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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: benchmarks/confinement_zones_test.py

confinement_zones_test.py

K_φ Confinement Zone Mapping Investigation

Test Task 2: Identify high |K_φ| zones as confinement regions and measure ΔNFR localization dynamics during operator sequences.

Source Code

python
#!/usr/bin/env python3
"""
K_φ Confinement Zone Mapping Investigation

Test Task 2: Identify high |K_φ| zones as confinement regions and measure
ΔNFR localization dynamics during operator sequences.
"""

import argparse
import json
import random
import sys
from pathlib import Path

import networkx as nx
import numpy as np


def _convert_numpy_types(obj):
    """Recursively convert NumPy types to native Python for JSON serialization.

    Ensures json.dumps does not raise TypeError for np.integer, np.floating,
    or ndarray objects. Leaves other types unchanged.
    """
    if isinstance(obj, dict):
        return {k: _convert_numpy_types(v) for k, v in obj.items()}
    if isinstance(obj, list):
        return [_convert_numpy_types(v) for v in obj]
    if isinstance(obj, tuple):
        return tuple(_convert_numpy_types(v) for v in obj)

    # NumPy scalar and array handling
    if isinstance(obj, np.integer):
        return int(obj)
    if isinstance(obj, np.floating):
        return float(obj)
    if isinstance(obj, np.ndarray):
        return obj.tolist()
    return obj


def confinement_zone_investigation(
    topologies=None, n_nodes=30, n_tests=10, high_resolution=False, seed=42, quiet=False
):
    """Investigate K_φ confinement zones and ΔNFR localization.

    Parameters
    ----------
    topologies : list[str] | None
        Topologies to test; uses default canonical subset if None.
    n_nodes : int
        Node count per topology.
    n_tests : int
        Number of seed experiments per topology.
    high_resolution : bool
        If True, include additional K_φ thresholds for finer mapping.
    seed : int
        Base RNG seed for reproducible per-test seeds.
    quiet : bool
        Suppress progress output (CI/test mode).
    """
    if topologies is None:
        topologies = ["ring", "scale_free", "ws"]

    rng = random.Random(seed)
    # Lazy project imports to satisfy linter and ensure sys.path is set
    PROJECT_ROOT = Path(__file__).parent.parent
    if str(PROJECT_ROOT) not in sys.path:
        sys.path.insert(0, str(PROJECT_ROOT))

    from benchmarks.benchmark_utils import (  # noqa: E402
        create_tnfr_topology,
        initialize_tnfr_nodes,
    )
    from src.tnfr.config import DNFR_PRIMARY  # noqa: E402
    from src.tnfr.operators.definitions import (  # noqa: E402
        Coherence,
        Dissonance,
        Mutation,
    )
    from src.tnfr.physics.fields import compute_phase_curvature  # noqa: E402

    if not quiet:
        print("🔒 K_φ Confinement Zone Mapping Investigation")
        print("=" * 50)
        print(f"Topologies: {topologies}")
        print(f"Nodes per topology: {n_nodes}")
        print(f"Tests per topology: {n_tests}")
        print(f"High-resolution: {high_resolution}")

    results = []
    k_phi_thresholds = [3.0, 4.0, 4.88, 5.5, 6.0]
    if high_resolution:
        # Add finer threshold granularity around revised 3.0 value
        extra_thresholds = [2.5, 3.25, 3.75, 5.25, 6.5]
        k_phi_thresholds = sorted(set(k_phi_thresholds + extra_thresholds))

    for topology in topologies:
        if not quiet:
            print(f"\n🌊 {topology.upper()} - Confinement Zone Analysis:")

        for test_id in range(n_tests):
            local_seed = rng.randint(1000, 9999)

            try:
                # Create and initialize graph
                G = create_tnfr_topology(topology, n_nodes, local_seed)
                initialize_tnfr_nodes(G, seed=local_seed)

                if not quiet:
                    print(f"  Test {test_id:2d}: ", end="")

                # === PHASE 1: Pre-disruption baseline ===
                k_phi_baseline = compute_phase_curvature(G)
                dnfr_baseline = {
                    node: G.nodes[node][DNFR_PRIMARY] for node in G.nodes()
                }

                baseline_stats = analyze_field_distribution(
                    k_phi_baseline, dnfr_baseline, "Baseline"
                )

                # === PHASE 2: Apply disruption sequence ===
                # Target nodes with various K_φ levels
                disruption_targets = select_disruption_targets(G, k_phi_baseline)

                for target_node in disruption_targets:
                    # Apply dissonance burst
                    dissonance = Dissonance()
                    dissonance(G, target_node)

                    # Random mutation
                    if random.random() < 0.4:
                        mutation = Mutation()
                        mutation(G, target_node)

                # === PHASE 3: Post-disruption analysis ===
                k_phi_disrupted = compute_phase_curvature(G)
                dnfr_disrupted = {
                    node: G.nodes[node][DNFR_PRIMARY] for node in G.nodes()
                }

                disrupted_stats = analyze_field_distribution(
                    k_phi_disrupted, dnfr_disrupted, "Disrupted"
                )

                # === PHASE 4: Confinement zone analysis ===
                confinement_analysis = {}

                for threshold in k_phi_thresholds:
                    zones = identify_confinement_zones(G, k_phi_disrupted, threshold)

                    dnfr_capture = measure_dnfr_localization(G, dnfr_disrupted, zones)

                    confinement_analysis[threshold] = {
                        "n_zones": len(zones),
                        "zone_sizes": [len(zone) for zone in zones],
                        "total_confined_nodes": sum(len(zone) for zone in zones),
                        "dnfr_capture_rate": dnfr_capture,
                        "zone_connectivity": analyze_zone_connectivity(G, zones),
                    }

                # === PHASE 5: Apply stabilization ===
                coherence = Coherence()
                for node in G.nodes():
                    if random.random() < 0.3:  # Stabilize 30% of nodes
                        coherence(G, node)

                k_phi_stabilized = compute_phase_curvature(G)
                dnfr_stabilized = {
                    node: G.nodes[node][DNFR_PRIMARY] for node in G.nodes()
                }

                stabilized_stats = analyze_field_distribution(
                    k_phi_stabilized, dnfr_stabilized, "Stabilized"
                )

                # === RESULTS COMPILATION ===
                result = {
                    "topology": topology,
                    "test_id": test_id,
                    "n_nodes": len(G.nodes()),
                    "n_edges": len(G.edges()),
                    "seed": local_seed,
                    "baseline_stats": baseline_stats,
                    "disrupted_stats": disrupted_stats,
                    "stabilized_stats": stabilized_stats,
                    "confinement_analysis": confinement_analysis,
                    "disruption_targets": disruption_targets,
                    "thresholds": k_phi_thresholds,
                    "high_resolution": high_resolution,
                }

                results.append(result)

                # Real-time summary
                best_threshold = max(
                    confinement_analysis.keys(),
                    key=lambda t: confinement_analysis[t]["dnfr_capture_rate"],
                )
                best_capture = confinement_analysis[best_threshold]["dnfr_capture_rate"]
                best_zones = confinement_analysis[best_threshold]["n_zones"]

                k_phi_evolution = {
                    "baseline_max": baseline_stats["k_phi_max"],
                    "disrupted_max": disrupted_stats["k_phi_max"],
                    "stabilized_max": stabilized_stats["k_phi_max"],
                }

                if not quiet:
                    print(
                        f"K_φ: {k_phi_evolution['baseline_max']:.1f}→"
                        f"{k_phi_evolution['disrupted_max']:.1f}→"
                        f"{k_phi_evolution['stabilized_max']:.1f} | "
                        f"Zones: {best_zones} | Capture: {best_capture:.2f}"
                    )

            except Exception as e:
                print(f"ERROR: {e}")
                continue

    # === COMPREHENSIVE ANALYSIS ===
    if results and not quiet:
        print("\n📊 CONFINEMENT ZONE ANALYSIS SUMMARY:")
        print(f"Total experiments: {len(results)}")

        # Threshold performance analysis
        print("\n🎯 Threshold Performance (ΔNFR Capture Rates):")
        print(f"{'Threshold':<10} {'Mean':<8} {'Std':<8} {'Max':<8} {'>75%':<6}")
        print("-" * 50)

        for threshold in k_phi_thresholds:
            capture_rates = []
            for result in results:
                if threshold in result["confinement_analysis"]:
                    capture_rates.append(
                        result["confinement_analysis"][threshold]["dnfr_capture_rate"]
                    )

            if capture_rates:
                mean_capture = np.mean(capture_rates)
                std_capture = np.std(capture_rates)
                max_capture = np.max(capture_rates)
                high_capture_count = sum(1 for r in capture_rates if r > 0.75)

                print(
                    f"{threshold:<10.1f} {mean_capture:<8.3f} "
                    f"{std_capture:<8.3f} {max_capture:<8.3f} {high_capture_count:<6d}"
                )

        # Zone dynamics analysis
        print("\n🌊 Zone Dynamics Across Phases:")
        phases = ["baseline", "disrupted", "stabilized"]

        print(f"{'Phase':<12} {'K_φ Mean':<10} {'K_φ Max':<10} {'ΔNFR Mean':<12}")
        print("-" * 50)

        for phase in phases:
            k_phi_means = []
            k_phi_maxs = []
            dnfr_means = []

            for result in results:
                stats = result[f"{phase}_stats"]
                k_phi_means.append(stats["k_phi_mean"])
                k_phi_maxs.append(stats["k_phi_max"])
                dnfr_means.append(stats["dnfr_mean"])

            print(
                f"{phase.title():<12} {np.mean(k_phi_means):<10.3f} "
                f"{np.mean(k_phi_maxs):<10.3f} {np.mean(dnfr_means):<12.6f}"
            )

        # Topology comparison
        print("\n🗺️ Topology-Specific Confinement Patterns:")
        for topology in topologies:
            topo_results = [r for r in results if r["topology"] == topology]

            if topo_results:
                # Best threshold for this topology
                best_capture_by_threshold = {}
                for threshold in k_phi_thresholds:
                    captures = []
                    for result in topo_results:
                        if threshold in result["confinement_analysis"]:
                            captures.append(
                                result["confinement_analysis"][threshold][
                                    "dnfr_capture_rate"
                                ]
                            )
                    if captures:
                        best_capture_by_threshold[threshold] = np.mean(captures)

                if best_capture_by_threshold:
                    best_threshold = max(
                        best_capture_by_threshold.keys(),
                        key=lambda t: best_capture_by_threshold[t],
                    )
                    best_performance = best_capture_by_threshold[best_threshold]

                    print(
                        f"   {topology:<12s}: Best threshold = {best_threshold:.1f} "
                        f"(capture = {best_performance:.3f})"
                    )

        # Save detailed results
        output_file = (
            PROJECT_ROOT / "benchmarks" / "results" / "confinement_zones_analysis.jsonl"
        )
        with open(output_file, "w") as f:
            for result in results:
                f.write(json.dumps(_convert_numpy_types(result)) + "\n")

        print(f"\n💾 Detailed results saved to: {output_file}")

        # === CONCLUSIONS ===
        print("\n🔍 CONFINEMENT MECHANISM CONCLUSIONS:")

        # Check for strong confinement evidence
        strong_evidence_threshold = 0.75  # 75% ΔNFR capture
        strong_evidence_cases = 0

        for result in results:
            for threshold, analysis in result["confinement_analysis"].items():
                if analysis["dnfr_capture_rate"] > strong_evidence_threshold:
                    strong_evidence_cases += 1

        total_threshold_tests = len(results) * len(k_phi_thresholds)
        strong_evidence_rate = strong_evidence_cases / total_threshold_tests

        print(
            f"\n   Strong Confinement Evidence: {strong_evidence_cases}/"
            f"{total_threshold_tests} ({strong_evidence_rate:.1%})"
        )

        # Moderate evidence band (partial confinement): capture > 0.20
        moderate_evidence_cases = 0
        for result in results:
            for threshold, analysis in result["confinement_analysis"].items():
                if analysis["dnfr_capture_rate"] > 0.20:
                    moderate_evidence_cases += 1
        moderate_rate = (
            moderate_evidence_cases / total_threshold_tests
            if total_threshold_tests > 0
            else 0.0
        )

        print(
            f"   Moderate Confinement Evidence (>20% capture): "
            f"{moderate_evidence_cases}/{total_threshold_tests} "
            f"({moderate_rate:.1%})"
        )

        if strong_evidence_rate > 0.2:  # 20% of cases show strong confinement
            print("   ✅ CONFINEMENT MECHANISM DETECTED")
            print("      - High |K_φ| zones successfully localize ΔNFR")
            print("      - Strong-like interaction regime validated")
            print("      - Supports canonical promotion pathway")
        elif strong_evidence_rate > 0.05:
            print("   ⚠️ WEAK CONFINEMENT EVIDENCE")
            print("      - Some localization observed but inconsistent")
            print("      - May need topology-specific thresholds")
            print("      - Requires further investigation")
        else:
            print("   ❌ NO CLEAR CONFINEMENT MECHANISM")
            print("      - ΔNFR remains distributed despite high |K_φ|")
            print("      - May not function as strong-like interaction")
            print("      - Consider alternative interpretations")


def analyze_field_distribution(k_phi_field, dnfr_field, phase_name):
    """Analyze statistical properties of K_φ and ΔNFR fields."""
    k_phi_values = list(k_phi_field.values())
    dnfr_values = list(dnfr_field.values())

    k_phi_abs = [abs(k) for k in k_phi_values]

    return {
        "phase": phase_name,
        "k_phi_mean": np.mean(k_phi_abs),
        "k_phi_max": np.max(k_phi_abs),
        "k_phi_std": np.std(k_phi_abs),
        "dnfr_mean": np.mean(dnfr_values),
        "dnfr_max": np.max(dnfr_values),
        "dnfr_std": np.std(dnfr_values),
        "n_nodes": len(k_phi_values),
    }


def select_disruption_targets(G, k_phi_field, n_targets=5):
    """Select nodes for disruption based on K_φ distribution."""
    # Target mix of high K_φ and random nodes
    k_phi_abs = {node: abs(k_phi_field[node]) for node in G.nodes()}

    # Top K_φ nodes
    sorted_by_k_phi = sorted(k_phi_abs.items(), key=lambda x: x[1], reverse=True)
    top_k_phi_nodes = [node for node, _ in sorted_by_k_phi[: n_targets // 2]]

    # Random nodes
    random_nodes = random.sample(list(G.nodes()), n_targets // 2)

    return list(set(top_k_phi_nodes + random_nodes))[:n_targets]


def identify_confinement_zones(G, k_phi_field, threshold):
    """Identify connected components of nodes with |K_φ| > threshold."""
    high_k_phi_nodes = [
        node for node, k_phi in k_phi_field.items() if abs(k_phi) > threshold
    ]

    if not high_k_phi_nodes:
        return []

    # Create subgraph of high K_φ nodes
    subgraph = G.subgraph(high_k_phi_nodes)

    # Find connected components (confinement zones)
    zones = [list(component) for component in nx.connected_components(subgraph)]

    return zones


def measure_dnfr_localization(G, dnfr_field, zones):
    """Measure what fraction of total ΔNFR is captured within zones."""
    if not zones:
        return 0.0

    confined_nodes = set()
    for zone in zones:
        confined_nodes.update(zone)

    # Total ΔNFR in system
    total_dnfr = sum(abs(dnfr_field[node]) for node in G.nodes())

    # ΔNFR within confinement zones
    confined_dnfr = sum(
        abs(dnfr_field[node]) for node in confined_nodes if node in dnfr_field
    )

    if total_dnfr == 0:
        return 0.0

    return confined_dnfr / total_dnfr


def analyze_zone_connectivity(G, zones):
    """Analyze connectivity properties of confinement zones."""
    if not zones:
        return {"avg_zone_size": 0, "max_zone_size": 0, "total_zones": 0}

    zone_sizes = [len(zone) for zone in zones]

    return {
        "avg_zone_size": np.mean(zone_sizes),
        "max_zone_size": np.max(zone_sizes),
        "total_zones": len(zones),
        "size_distribution": zone_sizes,
    }


if __name__ == "__main__":
    parser = argparse.ArgumentParser(
        description="K_phi confinement zone benchmark (ΔNFR localization)"
    )
    parser.add_argument(
        "--topologies",
        nargs="+",
        default=["ring", "scale_free"],
        help="Topologies to test (default: ring scale_free)",
    )
    parser.add_argument(
        "--nodes", type=int, default=30, help="Nodes per topology (default: 30)"
    )
    parser.add_argument(
        "--seeds",
        type=int,
        default=10,
        help="Number of seed runs per topology (default: 10)",
    )
    parser.add_argument(
        "--high-resolution",
        action="store_true",
        help="Add extra K_phi thresholds for finer mapping",
    )
    parser.add_argument("--seed", type=int, default=42, help="Base RNG seed")
    parser.add_argument("--quiet", action="store_true", help="Suppress progress output")
    cli_args = parser.parse_args()
    confinement_zone_investigation(
        topologies=cli_args.topologies,
        n_nodes=cli_args.nodes,
        n_tests=cli_args.seeds,
        high_resolution=cli_args.high_resolution,
        seed=cli_args.seed,
        quiet=cli_args.quiet,
    )