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Restructured from flat .tex/.pdf files into per-paper subdirectories. Added Antje Worring as co-author on all papers. Synced PDFs to pdfs/ for download site.
34 lines
1.9 KiB
TeX
34 lines
1.9 KiB
TeX
\section{Introduction}
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\label{sec:introduction}
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The metastable consensus protocols---Slush, Flare, and Wave---operate on binary conflicts:
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each conflict set has two possible outcomes, and the protocol converges to one. Many
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blockchain applications, however, involve $d$-valued conflicts: multiple conflicting
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transactions spending the same UTXO, multiple candidate blocks at the same height, or
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multi-party auction outcomes. Extending binary protocols to $d > 2$ requires either
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running $\log_2 d$ binary instances (inefficient) or redesigning the convergence mechanism.
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The Field protocol draws on the physics of electromagnetic alignment to provide a natural
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multi-valued extension. Instead of binary colors, each validator maintains a preference
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vector $\mathbf{p}_i \in \mathbb{R}^d$ on the $(d-1)$-simplex. Sampling interactions
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rotate preference vectors toward the sampled majority, analogous to magnetic dipoles
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aligning under an external field. The field potential function $\Phi$ provides a
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Lyapunov function for the dynamics, guaranteeing convergence without requiring
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binary decomposition.
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\paragraph{Contributions.}
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\begin{enumerate}[nosep]
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\item The Field protocol: a multi-valued metastable consensus mechanism with
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electromagnetic-inspired dynamics (\S\ref{sec:protocol}).
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\item A field potential function $\Phi$ that is non-increasing under the protocol,
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providing a Lyapunov convergence proof (\S\ref{sec:potential}).
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\item Extension to stake-weighted sampling via field strength gradients (\S\ref{sec:stake}).
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\item Phase transition analysis characterizing the convergence boundary (\S\ref{sec:phase}).
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\item Empirical evaluation of $d$-valued consensus for $d = 2, 4, 8, 16$ (\S\ref{sec:evaluation}).
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\end{enumerate}
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%% -----------------------------------------------------------------------
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%% 2. ELECTROMAGNETIC ANALOGY
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%% -----------------------------------------------------------------------
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