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68 lines
3.9 KiB
TeX
68 lines
3.9 KiB
TeX
% Hanzo HMM (Hamiltonian Market Maker) Paper
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% Expanded academic treatment with full Hamiltonian mechanics formulation
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\documentclass[11pt,twocolumn]{article}
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\usepackage{../shared/hanzocover}
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\usepackage{amsmath, amssymb, amsthm}
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\usepackage{mathtools}
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\usepackage{bm}
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\usepackage{graphicx}
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\usepackage{booktabs}
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\usepackage{hyperref}
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\usepackage{enumitem}
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\usepackage{algorithm}
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\usepackage{algpseudocode}
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\usepackage{xcolor}
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\usepackage{float}
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\usepackage{subcaption}
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\usepackage{multirow}
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\usepackage[numbers]{natbib}
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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{proposition}[theorem]{Proposition}
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{definition}{Definition}
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\newtheorem{remark}{Remark}
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\title{Hamiltonian Market Maker (HMM): Physics-Inspired Automated Market Making for AI Compute}
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\author{
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Antje Worring, Hanzo AI Research\thanks{Corresponding author: [email protected]} \quad
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David Wei \quad
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Marcus Chen \\
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\textit{Hanzo AI Research} \\
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\texttt{[email protected]}
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}
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\date{September 2025}
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\begin{document}
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\hanzocoverpage
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\begin{abstract}
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We present the \textbf{Hamiltonian Market Maker (HMM)}, a physics-inspired automated market maker (AMM) that leverages the mathematical structure of Hamiltonian mechanics to price heterogeneous AI compute resources on decentralized exchanges. Traditional AMMs such as Uniswap's constant product formula operate effectively for fungible token pairs but fail when applied to multi-dimensional resource bundles with quality constraints, SLA requirements, and rapidly shifting supply-demand dynamics characteristic of AI compute markets. HMM formulates the market state as a point in a symplectic phase space $(\bm{q}, \bm{p}) \in T^*\mathcal{M}$, where generalized coordinates $\bm{q}$ represent resource reserves and conjugate momenta $\bm{p}$ encode demand pressures. The Hamiltonian function $\mathcal{H}(\bm{q}, \bm{p})$ serves as a conserved invariant that determines endogenous prices without external oracle dependency. We derive the full equations of motion governing price evolution, prove conservation laws analogous to energy and momentum in classical mechanics, and construct symplectic integrators that preserve the geometric structure of the phase space under discrete trading updates. We extend the framework to multi-asset pools with weighted resources, prove impermanent loss bounds strictly tighter than constant product and stableswap alternatives, and introduce a MEV resistance mechanism grounded in the non-commutativity of phase space flows. Extensive simulations over 180 days of synthetic trading data demonstrate that HMM achieves 15.3\% higher capital efficiency than orderbook baselines, 98.7\% price stability versus 89.2\% for oracle-based AMMs, quote latency under 200ms, and impermanent loss 32\% lower than Uniswap v3 concentrated liquidity positions. We provide formal security proofs against flash loan attacks, sandwich attacks, and oracle manipulation, and present results from a live testnet deployment with 50 worker nodes and 100 client agents.
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\end{abstract}
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\input{sections/01-introduction}
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\input{sections/02-hamiltonian-formulation}
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\input{sections/03-conservation-laws}
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\input{sections/04-symplectic-integrators}
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\input{sections/05-phase-space-geometry}
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\input{sections/06-multi-asset-generalization}
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\input{sections/07-impermanent-loss-analysis}
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\input{sections/08-mev-resistance}
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\input{sections/09-system-architecture}
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\input{sections/10-liquidity-provision}
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\input{sections/11-experimental-evaluation}
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\input{sections/12-security-analysis}
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\input{sections/13-related-work}
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\input{sections/14-discussion}
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\input{sections/15-conclusion}
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\input{sections/16-proof-of-theorem-ref-thm-il}
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\input{sections/17-solidity-interface}
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\input{sections/18-hamiltonian-derivation-details}
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\input{sections/19-convergence-proofs-for-symplectic-integr}
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\input{sections/99-lyapunov-stability-proof}
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\end{document}
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