Implement CDT property validation checks

[acgetchell]

Overview

Complete the implementation of CDT property validation methods in src/cdt/triangulation.rs.

Background

The validate_cdt_properties() method currently has skeleton implementations for three critical validation checks that need to be completed:

1. Topology validation (validate_topology())
2. Causality constraints (validate_causality())
3. Foliation consistency (validate_foliation())

Implementation Details

1. Topology Validation (validate_topology())

Current state: Basic Euler characteristic check for 2D triangulations
Needs:

• Boundary detection to determine expected Euler characteristic
• Dimension-specific topology validation (currently only handles 2D)
• Support for different manifold topologies (sphere, torus, etc.)
• Validation of genus consistency

Reference: Lines 212-234 in src/cdt/triangulation.rs

2. Causality Validation (validate_causality())

Current state: Placeholder that always succeeds
Needs:

• Time slice assignment for each vertex
• Edge classification (timelike vs spacelike)
• Verification that timelike edges only connect adjacent time slices
• Detection of closed timelike curves (cycles in the timelike subgraph)
• Validation that causal structure is acyclic

Reference: Lines 236-256 in src/cdt/triangulation.rs

3. Foliation Validation (validate_foliation())

Current state: Placeholder that always succeeds
Needs:

• Vertex time label storage in geometry backend
• Verification that all vertices have valid time labels (0 to time_slices-1)
• Check that each time slice contains at least one vertex
• Validation of spatial topology consistency across slices
• Verification that spatial slices have the same genus

Reference: Lines 258-279 in src/cdt/triangulation.rs

Dependencies

• May require extending the TriangulationMut trait to expose time slice information
• May need to add vertex attribute storage to backends
• Consider adding a FoliationInfo structure to track time slice data

Testing Requirements

Each validation method should have:

• Unit tests for valid triangulations
• Unit tests for invalid cases (should return appropriate errors)
• Integration tests with actual CDT moves
• Property-based tests using Kani for formal verification

Related Code

• src/cdt/triangulation.rs: Lines 183-204 (main validation method)
• src/errors.rs: Error types (may need new variants)
• src/geometry/traits.rs: Trait definitions (may need extensions)

Acceptance Criteria

• All three validation methods have complete implementations
• Appropriate error types are returned for validation failures
• Unit tests cover both valid and invalid cases
• Documentation explains the validation criteria
• Integration tests verify validation works with ergodic moves
• Consider Kani proofs for critical properties