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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
36 lines
1.7 KiB
TeX
36 lines
1.7 KiB
TeX
\section{Introduction}
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\label{sec:nebula-introduction}
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Standard metastable consensus protocols assume a well-connected network where each
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validator can reach any other validator with bounded delay. This assumption fails in
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several important settings:
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\begin{itemize}[nosep]
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\item \textbf{Geographic distribution}: Validators in remote regions may have limited
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connectivity to the broader network.
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\item \textbf{Network partitions}: Temporary partitions create disconnected components
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that must eventually reconcile.
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\item \textbf{Bootstrap phase}: New blockchain networks start with few validators,
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gradually growing the validator set.
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\item \textbf{Appchains}: Lux appchains may have small validator sets (10--50 nodes)
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with high churn rates.
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\end{itemize}
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Nebula adapts the metastable consensus framework to operate under these conditions by
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replacing uniform random sampling with stratified neighborhood sampling, ensuring that
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even in sparse networks, the consensus dynamics converge to agreement.
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\paragraph{Contributions.}
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\begin{enumerate}[nosep]
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\item The Nebula stratified sampling protocol for sparse networks (\S\ref{sec:nebula-protocol}).
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\item A random geometric graph model of sparse network consensus (\S\ref{sec:nebula-model}).
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\item Convergence proofs under the expansion factor framework (\S\ref{sec:nebula-convergence}).
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\item Safety and liveness analysis for sparse and partitioned networks (\S\ref{sec:nebula-safety}).
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\item Empirical evaluation under packet loss and churn (\S\ref{sec:nebula-evaluation}).
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\end{enumerate}
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%% -----------------------------------------------------------------------
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%% 2. SPARSE NETWORK MODEL
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%% -----------------------------------------------------------------------
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