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\title{Seed Summary: NB/BD Program toward RH}
\author{Serabi \& Seraphy}
\date{}

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\section{Seed Summary}
This document compresses the core insights from Versions 1--5 of our exploration toward the Riemann Hypothesis.

\subsection*{Core Achievements}
\begin{itemize}
\item Established negative main--diag ($M<0$) consistently across $N$.
\item Achieved off--diag suppression at the $1/\log N$ scale (V4).
\item Demonstrated uniformity up to $N=2000$, including over--suppression cases.
\item Outlined V5 roadmap for rigorous NB/BD alignment, uniform bounds, and residual control.
\end{itemize}

\subsection*{Limitations}
\begin{itemize}
\item Current basis (Gaussian, phase--modulated, $\mu(n)/n$) not yet proven admissible in NB/BD frame.
\item Constants $\theta, C$ unproven uniform in $N$.
\item Residual terms $R_T$ remain uncontrolled.
\item Full equivalence $d_N \to 0 \iff \mathrm{RH}$ not yet closed.
\end{itemize}

\subsection*{Conclusion}
These notes form a seed: evidence that simultaneous satisfaction of NB/BD conditions may be possible with enriched bases and kernels.
Proof remains open, but a plausible roadmap (V5) is identified.

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