CHC-FRC-VP0: Official CHIME/FRB Catalog 1 Selection-Stress Gates

The FRC paper uses fast-radio-burst source counts and logarithmic-shell event-rate diagnostics only inside declared survey windows. For a homogeneous, non-evolving, Euclidean population the cumulative count diagnostic has the null form $\Ngt\propto F^{-3/2}$TeX\Ngt\propto F^{-3/2}, but a CHIME/FRB catalog window requires explicit selection controls before that diagnostic can be interpreted. VP0 therefore asks a limited question: whether a declared evaluation on the official CHIME/FRB public-catalog data object remains compatible with the near-Euclidean count/log-shell diagnostic under visible catalog exclusions, repeater policy, fluence-threshold, excess-DM, and exposure-context controls.

The CHIME/FRB Open Data tutorial states that Catalog 1 data can be downloaded from the official CHIME/FRB website in CSV and FITS formats and also accessed through the open-data Python route [citation]. The same tutorial lists catalog fields including sky position, exposure columns, SNR, DM and excess-DM proxies, fluence, repeater labels, and an exclusion flag. The First CHIME/FRB Catalog reports 536 FRBs detected between 2018 July 25 and 2019 July 1, including 62 bursts from 18 previously reported repeaters, and it reports a cumulative fluence index compatible with the Euclidean value after selection calibration [citation]. The present VP0 paper uses the official public table as the data object for a declared stress evaluation; its row counts below refer to the delivered CSV records and declared prepared windows, not to a new astrophysical census.

The declared evaluation used the official Catalog 1 CSV object center

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A direct raw evaluation without the repeater adapter returned an indeterminate label. The reason is that the official Catalog 1 CSV encodes missing repeater names by the sentinel value -9999. For the declared non-repeater policy, this sentinel is a missing-value marker rather than a physical repeater name.

The accepted sentinel-normalized evaluation converts only the missing repeater sentinel to a blank/NA value before applying the non-repeater policy. It leaves fluence, flux, DM, excess-DM, sky position, exposure, exclusion flag, event identifier, and subburst fields unchanged.

The resolved column map is center

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The accepted VP0 window is produced by four visible steps:

- Drop rows with the declared exclusion flag: 42 dropped, 558 kept. - Require positive finite fluence: 4 dropped, 554 kept. - Apply the non-repeater policy after sentinel normalization: 90 dropped, 464 kept. - Deduplicate by tns_name: 30 dropped, 434 prepared rows kept.

These steps define the primary analysis window. Repeater-policy variants are then evaluated as stress checks, not as replacements for the primary window.

For a declared high-fluence window, the source-count diagnostic fits

\log_{10} \Ngt = a + \alphac \log_{10} F.

The near-Euclidean value $\alphac^{(0)}=-3/2$TeX\alphac^{(0)}=-3/2 is used as a null diagnostic only.

The primary declared analysis returns center

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The fluence-threshold stress board is center

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The repeater-policy stress board is center

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The excess-DM log-shell proxy uses positive $\dmx$TeX\dmx values in six logarithmic bins. It returns counts $[19,66,123,131,76,19]$TeX[19,66,123,131,76,19] and positive-shell coefficient of variation 0.6118281691042171. This is a shell-count proxy only; it is not a redshift inversion or a physical shell-rate measurement.

The optional exposure-context analysis records positive exp_up values for all 434 prepared rows, with p10/median/p90 equal to 11.5, 19.0, and 88.7. This records exposure context but does not reconstruct the CHIME/FRB selection function.

The assigned VP0 label is

\boxed{\texttt{FRC-VP0-CHIME-SELECTION-STRESS-BOUNDED-NULLOVERTURN}}.

The declared reason is declared-window compatibility with the near-Euclidean count/rate diagnostic under visible selection controls. The label is supported by the primary count analysis, three stable fluence-threshold variants, three stable repeater-policy variants, the positive excess-DM shell proxy, and the exposure-context analysis.

The declared public-catalog stress result is identified in the companion source summaries by its source summary, gate configuration, and sentinel stress summary. These records identify the public-catalog route and the declared gate procedure; they do not strengthen the scientific label beyond . The companion source summaries identify the replay record and its public-source basis. These entries identify the public data surfaces used for the bounded gate; they do not strengthen the scientific label beyond .

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center It has only the bounded public-catalog selection-stress compatibility reading.

The selection-stress route constrains CHC-FRC only if the same frozen selection and population parameters control more retained summaries than their response rank. Let $S$TeXS be the Jacobian of the binned completeness, exposure, and count vector. Each $w\in\ker S^{\mathsf T}$TeXw\in\ker S^{\mathsf T} defines a first-order stress residual $w^{\mathsf T}\delta y$TeXw^{\mathsf T}\delta y that cannot be removed by admissible refitting.

Bin-specific nuisance amplitudes can make $S$TeXS full row rank, leaving no overidentifying restriction. Such a result is a selection reconstruction rather than a predictive source-count test. The status statement must therefore be read together with the frozen parameter count, rank estimate, and held-out left-null residuals; changing the selection family after those residuals are inspected starts a new analysis.

quote \ is classified as a declared public-catalog selection-stress result on CHIME/FRB Catalog 1. The declared sentinel-normalized evaluation gives \ with primary slope $-1.35455$TeX-1.35455, primary $R^2=0.974342$TeXR^2=0.974342, and stable declared fluence-threshold and repeater-policy stress boards. The result is a declared-window null-compatibility/stress label only; it is not a global FRB source-count-law verification, a luminosity-function reconstruction, a DM-to-redshift inversion, a full CHIME/FRB selection-function closure, or a CHC propagation-correction detection. 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 selection-stress 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 count and property residuals under the prescribed selection stresses. Let $a$TeXa range over the independent constitutive inputs comprising selection coordinates, threshold model, catalog cuts, and covariance.

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 selection map is frozen before stress contrasts are projected onto its left-null space.

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 retuning the threshold after each stress removes the very directions that test the selection model. 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.