Add Validated Topology And Sparse Surface Diffusion

[ryanwhois]

GeometryKit now has reusable numerical foundations for surface diffusion and future heat-method geodesics. TriangleMesh protects its backing arrays with read-only wrappers and caches validated internal half-edge adjacency. Edge geodesics reuse that cache. Topology-sensitive operations reject inconsistent winding, duplicate triangles, and disconnected or branched vertex fans; mesh health also rejects non-finite geometry.

The new LinearAlgebra boundary provides immutable CSR assembly, an ILinearSolver adapter contract, and a managed Jacobi-preconditioned conjugate-gradient baseline with cancellation, true-residual checks, iteration limits, and breakdown diagnostics. SurfaceOperators assembles cotangent stiffness and barycentric mass and performs backward-Euler scalar diffusion with natural zero-flux boundaries. Negative cotangent weights are retained; no general positivity guarantee is claimed on obtuse meshes.

Mathematics, sign conventions, units, boundary conditions, limits, class relationships, and an ADR are documented. Precise Special Functions supplies a high-precision Bessel reference for a future Neumann disc benchmark without becoming a runtime dependency. Full heat-method reconstruction and maintained solver adapters remain follow-up work.

Validation: library compiled with the .NET 8 C# compiler without XML documentation warnings; all 33 current C# cases passed locally using actual xUnit assertions via a reflection runner, including the 441-vertex sparse-grid case. Normal MSBuild execution is blocked by process-information restrictions in the local environment, so the standard test runner is verified by GitHub CI. Git diff --check passes, and the uploaded GitHub tree hash exactly matches the local commit.

Compatibility: graph geodesics now require consistent manifold topology; preliminary MeshHealthReport.IsQueryable does not itself certify vertex links. Inputs are rejected explicitly and are never silently repaired.