

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center The efficiency coefficient of variation is

S_{\rm inj}=0.05169329647427263.

The BOUNDED-NULLOVERTURN classification follows from the stability of the injection-efficiency grid.

The catalog exposure-context board is center

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center The catalog exposure summary records 600 rows with positive exposure and total exposure sum 47,923.4 in the staged exposure units of the input map and table. This analysis is an exposure-context diagnostic only.

The replay result reproduces the declared BOUNDED-NULLOVERTURN label. The replay public-source basis is recorded in the cited public references and companion statements and is not part of the scientific claim beyond the declared gate label.

The replay-confirmed official-data evaluation is summarized by declared replay-result, source-configuration, replay-procedure, and public-source basis records retained in the cited public references and companion statements. These records do not strengthen the scientific label beyond .

The assigned VP1 label is

\boxed{\substack{\mathrm{FRC\!\!\!-
VP1:}\ \mathrm{bounded\ exposure\!\!\!-
injection\ stress,}
[-1mm]\mathrm{no\ overturn}}}.

It means that the declared VP0 count/log-shell diagnostic survives this exposure-aware and injection-assisted public-data stress layer under the declared CHIME/FRB Catalog 1 window. It does not mean that the CHIME/FRB selection function is fully reconstructed.

center

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Exposure and injection corrections must enter one shared response map rather than two independently tuned surfaces. If their combined observable vector has dimension $m$TeXm and local sensitivity rank $r<m$TeXr<m, the $m-r$TeXm-r left-null directions are equality tests of the joint correction. They remain invariant under regular rebinning and nonsingular changes of summary coordinates.

A correction with independent coefficients for every exposure--injection cell can attain full row rank and reproduce an open set of outcomes. It then supplies no predictive constraint on the FRB population law. This test therefore requires a predeclared low-rank correction, covariance propagation into the null residuals, and evaluation on cells or catalog summaries not used to select the correction family.

quote \ is a CHIME/FRB exposure-aware, injection-assisted stress result. The evaluation gives \ on 600 catalog rows, 84,697 live-injected rows, and 29,641 detected injection rows; the injection-efficiency grid has coefficient of variation 0.0516933. The result establishes compatibility only within the declared window and controls. It does not close the selection function, infer a luminosity function, assign redshift from dispersion measure, verify a population law, or detect a CHC propagation correction. quote

Data and code availability..

This companion manuscript uses public CHIME/FRB data products and cited public references and companion statements as described in the text. Cited public references and companion statements, where provided, are identified by the companion source summaries cited in the text.

The closure test for the CHIME exposure--injection gates 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 injection recoveries, exposure-corrected counts, and cross-bin contrasts. Let $a$TeXa range over the independent constitutive inputs comprising exposure map, injection distribution, recovery efficiency, and weighting convention.

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 injection and exposure corrections share one finite map whose constrained directions are retained after profiling.

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 independent bin efficiencies saturate the observable rank and leave no catalog-level prediction. Failure of that condition therefore rejects the proposed microscopic closure before parameter estimation can be counted as evidence for it.

Funding and competing interests..

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