Formal
papers
& proofs

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.

Describes a biologically-inspired memory consolidation system for AI agents, combining episodic memory capture, dream-state compression, semantic extraction, and forgetting curves. Provides formal bounds on memory density and convergence criteria.

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.

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.

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 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.

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.

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.

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.

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.