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Resonant Fractal Nature Theory — a mathematical framework for coherent patterns on graph-coupled networks.

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© 2026 TNFR project — MIT licensed.DOI 10.5281/zenodo.17602860
docs
grammar
PHYSICS_VERIFICATION.md
API_CONTRACTS.mdCANONICAL_OZ_SEQUENCES.mdEMPIRICAL_CONFRONTATION_EEG.mdREADME.mdSTRUCTURAL_FIELDS_TETRAD.mdSTRUCTURAL_INTERFACE_THEORY.md
theory
APPLIED_STRUCTURAL_ANALYSIS.mdCATALOG_TYPE_HYGIENE_PROGRAMME.mdDISSIPATIVE_AND_OPEN_SYSTEMS.mdEMERGENT_ONTOLOGY.mdEXTENDED_FIELDS_AND_DERIVED_QUANTITIES.mdFUNDAMENTAL_THEORY.mdGAUGE_SYMMETRY_AND_UNIFICATION.mdGLOSSARY.mdMATHEMATICAL_DYNAMICS_BASIS.mdMINIMAL_STRUCTURAL_DEGREES.mdNUCLEUS_A_PRIME_LADDER_ATLAS.mdNUCLEUS_B_EQUIVARIANCE_OBSTRUCTIONS.mdPHYSICAL_REGIME_CORRESPONDENCES.mdREADME.mdREMESH_INFINITY_DERIVATION.mdSTRUCTURAL_CONSERVATION_THEOREM.mdSTRUCTURAL_OPERATORS.mdSTRUCTURAL_STABILITY_AND_DYNAMICS.mdTNFR_BSD_RESEARCH_NOTES.mdTNFR_HODGE_RESEARCH_NOTES.mdTNFR_NAVIER_STOKES_RESEARCH_NOTES.mdTNFR_NUMBER_THEORY.mdTNFR_P_VS_NP_RESEARCH_NOTES.mdTNFR_RIEMANN_RESEARCH_NOTES.mdTNFR_VARIATIONAL_PRINCIPLE.mdTNFR_YANG_MILLS_RESEARCH_NOTES.mdTNFR.pdfUNIFIED_GRAMMAR_RULES.md
factorization-lab
analysis
analyze_patterns.pycertificate_manifest.py
benchmarks
benchmark_analysis.pybenchmark_expansion_suite.pyfull_spectrum_factorization.pypaley_gap_extended.pypaley_gap_smoke.pytest_benchmark_suite.py
demos
experiment_contexts
exp_0b1663cd19b7.jsonexp_0bf0054b7474.jsonexp_75a4c8ca616a.jsonexp_848ee0fd1857.jsonexp_f6fe00562193.jsonexp_fdf3da424e1e.json
failure_telemetry_batch.pyfeedback_integration_demo.pyintegration_demo_snapshots.dbseed_management_integration_demo.pysnapshot_integration_demo.pytrajectory_143.jsontrajectory_77.jsontrajectory_89.jsontrajectory_91.jsontrajectory_97.json
docs
FACTORING_PLAYBOOK.mdFALSE_POSITIVE_TEST_SUITE.mdOPERATOR_CERTIFICATES.mdROADMAP.mdSPECTRAL_ROUTE.md
experiment_contexts
exp_cebe1d9e7d8e.json
notebooks
spectral_history.ipynb
scripts
run_false_positive_tests.py
tests
run_false_positive_test_suite.pytest_cli.pytest_false_positive_methodology.pytest_false_positive_verifier.pytest_feedback_integration.pytest_partitioning.pytest_seed_management.pytest_self_opt_support.pytest_snapshot_system.pytest_spectral_paley.pytest_verification_robustness.py
tnfr_factorization
__init__.pyapi.pycli.pyfailure_telemetry.pyfeedback_adapter.pyfeedback_integration.pypartitioning.pyself_opt_support.pyspectral_paley.py
demo_snapshots.dbLICENSE_SNAPSHOT.mdPACKAGE_SUMMARY.mdREADME.mdseed_management.pysnapshot_system.pytest_certificate_hashing.pytest_installation.pyverification_trajectory_77.json
benchmarks
analyze_tetrad_universality.pyb0star_alpha_canonical_product_graphs.pybenchmark_optimization_tracks.pybenchmark_utils.pyboundary_vibration.pybridge_primes_riemann.pychiral_involution.pycli_utils.pycoherence_projector_sense_index.pycommutant_bridge.pycomposition_arithmetic.pyconfinement_zones_test.pyconservation_law_validation.pydirected_paley_bridge.pyemergent_arithmetic_pulse.pyemergent_atom_dynamics.pyemergent_atomic_shells.pyemergent_base_dimension.pyemergent_dimension_dynamics.pyemergent_fractal_pulse.pyemergent_fractal_simplex_dimension.pyemergent_integers_symmetry.pyemergent_musical_nfr.pyemergent_nfr_geometry.pyemergent_nfr_where.pyemergent_rationals.pyemergent_rhythm.pyemergent_screening.pyemergent_shell_cardinals.pyemergent_shell_ordering.pyemergent_simplex_dimension.pyemergent_substrate_symmetry.pyequivariance_wall.pyexternal_phase_gate_validation.pyfield_methods_battery.pygolden_residue_remesh_bridge.pyintegrated_force_regime_study.pyinverse_spectrum_to_symmetry.pyk_phi_safety_demo.pykuramoto_farey_bridge.pymissing_piece_bridge.pymultichannel_interface_benchmark.pynavier_stokes_recipe_bridge.pynodal_propagator_residue_bridge.pyns_moment_hierarchy_cascade.pyoperational_irreducibility.pypaley_bridge.pyphase_curvature_investigation.pyphase_wall.pyphi_s_confinement_investigation.pyprimes_as_consequence.pypulse_phase_coherence_budget.pyREADME.mdremesh_infinity_riemann_baseline.pyremesh_infinity_riemann_composed.pyremesh_infinity_riemann_modified_graph.pyremesh_infinity_riemann_operator.pyremesh_infinity_riemann_spectral_basis.pyremesh_infinity_riemann_spectral_robustness.pyremesh_infinity_riemann_spectral.pyresidue_phase_vs_riemann.pystructural_interface_benchmark.pytemporal_interface_benchmark.pytetrad_results_aggregate.pyu2_destabilization_irreversibility.pyuniversality_clusters.pyxi_c_fast_experiment.py
primality-test
benchmarks
comprehensive_benchmark.py
docs
ADVANCED_INTEGRATION.mdmathematical_foundation.mdperformance_analysis.md
examples
advanced_examples.pybasic_usage.py
tnfr_primality
__init__.py__main__.pyadvanced_cli.pyadvanced_core.pycli.pyconstants.pycore.pyoptimized.py
MANIFEST.inPACKAGE_SUMMARY.mdREADME.mdRELEASE_NOTES_v1.0.mdsetup.pytest_installation.py
tests
core_physics
__init__.pytest_conservation_laws.pytest_delta_nfr_computation_paths.pytest_delta_nfr.pytest_dispersion_coherence_sign_invariance.pytest_emergent_constants_guard.pytest_lyapunov_operators.pytest_nodal_equation.pytest_structural_triad.py
data
replay_manifests
sample_run
_manifest_summary.json_manifest.json_partition_files.txt.gz
self_opt_validation
seed_alpha
paley.json
seed_beta
integration.json
seed_gamma
unknown.json
self_optimization
test_run
partitioned
test_run
test_run_p0.jsontest_run_p1.json
_manifest_summary.json_manifest.json
engines
test_pattern_discovery_manifest.pytest_self_optimization_engine.py
mathematics
__init__.pytest_autodiff.pytest_backends.pytest_dissipative_dynamics.pytest_epi.pytest_factory_patterns.pytest_metrics.pytest_navier_stokes_refounded.pytest_number_theory_canonical.pytest_operators.pytest_residue_networks.pytest_riemann_nodal_pulse.pytest_riemann_pulse_coherence.pytest_spaces.pytest_transforms.pytest_validator.py
operators
test_canonical_operators_modern.pytest_grammar_canon.pytest_grammar_canonical_consistency.pytest_grammar_dynamics.pytest_operator_contracts.pytest_operator_strategies.py
parallel
test_fractal_partition_manifest.py
physics
test_conservation_gauge_unification.pytest_dissipative_conservation.pytest_emergent_chemistry.pytest_field_cache_invalidation.pytest_gauge.pytest_phase_transition.pytest_signatures.pytest_spectral_conservation.pytest_structural_diffusion.pytest_structural_integrity.pytest_symplectic_substrate.pytest_tetrad_bounds.pytest_variational.pytest_yang_mills_closure.pytest_yang_mills_derivability.pytest_yang_mills_scaling.pytest_yang_mills_structural_gap.pytest_yang_mills_u6_sweep.py
scripts
test_run_self_opt_validation.pytest_run_self_optimization.py
sdk
__init__.pytest_simple_advanced.py
__init__.pyconftest.pyREADME.mdtest_breast_cancer_phase_gate_demo.pytest_classical_mechanics.pytest_distributed_fft.pytest_external_phase_gate_validation.pytest_factorization_entrypoint.pytest_multichannel_interface.pytest_nodal_optimizer.pytest_phase_gate_api.pytest_replay_register_manifest.pytest_signal_confrontation.pytest_structural_interface_api.pytest_structural_interface_baselines.pytest_structural_interface_benchmark.pytest_temporal_interface.pytest_vectorized_coherence_length_regression.pytest_wine_quality_phase_gate_demo.pyutils.py
examples
01_foundations
01_hello_world.py02_musical_resonance.py03_network_formation.py04_operator_sequences.py05_coherence_evolution.py06_network_topologies.py07_phase_transitions.py08_emergent_phenomena.py09_visualization_suite.py10_simplified_sdk_showcase.py
02_physics_regimes
11_classical_limit_comparison.py115_operator_contract_audit.py12_classical_mechanics_demo.py13_quantum_mechanics_demo.py14_uncertainty_and_interference.py15_train_crossing_demo.py17_conservation_law_demo.py26_gauge_structure_demo.py27_variational_principle_demo.py28_dissipative_systems_demo.py29_lyapunov_stability_demo.py30_self_optimization_demo.py31_mathematical_constants_basis.py33_complex_field_unification.py34_conservation_protocol_suite.py35_tetrad_irreducibility.py36_grammar_violation_detector.py37_operator_tetrad_synergy.py38_grammar_energy_landscape.py39_nodal_equation_decomposition.py
03_riemann_zeta
157_nodal_pulse_phase_attack.py41_von_mangoldt_zeta_demo.py42_riemann_zeros_as_resonances.py43_prime_ladder_hamiltonian_demo.py44_weil_explicit_formula_demo.py45_li_keiper_demo.py46_weil_tnfr_positivity_demo.py47_alpha_sweep_demo.py48_admissible_family_sweep_demo.py49_nodeaware_gauge_sweep_demo.py50_uniform_coercivity_demo.py51_adaptive_coercivity_demo.py52_paley_gap_coercivity_demo.py53_lyapunov_spectral_positivity_demo.py54_hilbert_polya_demo.py55_structural_zero_density_demo.py56_spectral_emergence_demo.py57_admissible_rescaling_demo.py58_oscillatory_correction_demo.py
04_riemann_L_twisted
59_dirichlet_l_function_demo.py60_dirichlet_l_continuation_demo.py61_dirichlet_l_hamiltonian_demo.py62_dirichlet_weil_explicit_formula_demo.py63_dirichlet_li_keiper_demo.py64_twisted_weil_positivity_demo.py65_twisted_alpha_sweep_demo.py66_twisted_admissible_family_sweep_demo.py67_twisted_nodeaware_gauge_sweep_demo.py68_twisted_hermite_family_demo.py69_twisted_coercivity_uniform_demo.py70_twisted_paley_gap_coercivity_demo.py71_twisted_lyapunov_spectral_demo.py72_twisted_hilbert_polya_demo.py73_twisted_structural_zero_density_demo.py74_twisted_spectral_emergence_demo.py75_twisted_admissible_rescaling_demo.py76_twisted_oscillatory_correction_demo.py
05_type_hygiene
77_remesh_infinity_residue_split_demo.py78_nuf_type_signature_demo.py79_epi_type_signature_demo.py80_phi_type_signature_demo.py81_dnfr_type_signature_demo.py82_remesh_window_type_signature_demo.py83_delta_phi_max_type_signature_demo.py84_coupling_weights_type_signature_demo.py85_tetrad_closure_signature_demo.py86_currents_closure_signature_demo.py87_aggregates_closure_signature_demo.py88_urules_consistency_signature_demo.py89_operator_catalog_discipline_signature_demo.py
06_navier_stokes
158_navier_stokes_two_face_refounded.py
07_number_theory
100_prime_families_orbits.py101_numbers_as_coupled_network.py102_nodal_flow_primes_equilibria.py116_nuf_emergent_prime_visibility.py146_primality_grammatical_inertness.py147_numbers_as_free_monoid_words.py148_capacity_arm_carries_von_mangoldt.py149_p14_is_the_capacity_arm_operator.py153_structural_frequency_rank_cyclotomy.py40_arithmetic_number_theory.py94_generative_number_construction.py95_primes_from_spectral_waves.py96_spectral_vibration_of_coherence.py97_goldbach_additive_multiplicative.pyemergent_chemistry_particles_demo.py
08_emergent_geometry
103_emergent_substrate_meets_riemann.py106_per_node_polarization_geometry.py107_orthogonal_structure_emergent_geometry.py108_emergent_field_generating_structure.py112_structure_predicts_coherence_flow.py113_overdamped_projection_bridge.py114_substrate_conserved_quantities.py117_emergent_geometry_residue_graph.py118_emergent_vs_classical_operator.py119_phase_sector_directed_residue.py120_symmetry_wall_substrate_vs_spectrum.py121_canonical_symmetry_break_negative.py122_factorization_phase_sector.py123_symmetry_sector_decomposition.py124_emergent_metric_fractal_consistency.py125_node_is_the_emergent_substrate.py126_two_layers_base_fiber.py127_base_is_emergent_not_imposed.py128_base_substrate_coemergence.py129_spectral_gap_base_fiber_clock.py130_operators_break_substrate_charges.py131_coemergent_loop_convergence.py132_geometric_phase_holonomy.py133_psi_topological_defects.py134_spectral_dimension_heat_kernel.py135_arrow_of_time_h_theorem.py136_heat_kernel_coefficients.py137_synchronization_transition.py138_structure_frequency_synchronization.py139_grammar_formal_language.py140_grammar_automaton.py141_grammar_rule_decomposition.py142_grammar_operator_quotient.py143_glyphic_function_sublanguage.py144_branching_combinator.py145_syntactic_monoid_starfree.py150_emergent_grammatical_pattern_parry.py151_grammar_in_emergent_geometry.py152_operator_contract_tetrahedron.py154_conductor_annotated_qr_spectrum.py155_ontological_position_of_numbers.py156_emergence_directness_law.py98_emergent_symplectic_substrate.py99_structural_diffusion.pyunified_fields_showcase.py
09_millennium
109_p_vs_np_coherence_synthesis.py110_bsd_rank_structural_pressure.py111_hodge_discrete_and_honest_gap.py
10_applications
159_empirical_confrontation_pipeline.py90_phase_gate_monitor_demo.py91_breast_cancer_phase_gate_demo.py92_wine_quality_phase_gate_demo.py93_structural_interface_demo.pypytorch_cuda_demo.py
README.md
scripts
replay
__init__.pyregister_manifest.py
__init__.pyREADME.mdrebuild_failure_manifest.pyrun_reproducible_benchmarks.pyrun_self_opt_validation.pyrun_self_optimization.pytnfr_is_prime.pyvalidate_conservation_law.pyverify_internal_references.py
src
core
__init__.pyevaluation.py
tnfr
backends
__init__.pyjax_backend.pynumpy_backend.pyoptimized_numpy.pyREADME.mdtorch_backend.py
cli
__init__.py__init__.pyiarguments.pyarguments.pyiexecution.pyexecution.pyiinteractive_validator.pyREADME.mdutils.pyutils.pyi
compat
__init__.pydataclass.pyjsonschema_stub.pymatplotlib_stub.pynumpy_stub.pyREADME.md
config
__init__.py__init__.pyiconstants.pyconstants.pyidefaults_core.pydefaults_init.pydefaults_metric.pydefaults.pyfeature_flags.pyfeature_flags.pyiglyph_constants.pyoperator_names.pyoperator_names.pyiphysics_derivation.pyprecision_modes.pypresets.pypresets.pyiREADME.mdsecurity.pythresholds.pytnfr_config.py
constants
__init__.py__init__.pyialiases.pyaliases.pyicanonical.pymetric.pymetric.pyioperational.py
core
__init__.pycontainer.pydefault_implementations.pyexceptions.pyinterfaces.pyREADME.md
dynamics
__init__.py__init__.pyiadaptation.pyadaptation.pyiadaptive_sequences.pyadaptive_sequences.pyiadelic.pyadvanced_cache_optimizer.pyadvanced_fft_arithmetic.pyaliases.pyaliases.pyibifurcation.pycache_aware_fft_engine.pycanonical.pycanonical.pyicomputational_hub.pycoordination.pycoordination.pyidistributed_fft.pydnfr.pydnfr.pyidynamic_limits.pyemergent_centralization.pyemergent_integration_engine.pyfeedback.pyfeedback.pyifft_backend.pyfft_cache_coordinator.pyfft_dispatchers.pyfft_engine.pyfft_workers.pyfused_dnfr.pyhomeostasis.pyhomeostasis.pyiintegrators.pyintegrators.pyilearning.pylearning.pyimetabolism.pymulti_modal_cache.pynbody_tnfr.pynbody.pynodal_optimizer.pyoptimization_orchestrator.pypropagation.pyREADME.mdruntime.pyruntime.pyisampling.pysampling.pyiselectors.pyselectors.pyiself_optimizing_engine.pyspectral_structural_fusion.pystructural_cache.pystructural_clip.pysymplectic.pyunified_backend.pyunified_mathematical_cache_orchestrator.py
engines
computation
__init__.pyfft_engine.pyunified_fft_engine.pyunified_gpu_system.py
constants
__init__.pycanonical.pyoperational.py
integration
__init__.pyemergent_integration.py
pattern_discovery
__init__.pymathematical_patterns.pymulti_modal_cache.py
self_optimization
__init__.pyengine.py
__init__.pyREADME.md
errors
__init__.pycontextual.py
factorization
__init__.py
flatten
README.md
gamma
README.md
glyph_history
README.md
glyph_runtime
README.md
immutable
README.md
initialization
README.md
io
README.md
math
__init__.pyfields_symbolic.pygrammar_validators.pyoptimizer.pyREADME.mdsymbolic.py
mathematics
__init__.pybackend.pybackend.pyidynamics.pydynamics.pyiepi.pyepi.pyigenerators.pygenerators.pyiliouville.pymetrics.pymetrics.pyinumber_theory.pyoperators_factory.pyoperators_factory.pyioperators.pyoperators.pyioptimized_primality.pyprojection.pyprojection.pyiREADME.mdruntime.pyruntime.pyispaces.pyspaces.pyispectral.pytransforms.pytransforms.pyiunified_cache.pyunified_numerical.pyzeta.py
metrics
__init__.py__init__.pyibuffer_cache.pybuffer_cache.pyicache_utils.pycoherence.pycoherence.pyicommon.pycommon.pyicore.pycore.pyidiagnosis.pydiagnosis.pyiemergence.pyexport.pyexport.pyiglyph_timing.pyglyph_timing.pyilearning_metrics.pylearning_metrics.pyilocal_coherence.pyphase_coherence.pyphase_compatibility.pyREADME.mdreporting.pyreporting.pyisense_index.pysense_index.pyitelemetry.pytetrad.pytrig_cache.pytrig_cache.pyitrig.pytrig.pyi
multiscale
__init__.pyhierarchical.pyREADME.md
navier_stokes
__init__.pyconservative_face.pyoperator.py
node
README.md
observers
README.md
operators
network_analysis
__init__.pysource_detection.py
postconditions
__init__.pymutation.py
preconditions
__init__.pycoherence.pydissonance.pyemission.pymutation.pyreception.pyresonance.py
strategies
__init__.pydefaults.pygpu_strategies.pystrategy.py
__init__.py__init__.pyialgebra.pycanonical_patterns.pycascade.pycoherence.pycontraction.pycoupling.pycycle_detection.pydefinitions_base.pydefinitions.pydefinitions.pyidissonance.pyemission.pyexpansion.pygrammar_application.pygrammar_canon.pygrammar_context.pygrammar_core.pygrammar_dynamics.pygrammar_error_factory.pygrammar_memoization.pygrammar_patterns.pygrammar_telemetry.pygrammar_types.pygrammar_u6.pygrammar_validate.pygrammar.pygrammar.pyihamiltonian.pyhealth_analyzer.pyintrospection.pyjitter.pyjitter.pyilifecycle.pymetabolism.pymetrics_basic.pymetrics_core.pymetrics_network.pymetrics_structural.pymetrics_u6.pymetrics.pymutation.pynodal_equation.pyoperator_contracts.pypattern_detection.pypatterns.pyREADME.mdreception.pyrecursivity.pyregistry.pyregistry.pyiremesh.pyremesh.pyiresonance.pyself_organization.pysilence.pystructural_units.pytransition.py
parallel
__init__.pyauto_scaler.pydistributed.pyengine.pymonitoring.pypartitioner.pyREADME.md
performance
guardrails.py
physics
__init__.py_helpers.pycalibration.pycanonical.pycell.pyclassical_mechanics.pyconservation_gauge_unification.pyconservation.pydissipative_conservation.pyemergent_chemistry.pyemergent_particles.pyextended.pyfields.pygauge.pyintegrity.pyinteractions.pylife.pylyapunov.pypatterns.pyphase_transition.pyquantum_mechanics.pyREADME.mdsignatures.pyspectral_conservation.pyspectral_metrics.pystructural_diffusion.pysymplectic_substrate.pytelemetry.pyunified.pyvariational.pyvectorized_ops.py
primality
__init__.py
recipes
__init__.pycookbook.pyREADME.md
riemann
__init__.pyadmissible_family_sweep.pyadmissible_rescaling.pyaggregates_closure_signature.pyalpha_sweep.pyanalytic_continuation_dirichlet.pyanalytic_continuation.pycoercivity_uniform.pycoupling_weights_type_signature.pycurrents_closure_signature.pydelta_phi_max_type_signature.pydirichlet_l.pydnfr_type_signature.pyepi_type_signature.pyhilbert_polya.pyli_keiper.pylyapunov_spectral_positivity.pynodal_pulse.pynodeaware_gauge_sweep.pynuf_type_signature.pyoperator_catalog_discipline_signature.pyoperator.pyoscillatory_correction.pypaley_gap_coercivity.pyphi_type_signature.pyprime_ladder_hamiltonian.pypulse_coherence.pyremesh_infinity_residue_split.pyremesh_window_type_signature.pyspectral_emergence.pystructural_zero_density.pytelemetry.pytetrad_closure_signature.pytwisted_admissible_family_sweep.pytwisted_admissible_rescaling.pytwisted_alpha_sweep.pytwisted_coercivity_uniform.pytwisted_hermite_family.pytwisted_hilbert_polya.pytwisted_li_keiper.pytwisted_lyapunov_spectral_positivity.pytwisted_nodeaware_gauge_sweep.pytwisted_oscillatory_correction.pytwisted_paley_gap_coercivity.pytwisted_prime_ladder_hamiltonian.pytwisted_spectral_emergence.pytwisted_structural_zero_density.pytwisted_weil_explicit_formula.pytwisted_weil_positivity.pyurules_consistency_signature.pyvon_mangoldt.pyweil_explicit_formula.pyweil_positivity.py
schemas
__init__.pygrammar.jsonREADME.md
sdk
__init__.py__init__.pyiadaptive_system.pyadaptive_system.pyibuilders.pybuilders.pyifluent.pyfluent.pyiREADME.mdself_opt.pysimple.pytemplates.pytemplates.pyiutils.py
security
__init__.pycrypto.pydatabase.pyREADME.mdsubprocess.pyvalidation.py
sequencing
__init__.pypatterns.pyREADME.md
services
__init__.pyorchestrator.pyREADME.md
sparse
__init__.pyREADME.mdrepresentations.py
structural
README.md
telemetry
__init__.pycache_metrics.pycache_metrics.pyiconstants.pynu_f.pynu_f.pyiREADME.mdunified_telemetry_system.pyverbosity.pyverbosity.pyi
tools
__init__.pydomain_templates.pyREADME.mdsequence_generator.pytnfr_is_prime_cli_optimized.pytnfr_is_prime_cli.py
topology
__init__.pyasymmetry.pyREADME.md
utils
cache_layers.pycache.pycache.pyicallbacks.pycallbacks.pyichunks.pychunks.pyidata.pydata.pyifast_diameter.pygraph.pygraph.pyiinit.pyinit.pyiio.pyio.pyinumeric.pynumeric.pyiREADME.mdtopology.pyunified_cache.py
validation
__init__.py__init__.pyiaggregator.pybase.pycompatibility.pycompatibility.pyiconfig.pygraph.pygraph.pyihealth.pyinput_validation.pyinterface_baselines.pyinvariants.pymultichannel_interface.pyphase_gate.pyREADME.mdrules.pyrules.pyiruntime.pyruntime.pyisequence_validator.pysignal_confrontation.pysoft_filters.pysoft_filters.pyispectral.pyspectral.pyistructural_interface.pytemporal_interface.pyunified_validation_system.pyvalidator.pywindow.pywindow.pyi
visualization
__init__.pycascade_viz.pyhierarchy.pyREADME.mdsequence_plotter.py
yang_mills
__init__.pyclosure.pyderivability.pyscaling.pystructural_gap.pyu6_sweep.py
__init__.py__init__.pyi_compat.py_version.py_version.pyialias.pyalias.pyibackend_config.pycache.pycache.pyiexecution.pyexecution.pyiflatten.pyflatten.pyigamma.pygamma.pyiglyph_history.pyglyph_history.pyiglyph_runtime.pyglyph_runtime.pyiimmutable.pyimmutable.pyiinitialization.pyinitialization.pyiio.pyio.pyilocking.pylocking.pyinode.pynode.pyiobservers.pyobservers.pyiontosim.pyontosim.pyipy.typedrng.pyrng.pyisecure_config.pyselector.pyselector.pyisense.pysense.pyistructural.pystructural.pyitokens.pytokens.pyitrace.pytrace.pyitypes.pytypes.pyiunits.pyunits.pyi
tetrad_evaluator.py
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FILE: src/tnfr/backends/torch_backend.py

torch_backend.py

PyTorch-based GPU-accelerated backend for TNFR computations (Experimental).

This module provides a PyTorch implementation of TNFR computational kernels with support for:

  • GPU acceleration via CUDA/ROCm
  • Automatic differentiation with autograd
  • Optimized tensor operations
  • Mixed precision training support

Status: Experimental - API may change in future releases.

The Torch backend currently delegates to the NumPy implementation but provides infrastructure for future GPU-optimized kernels.

Examples

from tnfr.backends import get_backend backend = get_backend("torch") # doctest: +SKIP backend.supports_gpu # doctest: +SKIP True

Source Code

python
"""PyTorch-based GPU-accelerated backend for TNFR computations (Experimental).

This module provides a PyTorch implementation of TNFR computational kernels
with support for:

- GPU acceleration via CUDA/ROCm
- Automatic differentiation with autograd
- Optimized tensor operations
- Mixed precision training support

**Status**: Experimental - API may change in future releases.

The Torch backend currently delegates to the NumPy implementation but provides
infrastructure for future GPU-optimized kernels.

Examples
--------
>>> from tnfr.backends import get_backend
>>> backend = get_backend("torch")  # doctest: +SKIP
>>> backend.supports_gpu  # doctest: +SKIP
True
"""

from __future__ import annotations

from typing import Any, MutableMapping

from ..alias import get_attr
from ..constants.aliases import ALIAS_EPI, ALIAS_THETA, ALIAS_VF
from ..types import TNFRGraph
from . import TNFRBackend


class TorchBackend(TNFRBackend):
    """PyTorch GPU-accelerated implementation of TNFR kernels (Experimental).

    This backend provides a foundation for GPU-accelerated TNFR computations
    using PyTorch. Current implementation delegates to NumPy backend while
    maintaining interface compatibility for future GPU implementations.

    Future optimizations planned:
    - GPU-accelerated ΔNFR computation using torch tensors
    - Sparse tensor operations for large-scale graphs
    - Mixed precision support (FP16/BF16) for memory efficiency
    - Automatic device placement (CPU/CUDA/ROCm)
    - Integration with PyTorch Geometric for graph operations

    Attributes
    ----------
    name : str
        Returns "torch"
    supports_gpu : bool
        True (PyTorch supports GPU acceleration)
    supports_jit : bool
        False (TorchScript not yet integrated)

    Notes
    -----
    Requires PyTorch to be installed: `pip install torch`

    For GPU support, install PyTorch with CUDA:
    `pip install torch --index-url https://download.pytorch.org/whl/cu118`
    """

    def __init__(self) -> None:
        """Initialize PyTorch backend."""
        try:
            import torch

            self._torch = torch
            self._device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
        except ImportError as exc:
            raise RuntimeError(
                "PyTorch backend requires torch to be installed. "
                "Install with: pip install torch"
            ) from exc

    @property
    def name(self) -> str:
        """Return the backend identifier."""
        return "torch"

    @property
    def supports_gpu(self) -> bool:
        """PyTorch supports GPU acceleration."""
        return True

    @property
    def supports_jit(self) -> bool:
        """TorchScript not yet integrated."""
        return False

    @property
    def device(self) -> Any:
        """Return the current PyTorch device (CPU or CUDA)."""
        return self._device

    def compute_delta_nfr(
        self,
        graph: TNFRGraph,
        *,
        cache_size: int | None = 1,
        n_jobs: int | None = None,
        profile: MutableMapping[str, float] | None = None,
    ) -> None:
        """Compute ΔNFR using PyTorch backend with GPU acceleration.

        Implements vectorized ΔNFR computation using PyTorch tensors with
        automatic device placement (CPU/CUDA). For large graphs (>1000 nodes),
        uses GPU if available for significant speedup.

        Parameters
        ----------
        graph : TNFRGraph
            NetworkX graph with TNFR node attributes
        cache_size : int or None, optional
            Cache size hint (ignored, PyTorch manages memory)
        n_jobs : int or None, optional
            Ignored (PyTorch uses GPU parallelism)
        profile : MutableMapping[str, float] or None, optional
            dict to collect timing metrics

        Notes
        -----
        Automatically moves tensors to GPU if available (backend.device).
        For small graphs (<1000 nodes), may use NumPy backend to avoid
        overhead of tensor conversion and device transfer.
        """
        import time

        import numpy as np

        if profile is not None:
            profile["dnfr_backend"] = "torch"
            profile["dnfr_device"] = str(self._device)

        n_nodes = graph.number_of_nodes()
        graph.number_of_edges()

        # For very small graphs, delegate to NumPy (tensor overhead not worth it)
        if n_nodes < 1000:
            if profile is not None:
                profile["dnfr_path"] = "numpy_fallback"
            from ..dynamics.dnfr import default_compute_delta_nfr

            default_compute_delta_nfr(
                graph, cache_size=cache_size, n_jobs=n_jobs, profile=profile
            )
            return

        if profile is not None:
            profile["dnfr_path"] = "torch_gpu"
            t0 = time.perf_counter()

        # Extract graph data
        node_list = list(graph.nodes())
        node_to_idx = {node: idx for idx, node in enumerate(node_list)}

        # Get node attributes as numpy arrays first
        phase = np.array(
            [get_attr(graph.nodes[node], ALIAS_THETA, 0.0) for node in node_list],
            dtype=np.float32,
        )
        epi = np.array(
            [get_attr(graph.nodes[node], ALIAS_EPI, 0.5) for node in node_list],
            dtype=np.float32,
        )
        vf = np.array(
            [get_attr(graph.nodes[node], ALIAS_VF, 1.0) for node in node_list],
            dtype=np.float32,
        )

        # Get edge list
        edges = list(graph.edges())
        if not edges:
            # No edges - all nodes get zero ΔNFR
            for node in node_list:
                graph.nodes[node]["ΔNFR"] = 0.0
            return

        edge_src = np.array([node_to_idx[src] for src, _ in edges], dtype=np.int64)
        edge_dst = np.array([node_to_idx[dst] for _, dst in edges], dtype=np.int64)

        # Get weights via the canonical mechanism (defaults + normalization),
        # mirroring optimized_numpy so both fast backends agree with the
        # serial ΔNFR path. Avoids the silent {}→all-zero fallback.
        from ..metrics.common import merge_and_normalize_weights

        weights = merge_and_normalize_weights(
            graph, "DNFR_WEIGHTS", ("phase", "epi", "vf", "topo"), default=0.0
        )
        w_phase = float(weights.get("phase", 0.0))
        w_epi = float(weights.get("epi", 0.0))
        w_vf = float(weights.get("vf", 0.0))
        w_topo = float(weights.get("topo", 0.0))

        if profile is not None:
            profile["dnfr_data_prep"] = time.perf_counter() - t0
            t0 = time.perf_counter()

        # Convert to PyTorch tensors and move to device
        phase_t = self._torch.tensor(
            phase, device=self._device, dtype=self._torch.float32
        )
        epi_t = self._torch.tensor(epi, device=self._device, dtype=self._torch.float32)
        vf_t = self._torch.tensor(vf, device=self._device, dtype=self._torch.float32)
        edge_src_t = self._torch.tensor(
            edge_src, device=self._device, dtype=self._torch.int64
        )
        edge_dst_t = self._torch.tensor(
            edge_dst, device=self._device, dtype=self._torch.int64
        )

        if profile is not None:
            profile["dnfr_to_device"] = time.perf_counter() - t0
            t0 = time.perf_counter()

        # Compute ΔNFR using PyTorch operations
        delta_nfr_t = self._compute_delta_nfr_torch(
            phase_t,
            epi_t,
            vf_t,
            edge_src_t,
            edge_dst_t,
            w_phase,
            w_epi,
            w_vf,
            w_topo,
            graph.is_directed(),
        )

        if profile is not None:
            profile["dnfr_compute"] = time.perf_counter() - t0
            t0 = time.perf_counter()

        # Convert back to numpy and write to graph
        delta_nfr = delta_nfr_t.cpu().numpy()

        if profile is not None:
            profile["dnfr_from_device"] = time.perf_counter() - t0
            t0 = time.perf_counter()

        for idx, node in enumerate(node_list):
            graph.nodes[node]["ΔNFR"] = float(delta_nfr[idx])

        if profile is not None:
            profile["dnfr_write_back"] = time.perf_counter() - t0

    def _compute_delta_nfr_torch(
        self,
        phase: Any,
        epi: Any,
        vf: Any,
        edge_src: Any,
        edge_dst: Any,
        w_phase: float,
        w_epi: float,
        w_vf: float,
        w_topo: float,
        is_directed: bool,
    ) -> Any:
        """Compute ΔNFR using PyTorch tensor operations.

        Implements the TNFR canonical formula:
        ΔNFR = νf · (w_phase·g_phase + w_epi·g_epi + w_vf·g_vf + w_topo·g_topo)

        Where:
        - g_phase = angle_diff(phase_mean, phase) / π (circular mean)
        - g_epi = epi_mean - epi
        - g_vf = vf_mean - vf
        - g_topo = neighbor_count · w_topo

        Parameters
        ----------
        phase, epi, vf : torch.Tensor
            Node attribute tensors on device
        edge_src, edge_dst : torch.Tensor
            Edge index tensors
        w_phase, w_epi, w_vf, w_topo : float
            Component weights
        is_directed : bool
            Whether graph is directed

        Returns
        -------
        torch.Tensor
            ΔNFR values for all nodes
        """
        n_nodes = phase.shape[0]
        torch = self._torch

        # Initialize accumulators
        neighbor_cos_sum = torch.zeros(
            n_nodes, device=self._device, dtype=torch.float32
        )
        neighbor_sin_sum = torch.zeros(
            n_nodes, device=self._device, dtype=torch.float32
        )
        neighbor_epi_sum = torch.zeros(
            n_nodes, device=self._device, dtype=torch.float32
        )
        neighbor_vf_sum = torch.zeros(n_nodes, device=self._device, dtype=torch.float32)
        neighbor_count = torch.zeros(n_nodes, device=self._device, dtype=torch.float32)

        # Accumulate neighbor statistics
        # For each edge, dst receives contributions from src
        neighbor_cos_sum.scatter_add_(0, edge_dst, torch.cos(phase[edge_src]))
        neighbor_sin_sum.scatter_add_(0, edge_dst, torch.sin(phase[edge_src]))
        neighbor_epi_sum.scatter_add_(0, edge_dst, epi[edge_src])
        neighbor_vf_sum.scatter_add_(0, edge_dst, vf[edge_src])
        neighbor_count.scatter_add_(
            0, edge_dst, torch.ones_like(edge_dst, dtype=torch.float32)
        )

        # For undirected graphs, also accumulate in reverse
        if not is_directed:
            neighbor_cos_sum.scatter_add_(0, edge_src, torch.cos(phase[edge_dst]))
            neighbor_sin_sum.scatter_add_(0, edge_src, torch.sin(phase[edge_dst]))
            neighbor_epi_sum.scatter_add_(0, edge_src, epi[edge_dst])
            neighbor_vf_sum.scatter_add_(0, edge_src, vf[edge_dst])
            neighbor_count.scatter_add_(
                0, edge_src, torch.ones_like(edge_src, dtype=torch.float32)
            )

        # Compute means
        has_neighbors = neighbor_count > 0

        # Circular mean for phase (using atan2)
        phase_mean = torch.zeros(n_nodes, device=self._device, dtype=torch.float32)
        phase_mean[has_neighbors] = torch.atan2(
            neighbor_sin_sum[has_neighbors], neighbor_cos_sum[has_neighbors]
        )

        # Arithmetic means for EPI and vf
        epi_mean = torch.zeros(n_nodes, device=self._device, dtype=torch.float32)
        vf_mean = torch.zeros(n_nodes, device=self._device, dtype=torch.float32)
        epi_mean[has_neighbors] = (
            neighbor_epi_sum[has_neighbors] / neighbor_count[has_neighbors]
        )
        vf_mean[has_neighbors] = (
            neighbor_vf_sum[has_neighbors] / neighbor_count[has_neighbors]
        )

        # Compute gradients using TNFR canonical formula
        # Phase: angle_diff with wrapping to [-π, π]
        phase_diff = (phase_mean - phase + torch.pi) % (2 * torch.pi) - torch.pi
        g_phase = phase_diff / torch.pi
        g_phase[~has_neighbors] = 0.0

        # EPI and vf gradients
        g_epi = epi_mean - epi
        g_epi[~has_neighbors] = 0.0

        g_vf = vf_mean - vf
        g_vf[~has_neighbors] = 0.0

        # Topology gradient
        g_topo = neighbor_count * w_topo

        # Combine gradients
        delta_nfr = w_phase * g_phase + w_epi * g_epi + w_vf * g_vf + g_topo

        # Apply structural frequency scaling (canonical TNFR)
        delta_nfr = vf * delta_nfr

        return delta_nfr

    def compute_si(
        self,
        graph: TNFRGraph,
        *,
        inplace: bool = True,
        n_jobs: int | None = None,
        chunk_size: int | None = None,
        profile: MutableMapping[str, Any] | None = None,
    ) -> dict[Any, float] | Any:
        """Compute sense index using PyTorch backend.

        **Current implementation**: Delegates to NumPy backend while maintaining
        interface compatibility.

        **Planned**: GPU-accelerated vectorized Si computation using torch tensors
        with optimized phase dispersion kernels and mixed precision support.

        Parameters
        ----------
        graph : TNFRGraph
            NetworkX graph with TNFR node attributes
        inplace : bool, default=True
            Whether to write Si values back to graph
        n_jobs : int or None, optional
            Ignored (PyTorch uses GPU parallelism)
        chunk_size : int or None, optional
            Chunk size hint (currently passed to NumPy backend)
        profile : MutableMapping[str, Any] or None, optional
            dict to collect timing metrics

        Returns
        -------
        dict[Any, float] or numpy.ndarray
            Node-to-Si mapping or array of Si values

        Notes
        -----
        When implemented, will support mixed precision (FP16/BF16) for
        memory-efficient computation on large graphs, selectable via
        graph.graph["TORCH_DTYPE"] = torch.float16
        """
        # PyTorch GPU implementation planned for v2.0 - mixed precision support
        # Currently delegates to NumPy backend for compatibility
        from ..metrics.sense_index import compute_Si

        return compute_Si(
            graph,
            inplace=inplace,
            n_jobs=n_jobs,
            chunk_size=chunk_size,
            profile=profile,
        )