# Hodge/Poincare Holographic Topology Module

This module implements two Millennium-inspired topological demos in the CATALYST phase-vector style.

Important: these are computational analogues and validation demos, not proofs of the Hodge conjecture or an alternative proof of Poincare.

## Hodge Decomposition Demo

- Hypervector dimension: 2048
- Mean absolute coefficient error: 0.011670
- Max coefficient error: 0.022804

## Poincare Ricci-Flow Demo

- Grid: 18^3 periodic manifold surrogate
- Initial curvature variance: 3.335549
- Final curvature variance: 0.006782
- Variance reduction: 99.797%
- Late log-decay slope: -0.028402

## Outputs

- `output/hodge_decomposition.csv`
- `output/hodge_decomposition.svg`
- `output/poincare_ricci_flow.csv`
- `output/poincare_ricci_flow.svg`