Theoretical Foundations and Reference Implementations Status: Active Research Programme (v1.0.0)Geometry of Reasoning is the first chapter in the broader Epistemic Dynamics research programme at RarePixel Research .While the intent of the Epistemic Dynamics programme is the study of thinking agents through a structural and methodological lens, this first chapter maily focuses on establishing a geometric framework for the formal characterization of such enteties. It formalizes reasoning as a gradient flow on the section spaces of fiber bundles and by mapping the locus of ontology to the locus of epistemology via Grothendieck fibration, the framework provides a calculus for managing the geometric invariants of this reasoning model. Taxonomy The theoretical core consists of seven texts: Foundational Commitments and Methodological Constraints of the Epistemic Dynamics Programme - Fixes the interpretive constraints and methodological commitments of the programme. Geometry of Reasoning: On the Dynamics of Epistemic Objects - As the formal foundation for the rest of the series, this paper introduces the primary formalism and key constructs of the framework. Geometry of Reasoning: Proofs - provides proofs ommited from the main body of the framework. Geometry of Reasoning: Extensions - Explores more advanced fibration-theoretic consequences of the framework, elaborates on Transformer Calculus ,Obstruction Sheaf and BlackBox Transformers. Geometry of Reasoning: Examples and Models - presents a set of concrete models and examples within the framework. Geometry of Reasoning: Conscious Systems - An engineering friendly document which defines system regimes and isolates the notion of conscious systems within these regimes as meta-problem parity and closure under self-application. Furthermore it explores derived characteristics, boundary phenomena and impossibility templates of such systems and finally presents a construction demonstrating the realization of such a regime through a reflective wrapper over an arbitrary pretrained language model. Geometry of Reasoning: Agents and Regime Interactions - An engineering friendly document that introduces a formalization for multi-regime agent architecture within the framework. It explores regime interactions, agent boundries and governance, also show cases examples of such architecture. Minimal Working Examples Along with the theoretical papers, this collection includes two Minimal Working Examples that provide hands-on demonstrations of the GoR framework and serve as deterministic, finite-dimensional existence proofs for the theoretical papers: GoRCon: A realization of the Conscious Regime. It implements the reflective wrapper architecture introduced in Conscious Systems paper, demonstrating how a system can achieve meta-context closure through iterative coherence loops and deterministic trace repairs. Artifact World: An implementation of a Governed Epistemic Institution, illustrating the implementation of a multi-agent system, the interaction of multi-regime agents, the translation of uncertified effects into a typed DSL, the mechanical generation of structured failure witnesses, and the promotion of verified sections into an authoritative state.
Nara Shiru (Tue,) studied this question.