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f4ee7a0525
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.
91 lines
3.9 KiB
TeX
91 lines
3.9 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[T1]{fontenc}
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\usepackage{amsmath,amssymb,amsthm}
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\usepackage{algorithm,algorithmic}
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\usepackage{graphicx}
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\usepackage{tikz}
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\usepackage{pgfplots}
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\usepackage{hyperref}
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\usepackage{listings}
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\input{../shared/lstlang}
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\usepackage{color}
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\usepackage{booktabs}
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\usepackage{multirow}
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\usepackage{subcaption}
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\usetikzlibrary{positioning,shapes,arrows}
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\pgfplotsset{compat=1.17}
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% Theorem environments
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\newtheorem{theorem}{Theorem}
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{definition}[theorem]{Definition}
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% Code listing style
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\definecolor{codegray}{rgb}{0.5,0.5,0.5}
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\definecolor{codegreen}{rgb}{0,0.6,0}
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\definecolor{codepurple}{rgb}{0.58,0,0.82}
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\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
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\lstdefinestyle{mystyle}{
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backgroundcolor=\color{backcolour},
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commentstyle=\color{codegreen},
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keywordstyle=\color{magenta},
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numberstyle=\tiny\color{codegray},
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stringstyle=\color{codepurple},
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basicstyle=\ttfamily\footnotesize,
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breakatwhitespace=false,
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breaklines=true,
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captionpos=b,
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keepspaces=true,
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numbers=left,
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numbersep=5pt,
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showspaces=false,
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showstringspaces=false,
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showtabs=false,
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tabsize=2
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}
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\lstset{style=mystyle}
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\title{Fast Probabilistic Consensus: Adaptive Threshold Consensus with Phase-Shift Dynamics}
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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{2025}
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\begin{document}
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\luxcoverpage
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\begin{abstract}
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We present Fast Probabilistic Consensus (FPC), a novel Byzantine fault-tolerant consensus protocol that achieves agreement through adaptive threshold voting with phase-shift dynamics. FPC employs a sigmoid cooling function to transition from exploration ($\theta = 0.5$) to exploitation ($\theta = 0.8$) phases, enabling rapid convergence while preventing metastability. The protocol achieves $\varepsilon$-consensus with $\varepsilon = 2^{-\lambda}$ where $\lambda = \beta \cdot k \cdot (\theta - 0.5)^2$, tolerating up to $f < n/3$ Byzantine nodes. Through committee sampling of size $k = 20$-$30$ validators and requiring $\beta = 5$-$10$ consecutive confident rounds, FPC finalizes transactions in 1-3 seconds with message complexity $O(k \log n)$. We demonstrate FPC's integration within the Lux consensus stack, where it operates as the ``wave'' layer in a physics-inspired consensus architecture. The Zero-copy Application Protocol (ZAP) replaces gRPC+Protobuf for consensus messaging, achieving 9.69M messages/second with a $14\times$ deserialization improvement over Protobuf. FPC's safety, liveness, and BFT tolerance properties have been formally verified in Lean~4 with machine-checked proofs. Simulation results show 99.999\% safety with logarithmic scaling properties suitable for global networks of 100,000+ nodes.
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\end{abstract}
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\input{sections/01-introduction}
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\input{sections/02-consensus-architecture-context}
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\input{sections/03-fpc-algorithm}
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\input{sections/04-adaptive-threshold-mechanism}
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\input{sections/05-threshold-calculation}
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\input{sections/06-pseudorandom-function-for-stability}
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\input{sections/07-termination-conditions}
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\input{sections/08-security-analysis}
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\input{sections/09-performance-characteristics}
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\input{sections/10-comparison-with-other-consensus-protocol}
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\input{sections/11-integration-with-lux}
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\input{sections/12-simulation-results}
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\input{sections/13-zap-zero-copy-wire-format-for-consensus-}
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\input{sections/14-mathematical-foundations}
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\input{sections/15-implementation-details}
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\input{sections/16-formal-verification}
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\input{sections/17-future-work}
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\input{sections/18-conclusion}
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\input{sections/99-acknowledgments}
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\end{document}
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