Formal
papers
& proofs

A compositional semantics of Steven Wright–style humor: the comic twist is the failure of literalization to be functorial on the pragmatic paraphrase category. Humor holds iff the incongruity gap is positive and the repair rank is bounded—the incongruity window. Proves paraphrase-stability as naturality, deadpan surprisal amplification, a Kolmogorov compression ceiling, and a terminating joke-debugger decision procedure.

Formalizes the shift from chat-grammar prompts to shell-grammar prompts, proving entropy reduction, reproducibility, and pipeline compositionality. Introduces the session quine—a fixed point of self-modification where a session reproduces its own governing instructions— proved via the Banach fixed-point theorem. Applies the MDA framework from game design to sessions, proving functorial propagation from mechanics to dynamics to aesthetics.

A formal K0--K5 benchmark for AI game creators. Proves fairness, monotonicity, boundedness, and telemetry information-gain properties. Outlines a triplex CAT VLM roadmap with teacher/student deplexing and VICReg-style collapse prevention.

Games are the oldest human activity. We formalise games as compressed worlds with rules that create meaning using information theory, graph theory, and dynamical systems. Proves the Rule Compression Lemma, Meaning Density Theorem, Literary Maximum Theorem for PnC games, Flow-Boundedness Theorem, and Primordial Precedence Theorem. Shows PnC games maximise literary meaning density.

Formalizes the Bijan Bowen Benchmark (B3), a practitioner-developed LLM evaluation methodology with nine generative coding tasks. Proves separability, coverage, and monotonicity. Introduces the Generative Separability Gap as a measure of ecological validity. Case study on Kimi K3.

Formal model of NPC intelligence composing six knowledge systems (emotion, cognitive bias, personality, social power, ethics, anxiety) into a behavioral stack. Proves emergence, signal distortion bounds for ecological rumor propagation, and affinity convergence. Companion to the "Building a Brain" frontier post.

Explores the neuroscience of creativity and its implications for artificial intelligence. Examines how spontaneous ideation emerges from memory consolidation, pattern recognition, and cross-domain analogy in biological and artificial systems.

Presents an ability system for AI agents inspired by video game design patterns. Abilities are relational graphs that abstract skill/workflow pairs into compact prompt context, achieving 10x token reduction versus flat file scanning. Formalizes token reduction bounds, compositionality, and evolution convergence.

Formal proof of the singleton law in distributed systems, showing that under network partition and message loss conditions, at most one leader can be elected. Provides correctness proof for Raft consensus algorithm variant.

Archive of GPU compute shaders for procedural universe generation, including galaxy formation, stellar evolution, and planetary surface generation. Provides formal analysis of procedural generation quality and performance characteristics.

Architecture for integrating reinforcement learning agents into real-time game engines. Describes observation spaces, action spaces, reward shaping, and training pipelines with formal convergence guarantees for policy gradient methods.

Describes a constraint-based rigid body physics system with formal correctness proofs for impulse-based constraint solvers. Proves that sequential impulse (SI) solver converges to feasible solution under bounded iteration count.

Formal proof that hierarchical collision detection with kinematic character controllers maintains stability under bounded velocity and acceleration. Provides sufficient conditions for collision response and proves no-tunneling guarantees.

Introduces a 4D holonomic memory model where knowledge is represented as points in (entity, attribute, time, value) space. Proves that this representation enables efficient temporal queries and supports forgetting curves via geometric decay.

Formal treatment of HFSM semantics, state transition correctness, and hierarchical composition. Proves that HFSM execution is equivalent to flattened FSM execution under specific conditions, enabling formal verification of game state machines.

Formal proof that directed acyclic graph (DAG) scheduling of game engine systems ensures deterministic frame execution across varying hardware. Provides sufficient conditions for DAG construction and proves bounded execution time.

Describes a biologically-inspired memory consolidation system for AI agents, combining episodic memory capture, dream-state compression, semantic extraction, and forgetting curves. Features a dream graph compiler with pulse propagation, trace-mode telemetry, dictionary-based engram compilation, top-k sequence generation, and concept-as-memory control flow replacing special tokens. Provides formal bounds on memory density, engram termination, and fingerprint uniqueness.

A formal treatment of cybernetic consciousness in artificial agents, defining self-model, mortality, continuity, agency, and endogenous persistence as measurable conditions. Introduces the cybernetic consciousness degree k(σ) and proves monotonic becoming under persistent memory.