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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/operators/preconditions/resonance.py

resonance.py

Strict precondition validation for RA (Resonance) operator.

This module implements canonical precondition validation for the Resonance (RA) structural operator according to TNFR theory. RA requires specific structural conditions to maintain TNFR operational fidelity:

  1. Coherent source EPI: Node must have sufficient structural form for propagation
  2. Network connectivity: Edges must exist for resonance to propagate through
  3. Phase compatibility: Node must be synchronized with neighbors (coupling)
  4. Controlled dissonance: ΔNFR must not be excessive (stable resonance)
  5. Sufficient νf: Structural frequency must support propagation dynamics

These validations protect structural integrity by ensuring RA is only applied to nodes in the appropriate state for coherence propagation through the network.

Source Code

python
"""Strict precondition validation for RA (Resonance) operator.

This module implements canonical precondition validation for the Resonance (RA)
structural operator according to TNFR theory. RA requires specific structural
conditions to maintain TNFR operational fidelity:

1. **Coherent source EPI**: Node must have sufficient structural form for propagation
2. **Network connectivity**: Edges must exist for resonance to propagate through
3. **Phase compatibility**: Node must be synchronized with neighbors (coupling)
4. **Controlled dissonance**: ΔNFR must not be excessive (stable resonance)
5. **Sufficient νf**: Structural frequency must support propagation dynamics

These validations protect structural integrity by ensuring RA is only applied to
nodes in the appropriate state for coherence propagation through the network.
"""

from __future__ import annotations

import warnings
from typing import TYPE_CHECKING, Any

from ...errors import TNFRValueError

if TYPE_CHECKING:
    from ...types import TNFRGraph

__all__ = ["validate_resonance_strict", "diagnose_resonance_readiness"]


def validate_resonance_strict(
    G: TNFRGraph,
    node: Any,
    *,
    min_epi: float | None = None,
    require_coupling: bool = True,
    max_dissonance: float | None = None,
    warn_phase_misalignment: bool = True,
) -> None:
    """Validate strict canonical preconditions for RA (Resonance) operator.

    According to TNFR theory, Resonance (RA - Resonancia) requires:

    1. **Coherent source**: EPI >= threshold (sufficient structure to propagate)
    2. **Network connectivity**: degree > 0 (edges for propagation)
    3. **Phase compatibility**: alignment with neighbors (synchronization)
    4. **Controlled dissonance**: |ΔNFR| < threshold (stable for resonance)
    5. **Sufficient νf**: νf > threshold (capacity for propagation dynamics)

    Canonical sequences that satisfy preconditions:
    - **UM → RA**: Coupling establishes connections, then resonance propagates
    - **AL → RA**: Emission activates source, then resonance broadcasts
    - **IL → RA**: Coherence stabilizes, then propagates stable form

    Parameters
    ----------
    G : TNFRGraph
        Graph containing the node to validate
    node : Any
        Node identifier for validation
    min_epi : float, optional
        Minimum EPI magnitude for resonance source
        Default: Uses G.graph["RA_MIN_SOURCE_EPI"] or 0.1
    require_coupling : bool, default True
        If True, validates that node has edges (connectivity)
    max_dissonance : float, optional
        Maximum allowed |ΔNFR| for resonance
        Default: Uses G.graph["RA_MAX_DISSONANCE"] or 0.5
    warn_phase_misalignment : bool, default True
        If True, warns when phase difference with neighbors is high

    Raises
    ------
    ValueError
        If EPI < min_epi (insufficient structure to propagate)
        If require_coupling=True and node has no edges
        If |ΔNFR| > max_dissonance (too unstable for resonance)
        If νf < threshold (insufficient structural frequency)

    Warnings
    --------
    UserWarning
        If phase misalignment with neighbors exceeds threshold (suboptimal resonance)
        If node is isolated but require_coupling=False

    Notes
    -----
    Thresholds are configurable via graph metadata:
    - ``RA_MIN_SOURCE_EPI``: Minimum EPI for source (default: 0.1)
    - ``RA_MAX_DISSONANCE``: Maximum |ΔNFR| (default: 0.5)
    - ``RA_MAX_PHASE_DIFF``: Maximum phase difference in radians (default: 1.0)
    - ``RA_MIN_VF``: Minimum structural frequency (default: 0.01)

    Examples
    --------
    >>> from tnfr.structural import create_nfr
    >>> from tnfr.operators.preconditions.resonance import validate_resonance_strict
    >>>
    >>> # Valid node for resonance
    >>> G, node = create_nfr("source", epi=0.8, vf=0.9)
    >>> neighbor = "neighbor"
    >>> G.add_node(neighbor, epi=0.5, vf=0.8, theta=0.1, dnfr=0.05, epi_kind="seed")
    >>> G.add_edge(node, neighbor)
    >>> G.nodes[node]["dnfr"] = 0.1
    >>> validate_resonance_strict(G, node)  # OK

    >>> # Invalid: EPI too low
    >>> G2, node2 = create_nfr("weak_source", epi=0.05, vf=0.9)
    >>> neighbor2 = "neighbor2"
    >>> G2.add_node(neighbor2, epi=0.5, vf=0.8, theta=0.1, dnfr=0.05, epi_kind="seed")
    >>> G2.add_edge(node2, neighbor2)
    >>> validate_resonance_strict(G2, node2)  # doctest: +SKIP
    Traceback (most recent call last):
        ...
    ValueError: RA requires coherent source with EPI >= 0.1 (current: 0.050). Apply IL or THOL first.

    >>> # Invalid: No connectivity
    >>> G3, node3 = create_nfr("isolated", epi=0.8, vf=0.9)
    >>> validate_resonance_strict(G3, node3)  # doctest: +SKIP
    Traceback (most recent call last):
        ...
    ValueError: RA requires network connectivity (node has no edges). Apply UM (Coupling) first.

    See Also
    --------
    tnfr.operators.definitions.Resonance : Resonance operator implementation
    tnfr.operators.definitions.Coupling : Establishes connectivity for RA
    diagnose_resonance_readiness : Diagnostic function for RA readiness
    """
    from ...alias import get_attr
    from ...constants.aliases import ALIAS_DNFR, ALIAS_EPI, ALIAS_THETA, ALIAS_VF
    from ...utils.numeric import angle_diff

    # Get configuration with defensive fallbacks
    if min_epi is None:
        min_epi = float(G.graph.get("RA_MIN_SOURCE_EPI", 0.1))
    if max_dissonance is None:
        max_dissonance = float(G.graph.get("RA_MAX_DISSONANCE", 0.5))
    min_vf = float(G.graph.get("RA_MIN_VF", 0.01))
    max_phase_diff = float(G.graph.get("RA_MAX_PHASE_DIFF", 1.0))  # ~60 degrees

    # 1. Validate coherent source EPI
    epi = abs(float(get_attr(G.nodes[node], ALIAS_EPI, 0.0)))
    if epi < min_epi:
        raise TNFRValueError(
            f"RA requires coherent source with EPI >= {min_epi:.1f} "
            f"(current: {epi:.3f}). Apply IL or THOL first.",
            context={"epi": epi, "min_epi": min_epi},
            suggestion="Apply IL or THOL first.",
        )

    # 2. Validate network connectivity
    neighbors = list(G.neighbors(node))
    if require_coupling:
        if not neighbors:
            raise TNFRValueError(
                "RA requires network connectivity (node has no edges). "
                "Apply UM (Coupling) first to establish resonant links.",
                suggestion="Apply UM (Coupling) first to establish resonant links.",
            )
    elif not neighbors:
        # Node is isolated but require_coupling=False - issue warning
        warnings.warn(
            f"Node {node} is isolated - RA will have no propagation effect. "
            "Consider applying UM (Coupling) first.",
            UserWarning,
            stacklevel=3,
        )

    # 3. Validate sufficient structural frequency
    vf = float(get_attr(G.nodes[node], ALIAS_VF, 0.0))
    if vf < min_vf:
        raise TNFRValueError(
            f"RA requires sufficient structural frequency νf >= {min_vf:.2f} "
            f"(current: {vf:.3f}). Apply AL (Emission) or VAL (Expansion) first.",
            context={"vf": vf, "min_vf": min_vf},
            suggestion="Apply AL (Emission) or VAL (Expansion) first.",
        )

    # 4. Validate controlled dissonance
    dnfr = abs(float(get_attr(G.nodes[node], ALIAS_DNFR, 0.0)))
    if dnfr > max_dissonance:
        raise TNFRValueError(
            f"RA requires controlled dissonance with |ΔNFR| <= {max_dissonance:.1f} "
            f"(current: {dnfr:.3f}). Apply IL (Coherence) first to stabilize.",
            context={"dnfr": dnfr, "max_dissonance": max_dissonance},
            suggestion="Apply IL (Coherence) first to stabilize.",
        )

    # 5. Validate phase compatibility (warning only, neighbors exist)
    if warn_phase_misalignment and neighbors:
        try:
            from ...metrics.trig import neighbor_phase_mean

            theta_node = float(get_attr(G.nodes[node], ALIAS_THETA, 0.0))
            theta_neighbors = neighbor_phase_mean(G, node)
            phase_diff = abs(angle_diff(theta_neighbors, theta_node))

            if phase_diff > max_phase_diff:
                warnings.warn(
                    f"RA phase misalignment: Δφ = {phase_diff:.2f} > {max_phase_diff:.2f}. "
                    "Consider applying UM (Coupling) first for better resonance.",
                    UserWarning,
                    stacklevel=3,
                )
        except Exception:
            # Phase validation is optional, don't fail if unavailable
            pass


def diagnose_resonance_readiness(G: TNFRGraph, node: Any) -> dict[str, Any]:
    """Diagnose node readiness for RA (Resonance) operator.

    Provides comprehensive diagnostic report with readiness status and
    actionable recommendations for RA operator application.

    Parameters
    ----------
    G : TNFRGraph
        Graph containing the node
    node : Any
        Node to diagnose

    Returns
    -------
    dict
        Diagnostic report with:
        - ``ready``: bool - overall readiness status
        - ``checks``: dict - individual check results (passed/failed/warning)
        - ``values``: dict - current node state values
        - ``recommendations``: list - actionable steps to achieve readiness
        - ``canonical_sequences``: list - suggested operator sequences

    Examples
    --------
    >>> from tnfr.structural import create_nfr
    >>> from tnfr.operators.preconditions.resonance import diagnose_resonance_readiness
    >>>
    >>> # Diagnose weak source
    >>> G, node = create_nfr("weak", epi=0.05, vf=0.9)
    >>> diag = diagnose_resonance_readiness(G, node)
    >>> diag["ready"]
    False
    >>> "coherent_source" in diag["checks"]
    True
    >>> diag["checks"]["coherent_source"]
    'failed'
    >>> "Apply IL (Coherence) or THOL (Self-organization)" in diag["recommendations"][0]
    True

    See Also
    --------
    validate_resonance_strict : Strict precondition validator
    """
    from ...alias import get_attr
    from ...constants.aliases import ALIAS_DNFR, ALIAS_EPI, ALIAS_THETA, ALIAS_VF
    from ...utils.numeric import angle_diff

    # Get thresholds
    min_epi = float(G.graph.get("RA_MIN_SOURCE_EPI", 0.1))
    max_dissonance = float(G.graph.get("RA_MAX_DISSONANCE", 0.5))
    min_vf = float(G.graph.get("RA_MIN_VF", 0.01))
    max_phase_diff = float(G.graph.get("RA_MAX_PHASE_DIFF", 1.0))

    # Get current state
    epi = abs(float(get_attr(G.nodes[node], ALIAS_EPI, 0.0)))
    vf = float(get_attr(G.nodes[node], ALIAS_VF, 0.0))
    dnfr = abs(float(get_attr(G.nodes[node], ALIAS_DNFR, 0.0)))
    theta = float(get_attr(G.nodes[node], ALIAS_THETA, 0.0))
    neighbors = list(G.neighbors(node))
    neighbor_count = len(neighbors)

    # Initialize checks
    checks = {}
    recommendations = []

    # Check 1: Coherent source
    if epi >= min_epi:
        checks["coherent_source"] = "passed"
    else:
        checks["coherent_source"] = "failed"
        recommendations.append(
            f"Apply IL (Coherence) or THOL (Self-organization) to increase EPI "
            f"from {epi:.3f} to >= {min_epi:.1f}"
        )

    # Check 2: Network connectivity
    if neighbor_count > 0:
        checks["network_connectivity"] = "passed"
    else:
        checks["network_connectivity"] = "failed"
        recommendations.append(
            "Apply UM (Coupling) to establish network connections before RA"
        )

    # Check 3: Structural frequency
    if vf >= min_vf:
        checks["structural_frequency"] = "passed"
    else:
        checks["structural_frequency"] = "failed"
        recommendations.append(
            f"Apply AL (Emission) or VAL (Expansion) to increase νf "
            f"from {vf:.3f} to >= {min_vf:.2f}"
        )

    # Check 4: Controlled dissonance
    if dnfr <= max_dissonance:
        checks["controlled_dissonance"] = "passed"
    else:
        checks["controlled_dissonance"] = "failed"
        recommendations.append(
            f"Apply IL (Coherence) to reduce |ΔNFR| from {dnfr:.3f} "
            f"to <= {max_dissonance:.1f}"
        )

    # Check 5: Phase alignment (warning only)
    phase_diff = None
    if neighbor_count > 0:
        try:
            from ...metrics.trig import neighbor_phase_mean

            theta_neighbors = neighbor_phase_mean(G, node)
            phase_diff = abs(angle_diff(theta_neighbors, theta))

            if phase_diff <= max_phase_diff:
                checks["phase_alignment"] = "passed"
            else:
                checks["phase_alignment"] = "warning"
                recommendations.append(
                    f"Consider applying UM (Coupling) to improve phase alignment "
                    f"(current: Δφ = {phase_diff:.2f}, optimal: <= {max_phase_diff:.2f})"
                )
        except Exception:
            checks["phase_alignment"] = "unavailable"
    else:
        checks["phase_alignment"] = "n/a"

    # Determine overall readiness
    critical_checks = [
        "coherent_source",
        "network_connectivity",
        "structural_frequency",
        "controlled_dissonance",
    ]
    ready = all(checks.get(check) == "passed" for check in critical_checks)

    # Canonical sequences
    canonical_sequences = [
        "UM → RA (Coupling then Resonance)",
        "AL → RA (Emission then Resonance)",
        "IL → RA (Coherence then Resonance)",
        "AL → EN → IL → UM → RA (Full activation sequence)",
    ]

    return {
        "ready": ready,
        "checks": checks,
        "values": {
            "epi": epi,
            "vf": vf,
            "dnfr": dnfr,
            "theta": theta,
            "neighbor_count": neighbor_count,
            "phase_diff": phase_diff,
        },
        "recommendations": recommendations,
        "canonical_sequences": canonical_sequences,
        "thresholds": {
            "min_epi": min_epi,
            "max_dissonance": max_dissonance,
            "min_vf": min_vf,
            "max_phase_diff": max_phase_diff,
        },
    }