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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
43 lines
2.0 KiB
TeX
43 lines
2.0 KiB
TeX
\section{Comparison with Slush and Flare}
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\label{sec:wave-comparison}
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\subsection{Slush: No Memory}
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Slush has no counters---it simply adopts the sampled majority in each round. While Slush
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converges in $O(\log n)$ rounds, it provides no finality guarantee. An adversary can
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continually perturb a Slush node by strategically timing equivocal responses.
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\subsection{Flare: Consecutive Counters}
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Flare tracks consecutive rounds of supermajority agreement. A counter $cnt$ increments
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when the supermajority matches the current preference and resets to 0 on a preference
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switch. Flare finalizes when $cnt \geq \beta_2$. While more robust than Slush, Flare
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is vulnerable to \emph{counter reset attacks}: an adversary who can occasionally force
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a preference switch resets the counter, potentially delaying finalization indefinitely.
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\subsection{Wave: Cumulative Advantage}
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Wave's confidence counters are cumulative---they never reset. Even if the adversary
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temporarily shifts some honest nodes, the historical confidence lead is preserved.
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This makes Wave strictly more robust than Flare against adaptive adversaries:
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\begin{proposition}[Wave Dominates Flare]
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\label{prop:dominance}
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For any adversary strategy $\sigma$ and any initial configuration, the expected
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finalization time under Wave is at most the expected finalization time under Flare.
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\end{proposition}
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\begin{proof}
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Flare finalizes when $\beta_2$ \emph{consecutive} supermajority rounds occur. Wave
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finalizes when $\beta_1$ \emph{total} supermajority rounds occur (for the leading color).
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Since $\beta_1$ total rounds of supermajority for a fixed color always occur before
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$\beta_2$ consecutive rounds (as consecutive is a stricter condition), and Wave needs
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only cumulative rather than consecutive counts, Wave's finalization time is stochastically
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dominated by Flare's for any $\beta_1 \leq \beta_2$.
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\end{proof}
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%% -----------------------------------------------------------------------
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%% 10. SECURITY CONSIDERATIONS
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%% -----------------------------------------------------------------------
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