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zeekay
1ecc25e9cf
The seven engine specifications (lux-{photon,wave,nova,nebula,prism,ray,field}-protocol)
were fragmented short notes documenting layers of the same Quasar consensus stack.
This commit merges them into a single canonical reference, lux-consensus-engines.tex,
that uses one preamble, one set of theorems, one bibliography, and one composition
chapter showing how the engines layer into the LP-020 finality pipeline.
The seven originals are reduced to single-page breadcrumb stubs pointing at the
consolidated paper; their sections/ content is preserved on disk for git history.
- new: lux-consensus-engines/ (50 pages, 646KB PDF, ~2900 lines tex)
- breadcrumbs: each original keeps cover + title + stub paragraph naming its chapter
- composition: chapter 9 records the layered contract Photon < Wave < Nova < ...
- bibliography: consolidated from the seven original thebibliography blocks
34 lines
1.9 KiB
TeX
34 lines
1.9 KiB
TeX
\section{Introduction}
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\label{sec:field-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:field-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:field-potential}).
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\item Extension to stake-weighted sampling via field strength gradients (\S\ref{sec:field-stake}).
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\item Phase transition analysis characterizing the convergence boundary (\S\ref{sec:field-phase}).
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\item Empirical evaluation of $d$-valued consensus for $d = 2, 4, 8, 16$ (\S\ref{sec:field-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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