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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: benchmarks/multichannel_interface_benchmark.py

multichannel_interface_benchmark.py

TNFR Multi-channel Structural-Interface Benchmark (coupled-oscillator networks).

This benchmark exercises the multi-channel extension of the TNFR Structural Interface Theory — the setting where the Structural Field Tetrad is genuinely native. Where the temporal benchmark embeds a single scalar series, here a set of simultaneously-measured channels is treated as a network of coupled oscillators: per-channel Hilbert phase/amplitude feed a phase-locking coupling graph, and the TNFR spatial tetrad (|∇φ|, K_φ, ξ_C, Φ_s) is tracked window by window and compared against the recognised synchronisation baselines (Kuramoto order parameter R, mean phase-locking value, spatial phase dispersion).

Real source: UCI "EEG Eye State"

14 EEG channels sampled at 128 Hz (Emotiv headset), with a binary label per sample: eyes open (0) vs eyes closed (1). Eye closure increases occipital alpha-band (8–12 Hz) synchronisation, so the two label states differ in multi-channel phase-coupling structure — a genuine regime change for which the spatial tetrad is the right tool. We band-pass to the alpha band before phase extraction.

Honest scope

  • The Kuramoto order parameter R is the gold-standard global synchrony measure and is included as a fair baseline, not a strawman.
  • |∇φ| is partially redundant with 1 − R (both fall as the network synchronises). The genuinely distinct TNFR fields are ξ_C (a spatial coherence length) and K_φ (phase-field curvature), which have no order-parameter analogue. The reported question is whether they add discriminative power; comparable or baseline-favourable outcomes are reported honestly.
  • The synthetic source is a test fixture only (a Kuramoto network switched from incoherent to coherent coupling). It validates pipeline mechanics and is never presented as evidence for the thesis.

Usage (PowerShell)::

text
$env:PYTHONPATH=(Resolve-Path -Path ./src).Path
# Real EEG data (downloaded + cached, bounded size):
python benchmarks/multichannel_interface_benchmark.py --source eeg \
    --output results/reports
# Offline synthetic Kuramoto fixture:
python benchmarks/multichannel_interface_benchmark.py --source synthetic

Source Code

python
#!/usr/bin/env python3
"""TNFR Multi-channel Structural-Interface Benchmark (coupled-oscillator networks).

This benchmark exercises the *multi-channel* extension of the TNFR Structural
Interface Theory — the setting where the Structural Field Tetrad is genuinely
native.  Where the temporal benchmark embeds a single scalar series, here a set
of simultaneously-measured channels is treated as a network of coupled
oscillators: per-channel Hilbert phase/amplitude feed a phase-locking coupling
graph, and the TNFR spatial tetrad (``|∇φ|``, ``K_φ``, ``ξ_C``, ``Φ_s``) is
tracked window by window and compared against the recognised synchronisation
baselines (Kuramoto order parameter ``R``, mean phase-locking value, spatial
phase dispersion).

Real source: UCI "EEG Eye State"
---------------------------------
14 EEG channels sampled at 128 Hz (Emotiv headset), with a binary label per
sample: eyes open (0) vs eyes closed (1).  Eye closure increases occipital
alpha-band (8–12 Hz) synchronisation, so the two label states differ in
multi-channel phase-coupling structure — a genuine regime change for which the
spatial tetrad is the right tool.  We band-pass to the alpha band before phase
extraction.

Honest scope
------------
- The Kuramoto order parameter ``R`` is the gold-standard global synchrony
  measure and is included as a *fair* baseline, not a strawman.
- ``|∇φ|`` is partially redundant with ``1 − R`` (both fall as the network
  synchronises).  The genuinely distinct TNFR fields are ``ξ_C`` (a spatial
  coherence *length*) and ``K_φ`` (phase-field curvature), which have no
  order-parameter analogue.  The reported question is whether they *add*
  discriminative power; comparable or baseline-favourable outcomes are reported
  honestly.
- The ``synthetic`` source is a **test fixture only** (a Kuramoto network
  switched from incoherent to coherent coupling).  It validates pipeline
  mechanics and is never presented as evidence for the thesis.

Usage (PowerShell)::

    $env:PYTHONPATH=(Resolve-Path -Path ./src).Path
    # Real EEG data (downloaded + cached, bounded size):
    python benchmarks/multichannel_interface_benchmark.py --source eeg \
        --output results/reports
    # Offline synthetic Kuramoto fixture:
    python benchmarks/multichannel_interface_benchmark.py --source synthetic
"""
from __future__ import annotations

import argparse
import json
import sys
import zipfile
from io import BytesIO
from pathlib import Path
from typing import Any
from urllib.request import Request, urlopen

# Ensure local src is importable ------------------------------------------------
_ROOT = Path(__file__).resolve().parents[1]
_SRC = _ROOT / "src"
if str(_SRC) not in sys.path:
    sys.path.insert(0, str(_SRC))

import numpy as np  # noqa: E402

from tnfr.validation.multichannel_interface import (  # noqa: E402
    MultichannelConfig,
    evaluate_synchrony_discrimination,
    multichannel_window_series,
)

# UCI EEG Eye State (dataset 264).  The post-2023 UCI layout serves a zip; the
# classic mirror serves the raw ARFF.  Both are tried in order; either yields
# the same 14-channel + label table.
EEG_EYE_STATE_URLS = (
    "https://archive.ics.uci.edu/static/public/264/eeg+eye+state.zip",
    "https://archive.ics.uci.edu/ml/machine-learning-databases/00264/"
    "EEG%20Eye%20State.arff",
)

DEFAULT_MAX_BYTES = 20_000_000  # bounded download guard (~20 MB)
EEG_SAMPLING_RATE_HZ = 128.0
ALPHA_BAND_HZ = (8.0, 12.0)
N_EEG_CHANNELS = 14
# Known acquisition spikes (sensor pops) are clipped at this robust z-threshold.
ROBUST_CLIP_SIGMA = 6.0


# ---------------------------------------------------------------------------
# Real data acquisition (bounded, cached, graceful-skip)
# ---------------------------------------------------------------------------
def download_eeg_eye_state(
    *,
    cache_path: Path | None = None,
    max_bytes: int = DEFAULT_MAX_BYTES,
    timeout: float = 60.0,
) -> Path | None:
    """Download the EEG Eye State dataset with a hard size bound.

    Tries each candidate URL in turn; the raw payload (zip or ARFF) is cached
    under ``results/data``.  Returns the cached path, or ``None`` on any failure
    (no network, HTTP error, oversized payload) so the caller can skip
    gracefully offline.
    """
    path = cache_path or _ROOT / "results" / "data" / "eeg_eye_state.raw"
    # Treat the cache as valid only if it holds a non-trivial payload; a stale
    # empty/truncated file from an aborted run must not short-circuit the fetch.
    if path.exists() and path.stat().st_size > 1024:
        return path
    path.parent.mkdir(parents=True, exist_ok=True)
    for url in EEG_EYE_STATE_URLS:
        try:
            request = Request(url, headers={"User-Agent": "tnfr-benchmark/1.0"})
            buffer = BytesIO()
            total = 0
            with urlopen(request, timeout=timeout) as response:  # noqa: S310
                while True:
                    chunk = response.read(1 << 16)
                    if not chunk:
                        break
                    total += len(chunk)
                    if total > max_bytes:
                        print(
                            f"  [skip] download exceeded {max_bytes} bytes; "
                            "aborting",
                            file=sys.stderr,
                        )
                        buffer = None  # type: ignore[assignment]
                        break
                    buffer.write(chunk)
                if buffer is None:
                    continue
        except Exception as exc:  # noqa: BLE001 - graceful offline skip
            print(f"  [skip] EEG download failed ({url}): {exc}", file=sys.stderr)
            continue
        if buffer is not None and total > 0:
            path.write_bytes(buffer.getvalue())
            return path
    return None


def _extract_arff_text(raw: bytes) -> str | None:
    """Return ARFF text from a raw payload that may be a zip or plain ARFF."""
    if raw[:2] == b"PK":  # zip magic
        try:
            with zipfile.ZipFile(BytesIO(raw)) as archive:
                names = [n for n in archive.namelist() if n.lower().endswith(".arff")]
                if not names:
                    names = [n for n in archive.namelist() if not n.endswith("/")]
                if not names:
                    return None
                return archive.read(names[0]).decode("utf-8", errors="ignore")
        except Exception as exc:  # noqa: BLE001 - corrupt/partial archive
            print(f"  [skip] could not read zip: {exc}", file=sys.stderr)
            return None
    return raw.decode("utf-8", errors="ignore")


def parse_arff(text: str) -> tuple[np.ndarray, np.ndarray] | None:
    """Parse EEG Eye State ARFF text into ``(signals, labels)``.

    ``signals`` has shape ``(n_channels, n_samples)`` (channels first); ``labels``
    is the per-sample binary eye-state.  ``@``/``%`` metadata lines are skipped;
    rows are read after ``@DATA``.  Returns ``None`` if too little data parses.
    """
    rows: list[list[float]] = []
    data_started = False
    for raw_line in text.splitlines():
        line = raw_line.strip()
        if not line:
            continue
        lowered = line.lower()
        if lowered.startswith("@data"):
            data_started = True
            continue
        if line.startswith("@") or line.startswith("%"):
            continue
        if not data_started:
            continue
        parts = [p.strip() for p in line.split(",")]
        if len(parts) < N_EEG_CHANNELS + 1:
            continue
        try:
            channels = [float(p) for p in parts[:N_EEG_CHANNELS]]
            label = int(float(parts[N_EEG_CHANNELS]))
        except ValueError:
            continue
        rows.append(channels + [float(label)])
    if len(rows) < 1024:
        print(f"  [skip] parsed only {len(rows)} usable rows", file=sys.stderr)
        return None
    table = np.asarray(rows, dtype=float)
    signals = table[:, :N_EEG_CHANNELS].T  # (channels, samples)
    labels = table[:, N_EEG_CHANNELS].astype(int)
    return signals, labels


def _robust_clip(
    signals: np.ndarray, *, sigma: float = ROBUST_CLIP_SIGMA
) -> np.ndarray:
    """Clip per-channel sensor spikes to a robust ``median ± σ·MAD`` band."""
    cleaned = np.array(signals, dtype=float, copy=True)
    for j in range(cleaned.shape[0]):
        row = cleaned[j]
        med = float(np.median(row))
        mad = float(np.median(np.abs(row - med)))
        if mad <= 0.0:
            continue
        scale = 1.4826 * mad  # MAD -> approx std for normal data
        lo = med - sigma * scale
        hi = med + sigma * scale
        cleaned[j] = np.clip(row, lo, hi)
    return cleaned


def load_eeg_eye_state(path: Path) -> tuple[np.ndarray, np.ndarray] | None:
    """Load and clean the cached EEG Eye State payload."""
    raw = path.read_bytes()
    text = _extract_arff_text(raw)
    if text is None:
        return None
    parsed = parse_arff(text)
    if parsed is None:
        return None
    signals, labels = parsed
    return _robust_clip(signals), labels


# ---------------------------------------------------------------------------
# Synthetic test fixture (mechanics only; never presented as evidence)
# ---------------------------------------------------------------------------
def kuramoto_simulate(
    n_oscillators: int,
    coupling: float,
    steps: int,
    *,
    dt: float = 0.05,
    mean_omega: float = 1.0,
    omega_spread: float = 0.2,
    seed: int = 0,
) -> np.ndarray:
    """Euler-integrate a Kuramoto network; observable is ``sin(θ_j(t))``.

    Returns shape ``(n_oscillators, steps)``.  Below the critical coupling the
    network stays incoherent; well above it the oscillators phase-lock.  The
    observable is the *signal* ``sin θ`` (not the latent phase), so the pipeline
    must recover phase via the Hilbert transform, exactly as for real data.
    """
    rng = np.random.default_rng(seed)
    omega = rng.normal(mean_omega, omega_spread, n_oscillators)
    theta = rng.uniform(-np.pi, np.pi, n_oscillators)
    out = np.empty((n_oscillators, steps), dtype=float)
    for t in range(steps):
        z = np.mean(np.exp(1j * theta))
        order = np.abs(z)
        psi = np.angle(z)
        theta = theta + dt * (omega + coupling * order * np.sin(psi - theta))
        out[:, t] = np.sin(theta)
    return out


def synthetic_kuramoto_regime_switch(
    *,
    n_oscillators: int = 14,
    block: int = 4096,
    coupling_low: float = 0.05,
    coupling_high: float = 2.0,
    seed: int = 0,
) -> tuple[np.ndarray, np.ndarray]:
    """Incoherent → coherent Kuramoto regime switch (mechanics fixture only).

    Concatenates a low-coupling (incoherent) block and a high-coupling
    (synchronised) block.  ``labels`` is 0 on the incoherent block and 1 on the
    coherent block.  Used to validate that the tetrad and the baselines both
    track synchronisation; never presented as evidence for the thesis.
    """
    incoherent = kuramoto_simulate(n_oscillators, coupling_low, block, seed=seed + 1)
    coherent = kuramoto_simulate(n_oscillators, coupling_high, block, seed=seed + 2)
    signals = np.concatenate([incoherent, coherent], axis=1)
    labels = np.concatenate([np.zeros(block), np.ones(block)]).astype(int)
    return signals, labels


# ---------------------------------------------------------------------------
# Benchmark orchestration
# ---------------------------------------------------------------------------
def _block_means(values: np.ndarray, labels: np.ndarray) -> dict[str, float]:
    """Mean indicator value within each label class (for a quick sanity view)."""
    values = np.asarray(values, dtype=float)
    labels = np.asarray(labels, dtype=bool)
    finite = np.isfinite(values)
    pos = values[finite & labels]
    neg = values[finite & ~labels]
    return {
        "label0": float(np.mean(neg)) if neg.size else float("nan"),
        "label1": float(np.mean(pos)) if pos.size else float("nan"),
    }


def run_multichannel_benchmark(
    *,
    source: str,
    config: MultichannelConfig,
    max_bytes: int = DEFAULT_MAX_BYTES,
    synthetic_block: int = 4096,
) -> dict[str, Any]:
    """Run the multi-channel structural-interface benchmark on the chosen source."""
    report: dict[str, Any] = {
        "source": source,
        "config": {
            "window": config.window,
            "step": config.step,
            "k_neighbours": config.k_neighbours,
            "sampling_rate": config.sampling_rate,
            "bandpass": list(config.bandpass) if config.bandpass else None,
        },
        "honest_scope": (
            "Multi-channel phase-coupled network: the native setting for the "
            "TNFR spatial tetrad. The Kuramoto order parameter R is the "
            "gold-standard synchrony baseline (fair, not a strawman). |∇φ| is "
            "partially redundant with 1−R; the genuinely distinct TNFR fields "
            "are ξ_C (spatial coherence length) and K_φ (phase-field curvature), "
            "which have no order-parameter analogue. Comparable or "
            "baseline-favourable outcomes are reported honestly."
        ),
    }

    if source == "eeg":
        cache = download_eeg_eye_state(max_bytes=max_bytes)
        if cache is None:
            report["status"] = "skipped"
            report["reason"] = (
                "EEG Eye State source unreachable in this environment. Re-run "
                "with network access; pipeline mechanics are validated offline "
                "via --source synthetic."
            )
            return report
        loaded = load_eeg_eye_state(cache)
        if loaded is None:
            report["status"] = "skipped"
            report["reason"] = "Downloaded EEG payload could not be parsed."
            return report
        signals, labels = loaded
        report["data"] = {
            "n_channels": int(signals.shape[0]),
            "n_samples": int(signals.shape[1]),
            "label_balance": float(np.mean(labels)),
            "cache": str(cache.relative_to(_ROOT)),
            "label_semantics": "0 = eyes open, 1 = eyes closed",
        }
        report["event_kind"] = "eyes open vs eyes closed (alpha synchronisation)"
    elif source == "synthetic":
        signals, labels = synthetic_kuramoto_regime_switch(
            n_oscillators=max(N_EEG_CHANNELS, 3), block=synthetic_block
        )
        report["data"] = {
            "n_channels": int(signals.shape[0]),
            "n_samples": int(signals.shape[1]),
            "label_balance": float(np.mean(labels)),
            "note": "Synthetic Kuramoto regime switch; mechanics only, not evidence.",
        }
        report["event_kind"] = "incoherent → coherent coupling (fixture)"
    else:  # pragma: no cover - argparse restricts choices
        raise ValueError(f"unknown source: {source}")

    if signals.shape[1] < config.window:
        report["status"] = "skipped"
        report["reason"] = (
            f"Signal length ({signals.shape[1]}) shorter than window "
            f"({config.window})."
        )
        return report

    discrimination = evaluate_synchrony_discrimination(signals, labels, config=config)
    series = multichannel_window_series(signals, config=config)

    report["status"] = "ok"
    report["n_windows"] = int(series.window_end.size)
    report["n_positive_windows"] = discrimination.n_positive_windows
    report["auc"] = {k: round(float(v), 4) for k, v in discrimination.auc.items()}
    report["best_tnfr"] = {
        "channel": discrimination.best_tnfr[0],
        "auc": round(float(discrimination.best_tnfr[1]), 4),
    }
    report["best_baseline"] = {
        "channel": discrimination.best_baseline[0],
        "auc": round(float(discrimination.best_baseline[1]), 4),
    }
    report["block_means"] = {
        name: _block_means(
            getattr(series, name), _series_labels(series, labels, config)
        )
        for name in (
            "grad_phi",
            "k_phi",
            "xi_c",
            "phi_s",
            "order_parameter",
            "mean_plv",
            "phase_dispersion",
        )
    }
    report["interpretation"] = discrimination.interpretation
    return report


def _series_labels(
    series: Any, labels: np.ndarray, config: MultichannelConfig
) -> np.ndarray:
    """Majority window labels aligned with the tetrad series (for block means)."""
    arr = np.asarray(labels, dtype=float)
    out = np.empty(series.window_end.size, dtype=bool)
    for i, end in enumerate(series.window_end):
        start = int(end) - config.window + 1
        segment = arr[max(0, start) : int(end) + 1]
        out[i] = bool(np.mean(segment) >= 0.5) if segment.size else False
    return out


def _build_arg_parser() -> argparse.ArgumentParser:
    parser = argparse.ArgumentParser(
        description="TNFR multi-channel structural-interface benchmark."
    )
    parser.add_argument(
        "--source",
        choices=("eeg", "synthetic"),
        default="eeg",
        help="Data source: real EEG Eye State or synthetic Kuramoto fixture.",
    )
    parser.add_argument("--window", type=int, default=512)
    parser.add_argument("--step", type=int, default=128)
    parser.add_argument("--k-neighbours", type=int, default=4)
    parser.add_argument("--max-bytes", type=int, default=DEFAULT_MAX_BYTES)
    parser.add_argument("--synthetic-block", type=int, default=4096)
    parser.add_argument(
        "--output",
        type=Path,
        default=_ROOT / "results" / "reports",
        help="Directory for the JSON report.",
    )
    return parser


def main(argv: list[str] | None = None) -> int:
    args = _build_arg_parser().parse_args(argv)
    if args.source == "eeg":
        config = MultichannelConfig(
            window=args.window,
            step=args.step,
            k_neighbours=args.k_neighbours,
            sampling_rate=EEG_SAMPLING_RATE_HZ,
            bandpass=ALPHA_BAND_HZ,
        )
    else:
        config = MultichannelConfig(
            window=args.window,
            step=args.step,
            k_neighbours=args.k_neighbours,
        )

    report = run_multichannel_benchmark(
        source=args.source,
        config=config,
        max_bytes=args.max_bytes,
        synthetic_block=args.synthetic_block,
    )

    print(json.dumps(report, indent=2))

    output_dir = Path(args.output)
    if not output_dir.is_absolute():
        output_dir = (Path.cwd() / output_dir).resolve()
    output_dir.mkdir(parents=True, exist_ok=True)
    out_path = output_dir / f"multichannel_interface_{args.source}.json"
    out_path.write_text(json.dumps(report, indent=2), encoding="utf-8")
    try:
        display = out_path.relative_to(_ROOT)
    except ValueError:
        display = out_path
    print(f"\nReport written to {display}")
    return 0


if __name__ == "__main__":  # pragma: no cover
    raise SystemExit(main())