Stewart Barteau

The Atlas: Phase-Locked Geometric Neural Manifolds on Mixed-Curvature Hyperbolic–Toroidal Product Spaces

We give a complete formal specification of Atlas, a phase-locked geometric representation substrate whose state space is the mixed-curvature Riemannian product M= Hn ×Tn. The hyperbolic factor carries semantic lineage (exponential volume growth, low-distortion hierarchy); the fla...

The Atlas: Phase-Locked Geometric Neural Manifolds on Mixed-Curvature Hyperbolic–Toroidal Product Spaces

We give a complete formal specification of Atlas, a phase-locked geometric representation substrate whose state space is the mixed-curvature Riemannian product M= Hn ×Tn. The hyperbolic factor carries semantic lineage (exponential volume growth, low-distortion hierarchy); the fla...