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Bylines, paper authorship, correspondence addresses and the founder blurb under each post named an individual. They name the organisation that published the work instead: the brand on posts and pages, the research byline on papers, and research@ in place of a personal address. Both are what these repositories already used elsewhere — nothing new was coined. Co-authors are untouched. Where a paper named someone else alongside, they stay named; only the one byline changed. Bibliography entries, running heads, PDF metadata and affiliations move with it, so a citation still resolves to whoever the cited paper names. Sample and fixture data uses the placeholder name these tests already use elsewhere, so no assertion changed meaning.
96 lines
3.4 KiB
TeX
96 lines
3.4 KiB
TeX
\documentclass[11pt,a4paper]{article}
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\usepackage{../shared/luxcover}
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\usepackage[utf8]{inputenc}
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\usepackage{amsmath,amssymb,amsfonts,amsthm}
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\usepackage{graphicx}
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\usepackage{hyperref}
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\usepackage{algorithm}
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\usepackage{algpseudocode}
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\usepackage{listings}
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\input{../shared/lstlang}
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\usepackage{xcolor}
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\usepackage{booktabs}
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\usepackage{multirow}
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\usepackage{array}
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\usepackage{tikz}
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\usepackage{pgfplots}
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\usepackage[numbers]{natbib}
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\usepackage{enumitem}
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\usepackage{subcaption}
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\pgfplotsset{compat=1.18}
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\newtheorem{theorem}{Theorem}[section]
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{definition}{Definition}[section]
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{remark}{Remark}[section]
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\lstset{
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basicstyle=\small\ttfamily,
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keywordstyle=\color{blue}\bfseries,
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commentstyle=\color{gray},
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stringstyle=\color{red},
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breaklines=true,
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frame=single,
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numbers=left,
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numberstyle=\tiny\color{gray},
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captionpos=b
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}
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\title{\textbf{Lux Consensus: Physics-Inspired Metastable Blockchain Consensus}}
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\author{
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Lux Research\thanks{Corresponding author: [email protected]}\\
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\textit{Lux Industries, Inc.}\\
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\texttt{[email protected]}
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}
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\date{Original: 2022\quad|\quad Revised: February 2026}
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\begin{document}
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\luxcoverpage
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\begin{abstract}
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We present Lux Consensus, a physics-inspired metastable consensus protocol that achieves
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sub-second finality with high throughput while tolerating up to $f < n/3$ Byzantine faults.
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Lux Consensus extends the metastable protocol family---Slush, Flare, Wave, and
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Lux---with a directed acyclic graph (DAG) ordering layer, adaptive confidence
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thresholds, and a novel metastability-breaking mechanism grounded in statistical mechanics
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and phase transition theory. The protocol operates through repeated random subsampling of
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the validator set, building confidence through emergent majority amplification rather than
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explicit leader election. We prove that Lux achieves probabilistic safety with $1 - e^{-\Omega(k)}$
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confidence, liveness under partial synchrony, and convergence in $O(\log n)$ communication
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rounds with high probability. Empirical evaluation on a 1,000-node testnet demonstrates
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sustained throughput of 4,500 transactions per second with median finality of 650
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milliseconds, outperforming PBFT-family protocols at scale while maintaining Byzantine fault
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tolerance equivalent to classical BFT systems. We provide formal proofs of safety, liveness,
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and convergence, alongside rigorous parameterization analysis of the sampling parameters
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$k$, $\alpha$, and $\beta$ that govern the protocol's security--performance trade-off.
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Additionally, we present a mechanized verification in Lean~4 with Mathlib, producing
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36 machine-checked theorems covering all protocol components, BFT threshold arithmetic,
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and cryptographic primitive axiomatization.
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\end{abstract}
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\tableofcontents
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\newpage
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%% -----------------------------------------------------------------------
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%% 1. INTRODUCTION
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%% -----------------------------------------------------------------------
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\input{sections/01-introduction}
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\input{sections/02-background-and-related-work}
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\input{sections/03-system-model}
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\input{sections/04-the-lux-protocol}
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\input{sections/05-formal-analysis}
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\input{sections/06-parameterization}
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\input{sections/07-implementation}
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\input{sections/08-evaluation}
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\input{sections/09-security-considerations}
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\input{sections/10-formal-verification}
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\input{sections/99-conclusion}
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\end{document}
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