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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
.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: examples/01_foundations/09_visualization_suite.py

09_visualization_suite.py

09 - TNFR Visualization Suite: Dynamic Nodal Evolution Graphics

Comprehensive visualization of TNFR dynamics with real-time plotting and animation.

PHYSICS: Visual representation of ∂EPI/∂t = νf · ΔNFR(t) evolution. LEARNING: Understanding through interactive graphics and dynamic plots.

Source Code

python
"""09 - TNFR Visualization Suite: Dynamic Nodal Evolution Graphics

Comprehensive visualization of TNFR dynamics with real-time plotting and animation.

PHYSICS: Visual representation of ∂EPI/∂t = νf · ΔNFR(t) evolution.
LEARNING: Understanding through interactive graphics and dynamic plots.
"""

import os

import matplotlib
import matplotlib.pyplot as plt
import networkx as nx
import numpy as np

# Configure font for better Unicode support
matplotlib.rcParams["font.family"] = "sans-serif"
matplotlib.rcParams["font.sans-serif"] = ["DejaVu Sans", "Arial", "sans-serif"]
# Suppress missing-glyph warnings
import warnings

warnings.filterwarnings("ignore", "Glyph .* missing from font.*")


def compute_coherence(G):
    """Network phase synchronization: the canonical Kuramoto order
    parameter R = |<e^{iθ}>|.

    R = 1 when phases are fully aligned, R -> 0 when desynchronized
    (random or antiphase). AGENTS.md frames TNFR phase coupling as
    Kuramoto synchronization, so this is the canonical phase-synchrony
    measure. The distinct total coherence
    C(t) = 1/(1 + mean|ΔNFR| + mean|dEPI|) lives in
    tnfr.metrics.coherence and requires the dynamics pipeline.
    """
    thetas = np.array(
        [G.nodes[n].get("theta", G.nodes[n].get("phase", 0.0)) for n in G.nodes()],
        dtype=float,
    )
    if thetas.size == 0:
        return 1.0
    return float(abs(np.mean(np.exp(1j * thetas))))


def compute_delta_nfr(G, node):
    """Compute ΔNFR (structural pressure) for a node."""
    if node not in G.nodes():
        return 0.0

    node_phase = G.nodes[node].get("phase", 0)
    neighbors = list(G.neighbors(node))

    if not neighbors:
        return 0.0

    neighbor_phases = [G.nodes[n].get("phase", 0) for n in neighbors]
    mean_neighbor_phase = np.mean(neighbor_phases)

    phase_diff = abs(node_phase - mean_neighbor_phase)
    return min(phase_diff, 2 * np.pi - phase_diff) / np.pi


def evolve_network_step(G, dt=0.1):
    """Single evolution step applying nodal equation."""
    new_phases = {}

    for node in G.nodes():
        current_phase = G.nodes[node].get("phase", 0)
        vf = G.nodes[node].get("vf", 1.0)

        neighbors = list(G.neighbors(node))
        if neighbors:
            neighbor_phases = [G.nodes[n].get("phase", 0) for n in neighbors]
            target_phase = np.mean(neighbor_phases)

            direction = target_phase - current_phase
            if direction > np.pi:
                direction -= 2 * np.pi
            elif direction < -np.pi:
                direction += 2 * np.pi

            delta_nfr = compute_delta_nfr(G, node)

            # Apply nodal equation: ∂EPI/∂t = νf · ΔNFR
            phase_change = vf * delta_nfr * dt * np.sign(direction)
            new_phases[node] = (current_phase + phase_change) % (2 * np.pi)
        else:
            new_phases[node] = current_phase

    for node, phase in new_phases.items():
        G.nodes[node]["phase"] = phase


def create_coherence_evolution_plot():
    """Create static plot showing coherence evolution across topologies."""

    print("🎨 Creating coherence evolution visualization...")

    # Create different topologies
    topologies = {
        "Ring": nx.cycle_graph(10),
        "Star": nx.star_graph(9),
        "Complete": nx.complete_graph(8),
        "Random": nx.erdos_renyi_graph(10, 0.4),
    }

    plt.figure(figsize=(12, 8))

    # Color scheme for topologies
    colors = {
        "Ring": "#FF6B6B",
        "Star": "#4ECDC4",
        "Complete": "#45B7D1",
        "Random": "#96CEB4",
    }

    for name, G in topologies.items():
        # Initialize
        np.random.seed(42)
        for node in G.nodes():
            G.nodes[node]["phase"] = np.random.uniform(0, 2 * np.pi)
            G.nodes[node]["nu_f"] = 1.0

        # Evolve and track
        steps = 50
        coherence_history = []

        for step in range(steps):
            coherence = compute_coherence(G)
            coherence_history.append(coherence)
            evolve_network_step(G)

        plt.plot(
            coherence_history,
            label=f"{name} Topology",
            color=colors[name],
            linewidth=3,
            alpha=0.8,
        )

    plt.xlabel("Evolution Steps", fontsize=14)
    plt.ylabel("Network Coherence", fontsize=14)
    plt.title(
        "🌊 TNFR Coherence Evolution Across Network Topologies", fontsize=16, pad=20
    )
    plt.legend(fontsize=12)
    plt.grid(True, alpha=0.3)
    plt.xlim(0, 49)
    plt.ylim(0, 1)

    # Add physics annotation
    plt.text(
        0.02,
        0.98,
        "Physics: ∂EPI/∂t = νf · ΔNFR(t)",
        transform=plt.gca().transAxes,
        fontsize=11,
        verticalalignment="top",
        bbox=dict(boxstyle="round,pad=0.3", facecolor="yellow", alpha=0.7),
    )

    plt.tight_layout()

    # Save to output directory
    os.makedirs("output", exist_ok=True)
    plt.savefig("output/coherence_evolution.png", dpi=300, bbox_inches="tight")
    plt.show()

    print("✅ Saved: output/coherence_evolution.png")


def create_phase_space_visualization():
    """Create phase space visualization showing nodal dynamics."""

    print("🎨 Creating phase space visualization...")

    # Create network
    G = nx.cycle_graph(6)

    # Initialize with specific pattern
    phases_init = [0, np.pi / 3, 2 * np.pi / 3, np.pi, 4 * np.pi / 3, 5 * np.pi / 3]
    for i, node in enumerate(G.nodes()):
        G.nodes[node]["phase"] = phases_init[i]
        G.nodes[node]["nu_f"] = 1.0

    # Track evolution
    steps = 30
    phase_trajectories = {node: [] for node in G.nodes()}
    time_points = []

    for step in range(steps):
        time_points.append(step * 0.1)

        # Record current phases
        for node in G.nodes():
            phase_trajectories[node].append(G.nodes[node]["phase"])

        # Evolve
        evolve_network_step(G, dt=0.1)

    # Create phase space plot
    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6))

    # Left plot: Phase trajectories over time
    colors = plt.cm.Set3(np.linspace(0, 1, len(G.nodes())))

    for i, node in enumerate(G.nodes()):
        ax1.plot(
            time_points,
            phase_trajectories[node],
            label=f"Node {node}",
            color=colors[i],
            linewidth=2,
            marker="o",
            markersize=3,
        )

    ax1.set_xlabel("Time", fontsize=12)
    ax1.set_ylabel("Phase (radians)", fontsize=12)
    ax1.set_title("🌊 Phase Evolution Over Time", fontsize=14)
    ax1.legend(bbox_to_anchor=(1.05, 1), loc="upper left")
    ax1.grid(True, alpha=0.3)
    ax1.set_ylim(0, 2 * np.pi)

    # Add π markers
    ax1.set_yticks([0, np.pi / 2, np.pi, 3 * np.pi / 2, 2 * np.pi])
    ax1.set_yticklabels(["0", "π/2", "π", "3π/2", "2π"])

    # Right plot: Circular phase representation (final state)
    ax2 = plt.subplot(122, projection="polar")

    final_phases = [phase_trajectories[node][-1] for node in G.nodes()]
    node_positions = np.array(final_phases)

    # Plot nodes on circle
    ax2.scatter(
        node_positions,
        np.ones(len(node_positions)),
        c=colors,
        s=200,
        alpha=0.8,
        edgecolors="black",
        linewidth=2,
    )

    # Add node labels
    for i, (node, phase) in enumerate(zip(G.nodes(), final_phases)):
        ax2.annotate(
            f"{node}",
            (phase, 1.15),
            ha="center",
            va="center",
            fontsize=10,
            fontweight="bold",
        )

    # Draw connections
    for edge in G.edges():
        phase1 = final_phases[edge[0]]
        phase2 = final_phases[edge[1]]
        ax2.plot([phase1, phase2], [1, 1], "gray", alpha=0.5, linewidth=1)

    ax2.set_title("🎯 Final Phase Configuration", fontsize=14, pad=20)
    ax2.set_ylim(0, 1.3)
    ax2.set_rticks([])

    plt.tight_layout()

    # Save
    plt.savefig("output/phase_space_dynamics.png", dpi=300, bbox_inches="tight")
    plt.show()

    print("✅ Saved: output/phase_space_dynamics.png")


def create_network_topology_comparison():
    """Create visual comparison of different network topologies."""

    print("🎨 Creating network topology comparison...")

    # Define topologies
    topologies = {
        "Ring": nx.cycle_graph(8),
        "Star": nx.star_graph(7),
        "Complete": nx.complete_graph(6),
        "Random": nx.erdos_renyi_graph(8, 0.3),
        "Small World": nx.watts_strogatz_graph(8, 3, 0.3),
        "Grid": nx.grid_2d_graph(3, 3),
    }

    fig, axes = plt.subplots(2, 3, figsize=(18, 12))
    axes = axes.flatten()

    for idx, (name, G) in enumerate(topologies.items()):
        ax = axes[idx]

        # Initialize with coherence visualization
        np.random.seed(42)
        for node in G.nodes():
            G.nodes[node]["phase"] = np.random.uniform(0, 2 * np.pi)
            G.nodes[node]["nu_f"] = 1.0

        # Evolve to show final state
        for _ in range(30):
            evolve_network_step(G)

        # Compute node colors based on phase
        node_phases = [G.nodes[node]["phase"] for node in G.nodes()]
        node_colors = plt.cm.hsv(np.array(node_phases) / (2 * np.pi))

        # Compute coherence
        coherence = compute_coherence(G)

        # Draw network
        pos = nx.spring_layout(G, seed=42)

        # Draw edges
        nx.draw_networkx_edges(G, pos, ax=ax, edge_color="gray", alpha=0.6, width=2)

        # Draw nodes
        nx.draw_networkx_nodes(
            G,
            pos,
            ax=ax,
            node_color=node_colors,
            node_size=500,
            edgecolors="black",
            linewidths=2,
        )

        # Add labels
        nx.draw_networkx_labels(G, pos, ax=ax, font_size=10, font_weight="bold")

        ax.set_title(
            f"{name}\nCoherence: {coherence:.3f}", fontsize=14, fontweight="bold"
        )
        ax.set_aspect("equal")
        ax.axis("off")

    # Add overall title and physics note
    fig.suptitle(
        "🕸️ TNFR Dynamics Across Network Topologies\n"
        + "Node colors represent phases | Higher coherence = better synchronization",
        fontsize=16,
        fontweight="bold",
    )

    # Add colorbar for phase
    cbar_ax = fig.add_axes([0.92, 0.15, 0.02, 0.7])
    sm = plt.cm.ScalarMappable(
        cmap=plt.cm.hsv, norm=plt.Normalize(vmin=0, vmax=2 * np.pi)
    )
    sm.set_array([])
    cbar = plt.colorbar(sm, cax=cbar_ax)
    cbar.set_label("Phase (radians)", fontsize=12)
    cbar.set_ticks([0, np.pi / 2, np.pi, 3 * np.pi / 2, 2 * np.pi])
    cbar.set_ticklabels(["0", "π/2", "π", "3π/2", "2π"])

    plt.tight_layout()
    plt.subplots_adjust(right=0.9)

    # Save
    plt.savefig("output/network_topology_comparison.png", dpi=300, bbox_inches="tight")
    plt.show()

    print("✅ Saved: output/network_topology_comparison.png")


def create_frequency_resonance_plot():
    """Create visualization of frequency resonance effects."""

    print("🎨 Creating frequency resonance visualization...")

    # Create network
    G = nx.cycle_graph(8)

    # Test different frequency distributions
    frequency_patterns = {
        "Uniform": [1.0] * 8,
        "Harmonic": [1.0, 2.0, 1.0, 2.0, 1.0, 2.0, 1.0, 2.0],
        "Golden Ratio": [1.0, 1.618, 1.0, 1.618, 1.0, 1.618, 1.0, 1.618],
        "Random": np.random.uniform(0.5, 2.0, 8),
    }

    fig, axes = plt.subplots(2, 2, figsize=(15, 12))
    axes = axes.flatten()

    results = {}

    for idx, (pattern_name, frequencies) in enumerate(frequency_patterns.items()):
        ax = axes[idx]

        # Initialize network
        np.random.seed(42)
        for i, node in enumerate(G.nodes()):
            G.nodes[node]["phase"] = np.random.uniform(0, 2 * np.pi)
            G.nodes[node]["nu_f"] = frequencies[i]

        # Track evolution
        steps = 60
        coherence_history = []
        freq_coherence_history = []

        for step in range(steps):
            # Compute coherences
            phase_coherence = compute_coherence(G)

            # Frequency coherence
            node_frequencies = [G.nodes[n]["nu_f"] for n in G.nodes()]
            freq_var = np.var(node_frequencies)
            freq_mean = np.mean(node_frequencies)
            freq_coherence = (
                1.0 / (1.0 + freq_var / freq_mean) if freq_mean > 0 else 0.0
            )

            coherence_history.append(phase_coherence)
            freq_coherence_history.append(freq_coherence)

            # Evolve
            evolve_network_step(G, dt=0.08)

        # Plot results
        ax.plot(coherence_history, label="Phase Coherence", color="blue", linewidth=2)
        ax.plot(
            freq_coherence_history,
            label="Frequency Coherence",
            color="red",
            linewidth=2,
            linestyle="--",
        )

        ax.set_xlabel("Evolution Steps")
        ax.set_ylabel("Coherence")
        ax.set_title(f"{pattern_name} Frequencies")
        ax.legend()
        ax.grid(True, alpha=0.3)
        ax.set_ylim(0, 1)

        # Store final coherence
        results[pattern_name] = {
            "final_phase": coherence_history[-1],
            "final_freq": freq_coherence_history[-1],
            "frequencies": frequencies,
        }

    plt.suptitle(
        "🎵 Frequency Resonance Effects on TNFR Dynamics",
        fontsize=16,
        fontweight="bold",
    )
    plt.tight_layout()

    # Save
    plt.savefig("output/frequency_resonance_effects.png", dpi=300, bbox_inches="tight")
    plt.show()

    # Print results summary
    print("📊 Frequency Pattern Results:")
    for pattern, result in results.items():
        print(
            f"  {pattern:12s}: Phase={result['final_phase']:.3f}, Freq={result['final_freq']:.3f}"
        )

    print("✅ Saved: output/frequency_resonance_effects.png")


def create_emergence_metrics_dashboard():
    """Create dashboard showing emergence metrics over time."""

    print("🎨 Creating emergence metrics dashboard...")

    # Create swarm network
    G = nx.watts_strogatz_graph(15, 4, 0.2)

    # Initialize with leader/follower structure
    np.random.seed(42)
    leaders = [0, 5, 10]

    for node in G.nodes():
        G.nodes[node]["phase"] = np.random.uniform(0, 2 * np.pi)
        if node in leaders:
            G.nodes[node]["nu_f"] = 2.0  # Leaders have higher frequency
            G.nodes[node]["role"] = "leader"
        else:
            G.nodes[node]["nu_f"] = 1.0
            G.nodes[node]["role"] = "follower"

    # Track metrics over time
    steps = 80
    metrics_history = {
        "order_parameter": [],
        "synchronization": [],
        "leader_coherence": [],
        "follower_coherence": [],
        "system_energy": [],
    }

    for step in range(steps):
        # Compute metrics
        phases = [G.nodes[n]["phase"] for n in G.nodes()]

        # Order parameter
        x_sum = sum(np.cos(p) for p in phases)
        y_sum = sum(np.sin(p) for p in phases)
        order_param = np.sqrt(x_sum**2 + y_sum**2) / len(phases)

        # Synchronization
        sync = compute_coherence(G)

        # Leader/follower coherence
        leader_phases = [
            G.nodes[n]["phase"] for n in G.nodes() if G.nodes[n]["role"] == "leader"
        ]
        follower_phases = [
            G.nodes[n]["phase"] for n in G.nodes() if G.nodes[n]["role"] == "follower"
        ]

        leader_coh = (
            1.0 - np.std(leader_phases) / np.pi if len(leader_phases) > 1 else 1.0
        )
        follower_coh = (
            1.0 - np.std(follower_phases) / np.pi if len(follower_phases) > 1 else 1.0
        )

        # System energy (based on phase mismatches)
        total_energy = sum(compute_delta_nfr(G, n) ** 2 for n in G.nodes())

        # Store metrics
        metrics_history["order_parameter"].append(order_param)
        metrics_history["synchronization"].append(sync)
        metrics_history["leader_coherence"].append(leader_coh)
        metrics_history["follower_coherence"].append(follower_coh)
        metrics_history["system_energy"].append(total_energy)

        # Evolve system
        evolve_network_step(G, dt=0.1)

        # Leaders occasionally change direction
        if step % 20 == 0:
            for leader in leaders:
                if np.random.random() < 0.3:
                    direction_change = np.random.uniform(-np.pi / 4, np.pi / 4)
                    current_phase = G.nodes[leader]["phase"]
                    G.nodes[leader]["phase"] = (current_phase + direction_change) % (
                        2 * np.pi
                    )

    # Create dashboard
    fig, axes = plt.subplots(2, 2, figsize=(16, 12))

    # Order parameter and synchronization
    axes[0, 0].plot(
        metrics_history["order_parameter"],
        label="Order Parameter",
        color="blue",
        linewidth=2,
    )
    axes[0, 0].plot(
        metrics_history["synchronization"],
        label="Synchronization",
        color="green",
        linewidth=2,
    )
    axes[0, 0].set_xlabel("Evolution Steps")
    axes[0, 0].set_ylabel("Metric Value")
    axes[0, 0].set_title("🎯 Global Coherence Metrics")
    axes[0, 0].legend()
    axes[0, 0].grid(True, alpha=0.3)
    axes[0, 0].set_ylim(0, 1)

    # Leader vs Follower coherence
    axes[0, 1].plot(
        metrics_history["leader_coherence"], label="Leaders", color="red", linewidth=2
    )
    axes[0, 1].plot(
        metrics_history["follower_coherence"],
        label="Followers",
        color="orange",
        linewidth=2,
    )
    axes[0, 1].set_xlabel("Evolution Steps")
    axes[0, 1].set_ylabel("Coherence")
    axes[0, 1].set_title("👑 Leader-Follower Dynamics")
    axes[0, 1].legend()
    axes[0, 1].grid(True, alpha=0.3)
    axes[0, 1].set_ylim(0, 1)

    # System energy
    axes[1, 0].plot(metrics_history["system_energy"], color="purple", linewidth=2)
    axes[1, 0].set_xlabel("Evolution Steps")
    axes[1, 0].set_ylabel("Total ΔNFR Energy")
    axes[1, 0].set_title("⚡ System Energy (Structural Pressure)")
    axes[1, 0].grid(True, alpha=0.3)

    # Phase portrait (final state)
    final_phases = [G.nodes[n]["phase"] for n in G.nodes()]
    leader_indices = [
        i for i, n in enumerate(G.nodes()) if G.nodes[n]["role"] == "leader"
    ]
    follower_indices = [
        i for i, n in enumerate(G.nodes()) if G.nodes[n]["role"] == "follower"
    ]

    axes[1, 1] = plt.subplot(224, projection="polar")

    # Plot leaders and followers differently
    if leader_indices:
        leader_phases = [final_phases[i] for i in leader_indices]
        axes[1, 1].scatter(
            leader_phases,
            [1.0] * len(leader_phases),
            c="red",
            s=200,
            alpha=0.8,
            label="Leaders",
            edgecolors="black",
        )

    if follower_indices:
        follower_phases = [final_phases[i] for i in follower_indices]
        axes[1, 1].scatter(
            follower_phases,
            [0.8] * len(follower_phases),
            c="lightblue",
            s=100,
            alpha=0.8,
            label="Followers",
            edgecolors="gray",
        )

    axes[1, 1].set_title("🌟 Final Swarm Configuration")
    axes[1, 1].set_ylim(0, 1.2)
    axes[1, 1].set_rticks([])
    axes[1, 1].legend(loc="upper left", bbox_to_anchor=(0.1, 1.1))

    plt.suptitle(
        "🐝 Swarm Intelligence: Emergence Metrics Dashboard",
        fontsize=16,
        fontweight="bold",
    )
    plt.tight_layout()

    # Save
    plt.savefig("output/emergence_metrics_dashboard.png", dpi=300, bbox_inches="tight")
    plt.show()

    print("✅ Saved: output/emergence_metrics_dashboard.png")


def visualization_suite_demo():
    """Run complete TNFR visualization suite."""

    print("=" * 80)
    print("                🎨 TNFR VISUALIZATION SUITE 🎨")
    print("=" * 80)
    print()
    print("Creating comprehensive visual representations of TNFR nodal dynamics...")
    print(
        "PHYSICS: Visual exploration of ∂EPI/∂t = νf · ΔNFR(t) across multiple scenarios"
    )
    print(
        "OUTPUT: High-resolution graphics showing evolution patterns and emergent behaviors"
    )
    print()

    try:
        # Create all visualizations
        create_coherence_evolution_plot()
        print()

        create_phase_space_visualization()
        print()

        create_network_topology_comparison()
        print()

        create_frequency_resonance_plot()
        print()

        create_emergence_metrics_dashboard()
        print()

        print("=" * 80)
        print("🎯 VISUALIZATION SUMMARY")
        print("=" * 80)
        print()
        print("📊 Generated visualizations:")
        print("  1. coherence_evolution.png - Topology-dependent coherence patterns")
        print("  2. phase_space_dynamics.png - Nodal phase trajectories over time")
        print("  3. network_topology_comparison.png - Visual network structure effects")
        print("  4. frequency_resonance_effects.png - Harmonic frequency influence")
        print("  5. emergence_metrics_dashboard.png - Swarm intelligence emergence")
        print()
        print("📁 All files saved to: output/ directory")
        print("🔬 Each graphic shows different aspects of TNFR nodal equation dynamics")
        print("🎨 High-resolution (300 DPI) suitable for presentations and papers")
        print()
        print("🚀 VISUAL INSIGHTS REVEALED:")
        print("━" * 60)
        print("• Complete graphs achieve fastest coherence convergence")
        print("• Phase trajectories show natural synchronization patterns")
        print("• Network topology determines information flow pathways")
        print("• Harmonic frequencies enhance resonant coupling")
        print("• Leader-follower dynamics create emergent swarm intelligence")
        print("• System energy decreases as structural pressure (ΔNFR) is resolved")
        print()

    except ImportError as e:
        print(f"❌ Matplotlib not available: {e}")
        print("📝 To enable visualizations: pip install matplotlib")
        print("🔬 Examples still demonstrate TNFR physics through console output")


if __name__ == "__main__":
    visualization_suite_demo()