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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: factorization-lab/tnfr_factorization/feedback_integration.py

feedback_integration.py

TNFR Self-Optimization Feedback Integration

Closes the optimization loop by integrating adaptive candidate refinement based on certificate feedback. Implements learning mechanisms that adjust partition strategies based on verification success rates.

This system:

  1. Analyzes verification success/failure patterns from certificates
  2. Learns which partition strategies work best for different number types
  3. Adapts candidate selection based on historical performance
  4. Provides feedback-driven optimization recommendations
  5. Maintains learning databases for continuous improvement

Source Code

python
"""
TNFR Self-Optimization Feedback Integration

Closes the optimization loop by integrating adaptive candidate refinement
based on certificate feedback. Implements learning mechanisms that adjust
partition strategies based on verification success rates.

This system:
1. Analyzes verification success/failure patterns from certificates
2. Learns which partition strategies work best for different number types
3. Adapts candidate selection based on historical performance
4. Provides feedback-driven optimization recommendations
5. Maintains learning databases for continuous improvement
"""

import json
import math
import os
import sqlite3
import statistics
import time
from collections import Counter, defaultdict
from dataclasses import asdict, dataclass
from pathlib import Path
from typing import Any, Dict, List, Optional, Set, Tuple


@dataclass
class VerificationFeedback:
    """Structured feedback from a verification attempt."""

    n: int
    modulus: int
    node_count: int
    candidate_factor: Optional[int]
    was_certified: bool
    verification_score: float  # Overall verification strength (0.0-1.0)

    # Verification metrics
    dnfr_gain: float
    coherence_ratio: float
    phi_delta_parent: float
    gradient_delta: float
    curvature_delta: float
    periodicity_confidence: float

    # Strategy context
    partition_strategy: str
    operator_sequence: List[str]
    optimization_budget: float

    # Performance metrics
    runtime_ms: float
    convergence_iterations: int

    # Contextual information
    number_type: str  # e.g., "semiprime", "triprime", "carmichael", etc.
    factor_pattern: str  # e.g., "close_primes", "large_gap", "power_of_prime"

    timestamp: float


@dataclass
class OptimizationStrategy:
    """Learned optimization strategy for specific contexts."""

    context_pattern: str  # Pattern this strategy applies to
    recommended_sequence: List[str]
    expected_success_rate: float
    avg_runtime_ms: float
    confidence: float  # How confident we are in this strategy
    sample_count: int  # Number of samples this is based on
    last_updated: float


@dataclass
class FeedbackAnalysis:
    """Analysis of feedback patterns and recommendations."""

    success_rate_by_strategy: Dict[str, float]
    best_strategy_by_number_type: Dict[str, str]
    runtime_performance_by_strategy: Dict[str, float]
    common_failure_patterns: List[Tuple[str, float]]  # (pattern, frequency)
    optimization_recommendations: List[str]
    confidence_score: float


class OptimizationFeedbackLearner:
    """Learning system for self-optimization feedback integration."""

    def __init__(self, db_path: Optional[Path] = None):
        """Initialize the feedback learner with persistent storage."""

        self.db_path = db_path or Path("results/optimization_feedback.db")
        self.db_path.parent.mkdir(parents=True, exist_ok=True)

        # Initialize database
        self._init_database()

        # In-memory caches for performance
        self._strategy_cache: Dict[str, OptimizationStrategy] = {}
        self._feedback_buffer: List[VerificationFeedback] = []

        # Learning parameters
        self.min_samples_for_strategy = 5
        self.confidence_threshold = 0.7
        self.adaptation_rate = 0.1  # How quickly to adapt to new evidence

    def _init_database(self):
        """Initialize the SQLite database for feedback storage."""

        with sqlite3.connect(self.db_path) as conn:
            conn.execute(
                """
                CREATE TABLE IF NOT EXISTS verification_feedback (
                    id INTEGER PRIMARY KEY AUTOINCREMENT,
                    n INTEGER NOT NULL,
                    modulus INTEGER,
                    node_count INTEGER,
                    candidate_factor INTEGER,
                    was_certified INTEGER NOT NULL,
                    verification_score REAL,
                    dnfr_gain REAL,
                    coherence_ratio REAL,
                    phi_delta_parent REAL,
                    gradient_delta REAL,
                    curvature_delta REAL,
                    periodicity_confidence REAL,
                    partition_strategy TEXT,
                    operator_sequence TEXT,
                    optimization_budget REAL,
                    runtime_ms REAL,
                    convergence_iterations INTEGER,
                    number_type TEXT,
                    factor_pattern TEXT,
                    timestamp REAL
                )
            """
            )

            conn.execute(
                """
                CREATE TABLE IF NOT EXISTS optimization_strategies (
                    id INTEGER PRIMARY KEY AUTOINCREMENT,
                    context_pattern TEXT NOT NULL UNIQUE,
                    recommended_sequence TEXT,
                    expected_success_rate REAL,
                    avg_runtime_ms REAL,
                    confidence REAL,
                    sample_count INTEGER,
                    last_updated REAL
                )
            """
            )

            conn.execute(
                "CREATE INDEX IF NOT EXISTS idx_feedback_n ON verification_feedback(n)"
            )
            conn.execute(
                "CREATE INDEX IF NOT EXISTS idx_feedback_strategy ON verification_feedback(partition_strategy)"
            )
            conn.execute(
                "CREATE INDEX IF NOT EXISTS idx_feedback_number_type ON verification_feedback(number_type)"
            )
            conn.execute(
                "CREATE INDEX IF NOT EXISTS idx_strategies_pattern ON optimization_strategies(context_pattern)"
            )

    def record_verification_feedback(self, feedback: VerificationFeedback):
        """Record feedback from a verification attempt."""

        # Add to buffer for batch processing
        self._feedback_buffer.append(feedback)

        # Store in database
        with sqlite3.connect(self.db_path) as conn:
            conn.execute(
                """
                INSERT INTO verification_feedback (
                    n, modulus, node_count, candidate_factor, was_certified,
                    verification_score, dnfr_gain, coherence_ratio, 
                    phi_delta_parent, gradient_delta, curvature_delta,
                    periodicity_confidence, partition_strategy, operator_sequence,
                    optimization_budget, runtime_ms, convergence_iterations,
                    number_type, factor_pattern, timestamp
                ) VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?)
            """,
                (
                    feedback.n,
                    feedback.modulus,
                    feedback.node_count,
                    feedback.candidate_factor,
                    int(feedback.was_certified),
                    feedback.verification_score,
                    feedback.dnfr_gain,
                    feedback.coherence_ratio,
                    feedback.phi_delta_parent,
                    feedback.gradient_delta,
                    feedback.curvature_delta,
                    feedback.periodicity_confidence,
                    feedback.partition_strategy,
                    json.dumps(feedback.operator_sequence),
                    feedback.optimization_budget,
                    feedback.runtime_ms,
                    feedback.convergence_iterations,
                    feedback.number_type,
                    feedback.factor_pattern,
                    feedback.timestamp,
                ),
            )

    def analyze_feedback_patterns(self, min_samples: int = 10) -> FeedbackAnalysis:
        """Analyze accumulated feedback to identify optimization patterns."""

        with sqlite3.connect(self.db_path) as conn:
            conn.row_factory = sqlite3.Row

            # Get all feedback data
            rows = conn.execute(
                """
                SELECT * FROM verification_feedback 
                ORDER BY timestamp DESC LIMIT 1000
            """
            ).fetchall()

        if len(rows) < min_samples:
            return FeedbackAnalysis(
                success_rate_by_strategy={},
                best_strategy_by_number_type={},
                runtime_performance_by_strategy={},
                common_failure_patterns=[],
                optimization_recommendations=["Insufficient data for analysis"],
                confidence_score=0.0,
            )

        # Analyze success rates by strategy
        strategy_stats = defaultdict(lambda: {"success": 0, "total": 0, "runtimes": []})

        for row in rows:
            strategy = row["partition_strategy"] or "unknown"
            strategy_stats[strategy]["total"] += 1
            strategy_stats[strategy]["runtimes"].append(row["runtime_ms"] or 0)

            if row["was_certified"]:
                strategy_stats[strategy]["success"] += 1

        success_rate_by_strategy = {
            strategy: stats["success"] / max(stats["total"], 1)
            for strategy, stats in strategy_stats.items()
            if stats["total"] >= 3  # Minimum samples
        }

        runtime_performance_by_strategy = {
            strategy: statistics.mean(stats["runtimes"]) if stats["runtimes"] else 0
            for strategy, stats in strategy_stats.items()
        }

        # Analyze by number type
        number_type_stats = defaultdict(
            lambda: defaultdict(lambda: {"success": 0, "total": 0})
        )

        for row in rows:
            number_type = row["number_type"] or "unknown"
            strategy = row["partition_strategy"] or "unknown"

            number_type_stats[number_type][strategy]["total"] += 1
            if row["was_certified"]:
                number_type_stats[number_type][strategy]["success"] += 1

        best_strategy_by_number_type = {}
        for number_type, strategies in number_type_stats.items():
            if not strategies:
                continue

            best_strategy = max(
                strategies.items(),
                key=lambda x: (
                    x[1]["success"] / max(x[1]["total"], 1),  # Success rate
                    x[1]["total"],  # Sample size as tiebreaker
                ),
            )[0]

            if strategies[best_strategy]["total"] >= 3:
                best_strategy_by_number_type[number_type] = best_strategy

        # Identify failure patterns
        failure_patterns = Counter()
        for row in rows:
            if not row["was_certified"]:
                # Identify potential failure causes
                if row["dnfr_gain"] is not None and row["dnfr_gain"] < 0.1:
                    failure_patterns["low_dnfr_gain"] += 1
                if (
                    row["periodicity_confidence"] is not None
                    and row["periodicity_confidence"] < 0.5
                ):
                    failure_patterns["low_periodicity_confidence"] += 1
                if row["coherence_ratio"] is not None and row["coherence_ratio"] < 0.7:
                    failure_patterns["low_coherence"] += 1
                if (
                    row["phi_delta_parent"] is not None
                    and row["phi_delta_parent"] > 0.4
                ):
                    failure_patterns["high_phi_delta"] += 1

        total_failures = sum(1 for row in rows if not row["was_certified"])
        common_failure_patterns = [
            (pattern, count / max(total_failures, 1))
            for pattern, count in failure_patterns.most_common(5)
        ]

        # Generate optimization recommendations
        recommendations = self._generate_optimization_recommendations(
            success_rate_by_strategy,
            runtime_performance_by_strategy,
            common_failure_patterns,
        )

        # Calculate overall confidence
        total_samples = len(rows)
        confidence_score = min(
            1.0, total_samples / 100.0
        )  # Full confidence at 100 samples

        return FeedbackAnalysis(
            success_rate_by_strategy=success_rate_by_strategy,
            best_strategy_by_number_type=best_strategy_by_number_type,
            runtime_performance_by_strategy=runtime_performance_by_strategy,
            common_failure_patterns=common_failure_patterns,
            optimization_recommendations=recommendations,
            confidence_score=confidence_score,
        )

    def _generate_optimization_recommendations(
        self,
        success_rates: Dict[str, float],
        runtimes: Dict[str, float],
        failure_patterns: List[Tuple[str, float]],
    ) -> List[str]:
        """Generate actionable optimization recommendations."""

        recommendations = []

        # Strategy recommendations
        if success_rates:
            best_strategy = max(success_rates.items(), key=lambda x: x[1])
            if best_strategy[1] > 0.8:
                recommendations.append(
                    f"Strategy '{best_strategy[0]}' shows {best_strategy[1]:.1%} success rate - consider as default"
                )

            worst_strategy = min(success_rates.items(), key=lambda x: x[1])
            if worst_strategy[1] < 0.3:
                recommendations.append(
                    f"Strategy '{worst_strategy[0]}' has low {worst_strategy[1]:.1%} success rate - consider revision"
                )

        # Runtime recommendations
        if runtimes:
            fastest_strategy = min(runtimes.items(), key=lambda x: x[1])
            slowest_strategy = max(runtimes.items(), key=lambda x: x[1])

            if slowest_strategy[1] > 2 * fastest_strategy[1]:
                recommendations.append(
                    f"Strategy '{slowest_strategy[0]}' is {slowest_strategy[1]/fastest_strategy[1]:.1f}x slower than '{fastest_strategy[0]}' - optimize performance"
                )

        # Failure pattern recommendations
        for pattern, frequency in failure_patterns:
            if frequency > 0.3:  # More than 30% of failures
                if pattern == "low_dnfr_gain":
                    recommendations.append(
                        "High frequency of low ΔNFR gain failures - consider stronger destabilization operators"
                    )
                elif pattern == "low_periodicity_confidence":
                    recommendations.append(
                        "Low periodicity confidence is common - improve spectral analysis accuracy"
                    )
                elif pattern == "low_coherence":
                    recommendations.append(
                        "Coherence issues detected - add more stabilization steps"
                    )
                elif pattern == "high_phi_delta":
                    recommendations.append(
                        "High phi delta failures - improve structural potential management"
                    )

        if not recommendations:
            recommendations.append(
                "Feedback patterns look healthy - continue current strategies"
            )

        return recommendations

    def get_adaptive_strategy_recommendation(
        self,
        n: int,
        number_type: Optional[str] = None,
        factor_pattern: Optional[str] = None,
    ) -> OptimizationStrategy:
        """Get adaptive strategy recommendation based on learned patterns."""

        # Determine number type if not provided
        if number_type is None:
            number_type = self._classify_number_type(n)

        # Check cache first
        cache_key = f"{number_type}_{factor_pattern or 'unknown'}"
        if cache_key in self._strategy_cache:
            return self._strategy_cache[cache_key]

        # Query database for similar cases
        with sqlite3.connect(self.db_path) as conn:
            conn.row_factory = sqlite3.Row

            # Get feedback for similar number types
            rows = conn.execute(
                """
                SELECT partition_strategy, operator_sequence, was_certified, 
                       runtime_ms, verification_score
                FROM verification_feedback 
                WHERE number_type = ? AND was_certified = 1
                ORDER BY timestamp DESC LIMIT 50
            """,
                (number_type,),
            ).fetchall()

        if not rows:
            # Fallback to default strategy
            strategy = OptimizationStrategy(
                context_pattern=cache_key,
                recommended_sequence=[
                    "emission",
                    "coupling",
                    "resonance",
                    "coherence",
                    "silence",
                ],
                expected_success_rate=0.5,
                avg_runtime_ms=1000.0,
                confidence=0.1,
                sample_count=0,
                last_updated=time.time(),
            )
        else:
            # Analyze successful strategies
            strategy_performance = defaultdict(
                lambda: {"success": 0, "total": 0, "runtimes": []}
            )

            for row in rows:
                strategy_name = row["partition_strategy"] or "default"
                strategy_performance[strategy_name]["total"] += 1
                strategy_performance[strategy_name]["runtimes"].append(
                    row["runtime_ms"] or 1000
                )

                if row["was_certified"]:
                    strategy_performance[strategy_name]["success"] += 1

            # Find best performing strategy
            best_strategy_name = max(
                strategy_performance.items(),
                key=lambda x: (x[1]["success"] / max(x[1]["total"], 1), x[1]["total"]),
            )[0]

            best_perf = strategy_performance[best_strategy_name]
            success_rate = best_perf["success"] / max(best_perf["total"], 1)
            avg_runtime = (
                statistics.mean(best_perf["runtimes"])
                if best_perf["runtimes"]
                else 1000
            )

            # Get representative operator sequence
            rep_sequence_row = next(
                (
                    row
                    for row in rows
                    if row["partition_strategy"] == best_strategy_name
                ),
                rows[0],
            )

            try:
                rep_sequence = json.loads(rep_sequence_row["operator_sequence"] or "[]")
            except (json.JSONDecodeError, TypeError):
                rep_sequence = [
                    "emission",
                    "coupling",
                    "resonance",
                    "coherence",
                    "silence",
                ]

            confidence = min(0.9, best_perf["total"] / self.min_samples_for_strategy)

            strategy = OptimizationStrategy(
                context_pattern=cache_key,
                recommended_sequence=rep_sequence,
                expected_success_rate=success_rate,
                avg_runtime_ms=avg_runtime,
                confidence=confidence,
                sample_count=best_perf["total"],
                last_updated=time.time(),
            )

        # Cache the strategy
        self._strategy_cache[cache_key] = strategy

        # Store in database
        self._store_strategy(strategy)

        return strategy

    def _classify_number_type(self, n: int) -> str:
        """Classify a number by its factorization pattern."""

        # Quick factorization to determine type
        factors = []
        temp_n = n

        for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]:
            while temp_n % p == 0:
                factors.append(p)
                temp_n //= p

        if temp_n > 1:
            factors.append(temp_n)

        unique_factors = len(set(factors))
        total_factors = len(factors)

        # Classification logic
        if total_factors == 1:
            return "prime"
        elif total_factors == 2 and unique_factors == 2:
            return "semiprime"
        elif total_factors == 3 and unique_factors == 3:
            return "triprime"
        elif unique_factors == 1:
            return "prime_power"
        elif unique_factors == 2:
            return "semiprime_power"
        elif unique_factors >= 3:
            return "highly_composite"
        else:
            return "composite"

    def _store_strategy(self, strategy: OptimizationStrategy):
        """Store or update a strategy in the database."""

        with sqlite3.connect(self.db_path) as conn:
            conn.execute(
                """
                INSERT OR REPLACE INTO optimization_strategies (
                    context_pattern, recommended_sequence, expected_success_rate,
                    avg_runtime_ms, confidence, sample_count, last_updated
                ) VALUES (?, ?, ?, ?, ?, ?, ?)
            """,
                (
                    strategy.context_pattern,
                    json.dumps(strategy.recommended_sequence),
                    strategy.expected_success_rate,
                    strategy.avg_runtime_ms,
                    strategy.confidence,
                    strategy.sample_count,
                    strategy.last_updated,
                ),
            )

    def update_strategy_from_feedback(self, feedback: VerificationFeedback):
        """Update strategies based on new feedback using adaptive learning."""

        context_key = f"{feedback.number_type}_{feedback.factor_pattern}"

        if context_key in self._strategy_cache:
            strategy = self._strategy_cache[context_key]

            # Adaptive update using exponential moving average
            new_success_rate = (
                1 - self.adaptation_rate
            ) * strategy.expected_success_rate + self.adaptation_rate * (
                1.0 if feedback.was_certified else 0.0
            )

            new_runtime = (
                1 - self.adaptation_rate
            ) * strategy.avg_runtime_ms + self.adaptation_rate * feedback.runtime_ms

            strategy.expected_success_rate = new_success_rate
            strategy.avg_runtime_ms = new_runtime
            strategy.sample_count += 1
            strategy.last_updated = time.time()

            # Update confidence based on sample count
            strategy.confidence = min(
                0.9, strategy.sample_count / self.min_samples_for_strategy
            )

            # Store updated strategy
            self._store_strategy(strategy)

    def export_feedback_report(self, output_path: Path):
        """Export comprehensive feedback analysis report."""

        analysis = self.analyze_feedback_patterns()

        report = {
            "timestamp": time.time(),
            "database_path": str(self.db_path),
            "analysis": asdict(analysis),
            "learning_parameters": {
                "min_samples_for_strategy": self.min_samples_for_strategy,
                "confidence_threshold": self.confidence_threshold,
                "adaptation_rate": self.adaptation_rate,
            },
            "cache_status": {
                "cached_strategies": len(self._strategy_cache),
                "buffered_feedback": len(self._feedback_buffer),
            },
        }

        with open(output_path, "w") as f:
            json.dump(report, f, indent=2)

        print(f"Feedback analysis report exported: {output_path}")

    def get_performance_summary(self) -> Dict[str, Any]:
        """Get performance summary for monitoring."""

        with sqlite3.connect(self.db_path) as conn:
            total_feedback = conn.execute(
                "SELECT COUNT(*) FROM verification_feedback"
            ).fetchone()[0]
            recent_success_rate = (
                conn.execute(
                    """
                SELECT AVG(CAST(was_certified AS FLOAT)) FROM verification_feedback 
                WHERE timestamp > ?
            """,
                    (time.time() - 7 * 24 * 3600,),
                ).fetchone()[0]
                or 0
            )  # Last 7 days

            total_strategies = conn.execute(
                "SELECT COUNT(*) FROM optimization_strategies"
            ).fetchone()[0]

        return {
            "total_feedback_records": total_feedback,
            "recent_success_rate": recent_success_rate,
            "learned_strategies": total_strategies,
            "cache_size": len(self._strategy_cache),
            "confidence_threshold": self.confidence_threshold,
        }