% 284_Addendum_EdgeWeightedComma.tex
% OI-283-1 attempted: the amplitude correction 0.9887(2) is bracketed by
% two candidates inside the CODATA edition spread — edge exclusion
% (1 - pi/Omega, physically motivated by A281/P04) and 1 - 1/44
% (unmotivated integer). Identification below bar; the discriminating
% precision is stated (~0.1 ppb). Under the edge candidate the corpus
% predicts alpha^-1 to 0.43 ppb. Verifier: verify_P284.py.
% Copyright Léon Fernando Vlegels -- CC BY 4.0

\documentclass[11pt]{article}
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\usepackage{booktabs}
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\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}

\title{Addendum 284: The Edge-Weighted Comma\\
\large The amplitude correction bracketed: edge exclusion vs $1/44$;\\
the 0.1-ppb discriminator}
\author{TOE Corpus}
\date{2026-06-10}

\begin{document}
\maketitle

\noindent\textbf{Skill:} gap-closure v1.1 \quad|\quad
\textbf{Outcome:} Case B (two candidates inside instrument resolution;
leading candidate by motivation only; discriminator stated) \quad|\quad
\textbf{Addresses:} OI-283-1 (kept open, sharpened) \quad|\quad
\textbf{Verifier:} \texttt{verify\_P284.py} --- all PASS

\begin{abstract}
A283 measured the oscillation amplitude as $A = c\,\kappa$ with
$c^2 = $ obs/pred $= 0.977561$ (CODATA-18) and $0.977263$ (CODATA-22).
A systematic scan of corpus-natural correction factors finds exactly
two candidates inside the CODATA edition spread ($3.0\times10^{-4}$):
\begin{center}
\begin{tabular}{lccc}
\toprule
candidate & value & vs 2018 & vs 2022 \\
\midrule
$1 - \pi/\Omega$ (edge exclusion) & $0.977075$ & $-4.9\times10^{-4}$ &
$-1.9\times10^{-4}$ \\
$1 - 1/44$ & $0.977273$ & $-2.9\times10^{-4}$ & $+1.0\times10^{-5}$ \\
\bottomrule
\end{tabular}
\end{center}
(All others miss by $10^{-3}$ or worse.) The \emph{edge exclusion}
reading has independent physical standing: A281 established that
observation vanishes at the universe boundary, and P04's edge fraction
$\pi/\Omega = 2.2925\%$ is precisely the sector where observation runs
out --- a measured average of the oscillating coupling would then be
collected over the observed fraction $1-\pi/\Omega$ only, giving
deficit $= \tfrac{\kappa^2}{2}(1-\pi/\Omega)$ with \emph{no new
constants}. The $1/44$ reading has a better 2022 fit and no motivation.
Per PSLQ-honesty neither is promoted: \textbf{the correction factor is
bracketed at $0.9773 \pm 0.0002$ and the identification is below the
corpus bar at current experimental precision.} The discriminator is
quantitative: the two candidates differ by $2.0\times10^{-4}$ in $c^2$,
i.e.\ $4.5\times10^{-10}$ in $\alpha^{-1}$ --- a $\sim$0.1-ppb
$\alpha$ measurement (one order beyond current) decides, and a CODATA
drift of one more edition may already. For the record: under the edge
candidate the corpus's closed-form prediction
$\alpha^{-1} = \Omega\sqrt{1 - \kappa^2(1-\pi/\Omega)} =
137.035999236$ sits $5.9\times10^{-8}$ ($2.8\,\sigma_{\rm exp}$,
$0.43$ ppb) from CODATA-22 --- the corpus's most precise contact with
experiment, carried entirely by derived quantities, and explicitly
\emph{not} claimed as exact. OI-283-1 remains open in sharpened form:
derive the averaging weight (prove or refute edge exclusion).
\end{abstract}

\begin{proposition}[The scan]
Among corpus-natural single corrections to $A = \kappa$
($1-\pi/\Omega$, $1-1/44$, $1-\kappa$, $1-2\kappa$, $1-\alpha$,
$(1-\kappa)^{10}$, $1-\Delta E/\Omega$, $31/32$), exactly the two
tabled above fall within the CODATA edition spread of the required
$c^2$; the rest miss by $\geq 10^{-3}$. Verified at 40 digits.
\end{proposition}

\begin{remark}[Why edge exclusion is the leading candidate ---
and why that is not enough]
The mechanism requires no invention: P03 supplies the oscillation,
A283 the averaging, A281/P04 the fact that the edge sector is
unobserved. ``The measured coupling is the oscillation average over
the observed sector'' is a one-line synthesis of three filed results,
and it lands within $1.9\times10^{-4}$ of the CODATA-22 requirement.
But $1-1/44$ lands closer still, and 44 has no derivation (the A44
Jordan cycle shares only the numeral; A255 discipline forbids the
conflation). When an unmotivated integer beats a motivated structure
inside the error bar, the honest statement is a bracket, not a claim.
\end{remark}

\begin{remark}[The prediction, recorded conditionally]
Under edge exclusion the corpus predicts, with zero adjustable
parameters: $\alpha^{-1} = \Omega\sqrt{1-\kappa^2(1-\pi/\Omega)}$.
Numerically $137.035999236$ vs CODATA-22 $137.035999177(21)$:
$+0.43$ ppb, $2.8\,\sigma_{\rm exp}$. Should future editions move
toward it, the edge reading strengthens; away, it dies. Either way the
corpus now owns a falsifiable sub-ppb statement about the most
precisely measured constant in physics --- conditional, dated, and
filed before the data that will judge it.
\end{remark}

\paragraph{Verifier.} \texttt{verify\_P284.py}: the scan (all eight
candidates against both editions); the bracket; the two survivors'
separations; the conditional prediction and its $\sigma$-distance; the
discriminator arithmetic. All PASS.

\end{document}
