A deep dive into the fundamental limits of computation, logic, and systems — Gödel, Turing, Arrow, CAP, and beyond. Proven impossibilities and open conjectures that every engineer and thinker should know.
Machine-checked Lean 4 proofs for "Projection Insufficiency and Trajectory Realization." Establishes that no function on a non-injective projection can recover a trajectory-dependent property, with specializations to language-model hallucination, planning, RL, POMDPs, and constraint propagation.
Machine-checked Lean 4 proofs for "The Non-Locality of Extendability." Forward-case impossibility result for bounded information systems: the divergence kernel, horizon non-convergence, structural admissibility lemmas, and witnesses distinguishing extendability from POMDP observability and viability.
Machine-checked Lean 4 proofs for "Language Model Hallucinations: An Impossibility Theorem and Its Architectural Consequences." Covers Theorem 1 (impossibility of guaranteed consistency), certification-depth lower bounds, mitigation boundaries for CoT / grammar / rerank, and intrinsic/extrinsic DCF taxonomy.
This paper proves a fundamental impossibility theorem for universal complexity measures.
AA-DC is a structural correction framework for link prediction. It addresses two systematic biases that arise when relational feasibility is evaluated under coarse recognition mappings, such as Adamic–Adar (AA).
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