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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
46 lines
1.9 KiB
TeX
46 lines
1.9 KiB
TeX
\section{Direct Voting Fast Path}
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\label{sec:prism-voting}
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For uncontested transactions (no conflict), the full metastable sampling process is
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unnecessary. Prism includes a direct voting fast path with $O(n)$ complexity.
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\begin{algorithm}[H]
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\caption{Prism Direct Voting --- Uncontested Fast Path}
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\label{alg:prism-voting}
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\begin{algorithmic}[1]
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\Function{DirectVote}{transaction $t$}
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\If{$\mathcal{C}(t) = \emptyset$} \Comment{no conflict detected}
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\State Broadcast $\text{vote}(v, t, \text{accept})$ to all validators
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\State Collect votes from $\geq 2n/3$ validators
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\If{all collected votes are accept}
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\State \textbf{finalize} $t$ immediately \Comment{$O(1)$ rounds}
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\Else
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\State Fallback to Photon pipeline for $t$ \Comment{conflict detected}
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\EndIf
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\EndIf
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{proposition}[Fast Path Safety]
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\label{prop:fast-path}
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The direct voting fast path maintains safety: if an honest validator finalizes $t$
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via direct vote, then no conflicting $t'$ can be finalized (via direct vote or Photon).
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\end{proposition}
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\begin{proof}
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Finalization via direct vote requires $2n/3$ accept votes. Since $f < n/3$, at least
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$n/3 + 1$ of these votes come from honest validators. If a conflicting $t'$ existed,
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honest validators would reject $t$ (detecting the conflict) and not send accept votes.
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Therefore, $2n/3$ accept votes implies no conflict exists, and finalization is safe.
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If a conflict is discovered after the direct vote begins (but before $2n/3$ votes are
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collected), the transaction falls back to the Photon pipeline, where the conflict is
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resolved through the standard metastable process.
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\end{proof}
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%% -----------------------------------------------------------------------
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%% 6. THROUGHPUT SCALING
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%% -----------------------------------------------------------------------
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