mirror of
https://github.com/lux-apps/papers.git
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zeekay
dd93cb41f7
Sweep across the non-Tier-1 paper catalogue (Tier-1 owned by parallel
agent and excluded). All 113 processed papers already had luxcover
wired up; this commit fixes 14 build breakers and produces fresh
PDFs across the catalogue.
Fixes:
- lux-blockchain-scaling-laws: em-dash inside lstlisting -> --
- lux-corona-pq: stale \input pointing at 03-the-corona-scheme renamed
to 03-the-corona-scheme (file already renamed on disk)
- lux-lattice-cryptography-primer: same Corona->Corona rename
- lux-formal-verification-lean4: Lean source uses unicode (×, ∀, ∃, ∈,
∧, ∨, ∩, ≠, ⟨, ⟩, ·, ¬) inside lstlistings. Added a literate map
so listings render the math glyphs without UTF-8 fault.
- lux-id-did-specification: ✓/✗ in tabular replaced with \ding{51}
/ \ding{55} (pifont). Added pifont package.
- lux-ntt-simd-implementation: middle-dot in Go assembly listings;
added literate {·}{\textperiodcentered}.
- lux-ntt-transform: μ, ×, –, — in regular text (no T1 fontenc).
Replaced with $\mu$/$\times$/--/--- via unicode->latex sweep.
- lux-perpetuals-derivatives, lux-quantum-consensus,
lux-quasar-consensus, lux-tee-computing-mesh: same unicode->latex
sweep across body text. Also fixed broken math segment
`$L_{avg} = 10$\times$$` -> `$L_{avg} = 10\times$`.
- lux-zchain: emoji glyphs in roadmap table replaced with
parenthetical text.
- lux-triple-proof-consensus: dropped duplicate \usepackage{geometry}
that clashed with luxcover (geometry option clash).
- pq: defined missing \Rq macro.
PDFs rebuilt for the full Tier-2/3 set.
Excluded (Tier-1, parallel agent): lp-073-pulsar, lp-stricte2epq,
dag-evm-formal, lp-010-quasar-stm-{3,4}, lp-020-quasar-consensus,
lux-institutional-custody, lux-nist-mptc-submission, pqsafe-il5,
pq-rns, plus shared/ and lps/.
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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Zach Kelling\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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