TNFR Logo
TheoryLearnSoftwareResearch

On this page

TNFR

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

About
  • Project history
  • Editorial policy
  • Contact
Resources
  • GitHub
  • PyPI
  • DOI · Zenodo
Legal
  • MIT License
  • Citation
© 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
.pre-commit-config.yaml.semgrep.yaml.zenodo.jsonARCHITECTURE.mdbandit.yamlCHANGELOG.mdCITATION.cffCONTRIBUTING.mdEMERGENT_CANON_AUDIT.mdEMERGENT_DERIVATION_PLAN.mdLICENSE.mdMakefileMANIFEST.inpyproject.tomlpyrightconfig.jsonPYTORCH_CUDA_INTEGRATION.mdREADME.mdSECURITY.mdTESTING.mdTNFR_Website_Content_Brief.md
FILE: src/tnfr/operators/self_organization.py

self_organization.py

SelfOrganization (THOL) operator.

Purpose: autonomous emergence; spawn sub-EPIs when d2_epi>tau. Physics: bifurcation + metabolic capture of network signals. Grammar: transformer (U4b) + handler (U4a) during bifurcation. Effects: adds sub-structure; parent epi increments; preserves identity. Preconditions: sufficient epi history; vf>0; elevated d2_epi; capacity. Typical: OZ->THOL; THOL->IL; EN->THOL; THOL->RA; THOL->IL->RA. Avoid: THOL without ΔNFR elevation; deep nesting beyond max depth.

Source Code

python
"""SelfOrganization (THOL) operator.

Purpose: autonomous emergence; spawn sub-EPIs when d2_epi>tau.
Physics: bifurcation + metabolic capture of network signals.
Grammar: transformer (U4b) + handler (U4a) during bifurcation.
Effects: adds sub-structure; parent epi increments; preserves identity.
Preconditions: sufficient epi history; vf>0; elevated d2_epi; capacity.
Typical: OZ->THOL; THOL->IL; EN->THOL; THOL->RA; THOL->IL->RA.
Avoid: THOL without ΔNFR elevation; deep nesting beyond max depth.
"""

from __future__ import annotations

from typing import Any, ClassVar

from ..config.operator_names import SELF_ORGANIZATION

# Import canonical constants
from ..constants.canonical import THOL_MIN_COLLECTIVE_COHERENCE
from ..types import Glyph, TNFRGraph
from .definitions_base import Operator

_THOL_SUB_EPI_SCALING = 0.3  # ≈ 0.309 (fractal scale)
_THOL_EMERGENCE_CONTRIBUTION = 0.1  # parent epi increment fraction


class SelfOrganization(Operator):
    """Spawn sub-EPIs on bifurcation; metabolic capture; update parent epi.

    Invariants: parent identity preserved; sub-EPIs coherent ensemble.
    Typical: OZ->THOL; THOL->IL; THOL->RA; EN->THOL; THOL->IL->RA.
    Metrics: d2_epi, sub_epi_value, bifurcation_level, collective_coherence.
    """

    __slots__ = ()
    name: ClassVar[str] = SELF_ORGANIZATION
    glyph: ClassVar[Glyph] = Glyph.THOL

    def __call__(self, G: TNFRGraph, node: Any, **kw: Any) -> None:
        """Apply THOL; if d2_epi>tau spawn sub-EPI; validate ensemble."""
        # Compute structural acceleration before base operator
        d2_epi = self._compute_epi_acceleration(G, node)

        # Get bifurcation threshold (tau) from kwargs or graph config
        tau = kw.get("tau")
        if tau is None:
            tau = float(G.graph.get("THOL_BIFURCATION_THRESHOLD", 0.1))

        # Apply base operator (includes glyph application and metrics)
        super().__call__(G, node, **kw)

        # Bifurcate if acceleration exceeds threshold
        if d2_epi > tau:
            # Validate depth before bifurcation
            self._validate_bifurcation_depth(G, node)
            self._spawn_sub_epi(G, node, d2_epi=d2_epi, tau=tau)

        # CANONICAL VALIDATION: Verify collective coherence of sub-EPIs
        # Ensemble must stay coherent and preserve parent identity.
        # Always validate if node has sub-EPIs (new or existing).
        if G.nodes[node].get("sub_epis"):
            self._validate_collective_coherence(G, node)

    def _compute_epi_acceleration(self, G: TNFRGraph, node: Any) -> float:
        """Finite diff second derivative abs value from epi_history."""

        # Get EPI history (maintained by node for temporal analysis)
        history = G.nodes[node].get("epi_history", [])

        # Need at least 3 points for second derivative
        if len(history) < 3:
            return 0.0

        # Finite difference: d²EPI/dt² ≈ (EPI_t - 2*EPI_{t-1} + EPI_{t-2})
        epi_t = float(history[-1])
        epi_t1 = float(history[-2])
        epi_t2 = float(history[-3])

        d2_epi = epi_t - 2.0 * epi_t1 + epi_t2

        return abs(d2_epi)

    def _spawn_sub_epi(
        self, G: TNFRGraph, node: Any, d2_epi: float, tau: float
    ) -> None:
        """Create sub-EPI node; apply metabolic weights; update parent epi."""
        from ..alias import get_attr, set_attr
        from ..constants.aliases import ALIAS_EPI, ALIAS_THETA, ALIAS_VF
        from .metabolism import capture_network_signals, metabolize_signals_into_subepi

        # Get current node state
        parent_epi = float(get_attr(G.nodes[node], ALIAS_EPI, 0.0))
        parent_vf = float(get_attr(G.nodes[node], ALIAS_VF, 1.0))
        parent_theta = float(get_attr(G.nodes[node], ALIAS_THETA, 0.0))

        # Check if vibrational metabolism is enabled
        metabolic_enabled = G.graph.get("THOL_METABOLIC_ENABLED", True)

        # CANONICAL METABOLISM: Capture network context
        network_signals = None
        if metabolic_enabled:
            network_signals = capture_network_signals(G, node)

        # Get metabolic weights from graph config
        gradient_weight = float(G.graph.get("THOL_METABOLIC_GRADIENT_WEIGHT", 0.15))
        complexity_weight = float(G.graph.get("THOL_METABOLIC_COMPLEXITY_WEIGHT", 0.10))

        # CANONICAL METABOLISM: Digest signals into sub-EPI
        sub_epi_value = metabolize_signals_into_subepi(
            parent_epi=parent_epi,
            signals=network_signals if metabolic_enabled else None,
            d2_epi=d2_epi,
            scaling_factor=_THOL_SUB_EPI_SCALING,
            gradient_weight=gradient_weight,
            complexity_weight=complexity_weight,
        )

        # Get current timestamp from glyph history length
        timestamp = len(G.nodes[node].get("glyph_history", []))

        # Determine parent bifurcation level for hierarchical telemetry
        parent_level = G.nodes[node].get("_bifurcation_level", 0)
        child_level = parent_level + 1

        # Construct hierarchy path for full traceability
        parent_path = G.nodes[node].get("_hierarchy_path", [])
        child_path = parent_path + [node]

        # ARCHITECTURAL: Create sub-EPI as independent NFR node
        # Enables fractality: recursive operators + hierarchical metrics.
        sub_node_id = self._create_sub_node(
            G,
            parent_node=node,
            sub_epi=sub_epi_value,
            parent_vf=parent_vf,
            parent_theta=parent_theta,
            child_level=child_level,
            child_path=child_path,
        )

        # Store sub-EPI metadata for telemetry and backward compatibility
        sub_epi_record = {
            "epi": sub_epi_value,
            "vf": parent_vf,
            "timestamp": timestamp,
            "d2_epi": d2_epi,
            "tau": tau,
            "node_id": sub_node_id,  # Reference to independent node
            "metabolized": network_signals is not None and metabolic_enabled,
            "network_signals": network_signals,
            "bifurcation_level": child_level,  # Hierarchical depth tracking
            "hierarchy_path": child_path,  # Full parent chain for traceability
        }

        # Keep metadata list for telemetry/metrics backward compatibility
        sub_epis = G.nodes[node].get("sub_epis", [])
        sub_epis.append(sub_epi_record)
        G.nodes[node]["sub_epis"] = sub_epis

        # Increment parent EPI using canonical emergence contribution
        # This reflects that bifurcation increases total structural complexity
        new_epi = parent_epi + sub_epi_value * _THOL_EMERGENCE_CONTRIBUTION
        set_attr(G.nodes[node], ALIAS_EPI, new_epi)

        # CANONICAL PROPAGATION: Enable network cascade dynamics
        if G.graph.get("THOL_PROPAGATION_ENABLED", True):
            from .metabolism import propagate_subepi_to_network

            propagations = propagate_subepi_to_network(G, node, sub_epi_record)

            # Record propagation telemetry for cascade analysis
            if propagations:
                G.graph.setdefault("thol_propagations", []).append(
                    {
                        "source_node": node,
                        "sub_epi": sub_epi_value,
                        "propagations": propagations,
                        "timestamp": timestamp,
                    }
                )

    def _create_sub_node(
        self,
        G: TNFRGraph,
        parent_node: Any,
        sub_epi: float,
        parent_vf: float,
        parent_theta: float,
        child_level: int,
        child_path: list,
    ) -> str:
        """Add sub-node with inherited state; record hierarchy metadata."""
        from ..constants import DNFR_PRIMARY, EPI_PRIMARY, THETA_PRIMARY, VF_PRIMARY

        # Generate unique sub-node ID
        sub_nodes_list = G.nodes[parent_node].get("sub_nodes", [])
        sub_index = len(sub_nodes_list)
        sub_node_id = f"{parent_node}_sub_{sub_index}"

        # Get parent hierarchy level
        parent_hierarchy_level = G.nodes[parent_node].get("hierarchy_level", 0)

        # Inherit parent's vf with slight damping (canonical: 95%)
        sub_vf = parent_vf * 0.95

        # Create the sub-node with full TNFR state
        G.add_node(
            sub_node_id,
            **{
                EPI_PRIMARY: float(sub_epi),
                VF_PRIMARY: float(sub_vf),
                THETA_PRIMARY: float(parent_theta),
                DNFR_PRIMARY: 0.0,
                "parent_node": parent_node,
                "hierarchy_level": parent_hierarchy_level + 1,
                "_bifurcation_level": child_level,
                "_hierarchy_path": child_path,  # Full ancestor chain
                "epi_history": [float(sub_epi)],
                "glyph_history": [],
            },
        )

        # Ensure ΔNFR hook is set for the sub-node
        # (inherits from graph-level hook, but ensure it's activated)
        if hasattr(G, "graph") and "_delta_nfr_hook" in G.graph:
            # Graph-level hook applies to sub-node automatically.
            pass

        # Track sub-node in parent
        sub_nodes_list.append(sub_node_id)
        G.nodes[parent_node]["sub_nodes"] = sub_nodes_list

        # Track hierarchy in graph metadata
        hierarchy = G.graph.setdefault("hierarchy", {})
        hierarchy.setdefault(parent_node, []).append(sub_node_id)

        return sub_node_id

    def _validate_bifurcation_depth(self, G: TNFRGraph, node: Any) -> None:
        """Warn if bifurcation depth exceeds configured max."""
        import logging

        # Get current bifurcation level
        current_level = G.nodes[node].get("_bifurcation_level", 0)

        # Get max depth from graph config (default: 5 levels)
        max_depth = int(G.graph.get("THOL_MAX_BIFURCATION_DEPTH", 5))

        # Warn if at or exceeding maximum
        if current_level >= max_depth:
            logger = logging.getLogger(__name__)
            logger.warning(
                f"Node {node}: Bifurcation depth ({current_level}) at/exceeds "
                f"maximum ({max_depth}). Deep nesting may impact performance. "
                f"Consider adjusting THOL_MAX_BIFURCATION_DEPTH if intended."
            )

            # Record warning in node for telemetry
            G.nodes[node]["_thol_max_depth_warning"] = True

            # Record event for analysis
            events = G.graph.setdefault("thol_depth_warnings", [])
            events.append(
                {
                    "node": node,
                    "depth": current_level,
                    "max_depth": max_depth,
                }
            )

    def _validate_collective_coherence(self, G: TNFRGraph, node: Any) -> None:
        """Compute ensemble coherence; warn if below threshold."""
        import logging

        from .metabolism import compute_subepi_collective_coherence

        # Compute collective coherence
        coherence = compute_subepi_collective_coherence(G, node)

        # Always store telemetry value (even if 0.0).
        G.nodes[node]["_thol_collective_coherence"] = coherence

        # Get threshold from graph config (fallback: canonical 1/(π+1) ≈ 0.2415)
        min_coherence = float(
            G.graph.get("THOL_MIN_COLLECTIVE_COHERENCE", THOL_MIN_COLLECTIVE_COHERENCE)
        )

        # Validate against threshold (only warn if we have multiple sub-EPIs)
        sub_epis = G.nodes[node].get("sub_epis", [])
        if len(sub_epis) >= 2 and coherence < min_coherence:
            # Log warning (but don't fail - allow monitoring)
            logger = logging.getLogger(__name__)
            logger.warning(
                f"Node {node}: THOL collective coherence ({coherence:.3f}) < "
                f"threshold ({min_coherence}). Sub-EPIs may be fragmenting. "
                f"Sub-EPI count: {len(sub_epis)}."
            )

            # Record event for analysis
            events = G.graph.setdefault("thol_coherence_warnings", [])
            events.append(
                {
                    "node": node,
                    "coherence": coherence,
                    "threshold": min_coherence,
                    "sub_epi_count": len(sub_epis),
                }
            )

    def _validate_preconditions(self, G: TNFRGraph, node: Any) -> None:
        """Validate THOL-specific preconditions."""
        from .preconditions import validate_self_organization

        validate_self_organization(G, node)

    def _collect_metrics(
        self, G: TNFRGraph, node: Any, state_before: dict[str, Any]
    ) -> dict[str, Any]:
        """Collect THOL-specific metrics."""
        from .metrics import self_organization_metrics

        return self_organization_metrics(
            G, node, state_before["epi"], state_before["vf"]
        )