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 CofaceAdjacent Coface adjacency: (max_dim)-cells containing the target (max_dim − 1)-cell as a face. CofaceAdjacentIter Concrete iterator returned by <CofaceAdjacent as Neighborhood<K>>::neighbors. CubicalReggeGeometry Cubical Regge geometry: discrete metric data on a D-dimensional cubical complex. 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. DualLatticeComplex 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). Edge An edge between two nodes, recording the endpoint mark at the lower-indexed
node (lo) and the higher-indexed node (hi). Euclidean Euclidean signature: all axes spacelike, signature (+, +, …, +). ExteriorDerivativeWitness Witness for the exterior derivative d: Ω^k → Ω^(k+1). FaceAdjacent Face adjacency on top-stratum cells, defined via ∂. FaceAdjacentIter Concrete iterator returned by <FaceAdjacent as Neighborhood<K>>::neighbors. 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>. GenericManifoldWitness Graph Represents a simple undirected graph (nodes and edges). GraphWitness HeavyHexLattice Heavy-Hex lattice (IBM quantum hardware topology). HodgeDecomposeOptions Caller-tunable knobs for Manifold::hodge_decompose_opts. HodgeDecomposition The three orthogonal components of a discrete Hodge–Helmholtz decomposition. 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 KRing Chebyshev-distance-≤-K neighborhood on LatticeComplex<D> top cells. KRingIter Concrete iterator returned by <KRing<K> as Neighborhood<LatticeComplex<D>>>::neighbors. KagomeLattice Kagome lattice in 2D.
Used in frustrated magnets, spin liquids. LatticeCell A k-cell in a D-dimensional regular lattice. LatticeComplex A combinatorial cubical lattice in D dimensions, paired with a metric precision R. LatticeComplexWitness HKT witness for LatticeComplex<D, R> as a functor over field values. LatticeGaugeField A gauge field on a D-dimensional lattice. LatticeGaugeFieldWitness HKT witness for LatticeGaugeField<G, D, M, R>. LinkVariable A link variable U_μ(n) ∈ G on a lattice edge. Lorentzian Lorentzian signature: at least one timelike axis, East-Coast convention
(−, +, …, +) (or equivalent permutation per the per-axis timelike_axes
flag carried on CubicalReggeGeometry). Manifold A newtype wrapper around any ChainComplex that represents a Manifold. ManifoldWitness MixedGraph A mixed graph over num_vertices nodes with typed edge endpoints. MixedGraphWitness HKT witness for MixedGraphType<T> = MixedGraph<T>. Moore Moore neighborhood on LatticeComplex<D> top cells (Chebyshev distance = 1). MooreIter Concrete iterator returned by <Moore as Neighborhood<LatticeComplex<D>>>::neighbors. 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. TopologicalInvariants Pure-topology invariants of a Hodge–Helmholtz decomposition. 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. VonNeumann Von Neumann neighborhood on LatticeComplex<D> top cells. VonNeumannIter Concrete iterator returned by <VonNeumann as Neighborhood<LatticeComplex<D>>>::neighbors. AcceptReject Outcome of a single Metropolis-Hastings step. CurvatureSymmetry Symmetry properties of curvature tensors. EdgeKind The classification of an edge by its (order-independent) pair of endpoint marks. FlowMethod Integration method for gradient flow. LightConeViolation Failure mode of the Lorentzian constructor on CubicalReggeGeometry. LinkVariableError Error type for link Mark The mark at one endpoint of an edge, in the typed-endpoint calculus shared by
CPDAGs, MAGs, and PAGs. RejectReason Reason a Metropolis proposal was rejected. TopologyErrorEnum BaseTopology A foundational trait for any topological structure. Cell Marker trait for cell types in a chain complex. ChainComplex Types that form a chain complex (a CW-style cellular decomposition).
This generalizes simplicial complexes, cubical lattices, and arbitrary cellular decompositions. GaugeGroup Marker trait for gauge groups. GraphTopology A trait for topological structures that exhibit graph-like properties. HasHodgeStar Capability trait for metric types that can vend a discrete Hodge star operator. HypergraphTopology A trait for topological structures that exhibit hypergraph-like properties. ManifoldTopology A trait for structures capable of evaluating manifold-specific criteria. MixedGraphTopology A trait for graph-like structures with typed edge endpoints (CPDAG/MAG/PAG). Neighborhood Strategy for enumerating the neighbors of a cell in a chain complex. RandomField A trait for generating random field elements uniformly. SignatureMarker Capability trait for CubicalReggeGeometry<D, R, S> signature markers. SimplicialTopology A trait for topological structures composed of simplices. CellId Stable identifier for a cell within a ChainComplex. Returned by Neighborhood::neighbors. CubicalCell Textbook alias for LatticeCell<D>. See CubicalComplex<D>. CubicalComplex Textbook alias: a cubical complex is the regular cellular decomposition of a
lattice. Both terms refer to the same structure here; LatticeComplex<D, R> is the
canonical name (it makes the underlying ℤᴰ grid and the metric precision explicit
and stays consistent with the physics vocabulary used elsewhere in the crate,
e.g. LatticeGaugeField). CurvatureTensorVector Type alias for generic curvature tensor SimplicialManifold Textbook alias for the simplicial case: Manifold<SimplicialComplex<R>, F>. SimplicialManifoldWitness Textbook alias for the simplicial case.