Quasi-local Angular-Momentum Compensation Grammar on Declared Cosmological Domains in the CHC Framework

Cosmic structures carry angular momentum across many scales, yet the largest accessible background appears close to statistically isotropic. Dark-matter haloes acquire angular momentum through tidal torques and subsequently develop mass-dependent spin--filament alignments [citation]. Controlled numerical experiments further show that proximity to a massive filament can strongly alter halo spin and orientation even when halo mass changes little [citation]. Haloes on void shells display statistically significant orientation patterns relative to the void-centric direction [citation]. Supermassive black-hole spin and host-galaxy orientation covary in modern cosmological simulations, and black-hole jets can remain coherent on cosmic-web scales [citation]. Recent observations also indicate that galaxy filaments can carry coherent rotational transport over multi-Mpc scales without implying a rigidly rotating Universe as a whole [citation]. At the same time, cosmic microwave background (CMB) isotropy and late-time vorticity searches strongly disfavor any large rigid rotation of the observable Universe [citation].

The relevant question is therefore whether substantial local angular-momentum observables can be organized on finite domains while the large-scale background remains close to isotropic. The construction below answers this question by replacing any putative global angular-momentum scalar with a declared quasi-local axial charge built from the CHC effective stress tensor. On that basis, the analysis establishes an exact declared-domain balance law, an exact FRW background-neutrality statement, a declared small-background-twist compatibility bound, and a declared compensation-bound theorem for one Hubble-domain visible-reservoir budget. An associated compensation-index corollary then supplies the coexistence reading on branches where that bound is small relative to the declared reservoir magnitudes. A transfer-network organizer then separates transport, storage, compaction, export, and compensation without turning the background itself into a dominant spin reservoir.

Companion public-data records QAC--VP0 through QAC--VP6 attach this declared proxy grammar to progressively more material public surfaces. The observational side uses MaNGA DAP/MAPS stellar-kinematic products and GEMA environment labels; the simulation side uses IllustrisTNG public API, group-catalog, cosmic-web, and stellar-particle cutout surfaces; the mass-weighted observational side uses MaNGA Pipe3D mass-like planes together with DAP stellar-velocity maps. These records are finite proxy and bridge checks only. They do not replace the exact balance theorem, do not close the finite-window compensation theorem, and do not convert local angular-momentum proxy agreement into global rotation or total cosmic angular-momentum evidence.

Only two imported CHC ingredients are used below: the conserved effective stress tensor and the homogeneous phase-flat background branch from the CHC dark-energy sector. Compact objects enter only through exterior spin/orientation reservoir proxies; no horizon equation, interior algebra, or evaporation dynamics is used or derived. The CMB isotropy and vorticity input enters only as an imported nearly-no-rotation admissibility envelope for the declared finite-domain compensation task; no primary-sector CMB transfer function, Boltzmann hierarchy, or likelihood fit is used or rederived here. No new tidal-torque law, no first-principles structure-formation closure, and no black-hole mechanics are proposed. The resulting statement is narrower in scope than a global-rotation or full-formation claim. It yields a declared-domain compensation bound, and only on branches where that bound is small relative to the declared reservoir magnitudes do large local spin observables remain admissible without rigid global rotation. The CMB input remains only as an imported nearly-no-rotation admissibility envelope and is not promoted here to a primary-sector transfer or likelihood claim.

Imported CHC objects

The imported CHC root object is the effective stress tensor

T^{\mu\nu}_{\mathrm{eff}} = T^{\mu\nu}_{\mathrm{m}}+T^{\mu\nu}_{\mathrm{rad}}+T^{\mu\nu}_{\HH},

where $T^{\mu\nu}_{\HH}$TeXT^{\mu\nu}_{\HH} is the phase-sector stress tensor on the admitted CHC branch and obeys local conservation with the material and radiation sectors,

\nabla_{\mu} T^{\mu\nu}_{\mathrm{eff}}=0.

The dark-energy branch supplies a homogeneous late-time phase-flatness regime in which $\HH=\HH(t)$TeX\HH=\HH(t) approaches a convex plateau and $\XiBG\to 0$TeX\XiBG\to 0 on the background branch. Compact objects enter below only through exterior spin and orientation reservoir proxies. No horizon equation, no interior algebra, and no evaporation dynamics are imported or derived here. [citation]

Declared quasi-local domains

definition: Declared quasi-local domain. A declared domain $\Ddom$TeX\Ddom consists of a spacetime world tube with spatial slices $\SigD$TeX\SigD, an outward boundary $\partial\SigD$TeX\partial\SigD, and a declared axial generator $\varphi^\mu$TeX\varphi^\mu appropriate to the symmetry class under consideration. The generator may be exact, approximate, or observationally declared; its status must remain fixed throughout one admitted family.

remark. No unique ADM-like angular momentum for generic cosmological spacetimes is introduced here. The conserved quantity is a quasi-local axial charge on declared domains. This choice is aligned with quasi-local angular-momentum constructions in general relativity and with the quasi-local-horizon program, where angular momentum is attached to finite surfaces and fluxes rather than to teleological event-horizon data [citation].

Declared environment family

definition: Declared environment family. A declared environment family is a tuple

\Fenv=(\mathcal W,\mathcal H,\mathcal V,\mathcal B,R_s,\mathcal S_{\mathrm{sign}}),

where $\mathcal W$TeX\mathcal W is the web/filament classifier, $\mathcal H$TeX\mathcal H the halo catalogue and spin proxy, $\mathcal V$TeX\mathcal V the void catalogue and shell prescription, $\mathcal B$TeX\mathcal B the black-hole spin/orientation proxy, $R_s$TeXR_s the smoothing or environment scale, and $\mathcal S_{\mathrm{sign}}$TeX\mathcal S_{\mathrm{sign}} the fixed sign convention used for all reservoir comparisons on that family. Changing any one of these defines a new family rather than a retuning within the same family.

definition: CHC quasi-local angular momentum. For a declared domain $\Ddom$TeX\Ddom and declared axial generator $\varphi^\mu$TeX\varphi^\mu, the CHC quasi-local angular momentum is

\Jql_{\Ddom}[\varphi]
:=
\int_{\SigD} d\Sigma_{\mu}\, T^{\mu}{}_{\nu,\mathrm{eff}}\,\varphi^{\nu}.

theorem: Declared-domain balance law for the quasi-local axial charge. Let $\Ddom$TeX\Ddom be a declared domain with generator $\varphi^\mu$TeX\varphi^\mu, and assume reference. Then

\nabla_{\mu}\bigl(T^{\mu}{}_{\nu,\mathrm{eff}}\varphi^{\nu}\bigr)
=
\frac12 T^{\mu\nu}_{\mathrm{eff}}\Lie_{\varphi} g_{\mu\nu}.

Consequently, between two slices $\SigD(t_1)$TeX\SigD(t_1) and $\SigD(t_2)$TeX\SigD(t_2),

\Jql_{\Ddom}(t_2)-\Jql_{\Ddom}(t_1)
=
-\int_{\mathcal W_{12}}\PhiJ
+
\frac12\int_{\mathcal W_{12}} dV\,T^{\mu\nu}_{\mathrm{eff}}\Lie_{\varphi} g_{\mu\nu},

where $\mathcal W_{12}$TeX\mathcal W_{12} is the spacetime slab between the two slices and the boundary flux is

\PhiJ:=n_{\mu}T^{\mu}{}_{\nu,\mathrm{eff}}\varphi^{\nu}.

If $\Lie_{\varphi}g_{\mu\nu}=0$TeX\Lie_{\varphi}g_{\mu\nu}=0 on the declared slab, the quasi-local angular momentum changes only by boundary flux.

proof. Using reference,

\nabla_{\mu}\bigl(T^{\mu}{}_{\nu,\mathrm{eff}}\varphi^{\nu}\bigr)
=
(\nabla_{\mu}T^{\mu}{}_{\nu,\mathrm{eff}})\varphi^{\nu}+T^{\mu}{}_{\nu,\mathrm{eff}}\nabla_{\mu}\varphi^{\nu}
=
T^{\mu\nu}_{\mathrm{eff}}\nabla_{\mu}\varphi_{\nu}.

Since $T^{\mu\nu}_{\mathrm{eff}}$TeXT^{\mu\nu}_{\mathrm{eff}} is symmetric,

T^{\mu\nu}_{\mathrm{eff}}\nabla_{\mu}\varphi_{\nu}
=
\frac12 T^{\mu\nu}_{\mathrm{eff}}(\nabla_{\mu}\varphi_{\nu}+\nabla_{\nu}\varphi_{\mu})
=
\frac12 T^{\mu\nu}_{\mathrm{eff}}\Lie_{\varphi}g_{\mu\nu},

which proves reference. Integrating over the declared slab and applying Stokes' theorem yields reference.

remark: Scientific status. reference is exact on the declared domain once the effective stress tensor and axial generator are fixed. It is not a theorem about a unique global angular momentum for arbitrary cosmological spacetimes.

proposition: Exact FRW background neutrality. Consider the homogeneous phase-flat branch from the CHC dark-energy sector used below, with FRW metric and $\HH=\HH(t)$TeX\HH=\HH(t). For any comoving axial generator $\varphi^\mu$TeX\varphi^\mu tangent to the spatial isometry of the slice, the global phase-field reference sector obeys

\Jbg=0
\qquad
\text{on the exact homogeneous branch.}

proof. On the exact homogeneous branch, $T^{0}{}_{i,\HH}=0$TeXT^{0}{}_{i,\HH}=0 and the spatial momentum density of the phase sector vanishes identically, so the integrand in reference vanishes for any comoving axial generator. This proves reference.

assumption: Declared small-background-twist compatibility bound. On an admitted small-background-twist branch, the background family used below satisfies

\frac{|\Jbg|}{\mathrm{Vol}(\SigD)}\le C_{\mathrm{bg}}\,\XiBG,

for a family-dependent constant $C_{\mathrm{bg}}$TeXC_{\mathrm{bg}} on the declared domain. This bound is used only as a declared compatibility estimate on the admitted branch; it is not promoted here to a new theorem about all late-time backgrounds.

remark: Interpretive status of the background branch. The global phase-field reference sector is not interpreted here as a rotating fluid or as a hidden reservoir of large net cosmic spin. On the admitted branch it serves as a nearly neutral global phase-field reference whose residual contribution is controlled by $\XiBG$TeX\XiBG. Local angular-momentum observables therefore arise as rotational responses of structured reservoirs on that reference sector, not as evidence for a rigidly rotating Universe.

definition: Reservoir decomposition. On a declared domain, write the bookkeeping decomposition

\Jtot
=
\Jweb+\Jhalo+\JBH+\Jvoid+\Jrad+\Jbg.

When the declared domain is the Hubble-domain window $\Ddom_H$TeX\Ddom_H used below, the total bookkeeping charge is identified with the same quasi-local axial charge,

\Jtot \equiv \Jql_{\Ddom_H}.

This is a decomposition of one quasi-local axial charge into observationally declared reservoirs, not an ontology of independent new fluids. Throughout, $\JBH$TeX\JBH denotes an exterior spin/orientation reservoir proxy associated with compact objects; it is not a horizon, interior, or evaporation charge.

theorem: Declared compensation-bound theorem on a Hubble-domain window. Let $\Ddom_H$TeX\Ddom_H be a declared Hubble-scale domain on an admitted background branch. Assume:

- the chosen CMB isotropy and vorticity admissibility map provides the upper envelope equation |\Jql_\Ddom_H| , equation where $\epsiso$TeX\epsiso is a declared upper envelope compatible with the adopted isotropy/vorticity tests on one fixed comparison convention, not a direct observational estimate of $\Jql_{\Ddom_H}$TeX\Jql_{\Ddom_H}; - the admitted background branch satisfies reference; - the boundary flux and symmetry-breaking bulk term in reference are bounded by equation |\int_ W_12| \epsilon_Phi, |\frac12\int_ W_12 dV T^munu_eff\Lie_phi g_munu| \epsilon_. equation

Then the visible-reservoir sum

\Jvis:=\Jweb+\Jhalo+\JBH+\Jvoid+\Jrad

obeys the declared bound

|\Jvis|\le \epsiso + C_{\mathrm{bg}}\XiBG\,\mathrm{Vol}(\SigDH)+\epsilon_{\Phi}+\epsilon_{\Lie}.

proof. Using the Hubble-domain identification reference, combine reference with reference and reference. The balance law reference contributes only through the declared boundary-flux and symmetry-breaking mismatch terms bounded in reference. Rearranging yields reference.

definition: Compensation index. The declared-domain compensation index is

\CJ(\Ddom)
:=
\frac{|\Jtot|}{|\Jweb|+|\Jhalo|+|\JBH|+|\Jvoid|+|\Jrad|+|\Jbg|}.

Here $\Jtot$TeX\Jtot denotes the same declared-domain quasi-local charge fixed in reference. A small value of $\CJ$TeX\CJ indicates that large local reservoir contributions coexist with a small net domain charge.

corollary: Conditional small compensation index on a declared Hubble-domain branch. Under the hypotheses of reference, if the denominator of reference is nonzero and the right-hand side of reference is small compared with the declared reservoir sum, then

\CJ(\Ddom_H)\ll 1.

Hence, on such branches, large local spins can coexist with a small Hubble-domain charge only through reservoir compensation.

proposition: No rigid-rotation inference from local spin covariance within one declared family. Within one declared family, the simultaneous presence of large local covariance observables for the web, halo, black-hole, or void-shell reservoirs does not by itself imply a large coherent global rotation. Under reference, such covariance is in particular admissible on branches for which the compensation index remains small.

proof. The statement is immediate from reference: on branches with a small compensation index, large reservoir magnitudes remain compatible with a small domain total through reservoir compensation. Hence local spin covariance cannot by itself be promoted to an inference of rigid global rotation without violating the declared Hubble-domain gate.

definition: Declared transfer network. A declared transfer network is a finite set of reservoirs $a\in\{\mathrm{web},\mathrm{halo},\mathrm{BH},\mathrm{void},\mathrm{rad},\HH\}$TeXa\in\{\mathrm{web},\mathrm{halo},\mathrm{BH},\mathrm{void},\mathrm{rad},\HH\} with antisymmetric internal transfer terms

\Pi_{ab}=-\Pi_{ba}

and reservoir equations

\dot J_a = \tau_a + \sum_{b\neq a}\Pi_{ba}-\Phi_a,

where $\tau_a$TeX\tau_a are source torques internal to the declared domain description and $\Phi_a$TeX\Phi_a are boundary leaks or exports. A declared transfer-network branch is effectively closed on an interval when

\sum_a \tau_a = 0,
\qquad
\sum_a \Phi_a = 0,

and it is nearly closed when

\left|\sum_a \tau_a-\sum_a \Phi_a\right|\le \epsilon_{\mathrm{close}}

for a declared tolerance $\epsilon_{\mathrm{close}}$TeX\epsilon_{\mathrm{close}} on the interval of interest.

theorem: Exact internal-transfer cancellation on the declared network. For any declared transfer network satisfying reference and reference, the summed reservoir charge obeys

\frac{d}{dt}\sum_a J_a = \sum_a \tau_a - \sum_a \Phi_a.

In particular, if the declared source torques are internal redistributions whose sum vanishes and the branch is effectively closed in the sense of reference, then the summed reservoir charge is conserved.

proof. Summing reference over all reservoirs gives

\frac{d}{dt}\sum_a J_a = \sum_a \tau_a + \sum_a\sum_{b\neq a}\Pi_{ba}-\sum_a\Phi_a.

The double sum over $\Pi_{ab}$TeX\Pi_{ab} vanishes pairwise by antisymmetry, leaving reference.

A representative declared compensation closure, used only as a bookkeeping organizer rather than as a first-principles structure-formation law, is

\dot \Jhalo = \Tide + \Pwh - \Phb - \Phv - \Phi_{\mathrm{halo}},

\dot \JBH = \Phb + \Tacc - \Phi_{\mathrm{BH}},

\dot \Jvoid = \Phv + \Pcomp - \Phi_{\mathrm{void}},

\dot \Jbg = -(\Tide+\Tacc+\Pcomp) - \Phi_{\HH},

\dot \Jweb = -\Pwh - \Phi_{\mathrm{web}},

\dot \Jrad = -\Phi_{\mathrm{rad}}.

The representative closure is not a first-principles structure-formation law. It is a declared bookkeeping organizer consistent with reference: within this representative organizer, the web acts as a transport layer, haloes as storage reservoirs, black-hole proxies as compaction channels, void shells as compensating reservoirs, radiation as an export channel, and the global phase-field reference sector as the nearly neutral residual-closure sector needed to keep the Hubble-domain branch nearly neutral. By construction it does not supply a unique microphysical torque budget or a full structure-formation dynamics.

corollary: Compact-object proxy compaction requires non-proxy compensation on a nearly closed declared Hubble-domain branch. On a declared nearly closed Hubble-domain branch in the sense of reference, with small $\epsiso$TeX\epsiso, if $\dot \JBH>0$TeX\dot \JBH>0 over an interval, then the sum of the non-proxy reservoirs must decrease by the same amount up to the declared closure tolerance:

\frac{d}{dt}\bigl(\Jweb+\Jhalo+\Jvoid+\Jrad+\Jbg\bigr)
= -\dot \JBH + \mathcal{O}(\epsclose).

proof. This follows immediately from reference together with the nearly closed condition reference.

definition: Sign-faithful observational proxies. Within one declared family, a proxy $A_a$TeXA_a for reservoir $J_a$TeXJ_a is sign-faithful if $dA_a/dJ_a$TeXdA_a/dJ_a has fixed sign on the admitted branch.

corollary: Conditional observable anti-coincidence under compact-object proxy compaction on one fixed family. Assume a nearly closed branch in the sense of reference, sign-faithful proxies for the compact-object reservoir proxy and at least one non-proxy reservoir, and $\dot \JBH>0$TeX\dot \JBH>0 over an interval. Then not all sign-faithful non-proxy observables can grow with the same sign over that interval unless an export channel $\Phi_a$TeX\Phi_a or a background term of comparable size is present.

proof. By reference, positive compact-object proxy compaction must be balanced by a decrease in the non-proxy sum up to the declared closure tolerance. If all sign-faithful non-proxy observables increased with the same sign while export and background corrections remained within that tolerance, the corresponding non-proxy reservoir sum would increase rather than decrease, contradicting reference.

remark: Status of the anti-coincidence corollary. reference is a supportive conditional consequence on one fixed family with sign-faithful proxies. It is not a catalogue-level fit, not a population-synthesis law, and not a replacement for the declared compensation-bound theorem itself.

The compensation framework is not tested against raw angular-momentum fields directly; it is tested against declared observable families with fixed comparison conventions.

definition: Declared alignment observables. Within one declared environment family $\Fenv$TeX\Fenv, define:

A_{\mathrm{halo|web}}(M;\Fenv) := \expval{\cos\theta(\mathbf J_{\mathrm{halo}},\hat{\mathbf e}_{\mathrm{fil}})}_{M,\Fenv},

A_{\mathrm{void|shell}}(r;\Fenv) := \expval{\cos\theta(\mathbf J_{\mathrm{shell}},\hat{\mathbf e}_{\mathrm{tan}})}_{r,\Fenv},

A_{\mathrm{BH|host}}(\Fenv) := \expval{\cos\theta(\mathbf J_{\mathrm{BH}},\hat{\mathbf e}_{\mathrm{host/web}})}_{\Fenv}.

These are declared same-family covariance observables exported from one fixed comparison convention, not detector-independent universal invariants.

proposition: No independent retuning inside one declared environment family. Within one fixed $\Fenv$TeX\Fenv, the smoothing scale, web finder, void-shell definition, halo spin proxy, and black-hole orientation proxy are held fixed. A change in any one of them defines a new family rather than a refinement inside the same family. Consequently, halo/web, void/shell, and BH/host orientation statements are coupled same-family tests and may not be calibrated independently within one declared family.

The compensation reading is admitted on a declared family only if every gate below passes on one unchanged comparison convention. If any gate fails, the branch is rejected.

- G1 (CMB nearly-no-rotation envelope). A viable Hubble-domain branch must satisfy the admissibility envelope reference; a branch requiring large rigid rotation is excluded [citation]. No primary-sector CMB transfer function, Boltzmann hierarchy, or likelihood fit is introduced here. - G2 (Background neutrality gate). On the declared late-time phase-flat background branch, the CHC background contribution must remain negligible in the sense of reference. A branch in which the background itself is the dominant spin reservoir is excluded. - G3 (Void-shell compensation gate). Compensation is assigned to void shells, not void centers. A claimed void contribution that does not survive a declared shell prescription inside one fixed family is excluded from the baseline compensation branch [citation]. - G4 (Linked web--halo--compact-object gate). If one claimed branch requires halo/web alignment, BH/host or BH/web covariance, and near-zero Hubble-domain net twist, then these statements must be tested within one fixed family; they may not be rescued by object-wise retuning of web, halo, or compact-object orientation proxies [citation]. - G5 (No structure-formation overclaim gate). No full simulation fit, no complete structure-formation pipeline, and no unique microphysical torque law are claimed here. Any such claim lies outside the admitted branch.

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

The exact statements above are declared-domain statements. The companion public-data records QAC--VP0 through QAC--VP6 instantiate only bounded proxy and bridge surfaces. They are read as public-data support for the declared observable-family grammar, not as independent proofs of finite-window compensation closure.

The public observational surfaces are MaNGA DR17 DAP/MAPS products, including stellar-kinematic maps, together with the GEMA environment value-added catalogue and Pipe3D mass-like or mass-to-light products where explicitly declared. The public simulation surfaces are IllustrisTNG group-catalog, API subhalo, cosmic-web, and stellar-particle cutout products. These data surfaces support projected and mass-weighted proxy construction; they do not by themselves define a unique environment family, shell/web/host prescription, covariance object, or theorem-level QAC certificate [citation].

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

The records in reference have a common boundary. They may support the existence of public proxy surfaces, finite projected proxy rows, environment/covariance partials, dual-environment harmonization intervals, mock-IFU observable-family bridges, and mass-weighted observable-family bridges. They do not assign a finite-window QAC closure, a theorem-level angular-momentum compensation result, a rotating-Universe model, a total cosmic angular-momentum law, a full structure-formation model, or a unique microphysical torque law. A closure claim would require one fixed environment family, one shell/web/host prescription, one observable-family convention, one proxy-sign convention set, and one covariance or interval object held fixed across the declared comparison.

The compensation branch removes the need to read local angular-momentum covariance as evidence for global rigid rotation. Large local reservoir contributions can coexist with a small Hubble-domain charge provided that transport, storage, compaction, export, and compensation are organized on one declared domain and one fixed comparison convention. Within the representative declared organizer, the web acts as a transport layer, haloes as storage reservoirs, compact-object proxies as compaction channels, void shells as compensating reservoirs, radiation as an export channel, and the global phase-field reference sector as a nearly neutral reference sector . This reading is compatible with strong CMB isotropy constraints because the background itself is not promoted to a dominant rotating reservoir.

The transfer network also ties otherwise separate empirical patterns into one finite-domain budget. Halo spin is not treated as an isolated object property, and black-hole orientation is not detached from the surrounding environment. Both become parts of the same domain bookkeeping once the web, void-shell, and background contributions are tracked simultaneously. The resulting interpretation is narrower than a global-rotation claim and narrower than a full structure-formation closure, but it is correspondingly sharper on the compensation question.

The QAC--VP0 through QAC--VP6 public-data records supply bounded material support for this restricted reading. They show that projected observational proxies, simulation proxies, environment labels, covariance or interval boards, mock-IFU observable operators, and mass-weighted observable operators can be constructed on declared public surfaces. They do not remove the need for a separately frozen finite-window certificate before a finite-window environment/proxy closure can be claimed.

The scope remains deliberately restricted. No posterior over joint web, halo, compact-object, and void catalogues is constructed here. No unique microphysical torque law is proposed. No structure-formation pipeline is replaced. No primary-sector CMB calculation, Boltzmann hierarchy, or likelihood fit is derived. The only admissible reading is the one enforced by the declared-domain balance law, the exact FRW neutrality statement, the admitted small-background-twist bound, and the same-family observational gates. In particular, no finite-window environment/proxy closure is assigned in the absence of a separately frozen finite-window certificate on one explicit environment family and proxy-sign convention set.

The relevant conserved quantity is a quasi-local axial charge on declared cosmological domains, not a generic ADM-like angular momentum of the whole Universe. From the conserved CHC effective stress tensor one obtains an exact declared-domain balance law. On the homogeneous phase-flat background branch, the background contribution vanishes exactly on the strict FRW branch, while an admitted small-background-twist family is constrained only through the compatibility bound reference. Under the declared CMB isotropy and vorticity admissibility envelope and bounded flux and symmetry-breaking terms, these ingredients yield the declared compensation-bound theorem reference, which places a declared bound on the Hubble-domain visible-reservoir sum. Combined with the compensation-index corollary reference on branches where that bound is small relative to the declared reservoir magnitudes, this admits large local angular-momentum observables without rigid global rotation.

The transfer-network organizer expresses the same statement in rate form. Within the representative declared organizer, the web acts as a transport layer, haloes as storage reservoirs, compact-object proxies as compaction channels, void shells as compensating reservoirs, radiation as an export channel, and the background closes the residual budget without becoming a dominant rotating reservoir. This organizer is not a first-principles structure-formation law. It is a declared bookkeeping closure consistent with the exact balance identity and with the admitted branch restrictions.

The CMB input is used only as a nearly-no-rotation admissibility envelope and is not promoted here to a primary-sector CMB transfer or likelihood claim. No claim is made here about a rigidly rotating Universe, a generic ADM-like total cosmic angular momentum, a full structure-formation fit, a unique microphysical torque law, black-hole horizon or interior dynamics, or a primary-sector CMB transfer analysis. The compensation reading is admitted only as a finite-domain compensation statement when the nearly-no-rotation envelope, the background compatibility bound, the void-shell prescription, and the linked web--halo--compact-object covariance tests all pass on one fixed comparison convention. The companion public-data records QAC--VP0 through QAC--VP6 provide bounded support for the declared proxy grammar: public simulation--observation proxy bridge partials, expanded proxy boards, environment/covariance partials, dual-environment harmonization, mock-IFU observable-family bridging, and mass-weighted observable-family bridging. These records do not assign a finite-window QAC closure. No finite-window environment/proxy closure is claimed unless a separate finite-window certificate freezes one explicit environment family, one proxy-sign convention set, one shell/web/host comparison prescription, one covariance or interval object, and one observable-family convention.

The imported CHC objects are restricted to the following minimal set.

- The effective stress tensor and local conservation law on the admitted CHC branch [citation]. - The homogeneous phase-flatness branch and the late-time small-background-twist variable $\XiBG$TeX\XiBG [citation].

Compact objects enter only as exterior reservoir proxies through the declared environment family and not through any imported horizon equation, interior algebra, or evaporation law. No new root-level standing assumption, dark-matter source law, detector law, or CMB likelihood is introduced.

The observable proxies reference--reference are intentionally family-relative. A change of web finder, shell prescription, spin proxy, or smoothing scale changes the declared environment family and therefore the comparison problem. This anti-flexibility rule is part of the declared comparison protocol: a branch that needs family changes to survive is rejected rather than silently retuned.

Funding and competing interests..

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