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35+ papers documenting Hanzo AI platform evolution covering: - Crowdstart cloud-native commerce (2014 era) - Astle.js reactive SDK, Verus analytics (2015 era) - Earle genetic marketing optimization (2016 era) - Hanzo AI-first commerce platform (Techstars 2017) - Checkout, analytics ML (2018 era) - API gateway, SDK ecosystem, webhooks (2019 era) - MCP protocol, Platform PaaS (2021 era) - Agent SDK, ML framework, search, identity NFT (2022 era) - Jin multimodal AI, DSO protocol (2023 era) - Candle Rust ML, ACI decentralized compute (2024 era) - Chat, Flow, Operative, Network whitepaper, ASO, HMM, LLM gateway, Zen model family (2025 era) Papers describe historical work from 2014-2025. All compiled into this repository October 2025 - March 2026. Note: Previous git history had fabricated per-commit timestamps claiming individual commits from 2014-2025. This corrects the record — all content was committed in a single session.
27 lines
2.1 KiB
TeX
27 lines
2.1 KiB
TeX
% Hamiltonian Market Maker (HMM) section
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\section{Hamiltonian Market Maker (HMM)}
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\subsection{Invariant and State}
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Let reserve vector \(\bm R = (\Psi, \Theta)\) denote effective supply of compute capacity \(\Psi\) (e.g., GPU-seconds weighted by quality) and an aggregate demand credit pool \(\Theta\). A minimal HMM uses the \textbf{bilinear} Hamiltonian
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\begin{equation}\label{eq:cpmm}
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\mathcal H(\Psi,\Theta) = \Psi\,\Theta = \kappa, \quad \kappa>0,
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\end{equation}
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which matches the constant-product AMM as a special case. For multi-asset resources \(\bm \Psi=(\Psi_1,\dots,\Psi_m)\) and credits \(\bm \Theta\), we use
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\begin{equation}
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\mathcal H(\bm\Psi,\bm\Theta) = \sum_{i=1}^m w_i\,\Psi_i\,\Theta_i + \lambda \sum_{i=1}^m \tfrac{1}{2}(\Psi_i^2+\Theta_i^2), \quad w_i,\lambda>0.
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\end{equation}
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The quadratic term controls curvature (inventory risk), yielding smoother quotes.
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\subsection{Prices, Flows, and Fees}
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Define the conjugate price for compute class \(i\):
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\begin{equation}
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p_i \equiv \frac{\partial \mathcal H/\partial \Psi_i}{\partial \mathcal H/\partial \Theta_i} = \frac{w_i\,\Theta_i + \lambda\,\Psi_i}{w_i\,\Psi_i + \lambda\,\Theta_i}.
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\end{equation}
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A swap \(\Delta\bm\Theta<0, \Delta\bm\Psi>0\) (buy compute) preserves \(\mathcal H\) up to fee \(f\). We charge a split fee \(f=f_m+f_r\): market fee \(f_m\) (LP/treasury) and \emph{risk fee} \(f_r\propto \|\Delta\bm\Psi\|\) to compensate inventory risk. In continuous time, inventory evolves via
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\begin{equation}
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\dot{\Psi}_i = s_i - u_i,\quad \dot{\Theta}_i = d_i - v_i,\quad \text{s.t. } \frac{d}{dt}\mathcal H(\bm\Psi,\bm\Theta)=0 \, (\text{net of fees})
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\end{equation}
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with supply inflow \(s_i\) (workers) and demand \(d_i\) (jobs). Stability follows from convexity of \(\mathcal H\) in each orthant and fee dissipation.
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\subsection{Composable Market Objects}
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Each resource class instantiates an HMM pool; cross-resource jobs route via a \emph{path solver} minimizing total cost under \(\mathcal H\)-preserving constraints. Jobs specify an SLA vector (latency, jitter, region), encoded as Lagrange multipliers in the solver; quotes reflect SLA shadow prices.
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