Welcome to PolyfdoS World.
Open-access research on topology, knowledge representation, and post-vector data systems. Every paper ships with an interactive animated explainer.
Live →Deep explorations in operating systems, low-level architecture, and systems design. Coming soon.
Coming soonCross-disciplinary thinking across mathematics, physics, philosophy, and computation. Coming soon.
Coming soonA topological–relational paradigm for post-vector data management. Replaces embedding similarity with sheaf-theoretic composition on dynamic graph manifolds — exact retrieval, no approximation.
Introducing realistic, a native type in the Matyos language implementing Kleene's three-valued logic. Extends Boolean logic with a third truth value ⊙ for uncertainty — with formal semantics, benchmarks, and applications in AI, quantum simulation, and paradox resolution.
A conjecture on the asymptotic bounds of half-prime gaps. Introduces the normalized half-gap sequence {rₙ} and proposes an exponential upper bound connecting gap growth to prime index — refining classical bounds on prime gaps.