Calera Computing derives cognitive architecture from mathematical first principles — not statistical approximation. We build systems where every output is provable, traceable, and deterministic.
Calera Computing, Inc. is a Delaware C-Corporation building the next generation of deterministic cognitive systems. Our architecture is organized around algebraic constants that emerge from lattice geometry — the same constants that govern energy propagation in simplicial structures across dimensions.
We don't approximate. We don't predict. We derive. Every architectural decision traces back to a mathematical proof. That's not a philosophy — it's a structural constraint.
Our first public paper establishes the dimensional hierarchy of algebraic constants that organize energy propagation on simplicial lattices.
We derive σ ≈ 1.22074, the unique positive real root of x⁴ − x − 1 = 0, and demonstrate that it is the geometry-native organizing constant for energy propagation on the A₄ root lattice. The result is validated through two independent methods: Hopfield recall optimization and spectral Laplacian analysis. Zero free parameters. The lattice geometry determines the constant.
| Dimension | Equation | Constant | Name | Geometry |
|---|---|---|---|---|
| 2 | x² = x + 1 | φ ≈ 1.618 | Golden Ratio | Triangle, Pentagon |
| 3 | x³ = x + 1 | ρ ≈ 1.325 | Plastic Constant | Tetrahedron |
| 4 | x⁴ = x + 1 | σ ≈ 1.221 | σ-Constant | Pentatope, A₄ Lattice |
| 5 | x⁵ = x + 1 | ≈ 1.167 | — | 5-Simplex |
| ∞ | — | → 1.0 | Isotropic Limit | — |