Public Environment/Covariance Bridge-Partial Gates in CHC

QAC-VP2 is a bounded public-data companion evaluation layer. Its purpose is not to prove a universal compensation theorem, but to ask whether the previously opened simulation/observation proxy analysis can be augmented by environment information and an explicit interval object. The admissible interpretation is therefore narrow: quote QAC-VP2 states a bounded public TNG-environment / MaNGA-proxy covariance bridge. It is not a finite-window closure, not a theorem-level QAC proof, not a rotating-Universe result, and not a full structure-formation model. quote This restriction is essential because QAC requires a fixed environment family, a proxy-sign convention, a shell/web/host comparison prescription, an observable-family definition, and a covariance or uncertainty object before stronger finite-window claims can be made. The present record partially states those prerequisites, but it does not close them all.

The simulation analysis uses IllustrisTNG public data access. The IllustrisTNG API documents public-access requests and object-level subhalo endpoints that expose flattened Subfind group-catalog values as public API fields [citation]. The evaluated route also uses a public TNG DisPerSE cosmic-web listing and a snapshot-99 HDF5 object. TNG supplementary catalog documentation identifies DisPerSE-style cosmic-web distance fields such as subhalo identifiers and distances to minima, saddles, nodes, and skeleton/filament structures [citation].

The observational analysis uses MaNGA DR17 products. MaNGA DR17 is the final MaNGA data release, and the MaNGA Data Analysis Pipeline provides stellar kinematics, emission-line properties, and spectral indices from the MaNGA data cubes [citation]. The DAP data model distinguishes three-dimensional calibrated datacubes from two-dimensional maps of derived quantities, which fixes the observational analysis here as a projected-proxy analysis [citation]. The SDSS DR17 value-added-catalog page also lists GEMA-VAC as a Galaxy Environment for MaNGA catalog providing environment characterisations for the MaNGA DR17 sample [citation]. In the present record the GEMA listing surface is available, but the GEMA table is not parsed, so observational environment assignment remains a follow-up target.

The declared QAC-VP2 gate has five operational stages.

- Source identification. TNG subhalo proxy source, TNG cosmic-web environment source, MaNGA MAPS/DAP source, and MaNGA environment source or listing surface must be identified or explicitly marked not parsed. - Identity alignment. TNG subhalo identifiers must be joinable to cosmic-web distance fields. MaNGA plate-IFU or MaNGA identifiers must be available for observational proxy rows. - Environment family. Environment bins are fixed before bridge evaluation. In this evaluation the TNG side is binned by filament distance, while the MaNGA side remains unbinned because the GEMA table is not parsed. - Proxy boards. The TNG analysis computes environment-binned radial spin-projection proxies. The MaNGA analysis computes projected line-of-sight kinematic proxies from MAPS files. - Covariance or interval object. A structured interval object must be produced. Here the method is bin-level standard error.

The final classification is only allowed to be one of the bounded companion-result labels. Labels such as QAC-FINITE-WINDOW-CLOSURE or QAC-THEOREM-LEVEL-CLOSURE are disallowed by construction.

The final public TNG analysis succeeds. The record reports the following simulation-side objects:

- public TNG DisPerSE listing endpoint: TNG-COSMIC-WEB-PUBLIC-SOURCE-SATISFIED; - snapshot-99 DisPerSE HDF5: identified from the public source and parsed; - parsed TNG cosmic-web board rows: 4,371,211; - TNG subhalo/environment join rows: 2,000; - TNG environment proxy: TNG-ENV-PROXY-CHECK-SATISFIED.

The TNG environment bins used in the final board are summarized in Table reference.

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

The MaNGA observational analysis returns five projected proxy rows from MAPS files. The diagnostic summary lists MANGA-ENV-PROXY-CHECK-SATISFIED, with five MAPS files found, five usable rows, and no parsed GEMA table present. The absence of a parsed GEMA table is not hidden: it is the principal reason why the result remains partial rather than a dual-side environment-resolved bridge.

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

The covariance object is a partial interval object. It has status QAC-VP2-COVARIANCE-OBJECT-PARTIAL. The bridge interval is summarized as

\bar p_{\rm MaNGA}=0.0134997,
\qquad
\bar p_{\rm TNG}=-0.0000838,

\Delta=0.0135835,
\qquad
\sigma_{\rm comb}=0.0761893,
\qquad
z_{\rm stress}=0.178286.

This small standardized stress does not constitute a physical closure. It records that the declared partial interval board does not produce a proxy-level contradiction in the available bridge object.

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

The companion source summary is the VP2 environment/covariance source-basis summary. It identifies the gate summary, cosmic-web parse summary, environment-proxy summary, covariance object, and public-source basis used for the declared partial label. The route type is an authorized public-data environment construction with a public-source basis check. Admissible interpretation: QAC-VP2-SIMOBS-COVARIANCE-BRIDGE-PARTIAL on the declared TNG environment and small MaNGA proxy handoff surfaces. Excluded interpretation: observational-environment completion, finite-window QAC closure, theorem-level compensation, rotating-Universe evidence, or full structure-formation modeling.

The final gate returns

\boxed{\texttt{QAC-VP2-SIMOBS-COVARIANCE-BRIDGE-PARTIAL}}.

The declared partial-level support conditions are satisfied: source check, environment partial, simulation/observation environment-proxy surface, and covariance partial. The public-source boundary is PUBLIC-SOURCE-ONLY; data-access mechanics are outside the manuscript claim.

This classification is deliberately conservative. The label SIM/OBS covariance bridge partial has the following bounded content: quote The TNG simulation side has a declared cosmic-web environment surface and environment-binned proxy board; the MaNGA side supplies a small projected observational proxy board; and the companion record supplies a structured partial interval object. The MaNGA GEMA environment table is not parsed in this record, so the bridge is not a full dual-side environment closure. quote

The present result remains a bounded simulation--observation covariance-bridge partial. A scientifically distinct follow-up would not repeat the same calculation with more objects; it would construct the missing observational-environment analysis by acquiring and parsing the MaNGA GEMA-VAC table, joining GEMA environment rows to a larger pre-registered MAPS sample, and building a dual-side environment-binned covariance object. Such a follow-up would be assessed as a separate observational-environment covariance study, not as a revision of the present VP2 classification.

If one compensation law applies across environments, its parameters generate a block response map whose rows contain the environment-specific observables. A common parameter shift moves every block through the same column space; contrasts in the left null space must vanish to first order. This supplies a direct test of environmental transportability rather than a comparison of separately calibrated trends.

Environment-specific nuisance coefficients enlarge the column space and may remove all such contrasts. They must be declared before the bridge is evaluated and counted in the response rank. A successful result therefore requires nonzero constrained dimension after nuisance projection, a fixed covariance model, and agreement of held-out environmental contrasts without changing the compensation map.

The closure test for the environment-covariance 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 within- and cross-environment angular-momentum contrasts. Let $a$TeXa range over the independent constitutive inputs comprising environment labels, block covariance, bridge parameters, and selection 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 one block response map and full cross-environment covariance are fixed before null contrasts are formed.

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 ignoring cross-block covariance or refitting each environment invalidates the claimed transport test. Failure of that condition therefore rejects the proposed microscopic closure before parameter estimation can be counted as evidence for it.

QAC-VP2 reaches its intended bounded construction target. It demonstrates that public simulation data can be connected to a cosmic-web environment board, that a small public MaNGA MAPS projected-proxy board can be evaluated within the declared bridge record, and that a structured partial covariance object can be formed. The final classification is QAC-VP2-SIMOBS-COVARIANCE-BRIDGE-PARTIAL. The result is a bounded companion record; it is not a finite-window QAC closure, not a theorem-level angular-momentum compensation closure, not a rotating-Universe result, and not a full 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.