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\usepackage{booktabs}
\usepackage{caption}
\usepackage{graphicx}
\usepackage{xurl}
\usepackage{hyperref}
\usepackage{placeins}
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\graphicspath{{figures/}}
\newcommand{\tablepath}{tables}
\newcommand{\Az}{A_z}
\newcommand{\sigz}{\langle\sigma_z\rangle}
\newcommand{\BW}{\mathrm{BW}}

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  colorlinks=true,
  linkcolor=blue!45!black,
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}

\title{\vspace{-1.0cm}Independent Reproduction of the Bell-Triplet Spin-Readout Notes}
\author{\rule{6em}{1.1ex}}
\date{\today}

\begin{document}
\maketitle

\begin{abstract}
This note reproduces the essential numerical claims in
\path{docs/internal_note/main.pdf} and \path{docs/internal_note/risk_audit.pdf}
from raw PIKOE tables, PIKOE outlists, Saclay-amplitude CSV grids, and the
saved risk-sweep JSON outputs.  No original source files were modified.  The
new code, plots, and tables live in \path{src/gpt-claude-reproduction/}.
\end{abstract}

\section{Scope and Provenance}

The reproduction uses the PWA93, AV18, and AV8' Saclay CSV files for the
elementary $pp$ amplitude, the PIKOE sample tables for
$^{7}$Li$(p,2p)^{6}$He and $^{17}$F$(p,2p)^{16}$O, and the risk-audit JSON
files for the already-run A2/A3/B1/D5 sweeps.  All Bell-readout quantities
below were recomputed in the new script
\path{src/gpt-claude-reproduction/reproduce_results.py}; generated tables
are in \path{src/gpt-claude-reproduction/tables/}.

At the free-$pp$ target point the reproduction gives
$S(151\,\mathrm{MeV},90^\circ)=0.9943$ and
$d\sigma/d\Omega=3.72$ mb/sr using PWA93 with Coulomb added.  The production
path is therefore a PWA93-based reproduction of the note's results; it is not
a fresh chiral-EFT amplitude calculation.

\section{Free $pp$ Bell Window}

\begin{figure}[!htbp]
  \centering
  \includegraphics[width=\linewidth]{fig01_free_pp_bell_window.pdf}
  \caption{Independent reconstruction of the elementary $pp$ Bell-window
  structure.  The PWA93 similarity island contains the intended
  $(E_{NN},\theta_{NN})=(151\,\mathrm{MeV},90^\circ)$ point; AV18 and AV8'
  track PWA93 closely near the central line but are used here as model-spread
  checks rather than as chiral truncation errors.}
\end{figure}

\FloatBarrier
\section{Production Scans}

\begin{table}[!htbp]
  \centering
  \caption{Beam-energy scan reproduced from the PIKOE tables and outlists.
  Stars mark the beam energies used for the production forecasts.}
  \resizebox{\linewidth}{!}{\input{\tablepath/beam_scan_table.tex}}
\end{table}

\begin{figure}[!htbp]
  \centering
  \includegraphics[width=\linewidth]{fig02_beam_energy_scans.pdf}
  \caption{Beam-energy scan diagnostics.  The reproduced optima are
  $130$ MeV/u for $^{7}$Li and $140$ MeV/u for $^{17}$F, matching the internal
  note.}
\end{figure}

\begin{figure}[!htbp]
  \centering
  \includegraphics[width=\linewidth]{fig03_yield_maps.pdf}
  \caption{Phase-space yield maps at the production energies.  Orange points
  are bins with $S(M,G_\odot)\ge 0.95$.  The right column weights the PIKOE TDX
  by a high power of the Bell similarity to make the useful kinematic ridge
  visually explicit.}
\end{figure}

\FloatBarrier
\section{Bell Readout and Counting}

\begin{table}[!htbp]
  \centering
  \caption{Scenario forecasts using the absolute-precision definition
  $\sigma(s_b^z)=0.05$.  The realistic rows reproduce the headline values:
  $^{7}$Li gives $\Az=0.130$, $\dot N=238$ s$^{-1}$, $t_{5\%}=42$ s; $^{17}$F
  gives $\Az=0.030$, $\dot N=2.33\times 10^{-2}$ s$^{-1}$, $t_{5\%}=119$ h.}
  \resizebox{\linewidth}{!}{\input{\tablepath/scenario_table.tex}}
\end{table}

\begin{figure}[!htbp]
  \centering
  \includegraphics[width=\linewidth]{fig04_bias_and_readout.pdf}
  \caption{Readout diagnostics at the production energies.  The full-amplitude
  physical readout gives $\Az=0.1231$ for $^{7}$Li and $\Az=0.0280$ for
  $^{17}$F at the $S_{\min}=0.95$ cut, while the ideal Bell-limit scenario
  table uses $P_TP_b=0.130$ and $0.030$.}
\end{figure}

\begin{figure}[!htbp]
  \centering
  \includegraphics[width=0.92\linewidth]{fig05_statistical_precision.pdf}
  \caption{Absolute statistical precision versus beam time for the conservative,
  realistic, and optimistic scenarios.}
\end{figure}

\FloatBarrier
\section{Systematics and Risk Audit}

\begin{table}[!htbp]
  \centering
  \caption{Risk-axis ranges reproduced from the saved JSON sweeps.  A1 is the
  active-proton spin-density band; A2, A3, B1, and D5 are the production
  pipeline sweeps.}
  \resizebox{\linewidth}{!}{\input{\tablepath/risk_range_table.tex}}
\end{table}

\begin{figure}[!htbp]
  \centering
  \includegraphics[width=\linewidth]{fig06_model_and_internal_systematics.pdf}
  \caption{Model and internal PIKOE systematics.  The on-shell prescription and
  optical-potential checks mostly move rates; the Bell-readout asymmetry is
  much less sensitive.}
\end{figure}

\begin{figure}[!htbp]
  \centering
  \includegraphics[width=\linewidth]{fig07_risk_audit_summary.pdf}
  \caption{Risk-audit reproduction.  The dominant horizontal range is the
  A1 $\sigz$ band; A2/A3/B1/D5 are sub-percent in the saved production sweeps.
  The lower panels reproduce the small A3 logarithmic Jacobians.}
\end{figure}

\begin{figure}[!htbp]
  \centering
  \includegraphics[width=\linewidth]{fig08_bookkeeping_and_crosschecks.pdf}
  \caption{Bookkeeping and cross-check reproductions.  The Pauli-blocking panel
  shows why the momentum convention matters; the carbon panel keeps the
  order-of-magnitude $S/B$ floor visible; the deuteron panel shows the effect
  of closing the $S+D$ probability; and the last panel reproduces the
  $^{17}$O pipeline check.}
\end{figure}

\FloatBarrier
\section{Mistake-Oriented Findings}

\begin{center}
\small
\begin{tabular}{p{0.22\linewidth}p{0.70\linewidth}}
\toprule
Topic & Reproduction finding \\
\midrule
Frame handling &
The reproduced BW bins are not exactly in a common lab spin frame:
$^{7}$Li has weighted $\theta(\mathbf{k}_i,-\hat z)=7.73^\circ$ and
$^{17}$F has $6.15^\circ$.  This is small enough to look like a few-percent
effect in the weighted $F_{zz}$ factor, but it is not the zero-rotation
assumption stated in the prose. \\
Pauli blocking &
Using the lab projectile momentum gives $Q=0.99986$ at $\rho_0$; using the
NN c.m. relative momentum gives $Q=0.871$.  The old ``$<0.01\%$'' statement is
a lab-momentum result, not the relative-momentum result. \\
Amplitude source &
The production runs reproduce PWA93-based Saclay amplitudes.  AV18/AV8' are
useful spread checks, but this package found no production use of a live
chiral-EFT amplitude path. \\
$t_{5\%}$ definition &
The scenario table above uses the main-note absolute definition
$\sigma(s_b^z)=0.05$.  The risk addendum also uses a relative definition that
scales as $(P_b\sigz)^{-2}$.  These are different observables and should not
share one label. \\
$^{17}$F significance &
The realistic $^{17}$F forecast remains $\Az=0.030$, below the addendum's
$\Az\ge 0.05$ discovery threshold.  It is a feasible signal estimate, not a
discovery-significance case under that threshold. \\
Carbon floor &
The reproduced arithmetic gives $S/B\simeq 0.002$ raw and about $0.02$ after
a $10\times$ BW rejection, not $0.2$--$0.5$. \\
Deuteron calibration &
The note bookkeeping values $P_S=0.89$ and $P_D=0.058$ sum to $0.948$.  Closing
$P_S+P_D=1$ shifts $\sigz_{\rm active}$ from $0.861$ to $0.913$. \\
$^{7}$Li valence wording &
The alpha-core $p$-shell picture is one valence proton plus two valence
neutrons, not three valence protons plus four valence neutrons in the
$1p$ shell. \\
\bottomrule
\end{tabular}
\end{center}

\section{Artifacts}

The code is \path{src/gpt-claude-reproduction/reproduce_results.py}.
The canonical machine-readable outputs are
\path{src/gpt-claude-reproduction/data/summary.json} and the CSV/TEX tables
under \path{src/gpt-claude-reproduction/tables/}.  The figure PDFs and PNGs
are under \path{src/gpt-claude-reproduction/figures/}.

\end{document}
