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% The Anti-Solipsism Theorem. Strong solipsism incoherent; weak solipsism true/located; two regimes
% (synchronicity=linking=correlation; action=cause). Seed for Paper 42. Author: Leon Fernando
% Vlegels. Text CC BY 4.0. Verifier: verify_P375.py (8/8 pass).
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\title{Addendum 375: The Anti-Solipsism Theorem\\
\large One statement consolidating the shared-boundary, enforcement, and\\
linking results --- solipsism as a category error\\[0.3em]
\normalsize (Consolidates Paper 04 with Addenda 373, 374; seed for Paper 42)}
\author{L\'eon Fernando Vlegels}
\date{2026-06-19}

\begin{document}
\maketitle

\begin{abstract}
The anti-solipsism result has been assembled in pieces: Paper~04 (multiple observers on a shared
boundary; privacy of monadic experience; communication via the classical layer; cardinality of
observers), Addendum~373 (shared reality enforced --- one $\Sthree$, disjoint fibers, the sole
inter-fiber channel through $\Sthree$), and Addendum~374 (linked-but-disjoint --- the Hopf linking as
acausal correlation, and the two regimes of efficacy). This addendum states it once, as a single named
theorem, and names the diagnosis it implies: solipsism is a \emph{category error}, the privacy of a
fiber mistaken for the privacy of the bundle. The result splits the solipsist thesis into a true,
exactly-located claim (the privacy of experience) and an incoherent one (that only the self exists),
and locates synchronicity and action as the two regimes of efficacy --- correlation through the
linking, causation only by action on the shared boundary. Theorem-grade as topology; the one hinge is
the interpretation that the fibers are observers. All claims pinned by \texttt{verify\_P375.py} (8/8).
This addendum is the seed consolidated into Paper~42.
\end{abstract}

\section{The theorem}
\label{sec:thm}

\begin{theorem}[Anti-Solipsism]
\label{thm:antisolipsism}
Let observers be the $S^1$ fibers of the Hopf fibration $\pi:\Sthree\to S^2$. Then:
\begin{enumerate}
\item[\textbf{(a)}] \textbf{Privacy (the solipsist's true datum).} Fibers are pairwise disjoint,
$M_i\cap M_j=\varnothing$; experience is fiber-local. The privacy of experience is true and exactly
located.
\item[\textbf{(b)}] \textbf{Embedding (the solipsist's false step).} Every fiber is a \emph{proper}
subset of the one shared total space $\Sthree$, which carries continuum-many fibers ($|S^2|=\mathfrak
c$). A perspective is by definition a fiber \emph{of} the bundle, so to be an observer is already to
be embedded in the shared arena. ``Only I exist'' is therefore not false-by-evidence but
\emph{incoherent}: it denies the very structure that constitutes the viewpoint it asserts.
\item[\textbf{(c)}] \textbf{Enforcement.} The only inter-fiber channel is the shared $\Sthree$
($M_i\to\Sthree\to M_j$); intersubjective consistency is enforced by the topology, and disjoint
private realities are excluded (Addendum~373).
\item[\textbf{(d)}] \textbf{Two regimes.} Distinct fibers are disjoint yet linked, with linking
number $1$: private viewpoints are acausally correlated through the bundle --- the structural form of
synchronicity (Addendum~374), an affectable layer --- while the shared $\Sthree$ changes only by
\emph{action} through $\Sthree$. The linking is correlation, not leverage.
\end{enumerate}
\end{theorem}

\begin{corollary}[Solipsism is a category error]
\label{cor:category}
Strong solipsism (only the self exists) is dissolved, not refuted: by (b) it is incoherent, since
being-an-observer is already being-embedded. Weak solipsism (the privacy of experience) is true and
exactly located by (a). The error is to read the privacy of a fiber (a, true) as the privacy of the
bundle (b, incoherent) --- a category error. By (d) the lever the solipsist covertly wants, a private
power over the shared world, is exactly what the topology forbids.
\end{corollary}

\begin{remark}[The hinge]
\label{rmk:hinge}
Parts (a)--(d) are theorems about the Hopf bundle --- disjointness, proper-subset embedding, the sole
$\Sthree$ channel, linking number $1$ --- and use no observer notion. The single interpretation, which
Paper~04 carries as such, is that the fibers \emph{are} conscious observers (monad $=$ consciousness);
a second, narrower reading identifies the linking with \emph{experienced} synchronicity. The corpus
establishes the topology and permits the readings; it asserts no paranormal phenomenon.
\end{remark}

\section*{Status}
The Anti-Solipsism Theorem (Theorem~\ref{thm:antisolipsism}) consolidates P04, 373, and 374 into one
statement: privacy is true and located (a), the self-only thesis is incoherent (b), consistency is
enforced (c), and efficacy splits into correlation (the linking) and causation (action on the shared
boundary) (d). The diagnosis is that solipsism is a category error (Corollary~\ref{cor:category}). The
result is theorem-grade as topology, with the monad $=$ observer interpretation as its one hinge
(Remark~\ref{rmk:hinge}). This addendum is the compact seed; Paper~42 expands it into a full treatment
with the philosophical and psychological context the result speaks to. No published number changes; no
new objects beyond the consolidation. Verifier: \texttt{verify\_P375.py}, 8/8 pass.

\end{document}
