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

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© 2026 TNFR project — MIT licensed.DOI 10.5281/zenodo.17602860
docs
grammar
PHYSICS_VERIFICATION.md
API_CONTRACTS.mdCANONICAL_OZ_SEQUENCES.mdEMPIRICAL_CONFRONTATION_EEG.mdREADME.mdSTRUCTURAL_FIELDS_TETRAD.mdSTRUCTURAL_INTERFACE_THEORY.md
theory
APPLIED_STRUCTURAL_ANALYSIS.mdCATALOG_TYPE_HYGIENE_PROGRAMME.mdDISSIPATIVE_AND_OPEN_SYSTEMS.mdEMERGENT_ONTOLOGY.mdEXTENDED_FIELDS_AND_DERIVED_QUANTITIES.mdFUNDAMENTAL_THEORY.mdGAUGE_SYMMETRY_AND_UNIFICATION.mdGLOSSARY.mdMATHEMATICAL_DYNAMICS_BASIS.mdMINIMAL_STRUCTURAL_DEGREES.mdNUCLEUS_A_PRIME_LADDER_ATLAS.mdNUCLEUS_B_EQUIVARIANCE_OBSTRUCTIONS.mdPHYSICAL_REGIME_CORRESPONDENCES.mdREADME.mdREMESH_INFINITY_DERIVATION.mdSTRUCTURAL_CONSERVATION_THEOREM.mdSTRUCTURAL_OPERATORS.mdSTRUCTURAL_STABILITY_AND_DYNAMICS.mdTNFR_BSD_RESEARCH_NOTES.mdTNFR_HODGE_RESEARCH_NOTES.mdTNFR_NAVIER_STOKES_RESEARCH_NOTES.mdTNFR_NUMBER_THEORY.mdTNFR_P_VS_NP_RESEARCH_NOTES.mdTNFR_RIEMANN_RESEARCH_NOTES.mdTNFR_VARIATIONAL_PRINCIPLE.mdTNFR_YANG_MILLS_RESEARCH_NOTES.mdTNFR.pdfUNIFIED_GRAMMAR_RULES.md
factorization-lab
analysis
analyze_patterns.pycertificate_manifest.py
benchmarks
benchmark_analysis.pybenchmark_expansion_suite.pyfull_spectrum_factorization.pypaley_gap_extended.pypaley_gap_smoke.pytest_benchmark_suite.py
demos
experiment_contexts
exp_0b1663cd19b7.jsonexp_0bf0054b7474.jsonexp_75a4c8ca616a.jsonexp_848ee0fd1857.jsonexp_f6fe00562193.jsonexp_fdf3da424e1e.json
failure_telemetry_batch.pyfeedback_integration_demo.pyintegration_demo_snapshots.dbseed_management_integration_demo.pysnapshot_integration_demo.pytrajectory_143.jsontrajectory_77.jsontrajectory_89.jsontrajectory_91.jsontrajectory_97.json
docs
FACTORING_PLAYBOOK.mdFALSE_POSITIVE_TEST_SUITE.mdOPERATOR_CERTIFICATES.mdROADMAP.mdSPECTRAL_ROUTE.md
experiment_contexts
exp_cebe1d9e7d8e.json
notebooks
spectral_history.ipynb
scripts
run_false_positive_tests.py
tests
run_false_positive_test_suite.pytest_cli.pytest_false_positive_methodology.pytest_false_positive_verifier.pytest_feedback_integration.pytest_partitioning.pytest_seed_management.pytest_self_opt_support.pytest_snapshot_system.pytest_spectral_paley.pytest_verification_robustness.py
tnfr_factorization
__init__.pyapi.pycli.pyfailure_telemetry.pyfeedback_adapter.pyfeedback_integration.pypartitioning.pyself_opt_support.pyspectral_paley.py
demo_snapshots.dbLICENSE_SNAPSHOT.mdPACKAGE_SUMMARY.mdREADME.mdseed_management.pysnapshot_system.pytest_certificate_hashing.pytest_installation.pyverification_trajectory_77.json
benchmarks
analyze_tetrad_universality.pyb0star_alpha_canonical_product_graphs.pybenchmark_optimization_tracks.pybenchmark_utils.pyboundary_vibration.pybridge_primes_riemann.pychiral_involution.pycli_utils.pycoherence_projector_sense_index.pycommutant_bridge.pycomposition_arithmetic.pyconfinement_zones_test.pyconservation_law_validation.pydirected_paley_bridge.pyemergent_arithmetic_pulse.pyemergent_atom_dynamics.pyemergent_atomic_shells.pyemergent_base_dimension.pyemergent_dimension_dynamics.pyemergent_fractal_pulse.pyemergent_fractal_simplex_dimension.pyemergent_integers_symmetry.pyemergent_musical_nfr.pyemergent_nfr_geometry.pyemergent_nfr_where.pyemergent_rationals.pyemergent_rhythm.pyemergent_screening.pyemergent_shell_cardinals.pyemergent_shell_ordering.pyemergent_simplex_dimension.pyemergent_substrate_symmetry.pyequivariance_wall.pyexternal_phase_gate_validation.pyfield_methods_battery.pygolden_residue_remesh_bridge.pyintegrated_force_regime_study.pyinverse_spectrum_to_symmetry.pyk_phi_safety_demo.pykuramoto_farey_bridge.pymissing_piece_bridge.pymultichannel_interface_benchmark.pynavier_stokes_recipe_bridge.pynodal_propagator_residue_bridge.pyns_moment_hierarchy_cascade.pyoperational_irreducibility.pypaley_bridge.pyphase_curvature_investigation.pyphase_wall.pyphi_s_confinement_investigation.pyprimes_as_consequence.pypulse_phase_coherence_budget.pyREADME.mdremesh_infinity_riemann_baseline.pyremesh_infinity_riemann_composed.pyremesh_infinity_riemann_modified_graph.pyremesh_infinity_riemann_operator.pyremesh_infinity_riemann_spectral_basis.pyremesh_infinity_riemann_spectral_robustness.pyremesh_infinity_riemann_spectral.pyresidue_phase_vs_riemann.pystructural_interface_benchmark.pytemporal_interface_benchmark.pytetrad_results_aggregate.pyu2_destabilization_irreversibility.pyuniversality_clusters.pyxi_c_fast_experiment.py
primality-test
benchmarks
comprehensive_benchmark.py
docs
ADVANCED_INTEGRATION.mdmathematical_foundation.mdperformance_analysis.md
examples
advanced_examples.pybasic_usage.py
tnfr_primality
__init__.py__main__.pyadvanced_cli.pyadvanced_core.pycli.pyconstants.pycore.pyoptimized.py
MANIFEST.inPACKAGE_SUMMARY.mdREADME.mdRELEASE_NOTES_v1.0.mdsetup.pytest_installation.py
tests
core_physics
__init__.pytest_conservation_laws.pytest_delta_nfr_computation_paths.pytest_delta_nfr.pytest_dispersion_coherence_sign_invariance.pytest_emergent_constants_guard.pytest_lyapunov_operators.pytest_nodal_equation.pytest_structural_triad.py
data
replay_manifests
sample_run
_manifest_summary.json_manifest.json_partition_files.txt.gz
self_opt_validation
seed_alpha
paley.json
seed_beta
integration.json
seed_gamma
unknown.json
self_optimization
test_run
partitioned
test_run
test_run_p0.jsontest_run_p1.json
_manifest_summary.json_manifest.json
engines
test_pattern_discovery_manifest.pytest_self_optimization_engine.py
mathematics
__init__.pytest_autodiff.pytest_backends.pytest_dissipative_dynamics.pytest_epi.pytest_factory_patterns.pytest_metrics.pytest_navier_stokes_refounded.pytest_number_theory_canonical.pytest_operators.pytest_residue_networks.pytest_riemann_nodal_pulse.pytest_riemann_pulse_coherence.pytest_spaces.pytest_transforms.pytest_validator.py
operators
test_canonical_operators_modern.pytest_grammar_canon.pytest_grammar_canonical_consistency.pytest_grammar_dynamics.pytest_operator_contracts.pytest_operator_strategies.py
parallel
test_fractal_partition_manifest.py
physics
test_conservation_gauge_unification.pytest_dissipative_conservation.pytest_emergent_chemistry.pytest_field_cache_invalidation.pytest_gauge.pytest_phase_transition.pytest_signatures.pytest_spectral_conservation.pytest_structural_diffusion.pytest_structural_integrity.pytest_symplectic_substrate.pytest_tetrad_bounds.pytest_variational.pytest_yang_mills_closure.pytest_yang_mills_derivability.pytest_yang_mills_scaling.pytest_yang_mills_structural_gap.pytest_yang_mills_u6_sweep.py
scripts
test_run_self_opt_validation.pytest_run_self_optimization.py
sdk
__init__.pytest_simple_advanced.py
__init__.pyconftest.pyREADME.mdtest_breast_cancer_phase_gate_demo.pytest_classical_mechanics.pytest_distributed_fft.pytest_external_phase_gate_validation.pytest_factorization_entrypoint.pytest_multichannel_interface.pytest_nodal_optimizer.pytest_phase_gate_api.pytest_replay_register_manifest.pytest_signal_confrontation.pytest_structural_interface_api.pytest_structural_interface_baselines.pytest_structural_interface_benchmark.pytest_temporal_interface.pytest_vectorized_coherence_length_regression.pytest_wine_quality_phase_gate_demo.pyutils.py
examples
01_foundations
01_hello_world.py02_musical_resonance.py03_network_formation.py04_operator_sequences.py05_coherence_evolution.py06_network_topologies.py07_phase_transitions.py08_emergent_phenomena.py09_visualization_suite.py10_simplified_sdk_showcase.py
02_physics_regimes
11_classical_limit_comparison.py115_operator_contract_audit.py12_classical_mechanics_demo.py13_quantum_mechanics_demo.py14_uncertainty_and_interference.py15_train_crossing_demo.py17_conservation_law_demo.py26_gauge_structure_demo.py27_variational_principle_demo.py28_dissipative_systems_demo.py29_lyapunov_stability_demo.py30_self_optimization_demo.py31_mathematical_constants_basis.py33_complex_field_unification.py34_conservation_protocol_suite.py35_tetrad_irreducibility.py36_grammar_violation_detector.py37_operator_tetrad_synergy.py38_grammar_energy_landscape.py39_nodal_equation_decomposition.py
03_riemann_zeta
157_nodal_pulse_phase_attack.py41_von_mangoldt_zeta_demo.py42_riemann_zeros_as_resonances.py43_prime_ladder_hamiltonian_demo.py44_weil_explicit_formula_demo.py45_li_keiper_demo.py46_weil_tnfr_positivity_demo.py47_alpha_sweep_demo.py48_admissible_family_sweep_demo.py49_nodeaware_gauge_sweep_demo.py50_uniform_coercivity_demo.py51_adaptive_coercivity_demo.py52_paley_gap_coercivity_demo.py53_lyapunov_spectral_positivity_demo.py54_hilbert_polya_demo.py55_structural_zero_density_demo.py56_spectral_emergence_demo.py57_admissible_rescaling_demo.py58_oscillatory_correction_demo.py
04_riemann_L_twisted
59_dirichlet_l_function_demo.py60_dirichlet_l_continuation_demo.py61_dirichlet_l_hamiltonian_demo.py62_dirichlet_weil_explicit_formula_demo.py63_dirichlet_li_keiper_demo.py64_twisted_weil_positivity_demo.py65_twisted_alpha_sweep_demo.py66_twisted_admissible_family_sweep_demo.py67_twisted_nodeaware_gauge_sweep_demo.py68_twisted_hermite_family_demo.py69_twisted_coercivity_uniform_demo.py70_twisted_paley_gap_coercivity_demo.py71_twisted_lyapunov_spectral_demo.py72_twisted_hilbert_polya_demo.py73_twisted_structural_zero_density_demo.py74_twisted_spectral_emergence_demo.py75_twisted_admissible_rescaling_demo.py76_twisted_oscillatory_correction_demo.py
05_type_hygiene
77_remesh_infinity_residue_split_demo.py78_nuf_type_signature_demo.py79_epi_type_signature_demo.py80_phi_type_signature_demo.py81_dnfr_type_signature_demo.py82_remesh_window_type_signature_demo.py83_delta_phi_max_type_signature_demo.py84_coupling_weights_type_signature_demo.py85_tetrad_closure_signature_demo.py86_currents_closure_signature_demo.py87_aggregates_closure_signature_demo.py88_urules_consistency_signature_demo.py89_operator_catalog_discipline_signature_demo.py
06_navier_stokes
158_navier_stokes_two_face_refounded.py
07_number_theory
100_prime_families_orbits.py101_numbers_as_coupled_network.py102_nodal_flow_primes_equilibria.py116_nuf_emergent_prime_visibility.py146_primality_grammatical_inertness.py147_numbers_as_free_monoid_words.py148_capacity_arm_carries_von_mangoldt.py149_p14_is_the_capacity_arm_operator.py153_structural_frequency_rank_cyclotomy.py40_arithmetic_number_theory.py94_generative_number_construction.py95_primes_from_spectral_waves.py96_spectral_vibration_of_coherence.py97_goldbach_additive_multiplicative.pyemergent_chemistry_particles_demo.py
08_emergent_geometry
103_emergent_substrate_meets_riemann.py106_per_node_polarization_geometry.py107_orthogonal_structure_emergent_geometry.py108_emergent_field_generating_structure.py112_structure_predicts_coherence_flow.py113_overdamped_projection_bridge.py114_substrate_conserved_quantities.py117_emergent_geometry_residue_graph.py118_emergent_vs_classical_operator.py119_phase_sector_directed_residue.py120_symmetry_wall_substrate_vs_spectrum.py121_canonical_symmetry_break_negative.py122_factorization_phase_sector.py123_symmetry_sector_decomposition.py124_emergent_metric_fractal_consistency.py125_node_is_the_emergent_substrate.py126_two_layers_base_fiber.py127_base_is_emergent_not_imposed.py128_base_substrate_coemergence.py129_spectral_gap_base_fiber_clock.py130_operators_break_substrate_charges.py131_coemergent_loop_convergence.py132_geometric_phase_holonomy.py133_psi_topological_defects.py134_spectral_dimension_heat_kernel.py135_arrow_of_time_h_theorem.py136_heat_kernel_coefficients.py137_synchronization_transition.py138_structure_frequency_synchronization.py139_grammar_formal_language.py140_grammar_automaton.py141_grammar_rule_decomposition.py142_grammar_operator_quotient.py143_glyphic_function_sublanguage.py144_branching_combinator.py145_syntactic_monoid_starfree.py150_emergent_grammatical_pattern_parry.py151_grammar_in_emergent_geometry.py152_operator_contract_tetrahedron.py154_conductor_annotated_qr_spectrum.py155_ontological_position_of_numbers.py156_emergence_directness_law.py98_emergent_symplectic_substrate.py99_structural_diffusion.pyunified_fields_showcase.py
09_millennium
109_p_vs_np_coherence_synthesis.py110_bsd_rank_structural_pressure.py111_hodge_discrete_and_honest_gap.py
10_applications
159_empirical_confrontation_pipeline.py90_phase_gate_monitor_demo.py91_breast_cancer_phase_gate_demo.py92_wine_quality_phase_gate_demo.py93_structural_interface_demo.pypytorch_cuda_demo.py
README.md
scripts
replay
__init__.pyregister_manifest.py
__init__.pyREADME.mdrebuild_failure_manifest.pyrun_reproducible_benchmarks.pyrun_self_opt_validation.pyrun_self_optimization.pytnfr_is_prime.pyvalidate_conservation_law.pyverify_internal_references.py
src
core
__init__.pyevaluation.py
tnfr
backends
__init__.pyjax_backend.pynumpy_backend.pyoptimized_numpy.pyREADME.mdtorch_backend.py
cli
__init__.py__init__.pyiarguments.pyarguments.pyiexecution.pyexecution.pyiinteractive_validator.pyREADME.mdutils.pyutils.pyi
compat
__init__.pydataclass.pyjsonschema_stub.pymatplotlib_stub.pynumpy_stub.pyREADME.md
config
__init__.py__init__.pyiconstants.pyconstants.pyidefaults_core.pydefaults_init.pydefaults_metric.pydefaults.pyfeature_flags.pyfeature_flags.pyiglyph_constants.pyoperator_names.pyoperator_names.pyiphysics_derivation.pyprecision_modes.pypresets.pypresets.pyiREADME.mdsecurity.pythresholds.pytnfr_config.py
constants
__init__.py__init__.pyialiases.pyaliases.pyicanonical.pymetric.pymetric.pyioperational.py
core
__init__.pycontainer.pydefault_implementations.pyexceptions.pyinterfaces.pyREADME.md
dynamics
__init__.py__init__.pyiadaptation.pyadaptation.pyiadaptive_sequences.pyadaptive_sequences.pyiadelic.pyadvanced_cache_optimizer.pyadvanced_fft_arithmetic.pyaliases.pyaliases.pyibifurcation.pycache_aware_fft_engine.pycanonical.pycanonical.pyicomputational_hub.pycoordination.pycoordination.pyidistributed_fft.pydnfr.pydnfr.pyidynamic_limits.pyemergent_centralization.pyemergent_integration_engine.pyfeedback.pyfeedback.pyifft_backend.pyfft_cache_coordinator.pyfft_dispatchers.pyfft_engine.pyfft_workers.pyfused_dnfr.pyhomeostasis.pyhomeostasis.pyiintegrators.pyintegrators.pyilearning.pylearning.pyimetabolism.pymulti_modal_cache.pynbody_tnfr.pynbody.pynodal_optimizer.pyoptimization_orchestrator.pypropagation.pyREADME.mdruntime.pyruntime.pyisampling.pysampling.pyiselectors.pyselectors.pyiself_optimizing_engine.pyspectral_structural_fusion.pystructural_cache.pystructural_clip.pysymplectic.pyunified_backend.pyunified_mathematical_cache_orchestrator.py
engines
computation
__init__.pyfft_engine.pyunified_fft_engine.pyunified_gpu_system.py
constants
__init__.pycanonical.pyoperational.py
integration
__init__.pyemergent_integration.py
pattern_discovery
__init__.pymathematical_patterns.pymulti_modal_cache.py
self_optimization
__init__.pyengine.py
__init__.pyREADME.md
errors
__init__.pycontextual.py
factorization
__init__.py
flatten
README.md
gamma
README.md
glyph_history
README.md
glyph_runtime
README.md
immutable
README.md
initialization
README.md
io
README.md
math
__init__.pyfields_symbolic.pygrammar_validators.pyoptimizer.pyREADME.mdsymbolic.py
mathematics
__init__.pybackend.pybackend.pyidynamics.pydynamics.pyiepi.pyepi.pyigenerators.pygenerators.pyiliouville.pymetrics.pymetrics.pyinumber_theory.pyoperators_factory.pyoperators_factory.pyioperators.pyoperators.pyioptimized_primality.pyprojection.pyprojection.pyiREADME.mdruntime.pyruntime.pyispaces.pyspaces.pyispectral.pytransforms.pytransforms.pyiunified_cache.pyunified_numerical.pyzeta.py
metrics
__init__.py__init__.pyibuffer_cache.pybuffer_cache.pyicache_utils.pycoherence.pycoherence.pyicommon.pycommon.pyicore.pycore.pyidiagnosis.pydiagnosis.pyiemergence.pyexport.pyexport.pyiglyph_timing.pyglyph_timing.pyilearning_metrics.pylearning_metrics.pyilocal_coherence.pyphase_coherence.pyphase_compatibility.pyREADME.mdreporting.pyreporting.pyisense_index.pysense_index.pyitelemetry.pytetrad.pytrig_cache.pytrig_cache.pyitrig.pytrig.pyi
multiscale
__init__.pyhierarchical.pyREADME.md
navier_stokes
__init__.pyconservative_face.pyoperator.py
node
README.md
observers
README.md
operators
network_analysis
__init__.pysource_detection.py
postconditions
__init__.pymutation.py
preconditions
__init__.pycoherence.pydissonance.pyemission.pymutation.pyreception.pyresonance.py
strategies
__init__.pydefaults.pygpu_strategies.pystrategy.py
__init__.py__init__.pyialgebra.pycanonical_patterns.pycascade.pycoherence.pycontraction.pycoupling.pycycle_detection.pydefinitions_base.pydefinitions.pydefinitions.pyidissonance.pyemission.pyexpansion.pygrammar_application.pygrammar_canon.pygrammar_context.pygrammar_core.pygrammar_dynamics.pygrammar_error_factory.pygrammar_memoization.pygrammar_patterns.pygrammar_telemetry.pygrammar_types.pygrammar_u6.pygrammar_validate.pygrammar.pygrammar.pyihamiltonian.pyhealth_analyzer.pyintrospection.pyjitter.pyjitter.pyilifecycle.pymetabolism.pymetrics_basic.pymetrics_core.pymetrics_network.pymetrics_structural.pymetrics_u6.pymetrics.pymutation.pynodal_equation.pyoperator_contracts.pypattern_detection.pypatterns.pyREADME.mdreception.pyrecursivity.pyregistry.pyregistry.pyiremesh.pyremesh.pyiresonance.pyself_organization.pysilence.pystructural_units.pytransition.py
parallel
__init__.pyauto_scaler.pydistributed.pyengine.pymonitoring.pypartitioner.pyREADME.md
performance
guardrails.py
physics
__init__.py_helpers.pycalibration.pycanonical.pycell.pyclassical_mechanics.pyconservation_gauge_unification.pyconservation.pydissipative_conservation.pyemergent_chemistry.pyemergent_particles.pyextended.pyfields.pygauge.pyintegrity.pyinteractions.pylife.pylyapunov.pypatterns.pyphase_transition.pyquantum_mechanics.pyREADME.mdsignatures.pyspectral_conservation.pyspectral_metrics.pystructural_diffusion.pysymplectic_substrate.pytelemetry.pyunified.pyvariational.pyvectorized_ops.py
primality
__init__.py
recipes
__init__.pycookbook.pyREADME.md
riemann
__init__.pyadmissible_family_sweep.pyadmissible_rescaling.pyaggregates_closure_signature.pyalpha_sweep.pyanalytic_continuation_dirichlet.pyanalytic_continuation.pycoercivity_uniform.pycoupling_weights_type_signature.pycurrents_closure_signature.pydelta_phi_max_type_signature.pydirichlet_l.pydnfr_type_signature.pyepi_type_signature.pyhilbert_polya.pyli_keiper.pylyapunov_spectral_positivity.pynodal_pulse.pynodeaware_gauge_sweep.pynuf_type_signature.pyoperator_catalog_discipline_signature.pyoperator.pyoscillatory_correction.pypaley_gap_coercivity.pyphi_type_signature.pyprime_ladder_hamiltonian.pypulse_coherence.pyremesh_infinity_residue_split.pyremesh_window_type_signature.pyspectral_emergence.pystructural_zero_density.pytelemetry.pytetrad_closure_signature.pytwisted_admissible_family_sweep.pytwisted_admissible_rescaling.pytwisted_alpha_sweep.pytwisted_coercivity_uniform.pytwisted_hermite_family.pytwisted_hilbert_polya.pytwisted_li_keiper.pytwisted_lyapunov_spectral_positivity.pytwisted_nodeaware_gauge_sweep.pytwisted_oscillatory_correction.pytwisted_paley_gap_coercivity.pytwisted_prime_ladder_hamiltonian.pytwisted_spectral_emergence.pytwisted_structural_zero_density.pytwisted_weil_explicit_formula.pytwisted_weil_positivity.pyurules_consistency_signature.pyvon_mangoldt.pyweil_explicit_formula.pyweil_positivity.py
schemas
__init__.pygrammar.jsonREADME.md
sdk
__init__.py__init__.pyiadaptive_system.pyadaptive_system.pyibuilders.pybuilders.pyifluent.pyfluent.pyiREADME.mdself_opt.pysimple.pytemplates.pytemplates.pyiutils.py
security
__init__.pycrypto.pydatabase.pyREADME.mdsubprocess.pyvalidation.py
sequencing
__init__.pypatterns.pyREADME.md
services
__init__.pyorchestrator.pyREADME.md
sparse
__init__.pyREADME.mdrepresentations.py
structural
README.md
telemetry
__init__.pycache_metrics.pycache_metrics.pyiconstants.pynu_f.pynu_f.pyiREADME.mdunified_telemetry_system.pyverbosity.pyverbosity.pyi
tools
__init__.pydomain_templates.pyREADME.mdsequence_generator.pytnfr_is_prime_cli_optimized.pytnfr_is_prime_cli.py
topology
__init__.pyasymmetry.pyREADME.md
utils
cache_layers.pycache.pycache.pyicallbacks.pycallbacks.pyichunks.pychunks.pyidata.pydata.pyifast_diameter.pygraph.pygraph.pyiinit.pyinit.pyiio.pyio.pyinumeric.pynumeric.pyiREADME.mdtopology.pyunified_cache.py
validation
__init__.py__init__.pyiaggregator.pybase.pycompatibility.pycompatibility.pyiconfig.pygraph.pygraph.pyihealth.pyinput_validation.pyinterface_baselines.pyinvariants.pymultichannel_interface.pyphase_gate.pyREADME.mdrules.pyrules.pyiruntime.pyruntime.pyisequence_validator.pysignal_confrontation.pysoft_filters.pysoft_filters.pyispectral.pyspectral.pyistructural_interface.pytemporal_interface.pyunified_validation_system.pyvalidator.pywindow.pywindow.pyi
visualization
__init__.pycascade_viz.pyhierarchy.pyREADME.mdsequence_plotter.py
yang_mills
__init__.pyclosure.pyderivability.pyscaling.pystructural_gap.pyu6_sweep.py
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tetrad_evaluator.py
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FILE: src/tnfr/sdk/README.md

README.md

🌊 TNFR SDK - Simplified & Powerful API ⭐ OPTIMIZED

The TNFR SDK provides an intuitive, production-ready interface for creating, evolving, and analyzing Resonant Fractal Networks with complete theoretical fidelity. 90% less code, 100% of the power.

🚀 Quick Start (New API)

python
from tnfr.sdk import TNFR

# One-line network creation and evolution
results = TNFR.create(20).random(0.3).evolve(5).results()
print(f'Coherence: {results.coherence:.3f}')

# Template-based approach
molecule = TNFR.template('molecule').auto_optimize()
print(molecule.summary())

# Ultra-compact with alias
from tnfr.sdk import T
net = T.create(10).complete().evolve(3)

PHILOSOPHY: Maximum power, minimum complexity.

📚 Core API (Simplified)

TNFR - Static Factory

Instant network creation with zero boilerplate:

python
from tnfr.sdk import TNFR

# Topology builders (chainable)
ring = TNFR.create(10).ring()              # Ring topology
star = TNFR.create(15).star()              # Star topology  
random = TNFR.create(20).random(0.3)       # Random connections
complete = TNFR.create(6).complete()       # All-to-all

# Templates for common patterns
molecule = TNFR.template('molecule')       # Molecular structure
small_net = TNFR.template('small')         # 5-node ring
large_net = TNFR.template('large')         # 50-node random

# Evolution and optimization
net.evolve(5)                              # TNFR dynamics
net.auto_optimize()                        # Self-optimization

# Metrics and analysis
result = net.results()                     # All metrics
coherence = net.coherence()                # Just coherence
summary = net.summary()                    # One-line overview

Power User Shortcuts

python
from tnfr.sdk import T  # Ultra-short alias

# Everything in one line
result = T.create(8).complete().evolve(2).results()

# Quick checks
if net.results().is_coherent():
    print("✅ Network is stable!")

# Comparison
comparison = TNFR.compare(net1, net2, net3)
print(f"Winner: {comparison['best']['name']}")7.5% reduction |
| **Learning Curve** | Steep | Gentle | Intuitive methods |
| **Import Complexity** | Multiple imports | Single import | Simplified |
| **Readability** | Technical | Natural English | Self-documenting |
| **Power** | Full TNFR | Full TNFR | No loss |
| **Performance** | Same | Same | Maintained |

## 🔄 Migration Guide

**OLD WAY (Complex):**
```python
from tnfr.sdk import TNFRNetwork

network = TNFRNetwork("test")
network.add_nodes(20, vf_range=(0.5, 2.0))
network.connect_nodes(0.3, "small_world")
network.apply_sequence("basic_activation", repeat=3)
results = network.measure()

NEW WAY (Simple):

python
from tnfr.sdk import TNFR

results = TNFR.create(20).random(0.3).evolve(3).results()

Backward Compatibility: Old API still works! New code should use TNFR class. print(f"Density: {network.get_density():.3f}") print(f"Avg degree: {network.get_average_degree():.2f}")

Clone network

cloned = network.clone()

Export data

data = network.export_to_dict()

Reset

network.reset()

text

### Advanced Examples

```python
# Molecular simulation
molecule = (TNFR.template('molecule')
           .evolve(10)
           .auto_optimize())
           
if molecule.results().is_stable():
    print("Molecule is stable!")

# Social network analysis
social_nets = {
    'family': TNFR.create(6).complete(),
    'friends': TNFR.create(15).ring().random(0.2),
    'community': TNFR.create(50).random(0.1)
}

for name, net in social_nets.items():
    evolved = net.evolve(5)
    print(f"{name}: {evolved.summary()}")

# Network comparison
comparison = TNFR.compare(*social_nets.values())
print(f"Most coherent: {comparison['best']['name']}")

Legacy API (TNFRTemplates)

For backward compatibility, the old API is still available:

TNFRTemplates - Domain-Specific Patterns

Pre-configured templates for common use cases:

python
from tnfr.sdk import TNFRTemplates

# Social network dynamics
social_results = TNFRTemplates.social_network_simulation(
    people=50,
    connections_per_person=6,
    simulation_steps=20,
    random_seed=42
)

# Neural network modeling
neural_results = TNFRTemplates.neural_network_model(
    neurons=100,
    connectivity=0.15,
    activation_cycles=30
)

# Ecosystem dynamics
ecosystem_results = TNFRTemplates.ecosystem_dynamics(
    species=25,
    evolution_steps=50
)

# Creative process modeling
creative_results = TNFRTemplates.creative_process_model(
    ideas=15,
    development_cycles=12
)

# Organizational networks
org_results = TNFRTemplates.organizational_network(
    agents=40,
    coordination_steps=25
)

TNFRExperimentBuilder - Research Patterns

Builder patterns for standard experiments:

python
from tnfr.sdk import TNFRExperimentBuilder

# Small-world network study
sw_results = TNFRExperimentBuilder.small_world_study(
    nodes=50,
    rewiring_prob=0.1,
    steps=10
)

# Synchronization analysis
sync_results = TNFRExperimentBuilder.synchronization_study(
    nodes=30,
    coupling_strength=0.5,
    steps=20
)

# Topology comparison
comparison = TNFRExperimentBuilder.compare_topologies(
    node_count=40,
    steps=10
)
for topology, results in comparison.items():
    print(f"{topology}: C(t) = {results.coherence:.3f}")

# Phase transition study
transition = TNFRExperimentBuilder.phase_transition_study(
    nodes=50,
    coupling_levels=5
)

# Resilience testing
resilience = TNFRExperimentBuilder.resilience_study(
    nodes=40,
    initial_steps=10,
    perturbation_steps=5,
    recovery_steps=10
)

Utility Functions

Analysis and Comparison

python
from tnfr.sdk import (
    compare_networks,
    compute_network_statistics,
    format_comparison_table,
)

# Create multiple networks
results1 = TNFRNetwork("net1").add_nodes(20).connect_nodes(0.3).measure()
results2 = TNFRNetwork("net2").add_nodes(20).connect_nodes(0.5).measure()

# Compare
comparison = compare_networks({"net1": results1, "net2": results2})
print(format_comparison_table(comparison))

# Extended statistics
stats = compute_network_statistics(results1)
print(f"Coherence: {stats['coherence']:.3f}")
print(f"Avg Si: {stats['avg_si']:.3f} ± {stats['std_si']:.3f}")
print(f"Range: [{stats['min_si']:.3f}, {stats['max_si']:.3f}]")

JSON Export/Import

python
from tnfr.sdk import export_to_json, import_from_json

# Export network
network = TNFRNetwork("test").add_nodes(10).connect_nodes(0.3)
export_to_json(network, "network.json")

# Import data
data = import_from_json("network.json")
print(f"Loaded: {data['name']} with {data['metadata']['nodes']} nodes")

Goal-Based Sequence Suggestions

python
from tnfr.sdk import suggest_sequence_for_goal

# Get recommendations
seq, desc = suggest_sequence_for_goal("stabilize")
print(f"Goal: stabilize")
print(f"Sequence: {seq}")
print(f"Description: {desc}")

# Use directly
network = TNFRNetwork().add_nodes(15).connect_nodes(0.3)
network.apply_sequence(seq, repeat=5)

Predefined Operator Sequences

All sequences follow TNFR grammar rules and maintain canonical invariants:


Theory ↔ SDK Cross-References

Each SDK feature derives from specific theoretical foundations:

SDK MethodPhysicsTheory Document
TNFR.create(n).ring()Network topology, nodal equationFUNDAMENTAL_THEORY.md
.tetrad() → TetradSnapshotΦ_s, |∇φ|, K_φ, ξ_CEXTENDED_FIELDS_AND_DERIVED_QUANTITIES.md
.conservation() → ConservationReportNoether charge, Lyapunov stabilitySTRUCTURAL_CONSERVATION_THEOREM.md
.evolve_grammar_aware(steps)U1–U6 proactive enforcementUNIFIED_GRAMMAR_RULES.md
.integrity_check() → IntegrityReport13/13 operator postconditionsSTRUCTURAL_STABILITY_AND_DYNAMICS.md
.tensor_invariants()Energy density ℰ, topological charge 𝒬EXTENDED_FIELDS_AND_DERIVED_QUANTITIES.md
.emergent_fields()Chirality χ, symmetry breaking 𝒮EXTENDED_FIELDS_AND_DERIVED_QUANTITIES.md
.telemetry()C(t), Si, phase, νfFUNDAMENTAL_THEORY.md
.auto_optimize()Gradient descent on structural manifoldAGENTS.md § Self-Optimizing Dynamics
TNFR.analyze(net)Comprehensive structural analysisAPPLIED_STRUCTURAL_ANALYSIS.md

Related Documentation

  • Theory hub: theory/README.md — all 12 theory documents with SDK pointers

  • Examples: examples/README.md — 30+ executable demonstrations with SDK links

  • Primary reference: AGENTS.md — complete TNFR theoretical framework

  • Glossary: theory/GLOSSARY.md — canonical terminology definitions

  • basic_activation: [emission, reception, coherence, resonance, silence]

    • Initiates network with fundamental operators
  • stabilization: [emission, reception, coherence, resonance, recursivity]

    • Establishes and maintains coherent structure
  • creative_mutation: [emission, dissonance, reception, coherence, mutation, resonance, silence]

    • Generates variation through controlled mutation
  • network_sync: [emission, reception, coherence, coupling, resonance, silence]

    • Synchronizes nodes through coupling
  • exploration: [emission, dissonance, reception, coherence, resonance, transition]

    • Explores phase space with transitions
  • consolidation: [recursivity, reception, coherence, resonance, silence]

    • Consolidates structure with recursive coherence

Network Results

The NetworkResults dataclass provides structured access to metrics:

python
results = network.measure()

# Direct access
print(f"Coherence: {results.coherence}")
print(f"Avg νf: {results.avg_vf} Hz_str")
print(f"Avg Phase: {results.avg_phase} rad")

# Node-level metrics
for node_id, si in results.sense_indices.items():
    print(f"{node_id}: Si = {si:.3f}")

# Convert to dict
data = results.to_dict()

# Human-readable summary
print(results.summary())

TNFR Compliance

All SDK components maintain full TNFR theoretical fidelity:

  • Structural Invariants: Preserved through validated operator sequences
  • Frequency Bounds: All νf values ≤ 1.0 Hz_str (structural hertz)
  • Operator Grammar: Sequences follow canonical TNFR rules
  • Metric Exposure: C(t), Si, νf, phase exposed without abstraction loss
  • Nodal Equation: ∂EPI/∂t = νf · ΔNFR(t) respected in all operations

Type Safety

Type stubs (.pyi files) are provided for better IDE support:

python
from tnfr.sdk import TNFRNetwork, NetworkResults

# Full type hints and autocomplete
network: TNFRNetwork = TNFRNetwork("typed")
results: NetworkResults = network.add_nodes(10).measure()

Examples

See examples/sdk_example.py for comprehensive usage demonstrations.

Testing

All SDK components are thoroughly tested:

bash
pytest tests/unit/sdk/ -v

Documentation

For detailed documentation on TNFR theory and canonical implementation:

  • See AGENTS.md for TNFR fundamentals
  • See tnfr.pdf for complete theoretical framework
  • See ARCHITECTURE.md for system architecture and SDK integration

Contributing

When extending the SDK, maintain TNFR canonicity:

  1. Validate all operator sequences against TNFR grammar
  2. Respect structural frequency bounds (νf ≤ 1.0 Hz_str)
  3. Preserve nodal equation semantics
  4. Expose canonical metrics without abstraction
  5. Add tests for new functionality

License

See repository LICENSE file.