The Generalized HKR Theory: Holonomic Context Realism in Open-Dimensional Context Fields — Non-Invariant Fact-Cores, Emergent Objectivity, and Topological Information Dynamics

The Generalized HKR Theory develops Holonomic Context Realism as a unified ontology, geometry, information theory, and computational research program for contextually manifest reality. Its central thesis has two inseparable components. First, the context field surrounding any fact is open-dimensional: every contextually effective influence can constitute a dimension, and no finite, predefined inventory exhausts the field. Second, the fact-core is the centering of this field and is therefore not invariant. As the distribution, geometry, weighting, and active dimensionality of context change, the centered fact-core may move along historical time. The framework models finite observable contexts as projections of an open-dimensional total field. Local fact manifestations inhabit a fact-state bundle over this field. A connection transports them between contexts; curvature measures local revision pressure; closed-loop holonomy measures path dependence; and the fact-core is formalized as a gauge-aware Fréchet centering of transported local manifestations. This permits contextual path independence at a given epoch to coexist with non-zero covariant drift of the fact-core through time. Objectivity is consequently treated as an epoch-local, low-holonomy, high-redundancy state rather than as temporal immutability. The construction incorporates the Hochschild–Kostant–Rosenberg filtration, Hopkins–Kuhn–Ravenel character-theoretic depth, Fisher–Rao information geometry, quantum Darwinism, active inference, and renormalization-group dynamics. The consolidated computational record exhibits a scalar-curvature basin with a minimum near −2.25, Wilson-loop concentration near 1.000, an 11.9-fold Fisher–Rao revision acceleration, a one-bit partial-information plateau with effective redundancy 117.6, and a revision-cascade transition near pc ≈ 0.593. Redundancy drives residual curvature downward while objectivity rises, while social, active-inference, biomimetic, and recursive sectors preserve revision without dissolving establishment. A prospective Claim-Field Validator translates the theory into an externally executable research program over real scientific claim histories. It defines temporally sliced claim states, context lattices, learned transport, loop holonomy, independent redundancy, stabilization targets, matched ablations, leakage controls, and cross-domain replication. The resulting architecture treats facts neither as arbitrary constructions nor as static substances, but as dynamically centered states within an open-dimensional context field. Document status: Independent research preprint, Version 1.0.