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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.
76 lines
2.7 KiB
TeX
76 lines
2.7 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,amsfonts,amsthm}
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\usepackage{graphicx}
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\usepackage{hyperref}
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\usepackage{booktabs}
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\usepackage{listings}
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\usepackage{xcolor}
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\usepackage{tikz}
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\usepackage{float}
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\usepackage{enumitem}
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\usepackage{array}
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\usepackage{tabularx}
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\input{../shared/lstlang}
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\hypersetup{colorlinks=true,linkcolor=black,citecolor=blue,urlcolor=blue}
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\newtheorem{theorem}{Theorem}
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{definition}{Definition}
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{remark}{Remark}
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\newtheorem{observation}[theorem]{Observation}
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\title{Blockchain Scaling Laws \\
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\large{Empirical Crossover Points for Post-Quantum Threshold Consensus on Heterogeneous Hardware}}
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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{2026-05-04 \quad\textit{Empirical CPU/Metal/WGSL crossover for the Lux Pulsar canonical NTT.}}
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\begin{document}
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\luxcoverpage
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\begin{abstract}
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\noindent We measure the per-polynomial throughput of the canonical
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post-quantum NTT used by the Lux Pulsar threshold signature
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($R_q = \mathbb{Z}_q[X]/(X^{256}+1)$, $q = 0x1000000004A01$) on Apple
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M1 Max across three backends — scalar CPU, Apple Metal, and a WGSL
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kernel via the host polyfill — and identify the empirical crossover
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where each GPU backend first beats CPU. We find that the CPU baseline
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is remarkably flat ($\sim 1.4$ \textmu s per NTT regardless of batch
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size); Metal pays a $\sim 1.5$ ms per-dispatch fixed cost that
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amortizes only beyond $n_\text{polys} \approx 16{,}384$, at which point
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Metal beats CPU by $\sim 1.4\times$ and grows monotonically with batch
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size. From these measurements we derive three empirical scaling laws
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that govern when GPU acceleration is profitable for blockchain workloads:
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(L1) the \emph{batch-size law} — GPU dispatch is fixed-cost per call,
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so per-poly speedup scales as $1 - C/n$; (L2) the \emph{validator-
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parallelism law} — single-validator workloads rarely cross the
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breakeven, but batched aggregation across $k$ validators amortizes
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linearly; (L3) the \emph{epoch-amortization law} — workloads that
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collect work over an epoch (block, finality round, FHE evaluation)
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trade latency for batch size and cross over far earlier than per-tx
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operations.
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\end{abstract}
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\tableofcontents
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\newpage
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\input{sections/01-introduction}
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\input{sections/02-methodology}
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\input{sections/03-measurements}
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\input{sections/04-scaling-laws}
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\input{sections/05-implications}
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\input{sections/06-honesty}
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\input{sections/99-conclusion}
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\end{document}
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