Research
Active research at Axiom Lab, papers, workstreams, and open questions in proof-native computing, neurosymbolic AI systems and infrastructure.
Imitation Is Not Intelligence: A Mathematical Case for Neurosymbolic Architecture
A mathematical case arguing that the limits of statistical approximation are structural: systems trained to imitate distributions cannot guarantee correctness outside observed support. The paper argues that out-of-distribution hallucination is not an implementation bug but a structural consequence, and motivates a shift toward architectures where correctness is derived through formal invariants and verification.
Imitation Is Not Intelligence: A Mathematical Case for Neurosymbolic Architecture
A mathematical case arguing that the limits of statistical approximation are structural: systems trained to imitate distributions cannot guarantee correctness outside observed support. The paper argues that out-of-distribution hallucination is not an implementation bug but a structural consequence, and motivates a shift toward architectures where correctness is derived through formal invariants and verification.
Flux: A Mathematical Programming Language with Paper-Native Syntax and OS-Level Integration
A dual-mode, math-native language architecture that attacks the two-language problem by preserving mathematical expressiveness while delivering compiled performance.
Tenet: A Domain-Specific Language for Game-Theoretic Process Scheduling
Treats strategic games as native language constructs with compile-time structural validation, turning invalid strategic models into syntax errors.
Alexitha: A Self-Bootstrapped Language Model for Novel DSL Fluency
Shows how language fluency can be manufactured from compiler-verified synthetic data, reducing reliance on internet-scale supervision.
Axiom OS: An AI-Native Operating System Architecture
Integrates Alexitha (language-facing), Flux (math substrate), and Tenet (scheduling/policy) into unified kernel execution where intelligence is architectural, not application-level.
The questions that drive the work. We publish these because the questions matter as much as the answers.
Can formal verification reach real-time AI inference without compromising soundness?
What is the minimal representational substrate required for structural truth in a neural system?
How do we design hardware that enforces computational contracts rather than merely executing them?
What does autonomy mean at each layer of the AI stack, and do those definitions compose?
Can neurosymbolic systems achieve full compositionality without sacrificing neural expressivity?
What kinds of environments most clearly reveal the difference between persuasive intelligence and verifiable intelligence?