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% Addendum 388 (falsification scorecard 2026; a dated living ledger like P40).
% Corpus attractor numbers vs current real data: Lambda_0 PASS, a_0/SPARC PASS, alpha near-pass;
% H_0=75.8 ~3 sigma TOO HIGH (tension), DE-evolution shape vs DESI (tension), delta_CP REFUTED,
% m_nu3 OPEN. Author: Leon Fernando Vlegels. Text CC BY 4.0. Verifier: verify_P388.py (10/10 pass).
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\theoremstyle{remark}
\newtheorem{remark}[section]{Remark}
\newcommand{\Lz}{\Lambda_0}

\title{Addendum 388: Falsification Scorecard (2026)\\
\large The corpus's attractor numbers confronted with current data\\[0.3em]
\normalsize (A dated living ledger, in the spirit of Paper 40 and the P39 falsifiers)}
\author{L\'eon Fernando Vlegels}
\date{2026-06-19}

\begin{document}
\maketitle

\begin{abstract}
The corpus makes numerical predictions that real data can falsify (Paper~39's pre-committed SPARC
falsifiers; Paper~40's refutation ledger). This addendum gathers the principal ``attractor numbers'' and
confronts each with a current (2025--2026) measurement, with an honest verdict. The result is a genuine
mix. The dark-energy \emph{density} lands cleanly: $\Lz=1-\pi^2/32=0.6916$ matches the observed
$\Omega_\Lambda\approx0.689$ to sub-percent (the new Addendum~387 result). The SPARC acceleration scale
holds: the corpus $a_0$ sits within the SPARC error bar (the BTFR confrontation of Paper~39, 175
galaxies). The fine-structure constant agrees to $0.43$~ppb ($2.8\sigma$, owned). But $H_0=2\alpha^2/
T_{\mathrm{breath}}=75.8$~km/s/Mpc is in tension with all current data --- it sits $\sim\!3\sigma$
\emph{above} even SH0ES (73.17), the local/high camp, so the corpus over-predicts $H_0$. And the
dark-energy \emph{evolution} conflicts both ways: DESI DR2 now prefers an evolving dark energy
($2.8$--$4.2\sigma$ over $\Lambda$CDM), which challenges the corpus's constant $\Lz$, while the corpus's
own evolving fold-to-redshift gives the wrong shape ($w_a$ far too small). One standing refutation
($\delta_{CP}$) and one open future test ($m_{\nu_3}$) round out the ledger. Headline: the corpus's
dark-energy density is its best current data hit; its $H_0$ and its DE-evolution are its worst. All
verdicts pinned by \texttt{verify\_P388.py} (10/10); this is a \emph{dated} confrontation, shifting as
the data shift.
\end{abstract}

\section{The scorecard}
\label{sec:card}

\begin{center}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{@{}p{3.0cm}p{3.4cm}p{3.4cm}p{2.4cm}@{}}
\toprule
\textbf{Prediction} & \textbf{Corpus value} & \textbf{Current data} & \textbf{Verdict} \\
\midrule
Dark-energy density $\Omega_\Lambda$ & $\Lz=1-\pi^2/32=0.6916$ (387/P38) & $\approx0.689$ ($\Lambda$CDM;
Planck $0.6847\!\pm\!0.0073$) & \textbf{PASS} ($\sim0.4\%$) \\
MOND scale $a_0$ & $0.976\times$ empirical (369) & $1.2\pm0.26\times10^{-10}\,\mathrm{m/s^2}$ (SPARC,
175 gal.) & \textbf{PASS} (within err.) \\
$\alpha^{-1}$ & $137.035999236$ (A288) & CODATA $137.035999177$ & near-pass, $2.8\sigma$ \\
$H_0$ & $2\alpha^2/T_{\mathrm{breath}}=75.8$ & SH0ES $73.17\!\pm\!0.86$; Planck $67.4$; DESI $68.53$ &
\textbf{consistent}$^\dagger$ ($0.3\sigma$, A393) \\
DE evolution $(w_0,w_a)$ & fold $\approx(-0.82,-0.25)$ (349a) & DESI DR2 $(-0.752,-0.86)$, evolving DE
$2.8$--$4.2\sigma$ & \textbf{TENSION} (both ways) \\
$\delta_{CP}$ & $\approx240^\circ$ & $\approx177^\circ$, CP-cons.\ within $1\sigma$ & \textbf{REFUTED}
(A344) \\
$m_{\nu_3}$ & $48.7$~meV & not yet measured & \textbf{OPEN} (JUNO/HK) \\
\bottomrule
\end{tabular}
\end{center}

\noindent{\footnotesize $^\dagger$\,\textbf{Patched 2026-06-19 (A393).} The $H_0$ row originally read
\textbf{TENSION} ($\sim\!3\sigma$ high). Addendum~393 showed that reading used an inconsistent error
budget: $H_0\propto\sqrt{a_0}$ through the chart's single dimensionful anchor, so the $H_0$ prediction
inherits the anchor's $\pm22\%$ ($75.8\pm8.2$); applying the same anchor error used to PASS $a_0$ gives
$0.32\sigma$ vs SH0ES ($0.88\sigma$ DESI, $1.02\sigma$ Planck). Consistent within the calibration
uncertainty --- though the central value still leans high (not a confirmation). The prose of
Sec.~\ref{sec:read} below is the dated original; the $\sim\!3\sigma$ figure there is the data-only number
A393 supersedes.}

\section{Reading the ledger}
\label{sec:read}

\begin{remark}[Where it lands, where it does not]
\label{rmk:read}
The honest summary has three registers. \emph{The hits.} The dark-energy density is the strongest current
confirmation, and it is new: Addendum~387 identified dark energy with the cokernel void $\Lz=1-\pi^2/32$,
and $0.6916$ matches the observed $\Omega_\Lambda\approx0.689$ to sub-percent. The SPARC acceleration
scale holds within its (large) error bar, and the fine-structure constant agrees to under half a
part-per-billion. \emph{The tensions.} $H_0=75.8$ is the clearest problem: it lies $\sim\!3\sigma$ above
even SH0ES, the highest measurement, so the corpus over-predicts $H_0$ relative to every current
determination --- it is most consistent with the local/high camp but still above it. And the dark-energy
\emph{evolution} cuts both ways: DESI DR2's preference for evolving dark energy ($2.8$--$4.2\sigma$ over a
cosmological constant) challenges the corpus's constant $\Lz$ even as it matches the density, while the
corpus's own evolving fold-to-redshift (Paper~32 / Addendum~349a) predicts an evolution with $w_a$ far too
small to match DESI. The corpus is, on present data, ``right that dark energy may evolve, wrong about
how'' --- and simultaneously ``right about the density, in a model the data are now questioning.''
\emph{The settled and the open.} $\delta_{CP}=240^\circ$ is refuted and recorded (A344); $m_{\nu_3}=48.7$~meV
awaits JUNO and Hyper-Kamiokande.
\end{remark}

\begin{remark}[The honest status of the $H_0$/DE tension]
\label{rmk:status}
Two of the corpus's worst results --- $H_0$ and the DE-evolution shape --- share a root: both descend from
the cosmological bridge (Addenda~358a/362/369), which is conditional on the SPARC closure hypothesis and
the de~Sitter $2\pi$, and which the corpus itself flags as resting on its single foundational posit
(Addendum~370). The density $\Lz$, by contrast, is the cokernel residual (Paper~38), a more directly
geometric quantity, and it is the one that lands. So the data are, suggestively, separating the corpus's
firmly-geometric predictions (the density, $a_0$, $\alpha$, the masses) from its bridge-conditional ones
($H_0$, DE-evolution): the former pass, the latter strain. That is a useful signal, not a verdict --- the
$H_0$ tension is real and could equally indict the bridge, the closure hypothesis, or the $2\pi$, none of
which the data here resolve.
\end{remark}

\section*{Status}
This is a falsification scorecard, a dated living ledger in the spirit of Paper~40 and the Paper~39
pre-committed falsifiers. Confronted with 2025--2026 data: the dark-energy density $\Lz=1-\pi^2/32=0.6916$
matches $\Omega_\Lambda\approx0.689$ (PASS, the new Addendum~387 result); the SPARC $a_0$ sits within its
error bar (PASS, Paper~39); $\alpha^{-1}$ agrees to $0.43$~ppb ($2.8\sigma$). But $H_0=75.8$ is $\sim\!3\sigma$
above even SH0ES (TENSION --- the corpus over-predicts), and the dark-energy evolution conflicts with DESI
both ways (TENSION); $\delta_{CP}=240^\circ$ is refuted (A344) and $m_{\nu_3}=48.7$~meV is open. The
geometric-density predictions pass; the bridge-conditional ones ($H_0$, DE-evolution, all descending from
the closure hypothesis of 369/370) strain (Remark~\ref{rmk:status}). The corpus is efficiently
falsifiable, and here it is being confirmed in places and falsified in others --- which is the point. No
published number changes; the new content is the dated confrontation. Verifier: \texttt{verify\_P388.py},
10/10 pass.

\paragraph{Sources.} $H_0$ (SH0ES $73.17\pm0.86$, Planck $67.4\pm0.5$, DESI $68.53\pm0.80$): Hubble-tension
status reports and DESI DR2 (2025). Dark energy: DESI DR2 evolving-DE preference ($w_0=-0.752$, $w_a=-0.86$,
$2.8$--$4.2\sigma$); $\Omega_\Lambda\approx0.689$ ($\Lambda$CDM). SPARC $a_0=1.2\pm0.26\times10^{-10}$~m/s$^2$
(175 late-type galaxies). $\alpha^{-1}$: CODATA. Retrieved 2026-06.

\end{document}
