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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/coherence.py

coherence.py

Strict precondition validation for IL (Coherence) operator.

This module implements canonical precondition validation for the Coherence (IL) structural operator according to TNFR.pdf §2.2.1. IL requires specific structural conditions to maintain TNFR operational fidelity:

  1. Active EPI: Node must have non-zero structural form (EPI > 0)
  2. Non-saturated EPI: EPI must be below maximum (leave room for stabilization increment)
  3. Active νf: Structural frequency must exceed minimum threshold
  4. ΔNFR presence: While IL reduces ΔNFR, some reorganization pressure should exist
  5. ΔNFR not critical: Excessive ΔNFR may require OZ (Dissonance) first
  6. Network coupling: Connections enable phase locking

These validations protect structural integrity by ensuring IL is only applied to nodes in the appropriate state for coherence stabilization.

Source Code

python
"""Strict precondition validation for IL (Coherence) operator.

This module implements canonical precondition validation for the Coherence (IL)
structural operator according to TNFR.pdf §2.2.1. IL requires specific structural
conditions to maintain TNFR operational fidelity:

1. **Active EPI**: Node must have non-zero structural form (EPI > 0)
2. **Non-saturated EPI**: EPI must be below maximum (leave room for stabilization increment)
3. **Active νf**: Structural frequency must exceed minimum threshold
4. **ΔNFR presence**: While IL reduces ΔNFR, some reorganization pressure should exist
5. **ΔNFR not critical**: Excessive ΔNFR may require OZ (Dissonance) first
6. **Network coupling**: Connections enable phase locking

These validations protect structural integrity by ensuring IL is only applied to
nodes in the appropriate state for coherence stabilization.
"""

from __future__ import annotations

from typing import TYPE_CHECKING, Any

if TYPE_CHECKING:
    from ...types import TNFRGraph

__all__ = ["validate_coherence_strict", "diagnose_coherence_readiness"]


def validate_coherence_strict(G: TNFRGraph, node: Any) -> None:
    """Validate strict canonical preconditions for IL (Coherence) operator.

    According to TNFR.pdf §2.2.1, Coherence (IL - Coherencia estructural) requires:

    1. **Active EPI**: EPI > 0 (node must have active structural form)
    2. **Non-saturated EPI**: EPI < maximum (leave room for stabilization)
    3. **Active νf**: νf > threshold (sufficient structural frequency)
    4. **ΔNFR presence**: ΔNFR > 0 (reorganization pressure to stabilize)
    5. **ΔNFR not critical**: ΔNFR < critical threshold (manageable instability)
    6. **Network coupling**: degree > 0 (connections for phase locking)

    Parameters
    ----------
    G : TNFRGraph
        Graph containing the node to validate
    node : Any
        Node identifier for validation

    Raises
    ------
    ValueError
        If EPI <= 0 (no structural form to stabilize)
        If EPI >= maximum (node saturated - consider NUL/Contraction)
        If νf <= 0 (no structural frequency - consider AL/Emission or NAV/Transition)

    Warnings
    --------
    UserWarning
        If ΔNFR == 0 (no reorganization pressure - IL may be redundant)
        If ΔNFR > critical threshold (high instability - consider OZ/Dissonance first)
        If node is isolated (no connections - phase locking will have no effect)

    Notes
    -----
    Thresholds are configurable via:
    - Graph metadata: ``G.graph["IL_PRECONDITIONS"]``
    - Module defaults: :data:`tnfr.config.thresholds.EPI_IL_MAX`, etc.

    Examples
    --------
    >>> from tnfr.structural import create_nfr
    >>> from tnfr.operators.preconditions.coherence import validate_coherence_strict
    >>> G, node = create_nfr("test", epi=0.5, vf=0.9)
    >>> G.nodes[node]["dnfr"] = 0.1
    >>> validate_coherence_strict(G, node)  # OK - active state with reorganization pressure

    >>> G2, node2 = create_nfr("inactive", epi=0.0, vf=0.9)
    >>> validate_coherence_strict(G2, node2)  # doctest: +SKIP
    Traceback (most recent call last):
        ...
    ValueError: IL precondition failed: EPI=0.000 <= 0.0. IL requires active structural form.

    See Also
    --------
    tnfr.config.thresholds : Configurable threshold constants
    tnfr.operators.preconditions : Base precondition validators
    tnfr.operators.definitions.Coherence : Coherence operator implementation
    diagnose_coherence_readiness : Diagnostic function for IL readiness
    """
    import warnings

    from ...alias import get_attr
    from ...config.thresholds import DNFR_IL_CRITICAL, EPI_IL_MAX, EPI_IL_MIN, VF_IL_MIN
    from ...constants.aliases import ALIAS_DNFR, ALIAS_EPI, ALIAS_VF

    # Get current node state
    epi = float(get_attr(G.nodes[node], ALIAS_EPI, 0.0))
    vf = float(get_attr(G.nodes[node], ALIAS_VF, 0.0))
    dnfr = float(get_attr(G.nodes[node], ALIAS_DNFR, 0.0))

    # Get configurable thresholds (allow override via graph metadata)
    config = G.graph.get("IL_PRECONDITIONS", {})
    min_epi = float(config.get("min_epi", EPI_IL_MIN))
    max_epi = float(config.get("max_epi", EPI_IL_MAX))
    min_vf = float(config.get("min_vf", VF_IL_MIN))
    dnfr_critical = float(config.get("dnfr_critical_threshold", DNFR_IL_CRITICAL))
    warn_isolated = bool(config.get("warn_isolated", True))
    warn_zero_dnfr = bool(config.get("warn_zero_dnfr", True))

    # Precondition 1: EPI must be active (non-zero structural form)
    # IL stabilizes existing structure - requires structure to exist
    if epi <= min_epi:
        raise ValueError(
            f"IL precondition failed: EPI={epi:.3f} <= {min_epi:.3f}. "
            f"IL requires active structural form (non-zero EPI). "
            f"Suggestion: Apply AL (Emission) first to activate node."
        )

    # Precondition 2: EPI must not be saturated (leave room for stabilization)
    # IL may increment EPI slightly during stabilization
    if epi >= max_epi:
        raise ValueError(
            f"IL precondition failed: EPI={epi:.3f} >= {max_epi:.3f}. "
            f"Node saturated, cannot stabilize further. "
            f"Suggestion: Consider NUL (Contraction) to consolidate structure."
        )

    # Precondition 3: νf must be active (sufficient structural frequency)
    # IL requires active reorganization capacity to effect stabilization
    if vf <= min_vf:
        raise ValueError(
            f"IL precondition failed: νf={vf:.3f} <= {min_vf:.3f}. "
            f"Structural frequency too low for coherence stabilization. "
            f"Suggestion: Apply AL (Emission) or NAV (Transition) to activate νf first."
        )

    # Precondition 4: Check for ΔNFR presence (warning only - not hard failure)
    # IL reduces ΔNFR, but if ΔNFR is already zero, IL is redundant
    if warn_zero_dnfr and dnfr == 0.0:
        warnings.warn(
            f"IL warning: Node {node!r} has ΔNFR=0. "
            f"No reorganization pressure to stabilize. "
            f"IL application may be redundant in this state.",
            UserWarning,
            stacklevel=3,
        )

    # Precondition 5: Check for critically high ΔNFR (warning only)
    # Excessive instability may require controlled dissonance (OZ) before stabilization
    if dnfr > dnfr_critical:
        warnings.warn(
            f"IL warning: Node {node!r} has ΔNFR={dnfr:.3f} > {dnfr_critical:.3f}. "
            f"High reorganization pressure - stabilization may be difficult. "
            f"Consider applying OZ (Dissonance) → IL sequence for better control.",
            UserWarning,
            stacklevel=3,
        )

    # Precondition 6: Check for network connections (warning only)
    # Isolated nodes can stabilize but phase locking will have no effect
    degree = G.degree(node)
    network_size = len(G)
    if warn_isolated and degree == 0 and network_size > 1:
        warnings.warn(
            f"IL warning: Node {node!r} isolated (degree=0). "
            f"Phase locking will have no effect. "
            f"Consider applying UM (Coupling) first to connect node to network.",
            UserWarning,
            stacklevel=3,
        )


def diagnose_coherence_readiness(G: TNFRGraph, node: Any) -> dict:
    """Diagnose node readiness for IL (Coherence) operator.

    Performs all canonical precondition checks and returns a diagnostic report
    with readiness status and actionable recommendations.

    Parameters
    ----------
    G : TNFRGraph
        Graph containing the node
    node : Any
        Node identifier for diagnosis

    Returns
    -------
    dict
        Diagnostic report with the following structure:

        - ``node``: Node identifier
        - ``ready``: bool - Overall readiness (all critical checks passed)
        - ``checks``: dict - Individual check results

          - ``epi_active``: bool - EPI > 0
          - ``epi_not_saturated``: bool - EPI < maximum
          - ``vf_active``: bool - νf > 0
          - ``dnfr_present``: bool - ΔNFR > 0 (warning only)
          - ``dnfr_not_critical``: bool - ΔNFR < critical (warning only)
          - ``has_connections``: bool - degree > 0 (warning only)

        - ``values``: dict - Current node attribute values

          - ``epi``: Current EPI value
          - ``vf``: Current νf value
          - ``dnfr``: Current ΔNFR value
          - ``degree``: Node degree

        - ``recommendations``: list[str] - Actionable suggestions

    Examples
    --------
    >>> from tnfr.structural import create_nfr
    >>> from tnfr.operators.preconditions.coherence import diagnose_coherence_readiness
    >>> G, node = create_nfr("test", epi=0.5, vf=0.9)
    >>> G.nodes[node]["dnfr"] = 0.1
    >>> report = diagnose_coherence_readiness(G, node)
    >>> report["ready"]
    True
    >>> "✓ Node ready" in report["recommendations"][0]
    True

    See Also
    --------
    validate_coherence_strict : Strict precondition validator
    """
    from ...alias import get_attr
    from ...config.thresholds import DNFR_IL_CRITICAL, EPI_IL_MAX, EPI_IL_MIN, VF_IL_MIN
    from ...constants.aliases import ALIAS_DNFR, ALIAS_EPI, ALIAS_VF

    # Get current node state
    epi = float(get_attr(G.nodes[node], ALIAS_EPI, 0.0))
    vf = float(get_attr(G.nodes[node], ALIAS_VF, 0.0))
    dnfr = float(get_attr(G.nodes[node], ALIAS_DNFR, 0.0))
    degree = G.degree(node)

    # Get configurable thresholds
    config = G.graph.get("IL_PRECONDITIONS", {})
    min_epi = float(config.get("min_epi", EPI_IL_MIN))
    max_epi = float(config.get("max_epi", EPI_IL_MAX))
    min_vf = float(config.get("min_vf", VF_IL_MIN))
    dnfr_critical = float(config.get("dnfr_critical_threshold", DNFR_IL_CRITICAL))

    # Perform checks
    checks = {
        "epi_active": epi > min_epi,
        "epi_not_saturated": epi < max_epi,
        "vf_active": vf > min_vf,
        "dnfr_present": dnfr > 0.0,
        "dnfr_not_critical": dnfr < dnfr_critical,
        "has_connections": degree > 0,
    }

    # Critical checks (hard failures)
    critical_checks = ["epi_active", "epi_not_saturated", "vf_active"]
    all_critical_passed = all(checks[key] for key in critical_checks)

    # Generate recommendations
    recommendations = []

    if not checks["epi_active"]:
        recommendations.append("Apply AL (Emission) to activate node")

    if checks["epi_active"] and not checks["epi_not_saturated"]:
        recommendations.append(
            "Apply NUL (Contraction) to consolidate saturated structure"
        )

    if not checks["vf_active"]:
        recommendations.append("Apply AL (Emission) or NAV (Transition) to activate νf")

    if checks["epi_active"] and not checks["dnfr_present"]:
        recommendations.append("⚠ ΔNFR=0 - IL may be redundant")

    if checks["dnfr_present"] and not checks["dnfr_not_critical"]:
        recommendations.append("⚠ High ΔNFR - consider OZ (Dissonance) → IL sequence")

    if not checks["has_connections"]:
        recommendations.append(
            "⚠ Isolated node - consider UM (Coupling) to enable phase locking"
        )

    if all_critical_passed:
        recommendations.insert(0, "✓ Node ready for IL (Coherence)")

    return {
        "node": node,
        "ready": all_critical_passed,
        "checks": checks,
        "values": {
            "epi": epi,
            "vf": vf,
            "dnfr": dnfr,
            "degree": degree,
        },
        "recommendations": recommendations,
    }