Mock-IFU Observable-Family Bridge Gates in CHC

QAC-VP0--VP4 progressively established public simulation/observation proxy, environment, covariance, and dual-environment harmonization surfaces. QAC-VP5 asks a different question: can the simulation and observational sides be brought closer to the same observable family? Instead of comparing only catalog-level spin or environment summaries, VP5 takes stellar-particle cutouts from IllustrisTNG and constructs a projected mock-IFU proxy, then compares that proxy family to projected MaNGA DAP/MAPS velocity-map proxies.

The scope is intentionally narrow. The result is a public-data observable-family bridge, not a finite-window QAC closure. It does not claim a theorem-level angular-momentum compensation law, a rotating Universe, total cosmic angular momentum closure, or a full structure-formation model. It also does not claim that the small VP5 sample is representative of the full MaNGA or TNG distributions.

The simulation-side data are TNG stellar-particle cutouts. The TNG public data release provides snapshots, group catalogs, subhalo catalogs, merger trees, and supplementary products, and its API supports public-access data retrieval and cutout-style retrievals for subhalo/snapshot fields [citation]. The observational-side data are MaNGA DR17 DAP/MAPS files. MaNGA DR17 is the final MaNGA release, and its DAP products include stellar kinematics, emission-line properties, and spectral-index maps derived from MaNGA datacubes [citation].

The VP5 gate board is organized as follows.

- V5-R0: TNG cutout acquisition. Fetch a preregistered small set of TNG stellar-particle cutouts and record public-source summaries. Passing label: QAC-VP5-TNG-CUTOUT-SOURCE-CHECK-SATISFIED. - V5-R1: TNG mock-IFU proxy. Project each stellar-particle cutout through the declared mock-IFU observable operator and produce one finite proxy row per cutout. Passing label: QAC-VP5-TNG-MOCKIFU-PROXY-CHECK-SATISFIED. - V5-R2: MaNGA MAPS acquisition. Fetch the declared MaNGA DR17 MAPS files. Passing label: QAC-VP5-MANGA-MAPS-SOURCE-CHECK-SATISFIED. - V5-R3: MaNGA observable proxy. Compute the projected observational proxy from MaNGA MAPS. Passing label: QAC-VP5-MANGA-OBSERVABLE-PROXY-CHECK-SATISFIED. - V5-R4: bridge summary. Compare the simulation and observational projected observable-family proxy boards and classify the bounded bridge.

The record reports all declared VP5 source and proxy labels. The exact final label board is:

- QAC-VP5-TNG-CUTOUT-SOURCE-CHECK-SATISFIED; - QAC-VP5-TNG-MOCKIFU-PROXY-CHECK-SATISFIED; - QAC-VP5-MANGA-MAPS-SOURCE-CHECK-SATISFIED; - QAC-VP5-MANGA-OBSERVABLE-PROXY-CHECK-SATISFIED; - QAC-VP5-MOCKIFU-OBSERVABLE-BRIDGE-PARTIAL.

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

The bridge stress is small in standardized units, while the deliberately tiny sample restricts the classification to a partial observable-family bridge. The simulation board contains five rows, and the observational board contains three rows. The result therefore establishes that the declared observable-family operators can be evaluated on both public data surfaces and compared under the declared partial bridge, not that QAC finite-window compensation has been empirically closed.

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

The public source basis for VP5 identifies the declared gate summary, TNG mock-IFU projection summary, MaNGA observable-proxy summary, public-source basis, source summaries, and non-claim boundary. The route type is a public-data mock/proxy observable-family bridge. Admissible interpretation: QAC-VP5-MOCKIFU-OBSERVABLE-BRIDGE-PARTIAL on the declared TNG stellar-particle cutout and MaNGA MAPS surfaces. Excluded interpretation: representative population inference, finite-window QAC closure, theorem-level compensation, rotating-Universe evidence, or full structure-formation modeling.

The TNG cutout and MaNGA MAPS public-source surfaces are large external scientific inputs. The companion source summary distinguishes the processed diagnostic boards used in the label from the larger external source surfaces. The scientific label uses only the declared processed boards and public-source boundary conditions.

The next valuable step is not to repeat the same comparison with only more rows. A larger sample would be useful as a robustness check, but it would thicken an existing analysis rather than supply a new object class. A genuinely new follow-up object is a mass-weighted observable bridge. This would combine MaNGA Pipe3D or FIREFLY spatially resolved stellar-population/mass maps with MaNGA DAP velocity maps, and compare them to mass-weighted projected TNG stellar-particle cutout proxies. Such a follow-up record would test whether the observable-family bridge remains stable after replacing light/velocity-style proxies with explicitly mass-weighted projected observables.

The mock-IFU bridge is identifiable only when its shared physical parameters control a higher-dimensional family of projected kinematic observables. The response Jacobian determines which perturbations can be produced by refitting; left-null combinations of velocity, dispersion, and angular-momentum summaries are the parameter-free first-order predictions.

Pixel-wise or observable-wise transfer coefficients can saturate the IFU data rank and make every nearby map reproducible. Such a bridge validates an interpolation procedure, not a common compensation law. The analysis therefore freezes the point-spread, projection, and mass-weighting maps, counts their nuisance directions, and evaluates residuals in the remaining transverse subspace on mock views not used for calibration.

The closure test for the mock-IFU 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 velocity, dispersion, and angular-momentum maps. Let $a$TeXa range over the independent constitutive inputs comprising mock-IFU forward model, point-spread response, kinematic extraction, 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 complete map cube is generated by one forward model and its joint sensitivity rank is used for testing.

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 pixel- or moment-specific corrections can erase the morphological correlations carrying the prediction. Failure of that condition therefore rejects the proposed microscopic closure before parameter estimation can be counted as evidence for it.

QAC-VP5 reaches QAC-VP5-MOCKIFU-OBSERVABLE-BRIDGE-PARTIAL. The companion record constructs a public-data bridge between five TNG stellar-particle mock-IFU proxies and three MaNGA projected observational proxies. With effective sample sizes five and three and a combined standard error larger than the reported mean offset, the statistic is a software and observable-definition check, not an inferential test of compensation. It does not establish finite-window QAC compensation, theorem-level angular-momentum compensation, rotating-Universe behavior, or a structure-formation model.

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.