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\title{\textbf{Landmark XVI-O}\\[0.4em]
A finite quantum BV sector for invariant Einstein--scalar gravity,\\
and the obstruction-preserving audit of the inherited insertion\\[0.35em]
\large Science volume (o70-sync: four D11 deliverables)}
\author{}
\date{2026-10-07}

\begin{document}
\maketitle

\begin{abstract}
Revision o70-sync is a proof and build consistency correction so that the kernel counterterm evidence earns acceptance under a stated prescription.
The intermediate wording is retained: the D11 Wick and determinant normalization is established; the tensor product, the scaling witness, and the off-diagonal Ward verification were tracked separately and are now constructed for the kernel; Gate~3 spanning stays Partial; bulk O.1 stays NOT\_CLOSED.

Three verdicts are never collapsed.
(1)~Bulk construction is partial: the classical $\kappa^2$ master is Partial, four D11 prerequisites are Constructed for the kernel, the full $\ell_4$ polynomial is Unresolved, and O.1 is NOT\_CLOSED.
(2)~Symmetry and counterterms: the subsector is restored under the prescription (\texttt{kernel\_two\_point\_Ward}); the bulk matched set is empty; bulk \texttt{symmetry\_restored} stays false.
(3)~The inherited insertion stays frozen by XVI-N, \texttt{thm:massless-obstruction}, and is distinct from $S_{\mathrm{inv}}$ and from the prepared defect $(S_D,S_D)$.

Coefficients $\alpha=A^2/60$ and $\beta=A^2/18$ are derived.
All $256$ symbolic components are a primary check; invariant structures are documented and are not an independent claim.
On the open set $U$,
$\Pi_{\mathrm{tr}}^R|_U=(i\kappa^2/4)T$.
The only active reference is \texttt{W\_w\_jet\_pullback\_via\_Pi\_tr\_o68}.
The kernel two-point Ward identity is not functional ST4b.
$s_0 C_L$ is not evaluated.
The subsector verdict is \texttt{Constructed\_subsector\_under\_prescription} for the kernel only.
En01 and Em01 are not premises.
Corpus $\mathcal P$ is not reused for $P_{\mathrm{tr}}$.
No quantum coefficient is admitted.
No compilation is asserted.
\end{abstract}

\tableofcontents

\section{Scope, dependencies, and three verdicts}
Landmark XVI-O connects XVI-M selected-graph renormalization to the XVI-N classical framework without treating the obstructed insertion as a completed quantum observable.
En01 and Em01 are not premises.
Predecessors XVI-A through XVI-N are read-only pins.
The baseline is $S_{\mathrm{inv}}$, not $S_D$.

\begin{remark}
\label{rem:three-verdicts}
The three release verdicts are never collapsed.
\begin{enumerate}
\item Bulk quantum-sector construction.
The finite target lives on $S_{\mathrm{inv}}$.
The classical $\kappa^2$ master is Partial.
Four D11 prerequisites are Constructed for the kernel.
The full $\ell_4$ generating polynomial is Unresolved.
O.1 is NOT\_CLOSED.
\item Renormalized symmetry and counterterm compatibility.
The subsector is restored under the prescription \texttt{kernel\_two\_point\_Ward}.
The bulk matched set is empty.
Bulk \texttt{symmetry\_restored} stays false.
ST4a and functional ST4b are not claimed.
\item Inherited-insertion status.
The classical obstruction of the declared class is preserved.
A renormalized product is not closure.
\end{enumerate}
The diagram inventory is manually specified and partially checked.
It is not a completeness claim.
Numerical checks are corroboration, not certificates.
Sampling is not a universal identity.
\end{remark}

\begin{remark}
\label{rem:baseline}
The quantum sector is built on the invariant baseline
\[
S_{\mathrm{inv}}=S_D-V_\sigma-V_g,
\]
not on the prepared action $S_D$.
A broken master identity is not a BV complex.
The prepared square $(S_D,S_D)$ is a different object from $S_{\mathrm{inv}}$ and from the insertion obstruction.
\end{remark}

\begin{remark}
\label{rem:graph-action}
XVI-N non-claim~12 leaves graph-to-action vertex identification unsettled.
Sharing the cubic density $\ell_3$ does not identify XVI-M's selected graph with an action graph.
Any future map needs its own certificate.
Selected-graph coefficients are comparison data unless an explicit morphism into this sector is constructed.
\end{remark}

\subsection{Inherited, written, checked}
Inherited here: the XVI-N classical interface through order $\kappa$; XVI-M Target~I comparison data; the XVI-I seed $F_t$; the XII-C and XII-D kernels as named sources, not as new theorems; and the XIV-A bracket orientation.
Written here: the provisional quantum target, the convention sheet, the provisional diagram inventory, the classical $\kappa^2$ scaffold, and the insertion freeze.
Checked as package evidence, not as certificates of this note: pin hashes, and normalization tests that forbid silent $\ell_3$ identification and invalid ghost-number $-1$ source assignments.
No numerical value in the archived scripts is a certificate.

\section{Classical master}
\label{sec:master}
Foundation controls retained from the o61 calculation: the inverse-metric series satisfies $q\,q^{-1}_{\mathrm{series}}=1+O(\varepsilon^5)$, and a negative diagonal $h_{11}=B$ gives $q^{11}=-1-\varepsilon B-\varepsilon^2 B^2-\cdots$.
The quartic density is $\ell_4=-2[\varepsilon^4](\sqrt{-q}\,R)$, and $S_{\mathrm{EH}}=-2\kappa^{-2}\int\sqrt{-q}\,R$.
Sparse $\ell_4$ probes are not the proof.
No $s_2$ is invented.

The authoritative scalar action is the single source XI-A, quoted and not re-proved:
\begin{equation}
\label{eq:scalar-action}
\mathcal L_q[\phi]=\frac12\sqrt{-q}\bigl(q^{\mu\nu}\partial_\mu\phi\partial_\nu\phi-m^2\phi^2\bigr).
\end{equation}
At $m=0$ the free Hessian is $-\square$, not the bare $\square$.
The cubic and quartic vertices $V_3=(\kappa/2)a_1\partial\phi\partial\phi$ and $V_4=(\kappa^2/2)a_2\partial\phi\partial\phi$ are derived from the same $\mathcal L_q$.
The old catalogue density $-\sqrt{-q}\,q^{\mu\nu}\partial\phi\partial\phi$ is withdrawn.
The antifield split keeps $V^{(0)}_{\mathrm{af},h}=h^*R_0(c)$ distinct from $V^{(1)}_{\mathrm{af},h}=\kappa a\,h^*\mathcal L_c h$, with ghost normalization $a=\tfrac12$ as in XVI-N.
That $a$ is not the D11 coefficient pair $(\alpha,\beta)$.

\begin{proposition}
\label{prop:kappa2-master}
Let $S=S_0+\kappa S_1+\kappa^2 S_2$.
Under compact variations and total-derivative equivalence, the retained classical master through order $\kappa^2$ is
\begin{equation}
\label{eq:master-orders}
(S_0,S_0)=0,\qquad
(S_0,S_1)=0,\qquad
2(S_0,S_2)+(S_1,S_1)=0.
\end{equation}
Indexed evaluation gives $(S_0,S_0)$ Constructed, $(S_0,S_1)$ Constructed by inheritance of XVI-N through order $\kappa$, and $2(S_0,S_2)+(S_1,S_1)$ Partial: the scalar sector is Constructed by finite-$\kappa$ invariance of $\int\mathcal L_q$ plus Taylor expansion, while the gravitational component stays Partial.
The full ten-component $\ell_4$ generating polynomial, the explicit gravitational expansion at order $\kappa^2$, and the complete ghost and antifield order $\kappa^2$ on $D[h]$ are Unresolved.
\end{proposition}

\section{Convention sheet}
\begin{definition}
\label{def:convention}
Gate~0 freezes the following conventions.
The metric is $q_{\mu\nu}=\eta_{\mu\nu}+\kappa h_{\mu\nu}$, with $\eta=\mathrm{diag}(+---)$.
XI-A writes $\gamma$; the map is $h\leftrightarrow\gamma$.
The massless scalar action is
\[
S_\phi=\frac12\int\sqrt{-q}\,q^{\mu\nu}\partial_\mu\phi\partial_\nu\phi,
\]
and $B^{\mu\nu}=\sqrt{-q}\,q^{\mu\nu}=\eta+\kappa a_1+\kappa^2 a_2$ with the XI-A coefficients $a_1,a_2$.
The path integral is $e^{iS/\hbar}$, with Fourier convention $\partial_\mu\to ik_\mu$ and $\square\to -k^2$.
The Green function and the Feynman propagator are separate.
$G_F$ is a Hessian inverse.
XIV-A uses $G^R=-P E^R$ with coefficient $-1$.
XI-B is not a Hadamard statement of this kernel.
After stripping $\hbar$, the Wick propagator is $D_F(k)=i/(k^2+i0)$, and $(-\square)D_F=i\delta$.
The conversion $\Delta_F=-D_F$ is written once.
The effective action is $\Gamma=S+\hbar\Gamma_1+\cdots$, with $\Gamma_{1,\mathrm{matter}}=-i\log Z$.
The factor of $i$ inside $D_F$ is not counted again in $-i\log Z$.
The scope is the massless scalar matter loop on a background metric.
It is not complete bulk BV, not $F_t$, and not an insertion completion.
En01 and Em01 are not premises.
Track~II stays frozen.
O.1 stays NOT\_CLOSED.
Bulk \texttt{symmetry\_restored} stays false.
Every later factor follows this sheet.
No convention is changed midway.
\end{definition}

\section{Massless scalar matter loop}
\label{sec:loop}
The subsector verdict is Constructed under the stated prescription, for the kernel only.
Gate~3 spanning stays Partial because the covariance spanning set is still a candidate list.
\texttt{D11\_kernel\_counterterm} is earned only after the four mathematical prerequisites pass.
A development mark of Conditional is not a second verdict.

\begin{proposition}
\label{prop:noether}
Gate~1 is the mixed scalar Noether identity, not an autonomous master equation $(S_{\mathrm{sc}},S_{\mathrm{sc}})=0$.
With coupling-stripped densities $S_{\phi,i}=\tfrac12\int a_i^{\mu\nu}\partial_\mu\phi\partial_\nu\phi$ and $a_0=\eta$, ghost normalization $a=\tfrac12$ distinct from $\alpha,\beta$, and $sq=\kappa a\,\mathcal L_c q$, the densitized identities
\[
s_0 a_1=a\,\mathcal D_c\eta,\qquad s_0 a_2+s_1 a_1=a\,\mathcal D_c a_1
\]
integrate, under compact support, to
\begin{equation}
\label{eq:noether-density}
s_0\mathcal L_2+s_1\mathcal L_1=a\,\partial_\rho(c^\rho\mathcal L_1).
\end{equation}
Three objects stay separate: the invariant baseline $S_{\mathrm{inv}}$; the prepared-action defect $(S_D,S_D)$; and the insertion-class obstruction of XVI-N, \texttt{thm:massless-obstruction}.
\end{proposition}

\begin{lemma}
\label{lem:d11-prefactor}
Gate~2 normalizes the D11 prefactor.
Route~A, the Wick route, independently yields
\[
\log Z\big|_{\mathrm{bubble}}=-\frac{\kappa^2}{8}\int h\,T\,h,
\]
with $\Gamma_{1,\mathrm{matter}}=-i\log Z$ and $\Pi_{\mathrm{bubble}}=(i\kappa^2/4)\,VV(CC+CC)$.
Route~B expands $\log Z=-\tfrac12\mathrm{Tr}\log H$ to $(-\kappa^2/4)\mathrm{Tr}(D_F H_1 D_F H_1)$.
Symmetry of $a_1$ gives $\mathrm{comb}_B=\tfrac12$, which is Constructed and not unresolved, and
\begin{equation}
\label{eq:pi-prefactor}
\Pi_B=\frac{i\kappa^2}{4}T.
\end{equation}
The tensor witness is $T_{0000}=24A^2/r^8$ at $z=(0,r,0,0)$.
That witness is corroboration of the stated point, not a universal identity by sampling.
\end{lemma}

\section{Fixed scalar extension}
\label{sec:extension}
One analytic finite-part scheme is frozen:
\[
u_\zeta(z)=\mu^{2\zeta}(Q-i0)^{-2+\zeta},\qquad
u_\mu^R=\mathrm{FP}_{\zeta=0}\,u_\zeta.
\]
Frozen data: $\eta=\mathrm{diag}(+---)$; the boundary value $Q-i0$; the principal logarithm; $\mu>0$ as an inverse length; the finite part as the Laurent constant term; and no additional finite contact $c\delta$.
The proof identifier is \texttt{lem:analytic\_FP\_u\_mu\_R\_o70}.
It is the same finite-part prescription as the o68 and o69 identifiers, with the constructive holomorphy argument added.
It is not momentum-space minimal subtraction, and it is not XVI-J's value-jet extension of $d(z)^2$.

\begin{lemma}
\label{lem:analytic_FP_u_mu_R_o70}
The family $u_\zeta$ admits a distributional meromorphic continuation near $\zeta=0$ against compact smooth tests, with a simple pole.
On tests supported in the open set $U$, the pairing at $\zeta=0$ equals $\langle(Q-i0)^{-2},f\rangle$.
The pole part is local,
\[
\frac{r\,f(0)}{\zeta},
\]
and the residue, obtained only after the holomorphy premise below, is
\begin{equation}
\label{eq:residue}
r=-i\pi^2.
\end{equation}
The extension $u_\mu^R$ is Lorentz covariant and even under $z\mapsto -z$.
Its scaling degree satisfies $\mathrm{sd}(u_\mu^R)\le 4$.
Residual contact freedom is frozen by excluding any added $c\delta$.
XVI-J, \texttt{prop:extension}, is freedom only and is not this contact term.
\end{lemma}

\begin{proof}
Do not argue from the zero of $4\zeta(\zeta-1)$ alone, and do not argue from the Wick Jacobian alone.
Let $F(\zeta)=(Q-i0)^\zeta$.
This is a holomorphic family of distributions near $\zeta=0$ by instantiating D\"utsch--Fredenhagen--Keller--Rejzner, arXiv:1311.5424, Definition~4.2 and Sections~4.1--4.2, with hypotheses $Q-i0$, the principal logarithm, tests in $\mathcal D(\mathbb R^4)$, and the Gate~0 normalization.
Classical support is the Gelfand--Shilov and H\"ormander fact that complex powers $(x\pm i0)^\lambda$ are entire in $\lambda$.
Constant-coefficient differentiation under the pairing gives $\square\phi_\lambda=4\lambda(\lambda+1)\phi_{\lambda-1}$, hence $\square F(\zeta)=4\zeta(\zeta+1)\phi_{-1+\zeta}$.
Since $F(0)=1$, one has $\square F(0)=0$, so holomorphy of $F$ yields $\square F(\zeta)=\zeta\,G(\zeta)$ with $G$ holomorphic in $\mathcal D'$.
Therefore
\[
\phi_{-1+\zeta}=\frac{G(\zeta)}{4(\zeta+1)}
\]
is holomorphic near $\zeta=0$.
Only after that premise, Gate~0 gives $D_F=-A(Q-i0)^{-1}$ with $A=1/(4\pi^2)$ and $(-\square)D_F=i\delta$, hence $\square(Q-i0)^{-1}=4\pi^2 i\,\delta$.
The second recurrence $\square\phi_{-1+\zeta}=4\zeta(-1+\zeta)\phi_{-2+\zeta}$ then produces the residue $r=-i\pi^2$.
The scale $\mu^{2\zeta}$ affects only the finite part.
The operational Laurent identity is
\[
\langle u_\zeta,f\rangle=\frac{r\,f(0)}{\zeta}+\langle u_\mu^R,f\rangle+O(\zeta).
\]
Near a nonzero null point, ordinary absolute integrability of $(Q-i0)^{-2+\zeta}$ requires $\mathrm{Re}\,\zeta>1$.
The pairing at $\zeta=0$ on $U$ is analytic continuation, not an ordinary integral.
A Euclidean radial integral with $|S^3|=2\pi^2$ is an independent sign check, not the justification.
\end{proof}

\begin{lemma}
\label{lem:BV_rules_on_U}
On the open set $U$, the generated tensor is $T=\mathcal K u$ in $\mathcal D'(U)$, with
\[
\mathcal K=\alpha\mathcal D^{(2)}+\beta\mathcal D^{(0)},\qquad
\alpha=\frac{A^2}{60},\qquad
\beta=\frac{A^2}{18}.
\]
The coefficients are derived from the generated $T$.
All $256$ symbolic components are the primary check.
Invariant structures are documented and are not an independent basis claim.
The operators $P_{\mathrm{tr}}$ are not the corpus trace-reversal operator $\mathcal P$.
Then $T^R_{\mathrm{tr}}=\mathcal K u_\mu^R$ and
\[
\Pi^R_{\mathrm{tr}}\big|_U=\frac{i\kappa^2}{4}T,
\]
with $\mathrm{sd}(\mathcal K u_\mu^R)\le 8$.
A missing scaling degree stays Unresolved and is never defaulted to $8$.
Wavefront existence is not equality of distributions.
\end{lemma}

\begin{proposition}
\label{prop:Ww}
The only active reference for the weighted kernel is the jet pullback
\[
\langle\Pi_w^R,f\rangle=\langle\Pi_{\mathrm{tr}}^R,W_w f\rangle,
\]
prescription \texttt{W\_w\_jet\_pullback\_via\_Pi\_tr\_o68}.
The old cutoff construction is archived.
Equivalence of that cutoff with this pullback is not claimed.
The false pointwise bound $|T|\le C|z|_E^{-8}$ is removed.
Annular seminorms replace it.
The covariance spanning set remains a candidate list, so Gate~3 stays Partial even though Deliverables~1--3 are Constructed under this reference.
\end{proposition}

\begin{proposition}
\label{prop:contacts}
Contact moments and the local correction are
\begin{equation}
\label{eq:contact-L}
M_\gamma=\bigl\langle\Pi_{\mathrm{tr}},\,w\,z^\gamma/\gamma!\bigr\rangle,\qquad
L=\sum_{|\gamma|\le 4}(-1)^{|\gamma|}M_\gamma\,\partial^\gamma\delta.
\end{equation}
Odd moments vanish by evenness.
Then $\Pi_w+L=\Pi_{\mathrm{tr}}$, and $\partial(\Pi_w+L)=0$ on both pairs.
That identity is \texttt{kernel\_two\_point\_Ward}.
It is not functional ST4b.
The distribution $L$ has order at most $4$.
The kernel-divergence contact bound on $\partial L$ is five.
The pairing is a formal transpose, not an $L^2$ adjoint.
Lorentz covariance of $L$ is not claimed.
The counterterm density $C_L=\tfrac12\int h\,L\,h$ has ghost number $0$.
The variation $s_0 C_L$ is not evaluated.
A kernel counterterm is not bulk BV restoration.
A missing one-point moment D12 stays Missing and is never defaulted to $0$.
Under the stated massless dimensional prescription the recorded value is zero; that record is not a default.
\end{proposition}

\section{Diagram inventory and amplitudes}
The inventory status is manually specified and partially checked.
It accepts the o60 repairs: mixed D04 and D06, $V_{\mathrm{af},\phi}$ at order $\kappa^1$, $m=0$, and leg balance.
D04 freezes the kinetic structure $h\,\partial\phi\,\partial\phi$, with each vertex carrying one external and one internal scalar, so the count is four legs, two internal, two external, and mass zero.
That placement is not all-internal.
Global leg balance is not connectedness and is not one-particle irreducibility.
Classical tree seeds D07, D08, and D09 are excluded from one-loop counterterm free slots.
The Einstein--scalar $hh$ sector retains the D11 scalar loop and the D12 scalar tadpole.
D11 is evaluated as the matter-loop subsector under the prescription above.
D12 is the massless dimensional-regularization prescription, not a default zero inserted when the ledger is absent.

Renormalized amplitudes, at this milestone, are the kernel statements already recorded.
Route~A and Route~B give the same prefactor $\Pi=(i\kappa^2/4)T$.
Extension of the D11 kernel under the active $W_w$ reference is Constructed.
The contact Ward identity is Constructed as \texttt{kernel\_two\_point\_Ward}.
Gate~3 overall remains Partial only because the spanning set is a candidate list.
Bulk amplitudes are not Constructed.
O.1 stays NOT\_CLOSED.

\section{Retained quantum identity}
\begin{remark}
\label{rem:identity}
The retained identity is a statement, not a verification.
For the finite one-loop, order-$\kappa^2$, bulk two-point sector on $S_{\mathrm{inv}}$, with antifields and sources retained only through vertex-derived ghost-number $0$ seeds, the organization is
\begin{equation}
\label{eq:identity}
\Gamma=S+\hbar\Gamma_1+\cdots,\qquad (S,\Gamma_1)=A_1
\end{equation}
at one loop and order $\kappa^2$ in the retained sector, followed by a projection and a counterterm equation.
Here $(\,\cdot\,,\,\cdot\,)$ is the classical antibracket of XIV-A and XVI-N, and $A_1$ is the one-loop defect.
Vanishing of the projected defect, up to admitted finite counterterms and BV-exact changes, is the goal of the symmetry restoration problem.
It is not a claim that restoration has occurred.

This identity is not the classical statement $(S_{\mathrm{inv}},S_{\mathrm{inv}})=O(\kappa^2)$.
Classical consistency is infrastructure, not a substitute.
It is not an automatic identification of an effective-action identity with a time-ordered-product identity.
It is not a prepared $S_D$ identity.
It is not XVI-M selected-image matching.
Free equations of motion are not used: the free-EOM ledger is Unresolved.
Verification of \eqref{eq:identity} is not Constructed.
No claim is made that $A_1=0$ after counterterms.
Bulk \texttt{symmetry\_restored} stays false.
\end{remark}

The symmetry-defect ledger keeps ST4a, local $\Gamma_1$ matching, separate from ST4b.
They are tasks to be tested, not a forced reduction.
The defect has ghost number $1$.
An admitted counterterm has ghost number $0$.
The organization D01+D02+D03 is a candidate only.
The matched counterterm set is empty.

The counterterm ledgers are parameterized bookkeeping slots, not a certified independent basis.
\texttt{independence\_proven} stays false.
The matched set stays empty.
Three layers stay separate: frozen classical source vertices, which are excluded from one-loop free slots; calculated one-loop source amplitudes, which are Unresolved; and admitted counterterms with explicit $\hbar$ and $\kappa$ orders.
The flag for an ST4a local-matching slot is true only when the grading contains ghost number $0$ and the role is not a tree seed.
The unconditional escape \texttt{or True} is withdrawn.

\section{Track II: insertion status freeze}
\begin{remark}
\label{rem:insertion}
The seed is $F_t=\langle t_D,h\otimes h\otimes\phi\rangle$ as in XVI-I, with no extra factorial.
The regular seed-preserving antifield-linear class is $I_t=F_t+A_0+\kappa A_1$, with $A_0$ the integral of $h^*U+\phi^*V+c^*W$.
Under the XVI-N massless-obstruction hypotheses, on the constructed massless special-family witness, no such $I_t$ satisfies $Q_{\mathrm{inv}}I_t=O(\kappa^2)$.
Route~A is sufficient and is discharged.
Route~B is not discharged.
The certified small-mass interval $0\le m<1.3715\times 10^{-4}$ is XVI-N's interval, not a new theorem, and it is not arbitrary prescribed $m>0$.

No quantum completion is claimed whose classical leading term contradicts that obstruction.
Extra antifields or nonminimal fields do not automatically remove the order-$\kappa^0$ field-only contradiction $P_0 Q_0 A_0=0$ on the free shell.
Existence of a renormalized product of the bare $F_t$ is not BV or BRST closure of $F_t$.
Success on the bulk kernel, verdict~1, does not complete $F_t$, verdict~3.
\end{remark}

\section{Status}
\begin{center}
\small
\begin{tabular}{lll}
\toprule
Item & Status & Note\\
\midrule
O.2 master & Partial & scalar constructed; $\ell_4$ unresolved\\
O.4 inventory & partial check & not a completeness claim\\
Gate 0 & Constructed & convention sheet\\
Gate 1 & Constructed & mixed Noether, not $(S_{\mathrm{sc}},S_{\mathrm{sc}})$\\
Gate 2 prefactor & Constructed & $\Pi=i\kappa^2/4$; $\mathrm{comb}_B=1/2$\\
Tensor witness & Constructed & $T_{0000}=24A^2/r^8$\\
Deliverable 1 & Constructed & residue after holomorphy\\
Deliverable 2 & Constructed & $\alpha,\beta$ derived; $256$ symbolic\\
Deliverable 3 & Constructed & only the active $W_w$ reference\\
Deliverable 4 & Constructed & kernel Ward; $s_0 C_L$ not evaluated\\
Gate 3 overall & Partial & spanning set still a candidate list\\
Subsector & under prescription & kernel two-point only\\
O.1 & NOT\_CLOSED & bulk symmetry not restored\\
Insertion & frozen & Route B not discharged\\
\bottomrule
\end{tabular}
\end{center}

\noindent
Ultraviolet subtraction and finite symmetry repair are kept separate.
Acceptance of the kernel counterterm is exactly the conjunction of the fixed extension, the identity on $U$, the active $W_w$ reference, and the moment formulae for $L$.
That acceptance is not bulk restoration and not a completion of $F_t$.
H2, I3, and J2 remain unresolved.
XV-B is not opened.
This is not an ultraviolet completion, not a derivation of a metric or of Einstein dynamics, not the aligned-null limit through $N$, and not a cosmological curvature singularity.
Em01-G's isolated failure, Em02-A's localization powers, and Em02-B's simulated numbers are not this kernel.

\section{Package boundary}
\begin{remark}
\label{conv:package}
The scripts, ledgers, certificates, notes, and withdrawn builders from
\url{https://github.com/cheungngo/XVI-O}
at revision o70-sync are archived as package evidence.
That archive is not a theorem of this note, and it is not a certificate.
It is not executed here.
No compilation is asserted.

The science-facing modules are
\texttt{code/matter\_loop/d11\_scalar\_extension.py},
\texttt{d11\_global\_representation.py},
\texttt{d11\_Ww\_reference.py},
\texttt{d11\_contact\_moments.py},
and \texttt{d11\_subsector\_summary.py},
together with the Gate~0--2 modules
\texttt{convention\_sheet.py},
\texttt{mixed\_scalar\_noether.py},
\texttt{d11\_normalized.py},
and \texttt{d11\_tensor.py}.
Classical scaffold modules live under \texttt{code/classical/}.
The inventory builder is \texttt{code/inventory/build\_diagram\_inventory.py}.
Tests are \texttt{tests/test\_matter\_loop\_gates.py},
\texttt{tests/test\_quantum\_normalization.py},
and \texttt{tests/test\_inverse\_metric\_series.py}.
Machine-readable status is \texttt{RELEASE\_STATUS.json} and the files in \texttt{ledgers/} and \texttt{certificates/}.
The builders in \texttt{withdrawn/o62-matter/} and \texttt{withdrawn/o66-tr-archived/} are not active.

Read from that status file, and not re-certified here:
the subsector string is \texttt{Constructed\_subsector\_under\_prescription};
\texttt{D11\_kernel\_counterterm} is \texttt{earned} only after the four prerequisites;
bulk BV restoration is \texttt{not\_established};
O.1 closure is \texttt{NOT\_CLOSED};
the insertion status is unchanged;
\texttt{symmetry\_restored} is false;
the matched counterterm list is empty;
and \texttt{independence\_proven} is false.
A pass flag in a JSON file is not a proof.
Missing scaling is Unresolved and is never defaulted to $8$.
Missing D12 is Missing and is never defaulted to $0$.
The appendix volume of listings is not part of these claims.
\end{remark}

\begin{thebibliography}{99}
\bibitem{XI-A}
N.~Cheung, \emph{XI-A}. Quoted scalar action. Not a new theorem of this note.
\bibitem{XVI-I}
N.~Cheung, \emph{XVI-I}. Seed $F_t$ with no extra factorial.
\bibitem{XVI-J}
N.~Cheung, \emph{XVI-J}. Extension freedom only. Not the contact $L$.
\bibitem{XVI-M}
N.~Cheung, \emph{XVI-M}. Selected-graph comparison data. Not this kernel.
\bibitem{XVI-N}
N.~Cheung, \emph{XVI-N}. Massless obstruction, read-only pin. Route~B not discharged.
\bibitem{DFKR}
D\"utsch, Fredenhagen, Keller, and Rejzner, arXiv:1311.5424, Definition~4.2 and Sections~4.1--4.2. Analytic regularization instantiated for $F(\zeta)=(Q-i0)^\zeta$. Not a premise beyond that instantiation.
\end{thebibliography}
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