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zeekay
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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
38 lines
1.5 KiB
TeX
38 lines
1.5 KiB
TeX
\section{Throughput Analysis}
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\label{sec:photon-throughput}
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\begin{theorem}[Sustained Throughput]
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\label{thm:photon-throughput}
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The Photon protocol sustains finalization throughput of:
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\[
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\Theta_{\text{sustained}} = \min\left(T, \frac{m \cdot q_1}{\Delta}\right)
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\]
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where $T$ is the transaction arrival rate, $m$ is the pipeline depth, $q_1$ is the
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per-round supermajority probability, and $\Delta$ is the round time.
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\end{theorem}
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\begin{proof}
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Each of the $m$ pipeline slots produces one finalization every $1/(q_1 \cdot \beta^{-1})$
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rounds, where $\beta$ rounds of supermajority are needed and each round succeeds with
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probability $q_1$. The expected slot cycle time is $\beta / q_1$ rounds = $\beta \Delta / q_1$
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seconds.
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With $m$ slots operating in parallel, the finalization rate is:
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\[
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\Theta_{\text{sustained}} = \frac{m}{\beta \Delta / q_1} = \frac{m q_1}{\beta \Delta}
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\]
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For $m = 100$, $q_1 = 0.63$, $\beta = 11$, $\Delta = 0.05$s:
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$\Theta_{\text{sustained}} = 100 \times 0.63 / (11 \times 0.05) \approx 114$ finalizations
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per round = $114 / 0.05 \approx 2{,}280$ per second per conflict-set pipeline.
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Since most transactions have independent conflict sets, the total throughput is
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$\Theta_{\text{sustained}} \times C$ where $C$ is the number of active conflict sets,
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easily reaching 10,000+ TPS.
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\end{proof}
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%% -----------------------------------------------------------------------
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%% 7. EVALUATION
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%% -----------------------------------------------------------------------
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