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/.
77 lines
2.8 KiB
TeX
77 lines
2.8 KiB
TeX
\documentclass[11pt,a4paper]{article}
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\usepackage{../shared/luxcover}
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\usepackage{amsmath,amssymb,amsthm}
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\DeclareMathOperator*{\argmin}{arg\,min}
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\usepackage{graphicx}
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\usepackage{algorithm,algorithmic}
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\usepackage{hyperref}
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\usepackage{tikz}
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\usepackage{pgfplots}
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\usepackage{booktabs}
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\usepackage{xcolor}
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\usepackage{listings}
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\input{../shared/lstlang}
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\usepackage{float}
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\usetikzlibrary{trees,positioning,calc,shapes.geometric}
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\pgfplotsset{compat=1.17}
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\definecolor{luxblue}{RGB}{0,122,255}
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\definecolor{luxgreen}{RGB}{0,200,83}
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\definecolor{luxgray}{RGB}{128,128,128}
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\lstset{
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basicstyle=\footnotesize\ttfamily,
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keywordstyle=\color{luxblue}\bfseries,
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commentstyle=\color{luxgray}\itshape,
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stringstyle=\color{luxgreen},
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numbers=left,
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numberstyle=\tiny\color{luxgray},
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frame=single,
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breaklines=true,
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captionpos=b
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}
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\theoremstyle{definition}
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\newtheorem{definition}{Definition}
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\newtheorem{theorem}{Theorem}
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\newtheorem{lemma}{Lemma}
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\newtheorem{corollary}{Corollary}
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\title{\textbf{Verkle Trees: Constant-Size Proofs for Stateless Clients on Lux}}
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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{2022}
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\begin{document}
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\luxcoverpage
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\begin{abstract}
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We present the design and implementation of Verkle trees in the Lux blockchain platform, enabling constant-size proofs for stateless clients. Verkle trees utilize polynomial commitments to achieve proof sizes of approximately 150 bytes, independent of tree depth or state size, representing a 4-5x reduction compared to traditional Merkle Patricia trees. Our implementation leverages KZG commitments on the BLS12-381 curve, providing efficient batch verification and enabling practical stateless client operation. We detail the cryptographic foundations, integration with Lux's multi-chain architecture, migration strategy from existing Merkle structures, and performance analysis showing 76\% bandwidth reduction for state proofs while maintaining sub-10ms verification times. This advancement enables light clients to verify state transitions with minimal storage requirements, improving network decentralization and accessibility.
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\end{abstract}
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\input{sections/01-introduction}
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\input{sections/02-merkle-tree-limitations}
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\input{sections/03-verkle-tree-background}
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\input{sections/04-verkle-tree-structure}
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\input{sections/05-polynomial-commitments-kzg}
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\input{sections/06-proof-generation}
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\input{sections/07-lux-implementation}
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\input{sections/08-performance-analysis}
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\input{sections/09-stateless-client-benefits}
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\input{sections/10-cryptographic-primitives}
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\input{sections/11-security-analysis}
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\input{sections/12-comparison-with-alternatives}
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\input{sections/13-economic-impact}
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\input{sections/14-migration-strategy}
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\input{sections/15-future-enhancements}
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\input{sections/99-conclusion}
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\end{document}
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