Toward a Contract-Governed Geometric Learning Paradigm

Contemporary deep learning systems store knowledge implicitly in distributed weights, making local updates, structural constraints, and causal interpretation difficult under continual change. This paper proposes a new learning substrate in which knowledge is represented as an explicit geometric state. In this paradigm, long-term knowledge is modeled as a base landscape, context acts as a geometric deformation, concepts correspond to stable attractors, reasoning is formalized as a route through attractor structure, and learning is defined as constrained geometric editing rather than global weight fitting. We introduce a minimal formal core specifying the state, deformation mechanism, dynamics, attractor graph, edit algebra, and route-and-cargo inference. Crucially, we argue that systems in this framework must be evaluated not only by output-level task metrics, but also by an internal contract governing state health, separability, and spurious-state control. The proposal is positioned adjacent to energy-based modeling, dynamical-systems approaches, and continual learning, but differs by making the geometry of the internal knowledge state itself the primary object of the theory. This work is presented as a paradigm paper with prototype-level mechanistic grounding, outlining its operational envelope for few-shot concept formation, local rule insertion, route-first reasoning, and contract-governed continual adaptation.