FRC-VP2: CHIME Catalog 1 Injection-Selection Surface Gates in CHC

FRC-VP2 is a companion public-data record for the CHC-FRC source-count diagnostic. It is deliberately narrower than a population-inference paper. The goal is not to infer a universal FRB luminosity function, all-sky rate law, or propagation correction. The goal is to determine whether the declared CHIME Catalog 1 count-law window remains selection-diagnostic when a public injection-response surface and exposure-map surface are joined to the count-law board.

The record is useful only because it opens a genuinely new surface relative to catalog-only and exposure-assisted stress gates. A mere repetition of the CHIME source-count slope, a fluence-threshold variant, or a repeater-policy sweep would not justify a distinct selection-response diagnostic. FRC-VP2 is therefore restricted to the injection-selection response surface: CHIME Catalog 1 events, live injected events, the full synthetic HDF5 injection set, and exposure maps must all be available and processed before the declared VP2 label can be considered.

The companion record uses four public-data surfaces, read through the CHIME/FRB open-data release route where applicable [citation].

- The CHIME/FRB Catalog 1 table in CSV or FITS form. The CHIME/FRB open-data documentation states that catalog data are available in both formats and gives direct examples for reading the table columns [citation]. - The live-injection data set. CHIME/FRB documentation states that the injection data set used for Catalog 1 includes a live-injected subset of roughly 85,000 events, stored as a pickle / pandas DataFrame [citation]. - The full synthetic-injection HDF5 data set. The same documentation states that the full set consists of 5 million synthetic FRBs and describes the HDF5 keys used in the data set [citation]. - The CHIME/FRB exposure map inputs. The exposure documentation provides NPZ exposure-map inputs and example code for rendering the exposure surface through the CHIME/FRB open-data package or through explicit HEALPix handling [citation].

The public result statement identifies the public input surfaces and the source conventions used for the declared gate. Large public inputs remain external public scientific sources; the manuscript uses only the declared summaries and public-source boundaries for the stated classification.

The public-source and diagnostic-summary record is: center

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The VP2 gate sequence is as follows.

FRC-R0: source basis and source summary..

The record identifies the catalog, live-injection, synthetic-injection, and exposure-map source bases used for the declared stress reading. In the present evaluation, all four required surfaces are represented by public-source basis records.

FRC-R1: event-selection policy reproduction..

Catalog rows are filtered by the declared policy. The diagnostic summary lists 600 raw catalog rows, 554 policy-filtered rows, 464 primary non-repeater rows, and 234 high-fluence fit rows above the declared fluence threshold.

FRC-R2: injection recovery and response-surface construction..

The primary detection policy is

\mathrm{bonsai\_snr} > 9
\quad\text{and}\quad
(\mathrm{l2\_rfi\_grade} > 7\;\text{or}\;\mathrm{bonsai\_snr}>30).

The analysis bins the live-injection and full-synthetic surfaces over fluence, dispersion measure, pulse width, and scattering-time coordinates. The surface contains 969 declared cells, 350 live-supported cells, 969 full-synthetic cells, and 676 to-inject cells.

FRC-R3: exposure/selection-weighted count-law residual..

For catalog events in the declared high-fluence window, the analysis computes an exposure/selection-adjusted cumulative count-law board. The output slope is a diagnostic of the declared CHIME Catalog 1 window only; it is not a global FRB population law.

FRC-R4: repeater-policy sensitivity..

The analysis separates the primary non-repeater board from all-event and repeater-sensitivity surfaces. Repeater treatment is not promoted to a repeater/non-repeater population theorem.

FRC-R5: classification boundary..

The final label is assigned by the response-surface and residual boards under the non-claim frontier. In this evaluation, the injection-efficiency coefficient of variation exceeds the declared stress threshold; the result is therefore a stress classification.

The primary result returns the following source summary.

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The declared stress threshold for the efficiency coefficient of variation is 0.3. Since

0.7211478539286401 > 0.3,

the response-surface gate records a selection stress. This is not a failure of acquisition or evaluation; it is a substantive result indicating that the declared CHIME Catalog 1 response surface is strongly structured over the declared bins.

The exposure/selection-weighted count-law residual gives:

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The final classification is therefore

\boxed{\texttt{FRC-SELECTION-STRESS}}.

The companion source summary identifies the declared injection-selection stress summaries, source-surface statement, and selection configuration used for the public-source replay reading. center

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center These entries identify the public data surfaces used for the bounded selection-stress gate. They do not strengthen FRC-SELECTION-STRESS into a pass label.

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The stress label is the correct conservative reading. FRC-VP2 successfully opens the bounded injection-selection response-surface analysis, but the response surface is sufficiently nonuniform that a simple Catalog 1 source-count slope cannot be transported as a selection-free count-law reading. The result supplies bounded public-data support for the FRC selection-response analysis by replacing a generic selection caution with an evaluated public-data selection-response board.

The resulting classification is quote FRC-VP2 returns a public CHIME Catalog 1 injection-selection stress result. The full synthetic injection set, live-injected subset, exposure maps, and catalog board are all available and processed. The high coefficient of variation in the injection-efficiency surface triggers the declared selection-stress label. This bounds the Catalog 1 source-count diagnostic and does not imply a global FRB population law or a full CHIME selection-function closure. quote

The following interpretations are explicitly disallowed:

- global FRB population law; - luminosity-function closure; - DM-to-redshift theorem; - repeater/non-repeater population theorem; - cross-survey universal rate law; - CHC propagation-correction detection; - full CHIME/FRB selection-function closure.

The injection-derived selection surface must be carried into the source-count law through one frozen parameter map. Let the binned completeness, exposure, and count predictions form an $m$TeXm-component vector with common sensitivity matrix $S$TeXS. Every $w\in\ker S^{\mathsf T}$TeXw\in\ker S^{\mathsf T} gives the first-order restriction $w^{\mathsf T}\delta y=0$TeXw^{\mathsf T}\delta y=0. These residuals test the joint selection--population construction rather than any single fitted histogram.

A selection surface with bin-wise nuisance amplitudes may attain full row rank and then imposes no local equality constraint on the data. Such a surface can still be useful descriptively, but it cannot support a predictive CHC-FRC claim. The declared test therefore requires reporting the frozen nuisance dimension, the numerical rank of $S$TeXS, and held-out left-null residuals in addition to goodness of fit on the injection sample.

The closure test for the injection selection-surface 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 the multidimensional recovery surface and held-out injection residuals. Let $a$TeXa range over the independent constitutive inputs comprising selection-surface parameters, injected population, recovery classifier, and binning map.

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 the joint sensitivity rank is computed before held-out injections are revealed and the same surface is used throughout.

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 a surface reconstructed with the held-out injections measures interpolation rather than prediction. Failure of that condition therefore rejects the proposed microscopic closure before parameter estimation can be counted as evidence for it.

FRC-VP2 is a successful external-data construction of the injection-selection response-surface analysis for CHC-FRC. It is successful because it uses the catalog, live-injection, full synthetic-injection, and exposure surfaces expected by the declared companion record. It is a stress result rather than a pass result because the injection-efficiency coefficient of variation exceeds the declared threshold. The final classification is

\boxed{\texttt{FRC-SELECTION-STRESS}}.

The result remains a bounded public-data stress record. It does not motivate a stronger selection-response diagnostic claim unless a genuinely new public selection surface becomes available, such as an injection-calibrated Catalog 2 response surface [citation] or a cross-survey response surface with comparable injection/exposure products.

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.

Funding and competing interests..

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