Skip to main content Crate deep_causality_topology Copy item path Source alias utils_tests Test utilities for deep_causality_topology tests ActionCoeffs Coefficients for improved gauge actions. BoundaryOperator The boundary operator ∂: C_k → C_{k-1} for a cell complex. BoundaryWitness Witness for the boundary operator ∂: C_k → C_(k-1). CellComplex A CW complex with arbitrary cell types. CellComplexWitness HKT witness for CellComplex<C> as a functor over field values. Chain Represents a weighted collection of simplices.
(e.g., A path is a Chain<f64> on the 1-skeleton where weights are 1.0). ChainWitness CurvatureTensor A rank-4 curvature tensor for RiemannMap operations. CurvatureTensorWitness HKT4 witness for CurvatureTensor<A, B, C, D>. DifferentialForm A differential k-form on a manifold. DualLattice For a D-dimensional lattice, a primal k-cell corresponds to a dual (D-k)-cell.
This structure is essential for discrete exterior calculus (Hodge star). ExteriorDerivativeWitness Witness for the exterior derivative d: Ω^k → Ω^(k+1). FlowParams Gradient flow parameters. GaugeField A gauge field over a base manifold. GaugeFieldHKT Wrapper type for GaugeField that can be used with HKT3Unbound. GaugeFieldWitness HKT3 witness for GaugeField<G, A, F>. Graph Represents a simple undirected graph (nodes and edges). GraphWitness HeavyHexLattice Heavy-Hex lattice (IBM quantum hardware topology). HoneycombLattice Honeycomb (hexagonal) lattice in 2D.
Used in graphene, Haldane model, Kitaev model. Hypergraph Represents a hypergraph where hyperedges can connect an arbitrary number of nodes. HypergraphWitness KagomeLattice Kagome lattice in 2D.
Used in frustrated magnets, spin liquids. Lattice A D-dimensional regular lattice. LatticeCell A k-cell in a D-dimensional regular lattice. LatticeGaugeField A gauge field on a D-dimensional lattice. LatticeGaugeFieldWitness HKT witness for LatticeGaugeField<G, D, M, R>. LatticeWitness HKT witness for Lattice<D> as a functor over field values. LinkVariable A link variable U_μ(n) ∈ G on a lattice edge. Manifold A newtype wrapper around SimplicialComplex that represents a Manifold. ManifoldWitness PointCloud Represents a collection of data points in a d-dimensional space. PointCloudWitness ReggeGeometry SE3 SE(3) gauge group marker. SO3_1 Lorentz SO(3,1) gauge group marker. SU2 SU(2) gauge group marker. SU3 SU(3) gauge group marker. SU2_U1 Electroweak SU(2)×U(1) gauge group marker. SU3_SU2_U1 Standard Model SU(3)×SU(2)×U(1) gauge group marker. Simplex A combinatorial simplex defined by sorted vertex indices.
Order is strictly increasing to ensure canonical representation. SimplicialComplex A simplicial complex representing a geometric structure. SimplicialComplexBuilder A builder for constructing SimplicialComplex instances incrementally. Skeleton A collection of all simplices of dimension K. SmearingParams Smearing parameters. StokesAdjunction Stokes Adjunction: d ⊣ ∂ StokesContext Context for Stokes theorem operations. TensorVector A concrete vector type for curvature and scattering operations. Topology Represents a discrete field defined on the k-skeleton. TopologyError TopologyWitness TriangularLattice Triangular lattice in 2D.
Used in antiferromagnetic systems, spin liquids. U1 U(1) gauge group marker. CurvatureSymmetry Symmetry properties of curvature tensors. FlowMethod Integration method for gradient flow. LinkVariableError Error type for link TopologyErrorEnum BaseTopology A foundational trait for any topological structure. CWComplex Types that form a CW complex (Closure-Finite Weak Topology).
This generalizes simplicial complexes, cubic lattices, and arbitrary cellular decompositions. Cell Marker trait for cell types in a CW complex. GaugeGroup Marker trait for gauge groups. GraphTopology A trait for topological structures that exhibit graph-like properties. HypergraphTopology A trait for topological structures that exhibit hypergraph-like properties. ManifoldTopology A trait for structures capable of evaluating manifold-specific criteria. RandomField A trait for generating random field elements uniformly. SimplicialTopology A trait for topological structures composed of simplices. CurvatureTensorVector Type alias for generic curvature tensor