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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
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tetrad_evaluator.py
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FILE: src/tnfr/operators/preconditions/dissonance.py

dissonance.py

Strict precondition validation for OZ (Dissonance) operator.

This module implements canonical precondition validation for the Dissonance (OZ) structural operator according to TNFR canonical theory. OZ requires specific structural conditions to enable productive dissonance without premature collapse:

  1. Minimum coherence base (EPI): Node must have sufficient structural form to withstand disruption (EPI >= threshold)
  2. ΔNFR not critically high: Avoid sobrecarga (overload) when ΔNFR already extreme
  3. Sufficient νf: Structural frequency must support reorganization response
  4. No overload pattern: Detect sobrecarga disonante (multiple OZ without resolution)
  5. Network connectivity: Warn if isolated (bifurcation requires alternative paths)

These validations implement the canonical warning from TNFR.pdf:

"OZ debe ir precedido por estabilización adecuada (IL). Genera nodos frágiles o fallidos si se aplica sobre estructuras sin coherencia interna."

References

  • TNFR.pdf §2.3.6: Catálogo de errores arquetípicos (Sobrecarga disonante)
  • TNFR.pdf §2.3.3: Reglas sintácticas R4 (Bifurcación)
  • Tabla de validación estructural: Condiciones de activación de OZ

Source Code

python
"""Strict precondition validation for OZ (Dissonance) operator.

This module implements canonical precondition validation for the Dissonance (OZ)
structural operator according to TNFR canonical theory. OZ requires specific
structural conditions to enable productive dissonance without premature collapse:

1. **Minimum coherence base (EPI)**: Node must have sufficient structural form to
   withstand disruption (EPI >= threshold)
2. **ΔNFR not critically high**: Avoid sobrecarga (overload) when ΔNFR already extreme
3. **Sufficient νf**: Structural frequency must support reorganization response
4. **No overload pattern**: Detect sobrecarga disonante (multiple OZ without resolution)
5. **Network connectivity**: Warn if isolated (bifurcation requires alternative paths)

These validations implement the canonical warning from TNFR.pdf:
> "OZ debe ir precedido por estabilización adecuada (IL). Genera nodos frágiles o
> fallidos si se aplica sobre estructuras sin coherencia interna."

References
----------
- TNFR.pdf §2.3.6: Catálogo de errores arquetípicos (Sobrecarga disonante)
- TNFR.pdf §2.3.3: Reglas sintácticas R4 (Bifurcación)
- Tabla de validación estructural: Condiciones de activación de OZ
"""

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_dissonance_strict"]


def validate_dissonance_strict(G: TNFRGraph, node: Any) -> None:
    """Validate strict canonical preconditions for OZ (Dissonance) operator.

    According to TNFR canonical theory, Dissonance (OZ - Disonancia) requires:

    1. **Coherence base**: EPI >= threshold (sufficient structure to withstand disruption)
    2. **ΔNFR safety**: |ΔNFR| < critical (avoid overload/collapse)
    3. **Active νf**: νf >= threshold (capacity to respond to dissonance)
    4. **No overload**: < 2 consecutive OZ without resolution (IL/THOL/NUL)
    5. **Network connectivity**: degree >= 1 (warning only - enables bifurcation paths)

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

    Raises
    ------
    ValueError
        If EPI < minimum (insufficient coherence base - apply IL first)
        If |ΔNFR| > maximum (reorganization pressure critical - apply IL first)
        If νf < minimum (cannot respond to dissonance)
        If overload detected (>= 2 OZ without resolver operators)

    Warnings
    --------
    UserWarning
        If node has low connectivity (degree < 1) - bifurcation paths limited

    Notes
    -----
    Thresholds are configurable via graph metadata:
    - ``G.graph["OZ_MIN_EPI"]``: Minimum EPI (default 0.2)
    - ``G.graph["OZ_MAX_DNFR"]``: Maximum |ΔNFR| (default 0.8)
    - ``G.graph["OZ_MIN_VF"]``: Minimum νf (default 0.1)
    - ``G.graph["OZ_MIN_DEGREE"]``: Minimum degree for warning (default 1)

    **Resolver operators** that integrate dissonance (reset overload counter):
    - IL (Coherence): Stabilizes structure
    - THOL (Self-organization): Creates sub-EPIs
    - NUL (Contraction): Simplifies structure

    Examples
    --------
    >>> from tnfr.structural import create_nfr
    >>> from tnfr.operators.preconditions.dissonance import validate_dissonance_strict
    >>> G, node = create_nfr("test", epi=0.5, vf=1.0)
    >>> G.nodes[node]["dnfr"] = 0.3
    >>> validate_dissonance_strict(G, node)  # OK - sufficient coherence base

    >>> G2, node2 = create_nfr("weak", epi=0.05, vf=1.0)
    >>> validate_dissonance_strict(G2, node2)  # doctest: +SKIP
    Traceback (most recent call last):
        ...
    ValueError: OZ precondition failed: EPI=0.050 < 0.2. Insufficient coherence base.

    See Also
    --------
    tnfr.operators.preconditions : Base precondition validators
    tnfr.operators.definitions.Dissonance : Dissonance operator implementation
    """
    from ...alias import get_attr
    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
    min_epi = float(G.graph.get("OZ_MIN_EPI", 0.2))
    max_dnfr = float(G.graph.get("OZ_MAX_DNFR", 0.8))
    min_vf = float(G.graph.get("OZ_MIN_VF", 0.1))
    min_degree = int(G.graph.get("OZ_MIN_DEGREE", 1))

    # Precondition 1: Minimum coherence base (EPI)
    # OZ requires existing structure to perturb - without it, OZ causes collapse
    if epi < min_epi:
        raise TNFRValueError(
            f"OZ precondition failed: EPI={epi:.3f} < {min_epi:.3f}. "
            f"Insufficient coherence base to withstand dissonance. "
            f"Suggestion: Apply IL (Coherence) first to stabilize node before introducing dissonance.",
            context={"epi": epi, "min_epi": min_epi},
            suggestion="Apply IL (Coherence) first to stabilize node before introducing dissonance.",
        )

    # Precondition 2: ΔNFR not critically high
    # Applying OZ when ΔNFR already extreme creates sobrecarga (overload) → collapse
    if abs(dnfr) > max_dnfr:
        raise TNFRValueError(
            f"OZ precondition failed: |ΔNFR|={abs(dnfr):.3f} > {max_dnfr:.3f}. "
            f"Reorganization pressure already critical - applying OZ risks collapse. "
            f"Suggestion: Apply IL (Coherence) first to reduce ΔNFR before introducing more dissonance.",
            context={"dnfr": dnfr, "max_dnfr": max_dnfr},
            suggestion="Apply IL (Coherence) first to reduce ΔNFR before introducing more dissonance.",
        )

    # Precondition 3: Sufficient νf for reorganization response
    # OZ triggers reorganization - node needs capacity (νf) to respond
    if vf < min_vf:
        raise TNFRValueError(
            f"OZ precondition failed: νf={vf:.3f} < {min_vf:.3f}. "
            f"Structural frequency too low - node lacks capacity to respond to dissonance. "
            f"Suggestion: Increase νf before applying OZ.",
            context={"vf": vf, "min_vf": min_vf},
            suggestion="Increase νf before applying OZ.",
        )

    # Precondition 4: Detect OZ overload (sobrecarga disonante)
    # Multiple OZ without resolution = entropic loop (violates R5)
    _validate_oz_no_overload(G, node)

    # Precondition 5: Network connectivity (warning only - not blocking)
    # Isolated nodes can experience dissonance but bifurcation paths are limited
    if degree < min_degree:
        warnings.warn(
            f"OZ warning: Node {node!r} has low connectivity (degree={degree} < {min_degree}). "
            f"OZ-induced bifurcation may have limited structural paths. "
            f"Consider applying UM (Coupling) first to increase network coupling.",
            UserWarning,
            stacklevel=3,
        )

    # Store validation context for telemetry
    G.nodes[node]["_oz_precondition_context"] = {
        "epi": epi,
        "dnfr": dnfr,
        "vf": vf,
        "degree": degree,
        "validation_passed": True,
    }


def _validate_oz_no_overload(G: TNFRGraph, node: Any) -> None:
    """Detect and prevent dissonance overload (sobrecarga disonante).

    Sobrecarga occurs when multiple OZ operators are applied in succession
    without intervening resolution operators (IL, THOL, NUL). This creates
    entropic loops that violate TNFR structural coherence requirements.

    Parameters
    ----------
    G : TNFRGraph
        Graph containing the node
    node : Any
        Node identifier to check for overload

    Raises
    ------
    ValueError
        If >= 1 OZ application detected in recent history without resolver
        (since we're about to apply another OZ, that would make it >= 2)

    Notes
    -----
    **Resolver operators** that integrate dissonance:
    - coherence (IL): Stabilizes structure, reduces ΔNFR
    - self_organization (THOL): Creates sub-EPIs via bifurcation
    - contraction (NUL): Simplifies structure

    This check examines the last 5 operators in glyph_history to detect
    overload patterns. Since validation is called BEFORE the operator is
    applied, if we find >= 1 OZ in history without a resolver, applying
    another OZ would create overload.

    References
    ----------
    TNFR.pdf §2.3.6 - Sobrecarga disonante: "acumulación excesiva de OZ sin
    paso a mutación"
    """
    from ...operators.grammar import glyph_function_name

    # Get glyph history from node
    history = G.nodes[node].get("glyph_history", [])
    if not history:
        # No history - first operator application, cannot be overload
        return

    # Convert deque to list and examine recent history (last 5 operations)
    history_list = list(history)
    recent_history = history_list[-5:] if len(history_list) >= 5 else history_list

    # Count OZ applications in recent history
    oz_count = sum(
        1 for glyph in recent_history if glyph_function_name(glyph) == "dissonance"
    )

    # If >= 1 OZ in history, check for resolver operators
    # (we're about to apply another OZ, so that would make >= 2 total)
    if oz_count >= 1:
        # Resolver operators that integrate dissonance
        resolvers = {"coherence", "self_organization", "contraction"}
        recent_names = [glyph_function_name(g) for g in recent_history]
        has_resolver = any(name in resolvers for name in recent_names)

        if not has_resolver:
            raise TNFRValueError(
                f"OZ precondition failed: Sobrecarga disonante detected. "
                f"Found {oz_count} OZ in recent history without resolution. "
                f"Applying another OZ without resolving previous dissonance risks collapse. "
                f"Suggestion: Apply IL (Coherence), THOL (Self-organization), or NUL (Contraction) "
                f"to integrate dissonance before introducing more.",
                context={"oz_count": oz_count, "recent_history": recent_names},
                suggestion="Apply IL (Coherence), THOL (Self-organization), or NUL (Contraction) to integrate dissonance before introducing more.",
            )