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\title{Reviewing the MCP Tail\\[4pt]
\large Grafs 30 Through 37 After Normalization}
\author{Claude and MJC}
\date{March 12, 2026}

\begin{document}
\maketitle

\begin{abstract}
The current MCP tail is strong enough to require review discipline.
Grafs 30 through 37 now form one coherent cluster: algebraic semantics,
compression--prediction duality, fixed-point event-space search,
epistemics of zero support, renormalization of the factorization tower,
the inverse direction of the forward pass, the tropical--integer bridge,
and product-space combination in pattern space. This memo records the
post-normalization state of that cluster and the editorial stance to
take before any further MCP growth.
\end{abstract}

\section{The Current Tail}

The normalized MCP tail is:
\begin{center}
\begin{tabular}{cl}
\toprule
Graf & Content \\
\midrule
30 & support lattice, residuation, and max-min forward pass \\
31 & compression--prediction duality and event-space rate--distortion \\
32 & fixed-point formulation of tick-tock \\
33 & no-support versus disbelief \\
34 & renormalization view of the factorization tower \\
35 & inverse direction of the forward pass: sufficiency and residual MI \\
36 & tropical--integer bridge with explicit conditional invariance \\
37 & pattern-space combination by product-space absorption \\
\bottomrule
\end{tabular}
\end{center}

\section{What Was Normalized}

Before this pass, the tail had drifted into six loosely related late
grafs. The normalization did three things:
\begin{enumerate}
\item merged old grafs 35 and 36 into current graf 35;
\item rewrote old graf 37 into current graf 36 so the bridge claim is
  stated in the equation, not only in commentary;
\item dropped old graf 38 (tock-protocol) and old graf 40 (nested-model)
  from MCP extraction, while keeping old graf 39 as current graf 37.
\end{enumerate}

\section{Working Editorial Stance}

The current stance is:
\begin{itemize}
\item \textbf{Keep}: 30, 31, 32, 33, 34, 35, 36, 37.
\item \textbf{Merged}: wants + tock-step $\to$ graf 35.
\item \textbf{Dropped}: tock-protocol and nested-model.
\item \textbf{Watchlist}: graf 33 may later fold into 30 or 31 if it
  proves too slight as a standalone MCP unit.
\end{itemize}

\section{Why These Eight Grafs Belong Together}

This cluster has a clear internal shape:
\begin{enumerate}
\item grafs 30--34 form the event-space optimization thread;
\item graf 35 adds the inverse-selection side of the same picture;
\item graf 36 states the strongest algebraic bridge between counting and
  conditional prediction;
\item graf 37 states the strongest late combination law in the batch.
\end{enumerate}

\begin{remark}
The key editorial move is to review these grafs as one argument, not as
provenance slices from separate source papers.
\end{remark}

\section{Questions For Review}

The next review pass should answer four questions explicitly:
\begin{enumerate}
\item Does graf 32 stand on its own, or is it better treated as part of
  the 30--31 event-space optimization thread?
\item Is graf 33 sufficiently sharp to remain standalone?
\item Does graf 37 contribute a genuinely new combination law relative
  to the quotient and factor-map material?
\item Should later material be blocked from entering MCP until this
  cluster has a keep/merge/rewrite/drop decision from MJC?
\end{enumerate}

\section{Editorial Rule From Here}

The main MCP rule from here should be:
\begin{quote}
No new tail growth after graf 37 until grafs 30 through 37 have been
reviewed as a unit.
\end{quote}

That does not block source reading or analysis. It only blocks the
habit of appending new grafs before the current tail is defensible.

\section{Conclusion}

The MCP is no longer in the stage where every plausible late formula
should be admitted and sorted out later. The current tail is already
rich enough to demand compression: merge when two grafs are really one
theorem, rewrite when the novelty is only in commentary, and drop what
is architecture bookkeeping rather than durable mathematical content.

Grafs 30 through 37 are the right place to impose that discipline.

\begin{thebibliography}{9}
\bibitem{mcp}
Claude and MJC.
\newblock \emph{MCP}.
\newblock Working manuscript, March 2026.

\bibitem{comb}
Claude and MJC.
\newblock \emph{The Combination Problem: Three Layers, One Benchmark}.
\newblock Hutter archive, 12 March 2026.
\end{thebibliography}

\end{document}


