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\newcommand{\Aether}{\AE{}ther}
\newcommand{\Aflow}{\AE{}ther-flow}
\newcommand{\TheoryName}{\Aflow{} Interpretation of Relativity}
\newcommand{\TheoryProgram}{\Aether{} / \Aflow{} framework}

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\title{The \TheoryName{}\\[0.4em]
Ontology: Exact-Closure Sequence Overview}
\author{}
\date{}
\input{tex_shared/aether_flow_apa_frontmatter.tex}

\begin{document}

\AetherFlowAPATitlePage

\begin{abstract}
This note presents the active exact-closure manuscript sequence for \TheoryName{} as the flagship public-facing deliverable of the repository. Its purpose is not to replace the individual root manuscripts, but to fix their common role, reading order, and shared claim boundary while packaging them as one coherent theory statement. In the active repository state, \TheoryName{} is the exact relativistic theory built on the \Aether{} / \Aflow{} ontology. At observable scale, the package is operationally identical to ordinary GR: it keeps the Einstein--Hilbert dynamics, one operative metric, universal matter coupling, ordinary diffeomorphism gauge structure, standard null / proper-time / redshift structure, and no extra preferred-frame, vector, or scalar graviton sector. Its late-time cosmological completion is correspondingly conservative: the ordinary cosmological constant or an equivalent GR-compatible dark-energy stress tensor inside the same one-metric law. It is therefore not Einstein-aether theory, not Ho\v{r}ava gravity, and not a new low-energy alternative to GR. Accordingly, the exact-closure sequence already provides a disciplined theory statement at the effective level even though the deeper substrate derivation remains open.

The overview makes four points explicit. First, this note is the canonical front door to the flagship exact-theory package. Second, the exact-closure note and the five companion modules on foundations, dynamics, consistency, relativistic recovery, and flow geometry should be read as one fixed coordinated line after that front door. Third, the predictive content of the active theory is exactly that of GR, while the \Aether{} / \Aflow{} vocabulary remains ontological and interpretive at the effective level. Fourth, the separate flagship public article is a release-facing synthesis built on that ordered core, while the derivational bridge manuscripts belong to an ongoing foundational recovery program answerable to this exact-closure benchmark rather than to the completed theory statement itself.
\end{abstract}

\section{Introduction}

The active repository has reached a stage at which the exact-closure line should be presented as the flagship scientific deliverable in its own right. The deeper framework still permits ongoing derivational work, but the project is no longer best described as ontology awaiting its first disciplined theory statement. That theory statement now exists in the exact-closure sequence.

At observable scale, that package is ordinary GR in operational content: Einstein--Hilbert dynamics, one operative metric, universal matter coupling, the ordinary ADM / diffeomorphism constraint structure, standard null / proper-time / redshift rules, and no extra preferred-frame, vector, or scalar graviton sector \cite{Einstein1916,ADM1962}. The congruence-based \Aflow{} dictionary belongs to the standard relativistic kinematics literature \cite{Raychaudhuri1955,EllisVanElst1999}, not to a second observer-level field law. For that reason the active package should be classified up front as not Einstein-aether theory, not Ho\v{r}ava gravity, and not any other low-energy preferred-structure alternative \cite{JacobsonMattingly2001,JacobsonMattingly2004,ElingJacobson2004,Jacobson2010,Jacobson2014,JacobsonSperanza2015,Horava2009}. The remaining derivational ambition belongs instead to the established emergent, induced, reconstruction, self-coupling, and analogue-gravity conversation \cite{Jacobson1995,Visser2002,HojmanKucharTeitelboim1976,Deser2004,Lovelock1971,BarceloLiberatiVisser2011,Sakharov1967}.

\paragraph{Framework and claim boundary.}
\TheoryProgram{} denotes the broader \Aether{} / \Aflow{} framework built on the claims that the \Aether{} is the underlying four-dimensional substrate of reality, the \Aflow{} is its intrinsic ordered motion, observed three-dimensional space is the local experiential slice of that deeper substrate, S-time is the experienced order of change arising from matter, light, and the \Aflow{}, and observed expansion is the three-dimensional appearance of deeper four-dimensional ordered motion. Within that framework, \TheoryName{} denotes the exact-closure theory in which the effective gravitational dynamics are adopted to be exactly Einsteinian with universal matter coupling. In the active sequence, \emph{adoption} means use of that established relativistic dynamics without claiming substrate derivation, while \emph{derivation} is reserved for a first-principles recovery from explicit substrate variables.

This distinction is the organizing principle of the overview. The active exact-closure line is already a positive deliverable. The still-open substrate program is a later foundational burden, not the condition for calling the effective theory statement real. The immediate packaging task is therefore consolidation of the flagship exact-theory sequence rather than another derivational bridge installment.

\paragraph{What is new here?}
What survives as novelty in the current package is interpretive and architectural, not a claim of new low-energy gravitational dynamics. The package enforces a strict adoption-versus-derivation distinction, makes the overview-first benchmark sequence the canonical front door, gives the \Aflow{} language a disciplined congruence-based dictionary, and keeps the positive benchmark package separate from the downstream bounded no-go on the frozen derivational line. None of those moves adds a second observer-level field law beyond GR.

\input{tex_shared/aether_flow_what_this_package_is_not.tex}

\section{Purpose of the Overview}

\begin{definition}[Exact-closure sequence overview]
An exact-closure sequence overview is a manuscript that presents the active root papers of \TheoryName{} as one coordinated theory statement, identifies the role of each paper within that statement, and fixes the boundary between completed exact closure and unfinished substrate derivation.
\end{definition}

\begin{proposition}[Current architectural status]
At the present stage of the repository, the canonical public-facing entry to \TheoryProgram{} is the exact-closure manuscript sequence rather than the derivational bridge program.
\end{proposition}

This proposition is not merely editorial. It reflects the scientific order now achieved in the repository. The exact operational theory, its consistency status, and its relation to relativistic phenomenology are already stated in disciplined manuscript form. What remains open is not whether the project has any exact theory statement, but whether that exact theory can later be recovered from a more primitive substrate dynamics.

\begin{corollary}[Flagship packaging rule]
The fixed flagship release package of the repository is this overview together with the six core exact-closure manuscripts and the public flagship article built on that ordered core, and any further derivational continuation must be presented only as downstream foundational work.
\end{corollary}

\section{Exact Theory Statement}

\begin{definition}[\TheoryName{}]
\TheoryName{} is the exact-closure, GR-consistent theory of \TheoryProgram{} in which the \Aether{} / \Aflow{} ontology is retained while the effective gravitational dynamics are exactly those of general relativity with universal matter coupling.
\end{definition}

Its effective action is
\begin{equation}
S_{\mathrm{eff}}
=
\frac{c^3}{16\pi G}\int d^4x\,\sqrt{-g}\,R
+
S_{\mathrm{matter}}[g,\psi],
\label{eq:SA}
\end{equation}
with field equations
\begin{equation}
G_{\mu\nu}
=
\frac{8\pi G}{c^4}T_{\mu\nu},
\label{eq:einstein}
\end{equation}
the standard null condition
\begin{equation}
0=g_{\mu\nu}\,dx^\mu dx^\nu,
\label{eq:null}
\end{equation}
and the standard proper-time rule
\begin{equation}
d\tau^2=-\frac{1}{c^2}g_{\mu\nu}\,dx^\mu dx^\nu.
\label{eq:propertime}
\end{equation}

\begin{proposition}[Operational identity]
For fixed matter sector, initial data, and boundary conditions, the effective observable content of \TheoryName{} is identical to that of GR.
\end{proposition}

\begin{remark}
This is an adoption statement, not a first-principles derivation statement. The exact-closure sequence does not claim that the Einstein sector has already been recovered uniquely from deeper substrate microphysics.
\end{remark}

For late-time cosmology, the same benchmark sector admits the ordinary conservative completion
\begin{equation}
S_{\mathrm{eff}}^{(\Lambda)}
=
\frac{c^3}{16\pi G}\int d^4x\,\sqrt{-g}\,\left(R-2\Lambda\right)
+
S_{\mathrm{matter}}[g,\psi],
\label{eq:SA_lambda}
\end{equation}
or, equivalently, a vacuum-energy / GR-compatible dark-energy stress tensor minimally coupled to the same operative metric. This sharpens the cosmological benchmark without changing the adoption-versus-derivation boundary: dark energy is incorporated inside exact GR rather than used to derive exact GR \cite{Riess1998,Perlmutter1999,Planck2018Parameters}.

\section{Flagship Package and Reading Order}

This note is the canonical front door to the exact-closure sequence. After it, the active core manuscripts should be read in the following fixed order and should be presented in this same order in repository-facing summaries.
\begin{enumerate}
    \item \textbf{Exact-closure note.} The standalone exact-closure note states the shortest complete version of the active scientific position, fixes the benchmark role of \TheoryName{}, and marks the nonclaims that preserve discipline.
    \item \textbf{Foundations.} The foundations manuscript fixes the ontological vocabulary, clarifies the original intent of the framework, and states why exact closure rather than unfinished deformation is the correct active stance.
    \item \textbf{Dynamics.} The dynamics manuscript states the adopted effective action, field equations, matter-coupling rule, weak-field structure, and benchmark role of the exact-closure theory.
    \item \textbf{Consistency.} The consistency manuscript makes explicit the gauge structure, degree-of-freedom count, and effective health conditions inherited from GR in the adopted exact-closure theory.
    \item \textbf{Relativistic recovery.} The relativistic-recovery manuscript states the exact relation to GR and the local relation to SR, including weak-field recovery, null propagation, redshift, clock behavior, and local inertial structure.
    \item \textbf{Flow geometry.} The flow-geometry manuscript supplies the disciplined congruence-based dictionary by which the \Aflow{} ontology is read inside exact relativistic geometry without introducing a second low-energy law.
\end{enumerate}

\begin{corollary}[Stable sequence logic]
Read in that order, the exact-closure papers supply one continuous argument: ontology is stated, exact dynamics are fixed, internal consistency is controlled, relativistic recovery is made explicit, and the \Aflow{} language is given formal geometric discipline.
\end{corollary}

This fixed reading order is part of the claim boundary of the flagship package. It prevents the effective theory statement from being blurred together with optional derivational continuation.
The flagship public article sits on top of this ordered core as a release-facing synthesis for first-time readers. It does not replace the overview as the canonical scientific front door, and it does not alter the reading order fixed above.

\section{What the Sequence Establishes}

The exact-closure sequence now establishes the following at the active theory level.
\begin{enumerate}
    \item The ontological vocabulary of \Aether{}, \Aflow{}, observed three-dimensional space, and S-time is fixed in disciplined form.
    \item The effective gravitational law is fixed exactly as Einsteinian with universal matter coupling.
    \item The late-time cosmological sector can be written conservatively as GR+\(\Lambda\), or equivalently with a GR-compatible dark-energy stress tensor, without changing the one-metric claim boundary.
    \item The active theory carries no independent low-energy non-GR observable signature.
    \item The effective gravitational sector has the ordinary massless spin-2 structure, standard relativistic causal order, and no additional established low-energy scalar or vector graviton sector.
    \item The observer-accessible weak-field, redshift, time-dilation, null-propagation, and local SR content is inherited exactly from the same metric structure.
    \item The \Aflow{} interpretation is formalized through congruence geometry rather than loose metaphor or a naive vector-wind picture.
\end{enumerate}

\begin{proposition}[Working theory standard]
At the effective level, \TheoryName{} already satisfies the working standard required for the project's main goal: ontology is matched by closed mathematical structure, effective dynamics are explicit, internal consistency is controlled, and observable relativistic structure is recovered without ambiguity.
\end{proposition}

\section{What the Sequence Does Not Establish}

The same discipline requires an explicit statement of what the consolidated exact-closure line does not yet claim.
\begin{enumerate}
    \item It does not claim a completed first-principles derivation of Einsteinian gravity from explicit substrate variables.
    \item It does not claim that dark energy by itself derives the Einsteinian metric sector from the \Aether{} / \Aflow{} ontology.
    \item It does not claim a unique underlying substrate action from which the exact relativistic sector has already been proved to emerge.
    \item It does not claim a distinct verified low-energy observable sector beyond GR.
    \item It does not claim that the broader bridge program has already solved uniqueness, mode control, or infrared emergence in full generality.
    \item It does not claim that ontology by itself constitutes empirical evidence for new low-energy physics.
\end{enumerate}

\begin{remark}
These nonclaims are not weaknesses of the overview. They are part of what makes the exact-closure sequence scientifically stable. The project now succeeds as an exact theory statement because it distinguishes completed effective structure from unfinished microphysical ambition.
\end{remark}

\section{Literature Positioning}

The benchmark package should not be misread as if \Aether{} / \Aflow{} language automatically made it a new low-energy alternative to GR. Its place relative to nearby literatures is narrower and should be stated directly.
\begin{enumerate}
    \item Relative to standard GR and its congruence / ADM baselines \cite{Einstein1916,Raychaudhuri1955,EllisVanElst1999,ADM1962}, the benchmark package keeps the same low-energy equations and observable content. The difference is interpretive ontology and package discipline, not a second low-energy field law. On the same logic, the consistency manuscript is an audit of the adopted GR sector against the ordinary ADM baseline, not a separate low-energy dynamics discovery.
    \item Relative to Einstein-aether theory, static post-Newtonian preferred-frame variants, and Ho\v{r}ava-type preferred-foliation gravity \cite{JacobsonMattingly2001,JacobsonMattingly2004,ElingJacobson2004,Jacobson2010,Jacobson2014,JacobsonSperanza2015,Horava2009}, the package is not a preferred-structure modification with a surviving observer-level vector or foliation field and extra propagating modes.
    \item Relative to thermodynamic, induced, reconstruction, self-coupling, uniqueness, and analogue-gravity programs \cite{Jacobson1995,Visser2002,HojmanKucharTeitelboim1976,Deser2004,Lovelock1971,BarceloLiberatiVisser2011,Sakharov1967}, the package is closer in spirit only at the level of the downstream derivation ambition: those programs ask how Einsteinian gravity emerges from deeper structure, just as the open derivational line here asks a related foundational question.
\end{enumerate}

Accordingly, the most accurate current literature label is: exact-GR interpretive package plus open emergent-gravity research program. Any novelty claim must therefore be narrower than ``new gravity theory'' and narrower than ``the general idea that GR might emerge from deeper microphysics.'' At current scope it can only lie, if anywhere, in the disciplined packaging of the benchmark package, the benchmark-gated derivation architecture, and the decision to preserve the frozen-line no-go explicitly.

A referee-facing summary is therefore short. The package is operationally GR by adoption; its novelty is interpretive and architectural rather than a new low-energy field law; and the first-principles substrate derivation remains open. The correct present assessment is acceptance of the exact-GR benchmark and bounded no-go / roadmap program, not acceptance of a completed derivation of GR from \Aether{} / \Aflow{} substrate variables.

\section{Relation to the Derivational Bridge Program}

The broader substrate manuscript line remains important, but its role must be read correctly. It is answerable to the exact-closure benchmark already fixed above. Its purpose is to ask whether the exact relativistic sector can be recovered from deeper substrate variables while preserving the same operational content and without generating a surviving deformation of that content.

This means the bridge program is no longer the repository's only route to theory status. It is a secondary foundational research program built downstream of an already stated exact theory. That ordering matters. If a future bridge candidate fails, the scientific status of the project contracts back to \TheoryName{} rather than back to ontology alone. If the bridge line is deliberately resumed, it should be introduced explicitly as optional continuation beyond the flagship package rather than as the next required milestone.

At the current routing stage, that downstream status has a sharper operational consequence. The bounded primitive-reservoir line has now been carried through its honest test and frozen in the current-line obstruction / no-go note. On that frozen bridge object, the verdict is \texttt{Not Derived On Current Line}: the line preserves adoption plus the recorded observer package, but it does not generate the observer-localizing law needed to recover Einsteinian observer dynamics from explicit substrate structure.

Accordingly, the correct architectural stance is consolidation rather than further blurring. The exact-closure sequence should be treated as the canonical flagship theory statement of the repository, and the current bounded derivation line should be read as a scoped no-go on the frozen bridge object rather than as an invitation to keep descending by same-output relay.

The next honest benchmark-facing move is therefore not another deeper same-output relay below the same frozen object. If no concrete new observer-localizing substrate law is already in hand, the correct action is to stop with that scoped no-go and present the exact-closure package as the positive theory statement already secured. If derivational work is resumed, it must begin as a genuinely new line or bridge-design manuscript that states the added law explicitly: how substrate structure localizes to observer spacetime fields, how the operative metric is generated locally, and how the Einsteinian observer equation together with relativistic recovery are supposed to emerge.

The claim boundary also remains fixed while that foundational continuation proceeds. The benchmark package keeps one operative metric, the ordinary matter route stays unchanged, there is no second operative metric, the low-energy matter law is not enlarged, and stronger first-principles promotion language is not yet licensed.

\begin{proposition}[Benchmark and reversion role]
Any admissible future extension of \TheoryProgram{} must remain answerable to \TheoryName{} as exact benchmark, and failure of such an extension contracts the framework back to \TheoryName{} rather than invalidating the exact-closure sequence.
\end{proposition}

\section{Editorial Use of This Note}

This overview is the canonical front-door manuscript for the flagship exact-closure line and should be used whenever a short but complete statement of the active project status is needed. It is especially appropriate when the repository must be introduced at sequence level rather than through one root paper in isolation.

The note does not replace the six core manuscripts. Instead, it fixes how they fit together:
\begin{itemize}
    \item the exact-closure note remains the shortest standalone anchor;
    \item the five companion papers remain the full modular statement of foundations, dynamics, consistency, relativistic recovery, and flow geometry;
    \item the flagship public article remains the release-facing synthesis built on this ordered core and does not replace it;
    \item the substrate notes remain an open derivational program downstream of the exact-closure benchmark and should be presented only after the flagship package is made explicit.
\end{itemize}

\section{Conclusion}

The main project goal is now best represented by the exact-closure sequence taken as one coordinated deliverable. \TheoryName{} is no longer merely an ontological suggestion awaiting its first disciplined theory statement. It is already the exact relativistic theory of the active framework at the effective level. Within that same benchmark, late-time accelerated expansion is handled conservatively by the ordinary cosmological constant or an equivalent GR-compatible dark-energy sector. What remains open is the deeper question of derivation from substrate first principles, not the existence of an exact operational theory.

Taken as one coordinated deliverable, the sequence makes the repository scientifically definite at effective scope. It fixes the public reading order, separates adoption from derivation, and supplies a stable exact benchmark against which any later continuation must be judged. The conclusion of the overview is therefore that the exact-closure package already stands as the canonical theory statement, with the deeper derivational question remaining open but explicitly downstream of that achieved result.

\input{tex_shared/aether_flow_product_a_references_apa.tex}

\end{document}
