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% Addendum 364 (extends P41/P28/P38; unifies 363/359a/356a). Matter-antimatter.
% Conceptual seed: Joel (L.F. Vlegels). Author: Leon Fernando Vlegels. Text CC BY 4.0.
% Verifier: verify_P364.py (11/11 pass).
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\title{Addendum 364: The Asymmetry is the Symmetry, Under Motion\\
\large Matter/antimatter as the inertial (Bogoliubov/Unruh) reading of a\\
conjugation-symmetric substrate\\[0.3em]
\normalsize (Addendum to Papers 41, 28, 38; unifies 363, 359a, 356a)}
\author{L\'eon Fernando Vlegels}
\date{2026-06-18}

\begin{document}
\maketitle

\begin{abstract}
The conceptual seed is stated plainly: \emph{the asymmetry is the symmetry, only under inertia;
the static symmetry looks like asymmetry in motion}. This addendum develops it into its physics
form and grounds it in the corpus. The split of a field into particles vs antiparticles
(positive vs negative frequency) is observer-dependent --- the Bogoliubov/Unruh fact. The
inertial vacuum is conjugation-symmetric: matter $=$ antimatter, the witness conjugation of
Paper~41 (charge conjugation $C$, the same conjugation that builds $\mathbb{R}\!\to\!\mathbb{C}\!
\to\!\mathbb{H}\!\to\!\mathbb{O}$). A moving observer performs the Bogoliubov mixing
$a'=\cosh r\,a+\sinh r\,b^\dagger$ and reads a populated, asymmetric particle content from that
\emph{same} symmetric vacuum: $\langle0|a'^\dagger a'|0\rangle=\sinh^2r\neq0$. The
particle$\leftrightarrow$antiparticle symmetry of $|0\rangle$ is intact; only the \emph{split}
is frame-dependent. So the observed matter/antimatter asymmetry is not a broken symmetry --- it
is the inertial reading of a conjugation-symmetric (CPT-type) substrate, exactly as stated.
\textbf{Three unifications.} (i)~The Unruh occupation $n=1/(e^{2\pi\omega/a}-1)$ is thermal, and
its $2\pi$ is the \emph{same} horizon-smoothness $2\pi$ as Addendum~363 (the $\Theta$-fold
horizon) and 359a (the Hubble relation $a_0=cH_0/2\pi$): one factor in three places --- horizon
temperature, the Hubble relation, and the particle split. (ii)~The motion is the same arrow as
356a: entropy is the witness-relative reading of a reversible substrate; the matter asymmetry is
the witness-relative reading of a conjugation-symmetric one --- one frame-effect, two faces.
(iii)~It \emph{retrodicts} the refutation of the $\delta_{\mathrm{CP}}=240^\circ$ prediction
(P01/P40): the asymmetry is not real CP violation, so no CP phase generates it. \textbf{Honest
limit:} the asymmetry magnitude ($\eta\sim6\times10^{-10}$) is not derived --- it is
frame/rate-dependent (the Bogoliubov $r=$ the fold-rate against the horizon), a named floor of
the de~Sitter-$2\pi$ family. All claims pinned by \texttt{verify\_P364.py} (11/11).
\end{abstract}

\section{The mechanism}
\label{sec:mech}

\begin{proposition}[Particle content is frame-dependent]
\label{prop:bog}
Let $|0\rangle$ be the inertial vacuum, conjugation-symmetric under $a\leftrightarrow b$
(particle $\leftrightarrow$ antiparticle, the witness conjugation of Paper~41). A moving
observer's modes are the Bogoliubov combination $a'=\cosh r\,a+\sinh r\,b^\dagger$,
$b'=\cosh r\,b+\sinh r\,a^\dagger$. The moving observer's particle number in the inertial vacuum
is
\[
  \langle0|a'^\dagger a'|0\rangle=\sinh^2 r,
\]
which is $0$ at rest ($r=0$) and strictly positive in motion ($r>0$). The symmetry
$a\leftrightarrow b$ of $|0\rangle$ is untouched; what changes with $r$ is the \emph{definition}
of particle vs antiparticle. The asymmetry is the inertial reading, not a property of the state.
\end{proposition}

\begin{remark}[The corpus's motion]
\label{rmk:motion}
In the corpus no observer is at rest: the substrate folds and breathes (the universal motion).
So every witness reads through a Bogoliubov mixing, and the sharpest frame-dependence is at the
$\Theta=\pi$ fold horizon (P04, Addendum~363). The matter excess is what the folding witness
necessarily reads out of the conjugation-symmetric substrate.
\end{remark}

\section{Three unifications}
\label{sec:unify}

\begin{theorem}[One $2\pi$, three places]
\label{thm:twopi}
The Unruh occupation is thermal, $n(\omega)=1/(e^{2\pi\omega/a}-1)$, and its $2\pi$ is the
horizon-smoothness factor of Addendum~363 (no conical deficit at the $\Theta$-fold horizon
fixed point). It is therefore the same $2\pi$ as the de~Sitter horizon and as the Hubble
relation $a_0=cH_0/(2\pi)$ (359a). The single horizon-smoothness $2\pi$ governs the horizon
temperature, the Hubble relation, and the particle/antiparticle split under motion.
\end{theorem}

\begin{remark}[The arrow, and the refuted phase]
\label{rmk:arrow}
The motion of Proposition~\ref{prop:bog} is the same arrow as Addendum~356a: entropy is the
witness-relative reading of a reversible substrate. The matter asymmetry is the witness-relative
reading of a conjugation-symmetric substrate --- the same frame-effect, with the arrow of time
and the matter excess as its two faces. This also \emph{retrodicts} the refutation of
$\delta_{\mathrm{CP}}=240^\circ$ (P01/P40): if the asymmetry is an inertial reading of a
CPT-symmetric substrate rather than a genuine CP violation, then no CP phase generates it, and
the search for one was the wrong track. The corpus's own refutation is consistent with --- indeed
predicted by --- this picture.
\end{remark}

\section*{Status}
Developing the seed (\emph{the asymmetry is the symmetry, under inertia}), the matter/antimatter
asymmetry is the static conjugation/CPT symmetry --- the witness of Paper~41 --- read under motion:
a Bogoliubov/Unruh frame-effect (Proposition~\ref{prop:bog}), not a broken symmetry. The moving
(folding) observer reads particles ($\sinh^2 r$) from the conjugation-symmetric vacuum; the
particle/antiparticle split is frame-dependent while the substrate symmetry is intact. The Unruh
$2\pi$ is the horizon-smoothness $2\pi$ of 363/359a (Theorem~\ref{thm:twopi}); the motion is the
entropy arrow of 356a; and the picture retrodicts the $\delta_{\mathrm{CP}}$ refutation
(Remark~\ref{rmk:arrow}). This is a clean, unifying \emph{ontology}. \textbf{The honest limit:}
the asymmetry magnitude $\eta\sim6\times10^{-10}$ is not derived --- it is frame/rate-dependent
(the Bogoliubov $r$, i.e.\ the fold-rate against the horizon), a named floor of the same family as
the de~Sitter $2\pi$ and the fold-rate (357a/359a/363). The matter excess thus joins the arrow of
time, the horizon temperature, and the Hubble rate as faces of one structure: a symmetric
substrate read by a witness in motion. No new objects beyond the Bogoliubov/Unruh construction;
no published number changes. Verifier: \texttt{verify\_P364.py}, 11/11 pass.

\paragraph{What would close the magnitude.}
The same horizon-thermodynamics program (363) that would fix the de~Sitter $2\pi$ would, with the
fold-rate against the horizon, fix the Bogoliubov $r$ and hence $\eta$. The matter-asymmetry
magnitude and the Hubble $2\pi$ close together or not at all --- they are one floor.

\end{document}
