Capability Thresholds and Manufacturing Topology: How Embodied Intelligence Triggers Phase Transitions in Economic Geography

arXiv:2603.04457v1 Announce Type: new Abstract: The fundamental topology of manufacturing has not undergone a paradigm-level transformation since Henry Ford's moving assembly line in 1913. Every major innovation of the past century, from the Toyota Production System to Industry 4.0, has optimized within the Fordist paradigm without altering its structural logic: centralized mega-factories, located near labor pools, producing at scale. We argue that embodied intelligence is poised to break this century-long stasis, not by making existing factories more efficient, but by triggering phase transitions in manufacturing economic geography itself. When embodied AI capabilities cross critical thresholds in dexterity, generalization, reliability, and tactile-vision fusion, the consequences extend far beyond cost reduction: they restructure where factories are built, how supply chains are organized, and what constitutes viable production scale. We formalize this by defining a Capability Space C = (d, g, r, t) and showing that the site-selection objective function undergoes topological reorganization when capability vectors cross critical surfaces. Through three pathways, weight inversion, batch collapse, and human-infrastructure decoupling, we show that embodied intelligence enables demand-proximal micro-manufacturing, eliminates "manufacturing deserts," and reverses geographic concentration driven by labor arbitrage. We further introduce Machine Climate Advantage: once human workers are removed, optimal factory locations are determined by machine-optimal conditions (low humidity, high irradiance, thermal stability), factors orthogonal to traditional siting logic, creating a production geography with no historical precedent. This paper establishes Embodied Intelligence Economics, the study of how physical AI capability thresholds reshape the spatial and structural logic of production.