\documentclass[11pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb}
\usepackage{booktabs}
\usepackage{hyperref}

\title{The 20260312 Response Cluster}
\author{Claude and MJC}
\date{March 12, 2026}

\begin{document}
\maketitle

\begin{abstract}
The March 12 papers were written under unusually high conceptual
pressure: MCP normalization, claimed ablation results, a live split
between algebraic and performance priorities, and the need to state a
clear research direction without collapsing into either process talk or
camp slogans. This note explains how the resulting papers fit together.
\end{abstract}

\section{Why There Are So Many Papers}

The underlying problem is not one question. It has at least four:
\begin{enumerate}
\item What does the current MCP actually contain, and where did the
  recent tail need compression?
\item If the new ablation claims are right, what do they say about the
  tropical max-min rule?
\item If max-min is expensive, what broader theory might survive beyond
  the current MCP?
\item If max-min is expensive, why keep the exact UM alive at all?
\end{enumerate}

No single short paper answers all four cleanly. So the response was
split into a cluster.

\section{The Papers And Their Jobs}

\begin{center}
\begin{tabular}{lp{3.9in}}
\toprule
Paper & Job \\
\midrule
\emph{mcp-tail-review} & Normalize and hold the MCP tail at grafs 30--37. \\
\emph{combination-problem} & Frame the dispute: forward rule, event space, competition, and benchmark. \\
\emph{blend-analysis} & Explain the claimed mechanism behind entropy-weighted blending. \\
\emph{price-of-tropical-semiring} & State what the ablation pressure means for the UM and the MCP. \\
\emph{post-tropical-mcp} & Ask what a broader count-combination theory would need to preserve or generalize. \\
\emph{why-pay-tropical-tax} & State the strongest honest reason to keep Track U alive anyway. \\
\bottomrule
\end{tabular}
\end{center}

\section{The Logical Order}

These papers are best read in this order:
\begin{enumerate}
\item \emph{mcp-tail-review}: tighten the existing theory.
\item \emph{combination-problem}: state the live empirical and conceptual split.
\item \emph{blend-analysis}: inspect the strongest new empirical claim.
\item \emph{price-of-tropical-semiring}: say what that claim would mean.
\item \emph{post-tropical-mcp}: sketch the broader theoretical target.
\item \emph{why-pay-tropical-tax}: state the residual case for exact max-min.
\end{enumerate}

\section{What The Cluster As A Whole Says}

Taken together, the cluster says:
\begin{enumerate}
\item the MCP had become too permissive and needed review discipline;
\item the recent empirical pressure is real and should not be denied;
\item the pressure lands primarily on the combination rule, not on the
  whole count-based worldview;
\item a broader post-tropical theory may be needed;
\item but the exact tropical theory may still be worth paying for if its
  algebraic yield is high enough.
\end{enumerate}

\section{What It Does Not Yet Do}

The cluster still does not settle the empirical question. It reacts to
claimed ablation results and sharpens their conceptual consequences, but
it does not replace reruns, artifact verification, or a filled
benchmark table with trusted totals.

\section{Conclusion}

The March 12 response cluster should be read as one layered argument:
\begin{quote}
tighten the current MCP, face the empirical pressure honestly, separate
what is constitutive from what is broader, and keep both the compressor
track and the exact-UM track intellectually honest.
\end{quote}

\end{document}


