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

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© 2026 TNFR project — MIT licensed.DOI 10.5281/zenodo.17602860
docs
grammar
PHYSICS_VERIFICATION.md
API_CONTRACTS.mdCANONICAL_OZ_SEQUENCES.mdEMPIRICAL_CONFRONTATION_EEG.mdREADME.mdSTRUCTURAL_FIELDS_TETRAD.mdSTRUCTURAL_INTERFACE_THEORY.md
theory
APPLIED_STRUCTURAL_ANALYSIS.mdCATALOG_TYPE_HYGIENE_PROGRAMME.mdDISSIPATIVE_AND_OPEN_SYSTEMS.mdEMERGENT_ONTOLOGY.mdEXTENDED_FIELDS_AND_DERIVED_QUANTITIES.mdFUNDAMENTAL_THEORY.mdGAUGE_SYMMETRY_AND_UNIFICATION.mdGLOSSARY.mdMATHEMATICAL_DYNAMICS_BASIS.mdMINIMAL_STRUCTURAL_DEGREES.mdNUCLEUS_A_PRIME_LADDER_ATLAS.mdNUCLEUS_B_EQUIVARIANCE_OBSTRUCTIONS.mdPHYSICAL_REGIME_CORRESPONDENCES.mdREADME.mdREMESH_INFINITY_DERIVATION.mdSTRUCTURAL_CONSERVATION_THEOREM.mdSTRUCTURAL_OPERATORS.mdSTRUCTURAL_STABILITY_AND_DYNAMICS.mdTNFR_BSD_RESEARCH_NOTES.mdTNFR_HODGE_RESEARCH_NOTES.mdTNFR_NAVIER_STOKES_RESEARCH_NOTES.mdTNFR_NUMBER_THEORY.mdTNFR_P_VS_NP_RESEARCH_NOTES.mdTNFR_RIEMANN_RESEARCH_NOTES.mdTNFR_VARIATIONAL_PRINCIPLE.mdTNFR_YANG_MILLS_RESEARCH_NOTES.mdTNFR.pdfUNIFIED_GRAMMAR_RULES.md
factorization-lab
analysis
analyze_patterns.pycertificate_manifest.py
benchmarks
benchmark_analysis.pybenchmark_expansion_suite.pyfull_spectrum_factorization.pypaley_gap_extended.pypaley_gap_smoke.pytest_benchmark_suite.py
demos
experiment_contexts
exp_0b1663cd19b7.jsonexp_0bf0054b7474.jsonexp_75a4c8ca616a.jsonexp_848ee0fd1857.jsonexp_f6fe00562193.jsonexp_fdf3da424e1e.json
failure_telemetry_batch.pyfeedback_integration_demo.pyintegration_demo_snapshots.dbseed_management_integration_demo.pysnapshot_integration_demo.pytrajectory_143.jsontrajectory_77.jsontrajectory_89.jsontrajectory_91.jsontrajectory_97.json
docs
FACTORING_PLAYBOOK.mdFALSE_POSITIVE_TEST_SUITE.mdOPERATOR_CERTIFICATES.mdROADMAP.mdSPECTRAL_ROUTE.md
experiment_contexts
exp_cebe1d9e7d8e.json
notebooks
spectral_history.ipynb
scripts
run_false_positive_tests.py
tests
run_false_positive_test_suite.pytest_cli.pytest_false_positive_methodology.pytest_false_positive_verifier.pytest_feedback_integration.pytest_partitioning.pytest_seed_management.pytest_self_opt_support.pytest_snapshot_system.pytest_spectral_paley.pytest_verification_robustness.py
tnfr_factorization
__init__.pyapi.pycli.pyfailure_telemetry.pyfeedback_adapter.pyfeedback_integration.pypartitioning.pyself_opt_support.pyspectral_paley.py
demo_snapshots.dbLICENSE_SNAPSHOT.mdPACKAGE_SUMMARY.mdREADME.mdseed_management.pysnapshot_system.pytest_certificate_hashing.pytest_installation.pyverification_trajectory_77.json
benchmarks
analyze_tetrad_universality.pyb0star_alpha_canonical_product_graphs.pybenchmark_optimization_tracks.pybenchmark_utils.pyboundary_vibration.pybridge_primes_riemann.pychiral_involution.pycli_utils.pycoherence_projector_sense_index.pycommutant_bridge.pycomposition_arithmetic.pyconfinement_zones_test.pyconservation_law_validation.pydirected_paley_bridge.pyemergent_arithmetic_pulse.pyemergent_atom_dynamics.pyemergent_atomic_shells.pyemergent_base_dimension.pyemergent_dimension_dynamics.pyemergent_fractal_pulse.pyemergent_fractal_simplex_dimension.pyemergent_integers_symmetry.pyemergent_musical_nfr.pyemergent_nfr_geometry.pyemergent_nfr_where.pyemergent_rationals.pyemergent_rhythm.pyemergent_screening.pyemergent_shell_cardinals.pyemergent_shell_ordering.pyemergent_simplex_dimension.pyemergent_substrate_symmetry.pyequivariance_wall.pyexternal_phase_gate_validation.pyfield_methods_battery.pygolden_residue_remesh_bridge.pyintegrated_force_regime_study.pyinverse_spectrum_to_symmetry.pyk_phi_safety_demo.pykuramoto_farey_bridge.pymissing_piece_bridge.pymultichannel_interface_benchmark.pynavier_stokes_recipe_bridge.pynodal_propagator_residue_bridge.pyns_moment_hierarchy_cascade.pyoperational_irreducibility.pypaley_bridge.pyphase_curvature_investigation.pyphase_wall.pyphi_s_confinement_investigation.pyprimes_as_consequence.pypulse_phase_coherence_budget.pyREADME.mdremesh_infinity_riemann_baseline.pyremesh_infinity_riemann_composed.pyremesh_infinity_riemann_modified_graph.pyremesh_infinity_riemann_operator.pyremesh_infinity_riemann_spectral_basis.pyremesh_infinity_riemann_spectral_robustness.pyremesh_infinity_riemann_spectral.pyresidue_phase_vs_riemann.pystructural_interface_benchmark.pytemporal_interface_benchmark.pytetrad_results_aggregate.pyu2_destabilization_irreversibility.pyuniversality_clusters.pyxi_c_fast_experiment.py
primality-test
benchmarks
comprehensive_benchmark.py
docs
ADVANCED_INTEGRATION.mdmathematical_foundation.mdperformance_analysis.md
examples
advanced_examples.pybasic_usage.py
tnfr_primality
__init__.py__main__.pyadvanced_cli.pyadvanced_core.pycli.pyconstants.pycore.pyoptimized.py
MANIFEST.inPACKAGE_SUMMARY.mdREADME.mdRELEASE_NOTES_v1.0.mdsetup.pytest_installation.py
tests
core_physics
__init__.pytest_conservation_laws.pytest_delta_nfr_computation_paths.pytest_delta_nfr.pytest_dispersion_coherence_sign_invariance.pytest_emergent_constants_guard.pytest_lyapunov_operators.pytest_nodal_equation.pytest_structural_triad.py
data
replay_manifests
sample_run
_manifest_summary.json_manifest.json_partition_files.txt.gz
self_opt_validation
seed_alpha
paley.json
seed_beta
integration.json
seed_gamma
unknown.json
self_optimization
test_run
partitioned
test_run
test_run_p0.jsontest_run_p1.json
_manifest_summary.json_manifest.json
engines
test_pattern_discovery_manifest.pytest_self_optimization_engine.py
mathematics
__init__.pytest_autodiff.pytest_backends.pytest_dissipative_dynamics.pytest_epi.pytest_factory_patterns.pytest_metrics.pytest_navier_stokes_refounded.pytest_number_theory_canonical.pytest_operators.pytest_residue_networks.pytest_riemann_nodal_pulse.pytest_riemann_pulse_coherence.pytest_spaces.pytest_transforms.pytest_validator.py
operators
test_canonical_operators_modern.pytest_grammar_canon.pytest_grammar_canonical_consistency.pytest_grammar_dynamics.pytest_operator_contracts.pytest_operator_strategies.py
parallel
test_fractal_partition_manifest.py
physics
test_conservation_gauge_unification.pytest_dissipative_conservation.pytest_emergent_chemistry.pytest_field_cache_invalidation.pytest_gauge.pytest_phase_transition.pytest_signatures.pytest_spectral_conservation.pytest_structural_diffusion.pytest_structural_integrity.pytest_symplectic_substrate.pytest_tetrad_bounds.pytest_variational.pytest_yang_mills_closure.pytest_yang_mills_derivability.pytest_yang_mills_scaling.pytest_yang_mills_structural_gap.pytest_yang_mills_u6_sweep.py
scripts
test_run_self_opt_validation.pytest_run_self_optimization.py
sdk
__init__.pytest_simple_advanced.py
__init__.pyconftest.pyREADME.mdtest_breast_cancer_phase_gate_demo.pytest_classical_mechanics.pytest_distributed_fft.pytest_external_phase_gate_validation.pytest_factorization_entrypoint.pytest_multichannel_interface.pytest_nodal_optimizer.pytest_phase_gate_api.pytest_replay_register_manifest.pytest_signal_confrontation.pytest_structural_interface_api.pytest_structural_interface_baselines.pytest_structural_interface_benchmark.pytest_temporal_interface.pytest_vectorized_coherence_length_regression.pytest_wine_quality_phase_gate_demo.pyutils.py
examples
01_foundations
01_hello_world.py02_musical_resonance.py03_network_formation.py04_operator_sequences.py05_coherence_evolution.py06_network_topologies.py07_phase_transitions.py08_emergent_phenomena.py09_visualization_suite.py10_simplified_sdk_showcase.py
02_physics_regimes
11_classical_limit_comparison.py115_operator_contract_audit.py12_classical_mechanics_demo.py13_quantum_mechanics_demo.py14_uncertainty_and_interference.py15_train_crossing_demo.py17_conservation_law_demo.py26_gauge_structure_demo.py27_variational_principle_demo.py28_dissipative_systems_demo.py29_lyapunov_stability_demo.py30_self_optimization_demo.py31_mathematical_constants_basis.py33_complex_field_unification.py34_conservation_protocol_suite.py35_tetrad_irreducibility.py36_grammar_violation_detector.py37_operator_tetrad_synergy.py38_grammar_energy_landscape.py39_nodal_equation_decomposition.py
03_riemann_zeta
157_nodal_pulse_phase_attack.py41_von_mangoldt_zeta_demo.py42_riemann_zeros_as_resonances.py43_prime_ladder_hamiltonian_demo.py44_weil_explicit_formula_demo.py45_li_keiper_demo.py46_weil_tnfr_positivity_demo.py47_alpha_sweep_demo.py48_admissible_family_sweep_demo.py49_nodeaware_gauge_sweep_demo.py50_uniform_coercivity_demo.py51_adaptive_coercivity_demo.py52_paley_gap_coercivity_demo.py53_lyapunov_spectral_positivity_demo.py54_hilbert_polya_demo.py55_structural_zero_density_demo.py56_spectral_emergence_demo.py57_admissible_rescaling_demo.py58_oscillatory_correction_demo.py
04_riemann_L_twisted
59_dirichlet_l_function_demo.py60_dirichlet_l_continuation_demo.py61_dirichlet_l_hamiltonian_demo.py62_dirichlet_weil_explicit_formula_demo.py63_dirichlet_li_keiper_demo.py64_twisted_weil_positivity_demo.py65_twisted_alpha_sweep_demo.py66_twisted_admissible_family_sweep_demo.py67_twisted_nodeaware_gauge_sweep_demo.py68_twisted_hermite_family_demo.py69_twisted_coercivity_uniform_demo.py70_twisted_paley_gap_coercivity_demo.py71_twisted_lyapunov_spectral_demo.py72_twisted_hilbert_polya_demo.py73_twisted_structural_zero_density_demo.py74_twisted_spectral_emergence_demo.py75_twisted_admissible_rescaling_demo.py76_twisted_oscillatory_correction_demo.py
05_type_hygiene
77_remesh_infinity_residue_split_demo.py78_nuf_type_signature_demo.py79_epi_type_signature_demo.py80_phi_type_signature_demo.py81_dnfr_type_signature_demo.py82_remesh_window_type_signature_demo.py83_delta_phi_max_type_signature_demo.py84_coupling_weights_type_signature_demo.py85_tetrad_closure_signature_demo.py86_currents_closure_signature_demo.py87_aggregates_closure_signature_demo.py88_urules_consistency_signature_demo.py89_operator_catalog_discipline_signature_demo.py
06_navier_stokes
158_navier_stokes_two_face_refounded.py
07_number_theory
100_prime_families_orbits.py101_numbers_as_coupled_network.py102_nodal_flow_primes_equilibria.py116_nuf_emergent_prime_visibility.py146_primality_grammatical_inertness.py147_numbers_as_free_monoid_words.py148_capacity_arm_carries_von_mangoldt.py149_p14_is_the_capacity_arm_operator.py153_structural_frequency_rank_cyclotomy.py40_arithmetic_number_theory.py94_generative_number_construction.py95_primes_from_spectral_waves.py96_spectral_vibration_of_coherence.py97_goldbach_additive_multiplicative.pyemergent_chemistry_particles_demo.py
08_emergent_geometry
103_emergent_substrate_meets_riemann.py106_per_node_polarization_geometry.py107_orthogonal_structure_emergent_geometry.py108_emergent_field_generating_structure.py112_structure_predicts_coherence_flow.py113_overdamped_projection_bridge.py114_substrate_conserved_quantities.py117_emergent_geometry_residue_graph.py118_emergent_vs_classical_operator.py119_phase_sector_directed_residue.py120_symmetry_wall_substrate_vs_spectrum.py121_canonical_symmetry_break_negative.py122_factorization_phase_sector.py123_symmetry_sector_decomposition.py124_emergent_metric_fractal_consistency.py125_node_is_the_emergent_substrate.py126_two_layers_base_fiber.py127_base_is_emergent_not_imposed.py128_base_substrate_coemergence.py129_spectral_gap_base_fiber_clock.py130_operators_break_substrate_charges.py131_coemergent_loop_convergence.py132_geometric_phase_holonomy.py133_psi_topological_defects.py134_spectral_dimension_heat_kernel.py135_arrow_of_time_h_theorem.py136_heat_kernel_coefficients.py137_synchronization_transition.py138_structure_frequency_synchronization.py139_grammar_formal_language.py140_grammar_automaton.py141_grammar_rule_decomposition.py142_grammar_operator_quotient.py143_glyphic_function_sublanguage.py144_branching_combinator.py145_syntactic_monoid_starfree.py150_emergent_grammatical_pattern_parry.py151_grammar_in_emergent_geometry.py152_operator_contract_tetrahedron.py154_conductor_annotated_qr_spectrum.py155_ontological_position_of_numbers.py156_emergence_directness_law.py98_emergent_symplectic_substrate.py99_structural_diffusion.pyunified_fields_showcase.py
09_millennium
109_p_vs_np_coherence_synthesis.py110_bsd_rank_structural_pressure.py111_hodge_discrete_and_honest_gap.py
10_applications
159_empirical_confrontation_pipeline.py90_phase_gate_monitor_demo.py91_breast_cancer_phase_gate_demo.py92_wine_quality_phase_gate_demo.py93_structural_interface_demo.pypytorch_cuda_demo.py
README.md
scripts
replay
__init__.pyregister_manifest.py
__init__.pyREADME.mdrebuild_failure_manifest.pyrun_reproducible_benchmarks.pyrun_self_opt_validation.pyrun_self_optimization.pytnfr_is_prime.pyvalidate_conservation_law.pyverify_internal_references.py
src
core
__init__.pyevaluation.py
tnfr
backends
__init__.pyjax_backend.pynumpy_backend.pyoptimized_numpy.pyREADME.mdtorch_backend.py
cli
__init__.py__init__.pyiarguments.pyarguments.pyiexecution.pyexecution.pyiinteractive_validator.pyREADME.mdutils.pyutils.pyi
compat
__init__.pydataclass.pyjsonschema_stub.pymatplotlib_stub.pynumpy_stub.pyREADME.md
config
__init__.py__init__.pyiconstants.pyconstants.pyidefaults_core.pydefaults_init.pydefaults_metric.pydefaults.pyfeature_flags.pyfeature_flags.pyiglyph_constants.pyoperator_names.pyoperator_names.pyiphysics_derivation.pyprecision_modes.pypresets.pypresets.pyiREADME.mdsecurity.pythresholds.pytnfr_config.py
constants
__init__.py__init__.pyialiases.pyaliases.pyicanonical.pymetric.pymetric.pyioperational.py
core
__init__.pycontainer.pydefault_implementations.pyexceptions.pyinterfaces.pyREADME.md
dynamics
__init__.py__init__.pyiadaptation.pyadaptation.pyiadaptive_sequences.pyadaptive_sequences.pyiadelic.pyadvanced_cache_optimizer.pyadvanced_fft_arithmetic.pyaliases.pyaliases.pyibifurcation.pycache_aware_fft_engine.pycanonical.pycanonical.pyicomputational_hub.pycoordination.pycoordination.pyidistributed_fft.pydnfr.pydnfr.pyidynamic_limits.pyemergent_centralization.pyemergent_integration_engine.pyfeedback.pyfeedback.pyifft_backend.pyfft_cache_coordinator.pyfft_dispatchers.pyfft_engine.pyfft_workers.pyfused_dnfr.pyhomeostasis.pyhomeostasis.pyiintegrators.pyintegrators.pyilearning.pylearning.pyimetabolism.pymulti_modal_cache.pynbody_tnfr.pynbody.pynodal_optimizer.pyoptimization_orchestrator.pypropagation.pyREADME.mdruntime.pyruntime.pyisampling.pysampling.pyiselectors.pyselectors.pyiself_optimizing_engine.pyspectral_structural_fusion.pystructural_cache.pystructural_clip.pysymplectic.pyunified_backend.pyunified_mathematical_cache_orchestrator.py
engines
computation
__init__.pyfft_engine.pyunified_fft_engine.pyunified_gpu_system.py
constants
__init__.pycanonical.pyoperational.py
integration
__init__.pyemergent_integration.py
pattern_discovery
__init__.pymathematical_patterns.pymulti_modal_cache.py
self_optimization
__init__.pyengine.py
__init__.pyREADME.md
errors
__init__.pycontextual.py
factorization
__init__.py
flatten
README.md
gamma
README.md
glyph_history
README.md
glyph_runtime
README.md
immutable
README.md
initialization
README.md
io
README.md
math
__init__.pyfields_symbolic.pygrammar_validators.pyoptimizer.pyREADME.mdsymbolic.py
mathematics
__init__.pybackend.pybackend.pyidynamics.pydynamics.pyiepi.pyepi.pyigenerators.pygenerators.pyiliouville.pymetrics.pymetrics.pyinumber_theory.pyoperators_factory.pyoperators_factory.pyioperators.pyoperators.pyioptimized_primality.pyprojection.pyprojection.pyiREADME.mdruntime.pyruntime.pyispaces.pyspaces.pyispectral.pytransforms.pytransforms.pyiunified_cache.pyunified_numerical.pyzeta.py
metrics
__init__.py__init__.pyibuffer_cache.pybuffer_cache.pyicache_utils.pycoherence.pycoherence.pyicommon.pycommon.pyicore.pycore.pyidiagnosis.pydiagnosis.pyiemergence.pyexport.pyexport.pyiglyph_timing.pyglyph_timing.pyilearning_metrics.pylearning_metrics.pyilocal_coherence.pyphase_coherence.pyphase_compatibility.pyREADME.mdreporting.pyreporting.pyisense_index.pysense_index.pyitelemetry.pytetrad.pytrig_cache.pytrig_cache.pyitrig.pytrig.pyi
multiscale
__init__.pyhierarchical.pyREADME.md
navier_stokes
__init__.pyconservative_face.pyoperator.py
node
README.md
observers
README.md
operators
network_analysis
__init__.pysource_detection.py
postconditions
__init__.pymutation.py
preconditions
__init__.pycoherence.pydissonance.pyemission.pymutation.pyreception.pyresonance.py
strategies
__init__.pydefaults.pygpu_strategies.pystrategy.py
__init__.py__init__.pyialgebra.pycanonical_patterns.pycascade.pycoherence.pycontraction.pycoupling.pycycle_detection.pydefinitions_base.pydefinitions.pydefinitions.pyidissonance.pyemission.pyexpansion.pygrammar_application.pygrammar_canon.pygrammar_context.pygrammar_core.pygrammar_dynamics.pygrammar_error_factory.pygrammar_memoization.pygrammar_patterns.pygrammar_telemetry.pygrammar_types.pygrammar_u6.pygrammar_validate.pygrammar.pygrammar.pyihamiltonian.pyhealth_analyzer.pyintrospection.pyjitter.pyjitter.pyilifecycle.pymetabolism.pymetrics_basic.pymetrics_core.pymetrics_network.pymetrics_structural.pymetrics_u6.pymetrics.pymutation.pynodal_equation.pyoperator_contracts.pypattern_detection.pypatterns.pyREADME.mdreception.pyrecursivity.pyregistry.pyregistry.pyiremesh.pyremesh.pyiresonance.pyself_organization.pysilence.pystructural_units.pytransition.py
parallel
__init__.pyauto_scaler.pydistributed.pyengine.pymonitoring.pypartitioner.pyREADME.md
performance
guardrails.py
physics
__init__.py_helpers.pycalibration.pycanonical.pycell.pyclassical_mechanics.pyconservation_gauge_unification.pyconservation.pydissipative_conservation.pyemergent_chemistry.pyemergent_particles.pyextended.pyfields.pygauge.pyintegrity.pyinteractions.pylife.pylyapunov.pypatterns.pyphase_transition.pyquantum_mechanics.pyREADME.mdsignatures.pyspectral_conservation.pyspectral_metrics.pystructural_diffusion.pysymplectic_substrate.pytelemetry.pyunified.pyvariational.pyvectorized_ops.py
primality
__init__.py
recipes
__init__.pycookbook.pyREADME.md
riemann
__init__.pyadmissible_family_sweep.pyadmissible_rescaling.pyaggregates_closure_signature.pyalpha_sweep.pyanalytic_continuation_dirichlet.pyanalytic_continuation.pycoercivity_uniform.pycoupling_weights_type_signature.pycurrents_closure_signature.pydelta_phi_max_type_signature.pydirichlet_l.pydnfr_type_signature.pyepi_type_signature.pyhilbert_polya.pyli_keiper.pylyapunov_spectral_positivity.pynodal_pulse.pynodeaware_gauge_sweep.pynuf_type_signature.pyoperator_catalog_discipline_signature.pyoperator.pyoscillatory_correction.pypaley_gap_coercivity.pyphi_type_signature.pyprime_ladder_hamiltonian.pypulse_coherence.pyremesh_infinity_residue_split.pyremesh_window_type_signature.pyspectral_emergence.pystructural_zero_density.pytelemetry.pytetrad_closure_signature.pytwisted_admissible_family_sweep.pytwisted_admissible_rescaling.pytwisted_alpha_sweep.pytwisted_coercivity_uniform.pytwisted_hermite_family.pytwisted_hilbert_polya.pytwisted_li_keiper.pytwisted_lyapunov_spectral_positivity.pytwisted_nodeaware_gauge_sweep.pytwisted_oscillatory_correction.pytwisted_paley_gap_coercivity.pytwisted_prime_ladder_hamiltonian.pytwisted_spectral_emergence.pytwisted_structural_zero_density.pytwisted_weil_explicit_formula.pytwisted_weil_positivity.pyurules_consistency_signature.pyvon_mangoldt.pyweil_explicit_formula.pyweil_positivity.py
schemas
__init__.pygrammar.jsonREADME.md
sdk
__init__.py__init__.pyiadaptive_system.pyadaptive_system.pyibuilders.pybuilders.pyifluent.pyfluent.pyiREADME.mdself_opt.pysimple.pytemplates.pytemplates.pyiutils.py
security
__init__.pycrypto.pydatabase.pyREADME.mdsubprocess.pyvalidation.py
sequencing
__init__.pypatterns.pyREADME.md
services
__init__.pyorchestrator.pyREADME.md
sparse
__init__.pyREADME.mdrepresentations.py
structural
README.md
telemetry
__init__.pycache_metrics.pycache_metrics.pyiconstants.pynu_f.pynu_f.pyiREADME.mdunified_telemetry_system.pyverbosity.pyverbosity.pyi
tools
__init__.pydomain_templates.pyREADME.mdsequence_generator.pytnfr_is_prime_cli_optimized.pytnfr_is_prime_cli.py
topology
__init__.pyasymmetry.pyREADME.md
utils
cache_layers.pycache.pycache.pyicallbacks.pycallbacks.pyichunks.pychunks.pyidata.pydata.pyifast_diameter.pygraph.pygraph.pyiinit.pyinit.pyiio.pyio.pyinumeric.pynumeric.pyiREADME.mdtopology.pyunified_cache.py
validation
__init__.py__init__.pyiaggregator.pybase.pycompatibility.pycompatibility.pyiconfig.pygraph.pygraph.pyihealth.pyinput_validation.pyinterface_baselines.pyinvariants.pymultichannel_interface.pyphase_gate.pyREADME.mdrules.pyrules.pyiruntime.pyruntime.pyisequence_validator.pysignal_confrontation.pysoft_filters.pysoft_filters.pyispectral.pyspectral.pyistructural_interface.pytemporal_interface.pyunified_validation_system.pyvalidator.pywindow.pywindow.pyi
visualization
__init__.pycascade_viz.pyhierarchy.pyREADME.mdsequence_plotter.py
yang_mills
__init__.pyclosure.pyderivability.pyscaling.pystructural_gap.pyu6_sweep.py
__init__.py__init__.pyi_compat.py_version.py_version.pyialias.pyalias.pyibackend_config.pycache.pycache.pyiexecution.pyexecution.pyiflatten.pyflatten.pyigamma.pygamma.pyiglyph_history.pyglyph_history.pyiglyph_runtime.pyglyph_runtime.pyiimmutable.pyimmutable.pyiinitialization.pyinitialization.pyiio.pyio.pyilocking.pylocking.pyinode.pynode.pyiobservers.pyobservers.pyiontosim.pyontosim.pyipy.typedrng.pyrng.pyisecure_config.pyselector.pyselector.pyisense.pysense.pyistructural.pystructural.pyitokens.pytokens.pyitrace.pytrace.pyitypes.pytypes.pyiunits.pyunits.pyi
tetrad_evaluator.py
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FILE: examples/02_physics_regimes/30_self_optimization_demo.py

30_self_optimization_demo.py

TNFR Self-Optimization — Intrinsic Agency on the Structural Manifold.

Demonstrates that TNFR networks possess intrinsic agency: the ability to analyse their own mathematical structure and select optimal transformation strategies via gradient descent on the structural manifold.

Key results shown:

  1. Mathematical optimisation landscape analysis (unified fields, conservation, graph structure, nodal-equation analysis, recommendations)
  2. Automatic strategy recommendation from learned policies
  3. Experience-based learning loop (record → policy extraction → adaptive config)
  4. Exported knowledge: policies, adaptive configuration, performance statistics
  5. Dry-run optimisation with structural telemetry snapshots before / after
  6. Conservation integrity feedback driving strategy reordering

Physics basis: This is NOT "AI magic." The self-optimising engine performs gradient descent on the structural manifold driven by the pressure term ΔNFR in the nodal equation ∂EPI/∂t = νf · ΔNFR(t). Unified-field telemetry (Ψ, χ, S, C) and conservation invariants (Noether charge, Lyapunov derivative) close the feedback loop.

See: AGENTS.md § Self-Optimizing Dynamics

Source Code

python
"""TNFR Self-Optimization — Intrinsic Agency on the Structural Manifold.

Demonstrates that TNFR networks possess intrinsic agency: the ability to
analyse their own mathematical structure and select optimal transformation
strategies via gradient descent on the structural manifold.

Key results shown:
1. Mathematical optimisation landscape analysis (unified fields, conservation,
   graph structure, nodal-equation analysis, recommendations)
2. Automatic strategy recommendation from learned policies
3. Experience-based learning loop (record → policy extraction → adaptive config)
4. Exported knowledge: policies, adaptive configuration, performance statistics
5. Dry-run optimisation with structural telemetry snapshots before / after
6. Conservation integrity feedback driving strategy reordering

Physics basis:
  This is NOT "AI magic."  The self-optimising engine performs *gradient
  descent on the structural manifold* driven by the pressure term ΔNFR
  in the nodal equation ∂EPI/∂t = νf · ΔNFR(t).  Unified-field telemetry
  (Ψ, χ, S, C) and conservation invariants (Noether charge, Lyapunov
  derivative) close the feedback loop.

See: AGENTS.md § Self-Optimizing Dynamics
"""

from __future__ import annotations

import os
import sys
import time

sys.path.insert(0, os.path.join(os.path.dirname(__file__), "..", "..", "src"))

import networkx as nx
import numpy as np

from tnfr.constants import inject_defaults
from tnfr.dynamics.self_optimizing_engine import (
    LearningStrategy,
    OptimizationExperience,
    OptimizationObjective,
    SelfOptimizationResult,
    TNFRSelfOptimizingEngine,
    auto_optimize_tnfr_computation,
    create_self_optimizing_engine,
)
from tnfr.metrics.common import compute_coherence
from tnfr.metrics.sense_index import compute_Si
from tnfr.operators import apply_glyph

SEED = 42
np.random.seed(SEED)

# ── helpers ──────────────────────────────────────────────────────────
HEADER = "=" * 72
SECTION = "-" * 60


def banner(title: str) -> None:
    print(f"\n{HEADER}")
    print(f"  {title}")
    print(HEADER)


def build_network(n: int = 20, p: float = 0.3, seed: int = SEED) -> nx.Graph:
    """Create and initialise a random TNFR network."""
    G = nx.erdos_renyi_graph(n, p, seed=seed)
    inject_defaults(G)
    # Bootstrap a few nodes so the graph has non-trivial EPI / ΔNFR
    for node in list(G.nodes())[:5]:
        apply_glyph(G, node, "AL")  # Emission
    for node in list(G.nodes())[:5]:
        apply_glyph(G, node, "IL")  # Coherence
    return G


def print_dict(d: dict, indent: int = 2) -> None:
    """Pretty-print a dict with controlled depth."""
    prefix = " " * indent
    for key, val in d.items():
        if isinstance(val, dict):
            print(f"{prefix}{key}:")
            print_dict(val, indent + 4)
        elif isinstance(val, (list, tuple)):
            if len(val) == 0:
                print(f"{prefix}{key}: []")
            elif len(val) <= 6:
                print(f"{prefix}{key}: {val}")
            else:
                print(f"{prefix}{key}: [{val[0]}, ... ({len(val)} items)]")
        elif isinstance(val, float):
            print(f"{prefix}{key}: {val:.6f}")
        else:
            print(f"{prefix}{key}: {val}")


# ── § 1  Optimisation Landscape Analysis ──────────────────────────────
banner("§ 1  Mathematical Optimisation Landscape")

G = build_network()
engine = TNFRSelfOptimizingEngine(
    learning_strategy=LearningStrategy.MATHEMATICAL_ANALYSIS,
    optimization_objective=OptimizationObjective.BALANCE_ALL,
)

landscape = engine.analyze_mathematical_optimization_landscape(G, "general")

print("\nLandscape keys:", sorted(landscape.keys()))

if "unified_field_analysis" in landscape:
    print(f"\n{SECTION}")
    print("  Unified Field Analysis  (Ψ, χ, S, C, E, Q)")
    print(SECTION)
    print_dict(landscape["unified_field_analysis"])

if "conservation_feedback" in landscape:
    print(f"\n{SECTION}")
    print("  Conservation Integrity Feedback")
    print(SECTION)
    print_dict(landscape["conservation_feedback"])

if "graph_structure" in landscape:
    print(f"\n{SECTION}")
    print("  Graph Structure")
    print(SECTION)
    print_dict(landscape["graph_structure"])

if "nodal_equation_analysis" in landscape:
    print(f"\n{SECTION}")
    print("  Nodal Equation Analysis")
    print(SECTION)
    nea = landscape["nodal_equation_analysis"]
    print(f"  EPI variance:    {nea.get('epi_variance', 0):.6f}")
    print(f"  νf range:        {nea.get('vf_range', 0):.6f}")
    print(f"  |ΔNFR| mean:    {nea.get('dnfr_magnitude', 0):.6f}")
    recs = nea.get("optimization_recommendations", [])
    print(f"  Recommendations ({len(recs)}):")
    for r in recs:
        print(f"    • {r}")

if "pattern_optimization_hints" in landscape:
    hints = landscape["pattern_optimization_hints"]
    print(f"\n  Pattern hints ({len(hints)}):")
    for h in hints:
        print(f"    • {h}")


# ── § 2  Strategy Recommendation ──────────────────────────────────────
banner("§ 2  Strategy Recommendation (SelfOptimizationResult)")

result: SelfOptimizationResult = engine.recommend_optimization_strategy(
    G, operation_type="general"
)

print(f"\n  Recommended strategies ({len(result.recommended_strategies)}):")
for s in result.recommended_strategies[:10]:
    speedup = result.predicted_speedups.get(s)
    extra = f"  (predicted speedup: {speedup:.2f}×)" if speedup else ""
    print(f"    • {s}{extra}")

print(f"\n  Learned policies (matching): {len(result.learned_policies)}")
print(f"  Adaptive configuration:")
print_dict(result.adaptive_configurations)
print(f"  Analysis time: {result.execution_time * 1000:.1f} ms")

if result.conservation_feedback is not None:
    print(f"\n  Conservation feedback:")
    print_dict(result.conservation_feedback)


# ── § 3  Experience-Based Learning Loop ───────────────────────────────
banner("§ 3  Experience-Based Learning Loop")

print("\n  Simulating 15 optimisation experiments ...\n")

topologies = [
    ("ring", lambda n, s: nx.cycle_graph(n)),
    ("random", lambda n, s: nx.erdos_renyi_graph(n, 0.3, seed=s)),
    ("star", lambda n, s: nx.star_graph(n - 1)),
]

strategies = ["spectral", "vectorized", "cache", "structural", "hybrid"]

for i in range(15):
    topo_name, topo_fn = topologies[i % len(topologies)]
    n = 10 + i * 5
    G_exp = topo_fn(n, SEED + i)
    inject_defaults(G_exp)

    # Bootstrap
    for node in list(G_exp.nodes())[:3]:
        apply_glyph(G_exp, node, "AL")  # Emission
        apply_glyph(G_exp, node, "IL")  # Coherence

    num_nodes = len(G_exp.nodes())
    num_edges = len(G_exp.edges())
    density = 2 * num_edges / (num_nodes * (num_nodes - 1)) if num_nodes > 1 else 0

    strategy = strategies[i % len(strategies)]
    speedup = 1.0 + np.random.exponential(0.5)

    exp = OptimizationExperience(
        graph_properties={"nodes": num_nodes, "edges": num_edges, "density": density},
        operation_type="general",
        strategy_used=strategy,
        parameters={"topology": topo_name},
        performance_metrics={
            "speedup_factor": float(speedup),
            "execution_time": 0.01 * n,
        },
        timestamp=time.time(),
        success=speedup > 1.05,
    )
    engine.learn_from_experience(exp)

print(f"  Experiences recorded: {len(engine.experience_history)}")
print(
    f"  Successful:           {engine.successful_optimizations} / {engine.optimization_attempts}"
)
print(f"  Learned policies:     {len(engine.learned_policies)}")

for p in engine.learned_policies[:5]:
    print(
        f"\n  Policy: {p.policy_name}"
        f"\n    conditions: {p.conditions}"
        f"\n    action:     {p.actions}"
        f"\n    confidence: {p.confidence:.2f}  |  avg improvement: {p.average_improvement:.3f}×"
    )


# ── § 4  Exported Knowledge ──────────────────────────────────────────
banner("§ 4  Exported Knowledge")

knowledge = engine.export_learned_knowledge()

print(f"\n  Performance statistics:")
print_dict(knowledge["performance_statistics"])

print(f"\n  Adaptive configuration:")
print_dict(knowledge["adaptive_configuration"])

print(f"\n  Policies exported: {len(knowledge['learned_policies'])}")
for p in knowledge["learned_policies"][:3]:
    print(f"    • {p['name']}  (confidence {p['confidence']:.2f})")


# ── § 5  Dry-Run Automatic Optimisation ───────────────────────────────
banner("§ 5  Dry-Run Automatic Optimisation")

G2 = build_network(n=30, p=0.25, seed=SEED + 100)
C_before = compute_coherence(G2)
si_result = compute_Si(G2)
Si_mean = (
    float(np.mean(list(si_result.values())))
    if isinstance(si_result, dict)
    else float(np.mean(si_result))
)

print(f"\n  Pre-optimisation telemetry:")
print(f"    C(t)  = {C_before:.6f}")
print(f"    Si    = {Si_mean:.6f}")
print(f"    Nodes = {len(G2.nodes())}  |  Edges = {len(G2.edges())}")

dry_result = engine.optimize_automatically(
    G2,
    operation_type="general",
    dry_run=True,
    seed=SEED,
)

print(f"\n  Dry-run mode: {dry_result.get('dry_run', False)}")
snapshot_path = dry_result.get("snapshot_path")
if snapshot_path:
    print(f"  Snapshot saved to: {snapshot_path}")
sig = dry_result.get("signature")
if sig:
    print(f"  Signature:         {sig[:40]}...")

recs_obj = dry_result.get("recommendations")
if recs_obj is not None and hasattr(recs_obj, "recommended_strategies"):
    print(f"\n  Recommended strategies:")
    for s in recs_obj.recommended_strategies[:8]:
        print(f"    • {s}")


# ── § 6  Convenience API ─────────────────────────────────────────────
banner("§ 6  Convenience API — auto_optimize_tnfr_computation()")

G3 = build_network(n=15, p=0.35, seed=SEED + 200)

auto_result = auto_optimize_tnfr_computation(G3, "general", dry_run=True, seed=SEED)

print(f"\n  dry_run: {auto_result.get('dry_run', '?')}")
recs_auto = auto_result.get("recommendations")
if recs_auto is not None and hasattr(recs_auto, "recommended_strategies"):
    strats = recs_auto.recommended_strategies
    print(f"  Strategies ({len(strats)}):")
    for s in strats[:6]:
        print(f"    • {s}")

print(f"\n  Conservation closed-loop:")
cf = auto_result.get("conservation")
if cf is not None:
    print_dict(cf)
else:
    print("    (no live conservation data in dry-run)")

# ── Summary ──────────────────────────────────────────────────────────
banner("Summary")
print(
    """
  Self-optimisation in TNFR is gradient descent on the structural manifold.
  The engine:
    1. Analyses the mathematical landscape (unified fields, conservation,
       graph structure, nodal equation properties).
    2. Recommends strategies — from learned policies and from mathematical
       analysis of Ψ, χ, S, C, E, Q.
    3. Records experiences and extracts optimisation policies.
    4. Reorders strategies when conservation health is stressed.
    5. Persists knowledge for reuse across sessions.

  Physics:  ∂EPI/∂t = νf · ΔNFR(t)  →  natural gradient on structural
  manifold.  Grammar rules (U1-U6) define the constraint sub-manifold.
  Conservation laws (Noether charge, Lyapunov derivative) close the
  feedback loop.

  See: AGENTS.md § Self-Optimizing Dynamics
"""
)