API inventory
This thematic inventory began with the 0.14.0a2 coordinate release and remains a human navigation aid. For the frozen 0.16.0a2 contract, use komorebi_math.stable, komorebi_math.v1, or komorebi_math.api.v1 together with public_api_stable_0_16.json. The source and committed manifests remain the authoritative signature references.
komorebi_math.core
Grammars and realizations
ArrowOperatorGrammarOperatorRelationOperatorWordOperatorRealization
Algebras and seed systems
OperatorAlgebraAlgebraBasisResultSeedSystemcyclic_spanmatrix_unitssemisimple_seed_ranksingle_operator_seed_rankshared_direct_sum_seed_boundsindependent_direct_sum_seed_ranktensor_seed_rank_upper_bound
Packets and transfers
PacketSystemPacketCoordinatesPacketOperatorTransferGraphSupportPreorderblock_from_pathspath_contributions
Morphisms
OperatorMorphismPacketMorphismSeedMorphism
komorebi_math.refinement
Towers and packet addresses
PacketRefinementRefinementTowercommon_refinementResidueCoordinatesresidue_analyzeresidue_packet_systemcrt_paircrt_many
Weighted transfer
WeightedTransferEdgeWeightedTransferGraph
Lattices and Smith congruences
LatticePacketDataSmithCongruenceProblem
Linear defects
LinearRefinementDefect
komorebi_math.nonlinear
Coordinates, defects, obstruction, lifting, and holonomy
NonlinearPacketMapNonlinearRefinementDefectLinearObstructionProblemLinearLiftProblemPolynomialLiftProblemFiniteLiftTreeTransportEdgeTransportGraphbuild_lift_treesolve_mod_prime
Derivative providers and composition
DerivativeProviderCallableDerivativeProviderPolynomialDerivativeProviderFiniteDifferenceDerivativeProviderSympyDerivativeProviderComposedDerivativeProviderfaa_di_brunopacket_faa_di_brunoset_partitionsstirling_second
Packet jets and trees
PacketJetPacketJetAddressPacketJetFamilyPacketJetSupportpacket_jet_supportpacket_taylorOrderedRootedTreePolynomialFixedPointProblemmajorant_convergencepacket_tree_reconstructionordered_rooted_treesordered_trees_with_leavescatalan_number
Graded nonlinear operations
FiniteAbelianGroupGradedPacketOperationmaurer_cartan_packetshigher_maurer_cartan_packetsdivided_square_packets
Correction and elimination
HilbertObstructionProjectorRightInverseCorrectionProblemLyapunovSchmidtReductionNonlinearSchurElimination
Filtered lifting and spectral sequences
FilteredVectorSpaceFilteredCorrectionProblemFiniteFilteredCochainComplexverify_finite_filtered_branchconditional_projective_limit_completion
Shared smooth transport
MovingPacketSystemKatoTransportdirect_packet_rotation
The transport objects are re-exported from komorebi_math.quantum for backward compatibility.
komorebi_math.algorithms
Layout and packet IR
PacketLayoutPacketBlockPacketIR
Structured operators
StructuredOperatorDenseOperatorIdentityOperatorDiagonalOperatorBlockDiagonalOperatorCirculantOperatorToeplitzOperatorKroneckerOperatorWalshHadamardOperatoras_structured_operator
Low rank algebra
LowRankOperatorRecompressionResultBlockDiagonalLowRankOperatorrecompress_corerecompress_factorsproduct_chain_error_boundaccumulated_recompression_bound
Support, Krylov, precision, compilation, and scheduling
The namespace includes structural support propagation, Krylov and conjugate gradient routines, block Jacobi certificates, continuous and discrete precision allocation, exact finite tree compilers, Pareto frontiers, task scheduling, complexity estimates, restricted structure discovery, NumPy execution, optional CuPy execution, and matched benchmark contracts.
komorebi_math.signals
Production finite DSP
WindowMetrics,get_window,window_metrics,overlap_profile,overlap_add_certificate,canonical_dual_windowFrameBatch,STFTResult,frame_signal,stft,istft,spectrogram,overlap_addPowerSpectrum,CrossSpectrum,periodogram,welch_psd,cross_spectrum,parseval_certificateFIRFilter,FrequencyResponse,StreamingFIR,design_fir,design_lowpass,design_highpass,design_bandpass,design_bandstop,fir_filter,stream_fir_filterRationalResamplingPlan,ResamplingResult,upsample,downsample,interpolate,decimate,design_resample_filter,resample_poly,resample_poly_resultAdaptiveFilterResult,lms_filter,nlms_filter,rls_filterHaarDecomposition,WaveletDenoiseResult,haar_decompose,wavelet_denoise,threshold_coefficients,denoising_risk_certificateStreamingSTFT,StreamingSTFTBatch,stream_stftLinearFilter,FilterOutput,StreamingLinearFilter,lfilter,stream_lfilter,design_biquadOverlapAddConvolver,fft_convolve,overlap_add_convolve,certified_overlap_add_convolve
Polyphase coordinates
PolyphaseCoordinatesLatticePolyphaseCoordinatesPolyphaseKernelPolyphaseSystempolyphase_analyzepolyphase_synthesizepolyphase_roundtrip_certificatelattice_polyphase_analyzelattice_polyphase_synthesizepolyphase_filter_kernelsmixed_radix_addresssplit_mixed_radix_addressrefinement_childrenresidue_project
Convolution
ConvolutionModePolyphaseConvolutionPolyphaseBlockMatrixFinitePolyphaseKernelconvolve_signalconvolution_matrixconvolution_output_lengthpolyphase_convolutionfinite_polyphase_blocksfinite_polyphase_filter_kernels
Filter banks and wavelets
PeriodicFilterBankFiniteFilterBankHaarFilterBankPeriodicLiftingSchemeFilterBankReportHaarPacketTreePrunedPacketCoefficientsBestBasisResulthaar_analyzehaar_synthesizehaar_matrixhaar_filter_bankperiodic_five_three_liftingbest_basisentropy_costlp_costpacket_energy
Singular packets and recovery
TruncatedPowerTermTruncatedPowerPacketSingularPacket1DRetainedPacketReconstructionRetainedPacketResultJumpDetectionJumpRecoveryResultVectorJumpRecoveryResultBreakpointBandResultretained_packet_reconstructretained_packet_reconstructionestimated_packet_reconstructrecover_separated_jumpsrecover_jumps_subgaussianrecover_vector_jumpsrecover_vector_jumps_subgaussiandetect_piecewise_polynomial_breaksfinite_differencescalar_region_errorscalar_region_lp_erroroverlap_matrix_erroroverlap_partition_lp_errorstep_location_lp_error
Secondary signal tools
- cyclic coefficient packet products
- shifted nonlinear filters
- Fourier low pass approximation
- Otsu thresholding
- the deliberately narrow positive contrast packet estimator
- Smith and Cayley phase coordinates
komorebi_math.dynamics
Semigroups and refinement
MatrixSemigroupPacketSemigroupSemigroupRefinementFiniteSemigroupTowerProjectiveSemigroupTowermatrix_exponentialsemigroup_refinement_defect
Markov and martingale systems
FiniteMarkovChainContinuousTimeMarkovChainAggregationMapMarkovLumpingConditionalExpectationConditionalExpectationTowerMartingaleToweraggregation_matrixcoordinate_lumpability_residualnormalize_partitionpartition_refines
Bayesian models
BayesianUpdateBayesianPartitionBayesianFlowHiddenMarkovFiltercoarsest_sufficient_partitionapproximate_likelihood_partitionrelative_entropyrelative_entropy_decomposition
Fractional and Green operators
FractionalDefectResultfractional_powerfractional_semigroupfractional_defectfractional_naturality_certificateDirichletGreen1D
Feynman Kac, Feshbach, memory, and survival
FiniteFeynmanKacFeshbachReductionMemoryKernelRationalMemoryKernelRationalMemoryRealizationmemory_kernel_error_boundkernel_l1_errorvolterra_trajectory_boundPhaseTypeSurvival
Infrastructure
Certificates and configuration
CertificateComputationResultConditionalResultExactnessSettingsconfigureget_settingssettings_context
Registries
FeatureSpecFeatureStatusfeaturefeaturesClaimStatusProvenanceRecorddescribe
Unified runtime
UnifiedStageStageSpecUnifiedSystemSTAGES
komorebi_math.analytic
Cyclic coordinates and sections
CyclicSectionFamilycyclic_project_coefficientscyclic_packetscyclic_reconstructcyclic_project_valuecyclic_product_packetscyclic_projection_certificatetransfer_sectionsigned_sectiontransfer_sectionssigned_sectionsdenominatordenominator_root_sumdenominator_derivativetransfer_shift_matrixsigned_shift_matrixcyclic_additionsection_certificate
Reciprocal and polynomial families
logarithmic_coefficientsreciprocal_coefficientsreciprocal_polynomialreciprocal_valuereciprocal_semigroup_certificatetransfer_tangenttransfer_tangent_coefficientscongruential_inversecongruential_reciprocal_coefficientsappell_polynomialappell_coefficientsappell_polynomial_symbolictheta_polynomialtheta_polynomial_symbolic
Zero diagnostics
CyclicDenominatorZeroStringResultasymptotic_positive_zeropositive_zero_stringzero_count_asymptotichadamard_partial_productreciprocal_coefficient_from_zerosreduced_zero_zeta
komorebi_math.quantum
Seeds, symmetry, and circuits
QuantumSeedSystemschmidt_ranklocal_orbit_dimensionobservable_seed_rankcomputational_basis_generationfinite_group_projectorcyclic_symmetry_projectorscharge_certificatecharge_selection_certificatetotal_charge_packetssymmetry_projector_certificateCircuitPacketExpansionCircuitPathAmplitudeInterferenceReport
Moving packets and leakage
LeakageResultfixed_packet_leakageMovingPacketSystemKatoTransportDirectRotationResultdirect_packet_rotationmoving_geometric_couplingmoving_packet_leakage_bound
Channels and error correction
ChannelPacketBlockQuantumChannelamplitude_dampingoperator_packetsreconstruct_operator_packetsdephaseLindbladGeneratorQuantumCodeKnillLaflammeReport
Effective dynamics and finite geometry
QuantumFeshbachReductionEuclideanTransferheat_tracespectral_dimensionperiodic_lattice_eigenvaluesperiodic_laplacianlow_mode_dispersion_boundConstraintClosureReportconstraint_closuretransported_constraint_defectBoundedHamiltonianTowerHamiltonianTowerReport
Arithmetic and sequences
Arithmetic and sequence interfaces cover exact local domains, valuations, Hurwitz convolution, standard windows, Euler coordinates, Mahler transfer, recurrence packets, lazy sequences, automatic models, holonomic recurrences, transforms, and compilation.
Deformation
The deformation namespace covers lift forests, visibility, counting charts, finite cochain complexes, packet cohomology, Fitting fibers, nested occupancy, Frobenius spines, companion forests, and compatible carriers.
Local Langlands finite models
Finite local models cover finite fields, tame Frobenius packets, monodromy chains, Gauss sums, Heisenberg models, alternating forms, quadratic refinements, projective envelopes, and finite bridges.
Finite image, ramification, and completion
The finite image namespace exports explicit groups, subgroups, linear characters, induced representations, orbit packets, Mackey packets, Clifford towers, conditional induction plans, and virtual character resolutions. The ramification namespace exports finite ramification tower diagnostics. The global and completion namespaces export finite Hecke packets, support comparisons, patching reports, dyadic sign diagnostics, five gate completion reports, and compatible propagation reports.
Portable exports and LaTeX
The export namespace provides document blocks, serialization adapters, JSON and tabular writers, text and web renderers, LaTeX renderers, LaTeX compiler discovery, PDF compilation, manifested export bundles with normalized ZIP metadata, and artifact certificates. See EXPORT_AND_LATEX.md for complete examples.
Scalable nonlinear execution
Scalable execution includes sparse derivative tensors and providers, lazy directional automatic-differentiation adapters, packet-jet plans, provider-independent snapshots, CuPy runtime diagnostics, versioned portable persistence and structural API compatibility tools.
Preferred public CuPy names use CuPy. Existing implementation spellings beginning with Cupy remain aliases inside the nonlinear modules and are not the preferred documented surface.
Streams and persistence
Streams support directory-backed packet-jet snapshots, resumable live capture, bounded chunking, adjacent codec migrations, behavioral fixtures, finite complexity counts and runtime profiles.
komorebi_math.generating
Bases and coefficient domains
WeightedMonomialBasis,BasisDescriptor,FiniteNormalizedSeries,FormalSeriesIntegerDomain,RationalDomain,ResidueRingDomain,PrimeFieldDomain,TruncatedPadicDomainordinary_basis,exponential_basis,factorial_power_basis,q_factorial_basis,fibonacci_factorial_basis,pochhammer_basis
Custom sources and recognition
CustomFunctionSpec,FunctionRegistry- recurrence, rational, hypergeometric, algebraic, Euler-product, composition, and factorial-power Bell constructors
- bounded recurrence, P-recursive, hypergeometric, algebraic, and quasipolynomial recognizers
Arithmetic compilers
FiniteMaskCarryPlan,CartierLinearRepresentation,CartierAutomatonmahler_mask_product,mahler_mask_inverse,compile_finite_mask_carry_plan,compile_digit_cauchy_productcompile_cartier_linear_representation,compile_rational_mask_automatonKummerLayerDistribution,PrimePowerUnitCompiler,PrimePowerKernelCompilerBellParityAutomaton,BellResidueAutomatonq_binomial_valuation_decomposition,q_binomial_support- cyclotomic collapse, trusted snapshots, and finite signal adapters
komorebi_math.coordinates
The coordinate namespace provides a general atlas with arbitrary finite bases and subspaces, path composition and commuting diagrams, normalized-series changes, combinatorial transforms, classical and custom polynomial families, recurrence and state-space coordinates, affine and formal charts, tensor and operator transport, prime-field maps, spectral and modal transforms, packet permutations, resource budgets, and trusted portable records. Euler-to-Fibonacci conversion remains one named bridge inside the general system.