Research

Papers, software and data.

Everything the systems rest on, by topic.

Model systems and reusable inference
Building Europe’s Frontier AI: Kolibri-1 Sharpness Governs the Substitutability of Attention Crystallized Attention The Holographic Causal Graph Machine No GPU, No KV Cache Compute Once Scarcity as Method: Attention, Replaced Organs, Not Weights
State-space models and operators
Geometric State Space Models One Operator, Three Switches Causal Prefix–Sinkhorn Attention O1FM: Verified Forecast Compilation
Exact discovery and tensor algorithms
Knowledge Is Compute Exact Tensor Ranks and Fast CPU Contractions Three Disjoint Boolean Balls for Every Tripartition Tensor Torus Chambers and Class Frames A Torus Ladder for Pratt’s Tripartition Tensor Breaking Pratt’s Bound for Balanced Tripartition Tensors False Endpoints in Numerical Border-Rank Search The Birkhoff Light Cone Smoothness Crossings in the CCF Model Sonic Termination of the Lower Kink Branch
Software, models and datasets
mrail Wirkung software repositories Model releases Verified Math Discovery Traces