Public Simulation-Observation Proxy Bridge Gates in CHC

The QAC sector is read here as a finite-domain angular-momentum compensation formalism with declared proxy families. A public-data companion record may test whether a proxy object can be identified, computed, and reported under a fixed sign convention. Such a record does not by itself close a finite-window environmental compensation theorem.

The present companion record has two active analyses. The observational analysis is a projected MaNGA analysis; it uses stellar-kinematic MAPS products only to build a line-of-sight proxy. The simulation analysis is a TNG public API analysis; it uses a bounded object-level subhalo sample only to build a minimal radial spin-projection proxy. The construction is rejected as a finite-window closure unless the environment family, sign convention, shell/web/host prescription, observable-family definition, and covariance object are all supplied under one fixed comparison convention. That stronger object is not supplied here.

MaNGA observational surface..

SDSS MaNGA DR17 is the final MaNGA data release and includes the complete MaNGA survey data products. The DAP provides stellar kinematic maps, including stellar velocity and dispersion maps, which are suitable for a projected line-of-sight proxy analysis but not for a three-dimensional angular-momentum closure [citation].

IllustrisTNG simulation surface..

IllustrisTNG publishes simulation snapshots, group catalogs, merger trees, and supplementary data products. The official specifications describe FoF halo and Subfind subhalo group-catalog products. The API documentation also defines object-level subhalo endpoints and the mapping of group-catalog vector fields into flattened returned quantities [citation]. These data surfaces are adequate for a bounded simulation proxy board. They are not, without a complete field-subset source and environmental prescription, a finite-window compensation closure.

For the observational analysis, a projected proxy is computed from the MaNGA velocity-map surface according to the declared proxy rule. The companion record lists this object as a projected line-of-sight proxy only:

\Pobs = \Jproxy^{\mathrm{MaNGA}}_{\mathrm{LOS}} .

For the simulation analysis, the object-level fallback uses the subhalo position and spin vector to define a bounded radial spin-projection proxy,

\Psim_i = \frac{\vect S_i\cdot \vect r_i}{\|\vect S_i\|\,\|\vect r_i\|},

for each public subhalo object for which the returned values are finite. This proxy is a diagnostic scalar board, not a halo-web compensation law.

The companion gate classification is reproduced in Table reference. The final status is QAC-BRIDGE-PARTIAL. This label means that both a public observational proxy analysis and a public simulation proxy analysis were evaluated under the declared non-claim boundary. It does not mean that the proxy families have been matched by a calibrated covariance object or that a finite environmental compensation law has been established.

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

The MaNGA projected-proxy analysis returns three finite rows. The TNG primary group-catalog field-subset route does not yield a complete public group-catalog field-subset surface on the declared source boundary. It is therefore not treated as supplying a completed group-catalog HDF5 data surface. The bounded fallback route then retrieves one hundred TNG100-1 snapshot-99 subhalo objects and returns one hundred finite radial spin-projection rows. The final gate classification records QAC-BRIDGE-PARTIAL.

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

The companion source summary identifies the primary gate classification, the source summaries, the declared MaNGA/TNG sample plans, and the public-source summaries used for the proxy evaluation. The route type is a public-data proxy evaluation with an explicitly incomplete group-catalog field-subset route and an object-level TNG fallback. Admissible interpretation: QAC-BRIDGE-PARTIAL on the declared MaNGA/TNG proxy surfaces. Excluded interpretation: finite-window QAC closure, theorem-level angular-momentum compensation, rotating-Universe evidence, total cosmic angular-momentum measurement, or a full structure-formation model.

The present result must be re-evaluated if any of the following occurs:

- the TNG object-level fallback sample is found to contain restricted-access source dependence or irreproducible public-source boundaries; - the MaNGA projected proxy row construction is found to use an undeclared sign convention; - the group-catalog field-subset route is later completed and changes the simulation proxy board materially; - a covariance object is supplied and the bridge classification is re-evaluated; or - the public record is read as a rotating-universe, total-angular-momentum, or finite-window closure claim.

A scientifically distinct follow-up record would require a completed TNG group-catalog field-subset acquisition, a larger preregistered MaNGA sample, an explicit shell/web/host environmental prescription, and a covariance object. Such a follow-up would be assessed separately and is not part of the present VP0 classification.

A simulation--observation bridge is predictive only if a predeclared parameter vector maps simulation summaries into more observational outputs than its local rank. For sensitivity matrix $S$TeXS, the vectors in $\ker S^{\mathsf T}$TeX\ker S^{\mathsf T} define first-order bridge residuals that are insensitive to admissible recalibration. These residuals test the bridge as a whole rather than agreement of any one proxy.

A separate calibration for every simulated halo, viewing angle, or observed environment can make the response full rank. The local image is then open and the bridge imposes no equality constraint. The partial-result classification should therefore preserve the frozen parameter count, covariance, and sensitivity rank, and should reserve at least one observable family or environment for a transverse test.

The closure test for the simulation--observation bridge 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 paired simulation and observational angular-momentum summaries. Let $a$TeXa range over the independent constitutive inputs comprising simulation proxy, observational proxy, matching variables, and bridge nuisance.

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 bridge is fixed on matched calibration objects and retains at least one unused transverse contrast.

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 full-row-rank proxy map is a translation device rather than a test of compensation dynamics. Failure of that condition therefore rejects the proposed microscopic closure before parameter estimation can be counted as evidence for it.

QAC-VP0 establishes a reproducible public simulation--observation proxy bridge for the CHC-QAC sector. The observational MaNGA analysis returns QAC-OBS-PROXY-CHECK-SATISFIED; the bounded TNG fallback analysis returns QAC-SIM-PROXY-CHECK-SATISFIED; and the combined bridge evaluation returns QAC-BRIDGE-PARTIAL. The result states a public proxy surface for QAC but does not claim finite-window compensation closure, covariance-object closure, shell/web/host closure, theorem-level QAC closure, global rotation, or total cosmic angular momentum.

Data and code availability..

This companion manuscript uses public observational, simulation, mock-observable, or supplementary bridge materials 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.