Public-Data Expansion and Covariance-Prep Proxy Gates in CHC

QAC-VP1 tests whether the public-data observation proxy surface can be expanded beyond the initial VP0 bridge partial while preserving the VP0 simulation fallback as the declared simulation-side support. The companion record remains within a proxy-gate interpretation. It does not assert three-dimensional observational angular momentum from MaNGA alone, does not identify a universal compensation mechanism, and does not assign a theorem-level QAC closure. The admissible result labels are restricted to public-data acquisition, proxy computation, fallback carry-forward, and covariance-preparation status.

The final assigned labels are center minipage0.95 QAC-VP1-OBS-EXPANDED-PROXY-CHECK-SATISFIED; QAC-VP1-SIM-FALLBACK-CARRIED-FROM-VP0; QAC-VP1-TNG-GROUPCAT-ROUTE-NOT-ADOPTED; QAC-VP1-COVARIANCE-PREP-PARTIAL. minipage center The combined public-data label is QAC-VP1-PUBLIC-DATA-EXPANSION-PARTIAL.

MaNGA observational proxy surface The observational analysis uses SDSS MaNGA DR17 MAPS products. MaNGA DR17 is the final MaNGA data release, and the MaNGA Data Analysis Pipeline provides science-ready products including stellar kinematics, emission-line properties, and spectral-index maps. The relevant DAP output is the MAPS FITS product, with files indexed by plate--IFU and DAP type. The VP1 companion record uses these MAPS products only to construct a projected line-of-sight proxy, not a three-dimensional angular-momentum vector.

For each admitted MAPS object, the companion record computes a signed projected proxy of the schematic form

\lambdaLOS = \frac{\sum_p w_p\,V_p\,R_p\,s_p}{\sum_p w_p\,|V_p|\,R_p+\epsilon},

where $p$TeXp indexes valid spaxels in the declared map window, $V_p$TeXV_p is the stellar line-of-sight velocity readout, $R_p$TeXR_p is a projected radial coordinate, $w_p$TeXw_p is the validity/weight mask inherited from the map window, $s_p$TeXs_p is the declared sign convention, and $\epsilon$TeX\epsilon is a numerical guard. Equation reference is a projected proxy definition only.

TNG simulation proxy surface The simulation analysis uses IllustrisTNG public data. IllustrisTNG provides snapshots, group catalogs, subhalo catalogs, merger trees, and supplementary products for the public TNG simulations. In the declared VP1 diagnostic surface, the group-catalog retry does not supply a completed public group-catalog HDF5 field object for the declared route. The VP1 declared diagnostic surface records QAC-VP1-TNG-GROUPCAT-ROUTE-NOT-ADOPTED and does not claim successful full group-catalog HDF5 field acquisition.

The simulation support used in VP1 is the object-level TNG fallback board carried forward from VP0. For each admitted subhalo object in that fallback board, the companion record computes a radial spin-projection proxy

\lambdaSIM = \frac{\mathbf{S}\cdot\mathbf{r}}{\|\mathbf{S}\|\,\|\mathbf{r}\|+\epsilon},

where $\mathbf{S}$TeX\mathbf{S} is the subhalo spin-vector readout and $\mathbf{r}$TeX\mathbf{r} is the position vector in the declared simulation coordinate convention. This is an object-level public simulation proxy. It is not a full web/void/host environmental closure.

MaNGA expanded observational analysis The expanded MaNGA request targeted fifty MAPS objects. All fifty rows produced finite projected-proxy values. The resulting observational proxy board is summarized in Table reference.

Figure or table content is omitted from the web reader; use the canonical manuscript for the exact object.

TNG group-catalog retry and object-level fallback The declared VP1 group-catalog retry does not supply a completed public group-catalog HDF5 field object for the declared route. The declared VP1 diagnostic surface therefore does not support a new five-hundred-object simulation expansion label. The simulation support used by VP1 is the VP0 TNG object-level fallback board. Table reference summarizes the carried-forward simulation proxy board.

Figure or table content is omitted from the web reader; use the canonical manuscript for the exact object.

Covariance-preparation board The covariance-preparation board compares the expanded MaNGA projected proxy summary with the carried-forward TNG fallback proxy summary without asserting a common physical covariance model. It records

\Delta\bar{\lambda} = \bar{\lambda}_{\rm MaNGA}-\bar{\lambda}_{\rm TNG}
=0.05944941755721009,

\Delta f_{+} = f_{+,\rm MaNGA}-f_{+,\rm TNG}=0.05999999999999994.

This constitutes QAC-VP1-COVARIANCE-PREP-PARTIAL. It prepares a comparison surface for later covariance-object work, but it does not close a joint uncertainty model.

The companion record passes the expanded observational proxy analysis and carries forward the VP0 simulation fallback for the simulation-side support. It records the declared TNG group-catalog retry as not supplying a completed public group-catalog HDF5 field object for that route. It also prepares a covariance board over the expanded MaNGA proxy and the carried-forward TNG fallback. The final classification is

\boxed{\texttt{QAC-VP1-PUBLIC-DATA-EXPANSION-PARTIAL}}.

This classification is deliberately bounded. It means that the public MaNGA proxy surface has been expanded and compared to the carried-forward VP0 TNG fallback surface. It does not mean that a finite-window angular-momentum compensation law has been empirically closed.

Figure or table content is omitted from the web reader; use the canonical manuscript for the exact object.

The companion source summary identifies the declared QAC-VP1 public-data expansion surface, the source summaries, the source status, and the companion-source boundary. The route type is a public-data proxy expansion with an incomplete group-catalog public-source limitation on the TNG group-catalog retry. Admissible interpretation: QAC-VP1-PUBLIC-DATA-EXPANSION-PARTIAL on an expanded MaNGA projected-proxy board plus a carried-forward VP0 simulation fallback. Excluded interpretation: finite-window compensation closure, same-window calibrated covariance certification, theorem-level empirical compensation, rotating-Universe evidence, total cosmic angular-momentum measurement, or full structure-formation modeling.

A stronger QAC result requires at least one of the following additional public-data records:

- successful full TNG group-catalog field acquisition or bulk-download reconstruction of the declared field set; - a fixed shell/web/host environment prescription using TNG environment products, including cosmic-web distance catalogs where admitted; - a larger preregistered MaNGA MAPS sample with reproducible selection from DAPall/DRPall; - a covariance or interval object for MaNGA projection errors, TNG sampling variance, and bridge-map uncertainty; - a simulation-to-observation bridge rule that fixes observable-family, sign convention, environment family, and uncertainty propagation before model comparison.

Until those objects are supplied, the present companion record remains a public-data expansion and covariance-preparation partial.

The public companion source summary identifies the public-source summary, source-detail records, processed proxy boards, gate classifications, and non-claim frontier used for the declared VP1 classification. Only public or authorized public-data routes described in the cited sources are used; private or restricted-source material is outside the manuscript claim.

Expanding the public data vector strengthens the theory only when it increases the number of constrained directions rather than the nuisance dimension. With a common QAC response map, the tangent space is the column space of its sensitivity matrix $S$TeXS; statistically meaningful discrepancies lie in the covariance-weighted complement of that space. The number of local equality restrictions is $m-\operatorname{rank}S$TeXm-\operatorname{rank}S.

Covariance preparation must precede inspection of these projected residuals. Adding dataset-specific offsets after expansion can increase the rank by the same amount as the data dimension and leave no overidentification. The analysis therefore reports whether each new block adds an independently testable left-null direction, and classifies a full-rank expanded fit as descriptive calibration rather than stronger support for angular-momentum compensation.

The closure test for the public-data expansion 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 baseline and added public-data summaries. Let $a$TeXa range over the independent constitutive inputs comprising dataset inclusion rule, expanded observation map, nuisance parameters, 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 new data count as theoretical leverage only when they increase the observable dimension faster than the profiled response rank.

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 adding one nuisance per datum enlarges coverage but leaves predictive codimension unchanged. Failure of that condition therefore rejects the proposed microscopic closure before parameter estimation can be counted as evidence for it.

QAC-VP1 extends the public-data proxy support for QAC on the MaNGA observational side. The MaNGA observational analysis now contains fifty finite projected-proxy rows, while the simulation-side support in the declared VP1 diagnostic surface is the VP0 TNG object-level fallback board carried forward under QAC-VP1-SIM-FALLBACK-CARRIED-FROM-VP0. The declared group-catalog retry is QAC-VP1-TNG-GROUPCAT-ROUTE-NOT-ADOPTED, and the covariance-preparation board records comparison statistics between the expanded MaNGA surface and the carried-forward TNG fallback surface. The final result is QAC-VP1-PUBLIC-DATA-EXPANSION-PARTIAL. No finite-window closure, shell/web/host closure, covariance-object closure, total cosmic angular-momentum claim, or rotating-universe claim is assigned.

Funding and competing interests..

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