Crate holos_tda 

Vietoris-Rips persistent homology and finite H1 degree-Rips modules over a prime field.

The scalar engine uses implicit persistent cohomology. Its tie-breaking and output conventions match Ripser. The degree-Rips path constructs every node and cover map on a declared finite grid.

Re-exports

pub use atlas::AtlasEvaluation;

pub use atlas::AtlasUpdate;

pub use atlas::ClassSensitivity;

pub use atlas::CoordinateDerivative;

pub use atlas::EdgeKey;

pub use atlas::EndpointGradient;

pub use atlas::EvaluatedClassSpace;

pub use atlas::LineageId;

pub use atlas::PersistenceAtlas;

pub use atlas::PointAtlasUpdate;

pub use atlas::PointClassSensitivity;

pub use atlas::PointEndpointGradient;

pub use atlas::PointPersistenceAtlas;

pub use atlas::TopologyEvent;

pub use atlas::TopologyEventKind;

pub use atlas::UpdateMode;

pub use atlas_wire::AtlasArtifact;

pub use atlas_wire::AtlasArtifactError;

pub use atlas_wire::AtlasArtifactRepair;

pub use atlas_wire::AtlasDecodeLimits;

pub use bifiltration::BifiltrationLimits;

pub use bifiltration::BifiltrationSlice;

pub use bifiltration::Bigrade;

pub use bifiltration::BirthAntichain;

pub use bifiltration::DegreeRipsBifiltration;

pub use bifiltration::DegreeRipsParams;

pub use bifiltration::MulticriticalBifiltration;

pub use bifiltration::MulticriticalSimplex;

pub use bipersistence::BipersistenceLimits;

pub use bipersistence::BipersistenceMap;

pub use bipersistence::BipersistenceMapColumn;

pub use bipersistence::BipersistenceModule;

pub use bipersistence::BipersistenceNode;

pub use bipersistence::BipersistenceRectangle;

pub use bipersistence::BipersistenceRegion;

pub use bipersistence::BipersistenceTerm;

pub use bipersistence::CircularCoordinateFamily;

pub use bipersistence::CircularCoordinateFamilyEntry;

pub use bipersistence::CircularCoordinateFamilyStatus;

pub use bipersistence::ClassExtension;

pub use bipersistence::ClassExtensionKind;

pub use bipersistence::ClassExtensionRegion;

pub use bipersistence::CohomologyClassAtlas;

pub use bipersistence_artifact::BipersistenceArtifact;

pub use bipersistence_artifact::BipersistenceArtifactLimits;

pub use bipersistence_artifact::BipersistenceArtifactSummary;

pub use bipersistence_artifact::BipersistenceRectangleClaim;

pub use bipersistence_artifact::BipersistenceRegionClaim;

pub use certificate::CertificateError;

pub use certificate::CertificateLimits;

pub use certificate::CertificateTerm;

pub use certificate::CertifiedReductionRegion;

pub use certificate::CertifiedRegionEvaluation;

pub use certificate::ChangeColumn;

pub use certificate::FiltrationSimplex;

pub use certificate::ReductionCertificate;

pub use certificate::ReductionGuard;

pub use certificate::ReductionGuardKind;

pub use certificate::ReductionRepair;

pub use certificate::ReductionRepairMode;

pub use certificate::ReductionRepairWork;

pub use certificate::RegionViolation;

pub use certificate::RegionViolationKind;

pub use circular::CircularClassTerm;

pub use circular::CircularCoordinate;

pub use circular::CircularCoordinateContinuation;

pub use circular::CircularCoordinateParams;

pub use circular::IntegralCocycleTerm;

pub use circular::circular_coordinate;

pub use circular::circular_coordinate_for_class;

pub use circular::circular_coordinate_with_integral_lift;

pub use circular::cocycle_from_ripser_terms;

pub use circular::continue_circular_coordinate;

pub use circular_artifact::CircularArtifactError;

pub use circular_artifact::CircularArtifactSummary;

pub use circular_artifact::CircularCoordinateArtifact;

pub use classes::BasisClassId;

pub use classes::Cocycle;

pub use classes::CocycleTerm;

pub use classes::CriticalPair;

pub use classes::CriticalSimplex;

pub use classes::ExplainedDiagram;

pub use classes::IntervalGroupId;

pub use classes::PersistentClass;

pub use classes::PersistentClassProvenance;

pub use classes::PersistentClassSpace;

pub use classes::lift_h1_classes;

pub use classes::rips_persistence_with_classes_sparse;

pub use cohomology::CochainTerm;

pub use cohomology::CohomologyClass;

pub use cohomology::CohomologyClassId;

pub use cohomology::CohomologyContinuation;

pub use cohomology::CohomologyContinuationKind;

pub use cohomology::CohomologyLimits;

pub use cohomology::CohomologyMapColumn;

pub use cohomology::CohomologyMapTerm;

pub use cohomology::CohomologyRelation;

pub use cohomology::CohomologyRelationTerm;

pub use cohomology::CohomologyRelationVector;

pub use cohomology::CohomologyRestriction;

pub use cohomology::CohomologySpace;

pub use cohomology::CohomologySpaceId;

pub use cohomology::CohomologySubspace;

pub use cohomology::CohomologySubspaceGenerator;

pub use cohomology::CohomologySubspaceTerm;

pub use cohomology::cohomology_continuation;

pub use cohomology::cohomology_relation;

pub use cohomology::cohomology_restriction;

pub use cohomology::cohomology_space;

pub use cohomology_intervention::CohomologyInterventionArtifact;

pub use cohomology_intervention::CohomologyInterventionCandidate;

pub use cohomology_intervention::CohomologyInterventionLimits;

pub use cohomology_intervention::CohomologyInterventionScenario;

pub use cohomology_intervention::CohomologyInterventionStatus;

pub use correspondence::ClassCorrespondence;

pub use correspondence::CorrespondenceTerm;

pub use correspondence::CorrespondenceVector;

pub use correspondence::class_correspondences;

pub use coverage::CoverageEvaluation;

pub use coverage::CoverageFence;

pub use coverage::CoverageLimits;

pub use coverage::CoverageTriangleTerm;

pub use coverage::PlanarCoverageModel;

pub use coverage::evaluate_planar_coverage;

pub use coverage_frontier::CoverageComponentFrontier;

pub use coverage_frontier::CoverageComposition;

pub use coverage_frontier::CoverageCompositionStatus;

pub use coverage_frontier::CoverageFrontierEntry;

pub use coverage_frontier::compose_coverage_frontiers;

pub use coverage_geometry::CoverageGeometry;

pub use coverage_geometry::CoverageGeometryLimits;

pub use coverage_geometry::GeometryBoundCoverageArtifact;

pub use coverage_geometry::GeometryBoundCoverageDecodeLimits;

pub use coverage_geometry::PlanarPoint;

pub use coverage_synthesis::CoverageAction;

pub use coverage_synthesis::CoverageComponent;

pub use coverage_synthesis::CoverageCounterexample;

pub use coverage_synthesis::CoveragePlanEvaluation;

pub use coverage_synthesis::CoverageSource;

pub use coverage_synthesis::CoverageSpecification;

pub use coverage_synthesis::CoverageState;

pub use coverage_synthesis::CoverageSynthesisArtifact;

pub use coverage_synthesis::CoverageSynthesisLimits;

pub use coverage_synthesis::CoverageSynthesisStatus;

pub use coverage_synthesis::evaluate_coverage_plan;

pub use distances::DistanceMatrix;

pub use distances::PointCloudGraph;

pub use distances::PointCloudParams;

pub use distances::PointCloudStats;

pub use distances::PointCloudStrategy;

pub use distances::SparseDistanceMatrix;

pub use distributed::ArtifactId;

pub use distributed::DistributedInterfaceCommit;

pub use distributed::DistributedInterfaceError;

pub use distributed::DistributedInterfaceManifest;

pub use distributed::DistributedInterfaceWork;

pub use distributed::DurableInterfaceStore;

pub use explicit_certificate::ExplicitReductionCertificate;

pub use filtration::ComplexLimits;

pub use filtration::CoordinateProjection;

pub use filtration::FilteredSimplex;

pub use filtration::FilteredSimplicialComplex;

pub use filtration::FiltrationError;

pub use filtration::FiltrationGrade;

pub use filtration::FlagComplexParams;

pub use filtration::LinearFiltrationGrade;

pub use filtration::ProductGrade;

pub use filtration::ScalarGrade;

pub use filtration::ScalarProjection;

pub use graded_certificate::GradedDimensionWork;

pub use graded_certificate::GradedReductionCertificate;

pub use graded_certificate::GradedReductionRepair;

pub use graded_certificate::GradedReductionRepairWork;

pub use index::DiagramDelta;

pub use index::IndexBranch;

pub use index::IndexDiff;

pub use index::IndexEdit;

pub use index::IndexEvent;

pub use index::IndexEventKind;

pub use index::IndexParams;

pub use index::IndexSummary;

pub use index::IndexTransition;

pub use index::IndexUpdateMode;

pub use index::IndexWork;

pub use index::InterfaceMode;

pub use index::InterfacePolicy;

pub use index::InterfaceSummary;

pub use index::PersistenceIndex;

pub use index::TopologyPatch;

pub use index_proof::IndexDeltaProof;

pub use index_proof::IndexProofError;

pub use index_proof::IndexProofSummary;

pub use index_proof::IndexSnapshotProof;

pub use index_stream::IndexStream;

pub use index_stream::IndexStreamProof;

pub use index_stream::IndexStreamStep;

pub use intervention::EdgeWeightEdit;

pub use intervention::H1Intervention;

pub use intervention::InterventionArtifact;

pub use intervention::InterventionBudget;

pub use intervention::InterventionDecodeLimits;

pub use intervention::InterventionError;

pub use intervention::InterventionStatus;

pub use intervention::VerifiedIntervention;

pub use kinetic::KineticCohomologyEvent;

pub use kinetic::KineticEdge;

pub use kinetic::KineticEdgeKey;

pub use kinetic::KineticEvent;

pub use kinetic::KineticEventKind;

pub use kinetic::KineticFiltration;

pub use kinetic::KineticGraphState;

pub use kinetic::KineticGraphStateKind;

pub use kinetic::KineticLimits;

pub use kinetic::KineticSchedule;

pub use kinetic::KineticZigzag;

pub use kinetic::KineticZigzagArrow;

pub use kinetic::KineticZigzagNode;

pub use kinetic::KineticZigzagNodeKind;

pub use kinetic_zigzag_artifact::KineticZigzagArtifact;

pub use kinetic_zigzag_artifact::KineticZigzagArtifactLimits;

pub use kinetic_zigzag_artifact::KineticZigzagArtifactSummary;

pub use kinetic_zigzag_artifact::KineticZigzagIntervalClaim;

pub use persistent_class_artifact::PersistenceCycleTerm;

pub use persistent_class_artifact::PersistenceTriangleTerm;

pub use persistent_class_artifact::PersistentClassArtifact;

pub use persistent_coordinate_artifact::PersistentCoordinateArtifact;

pub use persistent_coordinate_artifact::PersistentCoordinateArtifactError;

pub use persistent_coordinate_artifact::PersistentCoordinateArtifactSummary;

pub use program::BasisTransport;

pub use program::ClassContinuation;

pub use program::ContinuationKind;

pub use program::CorrespondenceMode;

pub use program::PersistenceProgram;

pub use program::ProgramAtomInfo;

pub use program::ProgramBranch;

pub use program::ProgramCheckpoint;

pub use program::ProgramDiagramState;

pub use program::ProgramDiagramUpdate;

pub use program::ProgramDiagramUpdateMode;

pub use program::ProgramEvaluation;

pub use program::ProgramEvent;

pub use program::ProgramEventKind;

pub use program::ProgramSummary;

pub use program::ProgramUpdate;

pub use program::ProgramUpdateMode;

pub use program::ProgramWork;

pub use program_trace::ProgramTraceArtifact;

pub use program_trace::ProgramTraceDecodeLimits;

pub use program_trace::ProgramTraceError;

pub use program_trace::ProgramTraceStep;

pub use program_trace::VerifiedProgramTrace;

pub use program_trace::VerifiedProgramTraceStep;

pub use program_wire::ProgramArtifact;

pub use program_wire::ProgramArtifactError;

pub use program_wire::ProgramAtomArtifact;

pub use program_wire::ProgramDecodeLimits;

pub use proof::ProofArtifact;

pub use proof::ProofArtifactError;

pub use proof::ProofArtifactSummary;

pub use relative_interface::InterfaceCancellation;

pub use relative_interface::InterfaceCell;

pub use relative_interface::InterfaceChainTerm;

pub use relative_interface::RelativeInterfaceCertificate;

pub use relative_interface::RelativeInterfaceWork;

pub use synthesis::SynthesisAction;

pub use synthesis::SynthesisArtifact;

pub use synthesis::SynthesisComponent;

pub use synthesis::SynthesisCoordinate;

pub use synthesis::SynthesisLimits;

pub use synthesis::SynthesisSource;

pub use synthesis::SynthesisState;

pub use synthesis::SynthesisStatus;

pub use synthesis::TopologicalSpecification;

pub use trajectory::TrajectoryArtifact;

pub use trajectory::TrajectoryDecodeLimits;

pub use trajectory::TrajectoryError;

pub use trajectory::TrajectoryStep;

pub use trajectory::VerifiedTrajectory;

pub use trajectory::VerifiedTrajectoryStep;

pub use zigzag::ZigzagBarcode;

pub use zigzag::ZigzagDirection;

pub use zigzag::ZigzagInterval;

pub use zigzag::ZigzagIntervalId;

pub use zigzag::ZigzagLimits;

pub use zigzag::ZigzagMap;

pub use zigzag::ZigzagModule;

pub use zigzag::ZigzagModuleId;

pub use zigzag::ZigzagTerm;

Modules

atlas

Certified local models of H1 persistence under changing inputs. Certified local models of H1 persistence under changing edge weights.

atlas_wire

Wire format for persistence atlases. Wire format for persistence atlases.

bifiltration

Finite multicritical bifiltrations and exact degree-Rips construction. Finite multicritical bifiltrations and exact degree-Rips construction.

bipersistence

Exact finite H1 modules over degree-Rips parameter grids. Exact finite H1 modules over a degree-Rips parameter grid.

bipersistence_artifact

Wire format for checked finite degree-Rips bipersistence modules. Wire format for checked finite degree-Rips bipersistence modules.

certificate

Algebraic reduction certificates. Algebraic certificates for exact H0 and H1 persistence.

circular

Checked circular coordinates and conservative continuation. Checked circular coordinates from canonical fixed-scale H1 classes.

circular_artifact

Wire format for checked circular coordinates and continuation. Wire format for checked circular coordinates and continuation.

classes

Stable H1 classes and cocycle validation. Stable H1 classes and cocycles on the caller’s graph.

cli

The holos CLI as a library function (shared with the Python bindings). The holos command-line interface, callable as a library function.

cohomology

Canonical cohomology and exact relations in any bounded dimension. Canonical cohomology spaces and exact relations in any bounded dimension.

cohomology_intervention

Weighted fixed-scale interventions across declared graph scenarios. Weighted fixed-scale class interventions across declared scenarios.

collapse

Filtered edge collapse for flag filtrations.

correspondence

Exact class-space correspondences across persistence updates. Exact class-space correspondences across persistence updates.

coverage

Relative topological coverage criteria for fenced planar sensor networks. Exact relative coverage witnesses for fenced planar Rips complexes.

coverage_frontier

Exact component frontiers for failure-tolerant coverage synthesis. Exact component frontiers for failure-tolerant coverage synthesis.

coverage_geometry

Exact planar geometry bindings for finite coverage specifications. Exact planar geometry bindings for finite coverage specifications.

coverage_synthesis

Failure-tolerant finite and kinetic relative coverage specifications. Failure-tolerant specifications for exact relative coverage.

distances

Distance-matrix construction and storage. Distance-matrix storage and exact point-cloud graph construction.

distributed

Durable content-addressed execution for relative interfaces. Durable content-addressed execution for relative interfaces.

explicit_certificate

Proof-carrying persistence for explicit scalar filtered complexes. Proof-carrying persistence for explicit scalar filtered complexes.

factorization

Vertex-biconnected factorization of sparse flag filtrations. Vertex-biconnected factorization of sparse flag filtrations.

filtration

Explicit filtered simplicial complexes and filtration grades. Explicit filtered simplicial complexes and filtration grades.

graded_certificate

Dimension-generic algebraic certificates for separator indexes. Dimension-generic algebraic certificates for separator interfaces.

index

Versioned exact persistence over checked separator interfaces. Versioned exact persistence over checked separator interfaces.

index_proof

Cold snapshots and warm deltas for persistence indexes. Cold snapshots and warm deltas for versioned persistence indexes.

index_stream

Stateful exact index streams with proof output. Stateful index streams with proof output.

intervention

Certified finite H1 lifetime interventions. Finite H1 lifetime interventions.

io

File formats and diagram output. Readers for point clouds and for dense or sparse distance matrices. Writers for the diagram output formats.

kinetic

Exact events for affine edge-weight trajectories. Exact event schedules for affine edge-weight trajectories.

kinetic_zigzag_artifact

Certificates for kinetic cohomology zigzags. Certificates for exact kinetic cohomology zigzags.

oracle

Brute-force reference implementation used by the test gates. Independent correctness oracle: explicit simplex enumeration and textbook boundary-matrix reduction over a prime field. Deliberately naive. It shares nothing with the solver path except the input and output types, down to the modular inverses (Fermat exponentiation here, a Euclid-style table there).

persistent_class_artifact

Source-bound persistent H1 class and cycle artifacts. Wire format and producer for one source-bound persistent H1 class.

persistent_coordinate_artifact

Harmonic coordinates bound to persistent H1 class artifacts. Wire format for one selected persistent circular coordinate.

program

Compositional H0 and H1 persistence programs. Compositional, change-sensitive H0 and H1 persistence programs.

program_trace

Update traces for persistence programs. Update traces for persistence programs.

program_wire

Wire format for persistence programs. Wire format for persistence programs.

proof

Unified proof DAGs for checked persistence trajectories. Unified proof DAGs for checked persistence trajectories.

relative_interface

Exact filtered chain cores relative to separator subcomplexes. Exact filtered chain cores relative to separator subcomplexes.

synthesis

Proof-carrying synthesis for finite temporal topology specifications. Proof-carrying synthesis for finite temporal cohomology specifications.

trajectory

Trajectories across atlas regions. Persistence trajectories across atlas regions.

zigzag

Exact interval decomposition of finite zigzag modules. Exact interval decomposition of finite zigzag vector-space modules.

Structs

Bar

One persistence interval. death is f64::INFINITY for essential classes.

Diagram

A persistence diagram: the multiset of bars across dimensions.

RipsParams

Parameters for crate::rips_persistence.

Enums

CollapseSchedule

The collapse the pipeline runs with RipsParams::collapse_edges set.

DenseStorage

Which storage form the dense engine reduces from.

Engine

Which engine reduces a dense input.

Error

Errors from construction, validation, and IO.

GraphFactorization

Structural routing for positive-dimensional sparse persistence.

Constants

BUILD_PROFILE

Cargo build profile recorded at build time.

GIT_HASH

Short git commit hash recorded at build time (“unknown” outside a repo).

VERSION

Crate version.

Functions

rips_persistence

Compute the Rips persistence diagram of a distance matrix.

rips_persistence_sparse

Compute the Rips persistence diagram of a sparse distance matrix.

rips_persistence_with_classes

Compute a diagram and stable H1 classes from a dense distance matrix.

Type Aliases

Result

Crate-wide result alias.