This paper develops a dual-channel framework for analyzing technology diffusion that integrates spatial decay mechanisms from continuous functional analysis with network contagion dynamics from spectral graph theory. Building on our previous studies, which establish Navier-Stokes-based approaches to spatial treatment effects and financial network fragility, we demonstrate that technology adoption spreads simultaneously through both geographic proximity and supply chain connections. Using comprehensive data on six technologies adopted by 500 firms over 2010-2023, we document three key findings. First, technology adoption exhibits strong exponential geographic decay with spatial decay rate $\kappa \approx 0.043$ per kilometer, implying a spatial boundary of $d^* \approx 69$ kilometers beyond which spillovers are negligible (R-squared = 0.99). Second, supply chain connections create technology-specific networks whose algebraic connectivity ($\lambda_2$) increases 300-380 percent as adoption spreads, with correlation between $\lambda_2$ and adoption exceeding 0.95 across all technologies. Third, traditional difference-in-differences methods that ignore spatial and network structure exhibit 61 percent bias in estimated treatment effects. An event study around COVID-19 reveals that network fragility increased 24.5 percent post-shock, amplifying treatment effects through supply chain spillovers in a manner analogous to financial contagion documented in our recent study. Our framework provides micro-foundations for technology policy: interventions have spatial reach of 69 kilometers and network amplification factor of 10.8, requiring coordinated geographic and supply chain targeting for optimal effectiveness.

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