The Geometry of Discovery: Locating Scientific Structure Beyond LLMs and Knowledge Graphs-S. Rahman

Description: We present a discovery engine that extracts governing mathematical structure initiated from scientific corpora using topological and geometric methods. Seeded with 2.5M+ arXiv papers, the system produces a living manifold distinct from both the stochastic interpolation of LLMs and the rigid ontologies of traditional knowledge graphs, identifying 130 emergent mathematical fields and over 36,000 structural gaps across domains. We demonstrate how the manifold dynamically reorganizes around user context, and as a case study, examine where Active Inference is structurally located on the manifold relative to its parent fields in variational calculus, stochastic dynamics, and Bayesian inference. We also present applications in multi-agent simulation (extending standard POMDPs with mean-field stochastic coupling) and non-equilibrium macro-finance. Presenters: Vladimir Baulin, PhD is Chief Scientist at the Synthetix Institute and architect of the Discovery Engine protocol. Distinguished Researcher at Universitat Rovira i Virgili with 150+ publications and over 8,000 citations in soft matter physics, biophysics, and complex systems. Board member of the Active Inference Institute. His recent work includes a framework for AI-driven synthesis of scientific knowledge landscapes and a lead contribution to the Intelligent Soft Matter roadmap (2025). Shagor Rahman is Head of Product at the Synthetix Institute, where he leads the design of the Atlas research platform. His work spans product design and management, with publications in Frontiers on transcendent model selection and cognitive simulation methods. Also joining from the Synthetix team: Andrew Pashea (Chief Agentic Architect), Austin Cook (Head of Engineering), and Jonathan Minchin (COO).