Mass-Weighted Observable-Family Bridge Gates in CHC

QAC concerns quasi-local angular-momentum compensation on declared cosmological domains. In this companion public-data record, the target is deliberately narrower: a public-data bridge between a mass-weighted TNG mock-IFU proxy and a mass-weighted MaNGA observational proxy. The record is evaluated only as a bounded public-data source basis.

The value condition for VP6 was that it must not be a mere enlargement of VP5 sample size. It had to introduce a genuine mass-weighted observable operator. The accepted evaluation satisfies that condition: TNG uses stellar-particle coordinates, velocities, and masses from public-access cutouts, while MaNGA uses explicit Pipe3D mass-like planes or a declared mass-to-light plane together with the DAP STELLAR_VEL map. Unlabeled Pipe3D planes are not promoted to mass-map proxies.

The simulation-side input is the IllustrisTNG public data release. TNG releases snapshots, group catalogues, subhalo catalogues, merger trees, and supplementary catalogues; the API supports subhalo-level access and snapshot cutout queries for selected particle fields [citation]. The observational input is SDSS-IV MaNGA DR17. MaNGA DAP MAPS files provide two-dimensional derived maps, including stellar kinematics, while the Pipe3D value-added catalogue provides stellar-population dataproducts, including per-galaxy/datacube FITS products and stellar-population property planes [citation]. FIREFLY is noted as an alternative mass-map source, but it is not required for the present VP6 result [citation].

The VP6 gate sequence is:

- Source check. Verify that TNG cutout, MaNGA Pipe3D, and MaNGA DAP/MAPS surfaces are present or identifiable. - TNG mass-weighted mock-IFU proxy. From stellar-particle coordinates, velocities, and masses, compute a mass-weighted projected proxy. - MaNGA mass-map proxy. Combine declared Pipe3D mass-like or mass-to-light planes with MaNGA DAP STELLAR_VEL on the declared map support. - Bridge stress. Compare the TNG and MaNGA proxy boards through the declared summary stress object. - Non-claim and public-source boundary check. Confirm that only public-source surfaces support the displayed classification and that no finite-window or theorem-level closure is claimed.

Table reference summarizes the analysis status. Table reference records the bridge stress object.

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

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

The MaNGA mass-map validation records are intentionally conservative. For 7443-12703 and 8138-12704, the record uses Pipe3D SSP HDU 1, plane 18, with explicit Mass_ssp file labels and DAP STELLAR_VEL. For 8485-1901, the record uses Pipe3D SSP HDU 1, plane 17, identified as an average stellar mass-to-light-ratio plane, again paired with DAP STELLAR_VEL. The valid-pixel counts are 2997, 3218, and 503, respectively. This is sufficient for the declared bounded partial-bridge gate, but not for a population-level or global inference claim.

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

The public source basis for VP6 identifies the declared gate summary, the mass-weighted TNG mock-IFU summary, the MaNGA mass-weighted proxy summary, the MaNGA mass-map source summary, and the non-claim boundary. The route type is a public-data mass-weighted observable-family bridge. Admissible interpretation: QAC-VP6-MASSWEIGHTED-OBSERVABLE-BRIDGE-PARTIAL on explicitly declared mass-weighted TNG and MaNGA surfaces. Excluded interpretation: finite-window QAC closure, theorem-level compensation, rotating-Universe evidence, total cosmic angular-momentum measurement, full structure-formation modeling, or promotion of unlabeled Pipe3D planes to mass maps.

The record reports

\boxed{\texttt{QAC-VP6-MASSWEIGHTED-OBSERVABLE-BRIDGE-PARTIAL}}.

The result states a mass-weighted observable-family bridge that was not present in VP5. It should not be read as a finite-window compensation closure. It should not be read as theorem-level angular-momentum compensation, rotating-Universe evidence, or a full structure-formation model. The stress value is small in the declared summary record, but the sample sizes are deliberately small and the result remains a partial construction surface.

Under the declared public-data criterion, QAC-VP6 supplies a bounded mass-weighted observable-family bridge partial based on a different observable object rather than on sample thickening. Further public-data extensions that merely increase the number of TNG cutouts, MaNGA MAPS files, Pipe3D products, or FIREFLY products should be treated as robustness analyses within the same gate family, not as a separate gate-family result. A stronger empirical claim would require a genuinely new missing object, such as an independently calibrated finite-window covariance closure or a same-window environment--observable calibration object. No such object is identified here.

Mass weighting is part of the observation map and must not become an independent response law for each reported quantity. With one frozen weighting prescription, the sensitivities of the mass-weighted angular momentum, rotation support, and related summaries form a common matrix $S$TeXS. Its left null space supplies the combinations that a shared compensation parameterization cannot change.

Changing the mass definition or radial weighting after seeing those combinations adds nuisance directions and may eliminate the test. The test should therefore propagate uncertainty in the declared weighting through the covariance while keeping its functional form fixed. Support for the bridge requires at least one nonzero transverse direction and successful prediction of that direction on an unused observable or environment.

The closure test for the mass-weighted observable 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 mass-weighted angular momentum and its environmental contrasts. Let $a$TeXa range over the independent constitutive inputs comprising stellar-mass weights, light-to-mass conversion, selection, and kinematic 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 mass weighting is fixed as part of the observation operator before calibration and null-space evaluation.

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 post hoc weights act as additional functional nuisance directions. Failure of that condition therefore rejects the proposed microscopic closure before parameter estimation can be counted as evidence for it.

QAC-VP6 records a mass-weighted observable-family bridge on the declared public-data surfaces. It evaluates five simulated and three observed objects. The resulting $z=-0.2045$TeXz=-0.2045 is not evidential because these effective sample sizes are too small to characterize either population or the proxy covariance, and the construction was not an independently powered hypothesis test. It demonstrates that the mass-weighted operator can be evaluated on both data types; it does not test finite-window compensation. The declared final classification is QAC-VP6-MASSWEIGHTED-OBSERVABLE-BRIDGE-PARTIAL.

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.