papers/lux-consensus-engines/lux-consensus-engines.tex

\documentclass[11pt,a4paper]{report}
\usepackage{../shared/luxcover}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amssymb,amsfonts,amsthm}
\usepackage{graphicx}
\usepackage{hyperref}
\usepackage{algorithm}
\usepackage{algpseudocode}
\usepackage{xcolor}
\usepackage{booktabs}
\usepackage{enumitem}
\usepackage{tikz}

\hypersetup{colorlinks=true,linkcolor=black,citecolor=blue,urlcolor=blue}

\newtheorem{theorem}{Theorem}[chapter]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{definition}{Definition}[chapter]
\newtheorem{remark}{Remark}[chapter]

\title{\textbf{Lux Consensus Engines}\\[6pt]
\large Photon, Wave, Nova, Nebula, Prism, Ray, Field\\
A Unified Reference for the Quasar Stack}

\author{
Zach Kelling\thanks{Corresponding author: [email protected]}\\
\textit{Lux Industries, Inc.}\\
\texttt{[email protected]}
}

\date{2026}

\begin{document}

\luxcoverpage

\begin{abstract}
The Lux primary network finalises blocks through a stack of seven
metastable consensus engines collectively named \emph{Quasar}. Each
engine specialises one regime of the consensus design space and each
serves as a reusable primitive on its own. \textbf{Photon} pipelines
binary sampling so that per-conflict throughput is decoupled from
per-transaction finality latency, sustaining $10{,}000$ TPS at fixed
$500$\,ms finality. \textbf{Wave} establishes the safety primitive of
the family: cumulative confidence counters whose monotonicity makes
decision reversal exponentially unlikely once a colour establishes a
lead. \textbf{Nova} extends sampling from individual vertices to DAG
cones via a supernova-burst finalisation that closes the entire
ancestor cone in a single round, achieving $8{,}500$ TPS at $1{,}000$
validators. \textbf{Nebula} retains the same machinery under network
sparsity, packet loss, validator churn and partition: stratified
sampling with bridge validators gives graceful degradation from
$O(\log n)$ rounds in well-connected graphs to $O(n \log n)$ at the
connectivity threshold. \textbf{Prism} parallelises the family by
spectral decomposition into $B$ bands: conflicting transactions land
in the same band by construction, independent transactions are
distributed across bands, and the aggregate throughput scales as
$B \cdot \Theta_{\text{band}}$, reaching $50{,}000$ TPS at
$B = 16$. \textbf{Ray} closes a feedback loop on top of any of the
above: it estimates the live adversary fraction from the confidence
velocity and adapts $\beta$ down to the light-speed bound of three
rounds under benign conditions, cutting median finality by up to
$64\%$. \textbf{Field} generalises the family to $d > 2$ colours
through an electromagnetic potential function whose phase transition
characterises the exact $(k, \alpha, \beta)$ regime where consensus is
achievable, enabling validator-set elections, DAO governance and
multi-party auction resolution under the same safety guarantees.

This paper supersedes the seven individual engine specifications
(\texttt{lux-photon-protocol} through \texttt{lux-field-protocol})
that previously circulated as separate research notes. Each chapter
here is the canonical description of one engine; a final composition
chapter records the contract by which the engines layer into the
Quasar 3.0 finality pipeline activated on the Lux primary network on
25~December 2025 (LP-020).
\end{abstract}

\tableofcontents
\clearpage

%% ============================================================================

\input{sections/00-introduction}
\input{sections/01-photon}
\input{sections/02-wave}
\input{sections/03-nova}
\input{sections/04-nebula}
\input{sections/05-prism}
\input{sections/06-ray}
\input{sections/07-field}
\input{sections/08-composition}
\input{sections/99-conclusion}

\end{document}