TNFR Logo
TheoryLearnSoftwareResearch

On this page

TNFR

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

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

cli.py

Advanced Command Line Interface for TNFR Primality Testing

Provides access to both standard and advanced TNFR algorithms with repository integration. Supports performance analysis, benchmarking, caching, and infrastructure diagnostics.

Usage: python -m tnfr_primality.cli 17 97 997 --timing python -m tnfr_primality.cli --benchmark 10000 --advanced python -m tnfr_primality.cli --validate 1000 --infrastructure-status python -m tnfr_primality.cli --batch 2 3 5 7 11 13 17 --cached

Source Code

python
"""
Advanced Command Line Interface for TNFR Primality Testing

Provides access to both standard and advanced TNFR algorithms with repository integration.
Supports performance analysis, benchmarking, caching, and infrastructure diagnostics.

Usage:
    python -m tnfr_primality.cli 17 97 997 --timing
    python -m tnfr_primality.cli --benchmark 10000 --advanced
    python -m tnfr_primality.cli --validate 1000 --infrastructure-status
    python -m tnfr_primality.cli --batch 2 3 5 7 11 13 17 --cached
"""

from __future__ import annotations

import argparse
import time
from typing import List

# Import standard implementations
from .core import tnfr_is_prime, validate_tnfr_theory
from .optimized import OptimizedTNFRPrimality, performance_comparison

# Try to import advanced implementations
try:
    from .advanced_core import (
        HAS_TNFR_INFRASTRUCTURE,
        cached_tnfr_is_prime_advanced,
        get_infrastructure_status,
        get_system_info,
        tnfr_is_prime_advanced,
        validate_tnfr_theory_advanced,
    )

    HAS_ADVANCED = True
except ImportError:
    HAS_ADVANCED = False


def main(argv: List[str] | None = None) -> int:
    """Main CLI entry point."""
    parser = argparse.ArgumentParser(
        description="TNFR-based primality testing using arithmetic pressure equations",
        formatter_class=argparse.RawDescriptionHelpFormatter,
        epilog="""
Examples:
  python -m tnfr_primality.cli 17 97 997 9973          # Test specific numbers
  python -m tnfr_primality.cli --timing 982451653      # With timing info
  python -m tnfr_primality.cli --benchmark 10000       # Performance benchmark  
  python -m tnfr_primality.cli --batch --optimized 2 3 5 7  # Batch mode
  python -m tnfr_primality.cli --validate 1000         # Validate theory

TNFR Theory:
  A number n is prime ⟺ ΔNFR(n) = 0, where:
  ΔNFR(n) = ζ·(ω(n)−1) + η·(τ(n)−2) + θ·(σ(n)/n − (1+1/n))
  
  This represents arithmetic pressure in structural coherence systems.
        """,
    )

    parser.add_argument(
        "numbers", nargs="*", type=int, help="Integers to test for primality"
    )
    parser.add_argument(
        "--timing", action="store_true", help="Show detailed timing information"
    )
    parser.add_argument(
        "--optimized",
        action="store_true",
        help="Use optimized implementation with caching",
    )
    parser.add_argument(
        "--batch",
        action="store_true",
        help="Batch processing mode for multiple numbers",
    )
    parser.add_argument(
        "--benchmark", type=int, metavar="N", help="Run performance benchmark up to N"
    )
    parser.add_argument(
        "--validate",
        type=int,
        metavar="N",
        help="Validate TNFR theory against traditional methods up to N",
    )
    parser.add_argument(
        "--compare", action="store_true", help="Compare basic vs optimized performance"
    )
    parser.add_argument("--stats", action="store_true", help="Show detailed statistics")
    parser.add_argument(
        "--sieve",
        type=int,
        metavar="N",
        help="Generate primes up to N using TNFR-verified sieve",
    )

    args = parser.parse_args(argv)

    # Validation mode
    if args.validate:
        print(
            f"Validating TNFR theory against traditional primality testing up to {args.validate}..."
        )
        print("=" * 70)

        start_time = time.perf_counter()
        results = validate_tnfr_theory(args.validate)
        elapsed = time.perf_counter() - start_time

        print(f"Numbers tested: {results['tested']:,}")
        print(f"Correct results: {results['correct']:,}")
        print(f"Accuracy: {results['accuracy']:.6f} ({results['accuracy']*100:.4f}%)")
        print(f"False positives: {results['false_positives']}")
        print(f"False negatives: {results['false_negatives']}")
        print(f"Error rate: {results['error_rate']:.8f}")
        print(f"Validation time: {elapsed*1000:.2f} ms")

        if results["accuracy"] == 1.0:
            print("✅ TNFR theory validation: PERFECT ACCURACY")
        else:
            print("❌ TNFR theory validation: ERRORS DETECTED")

        return 0

    # Benchmark mode
    if args.benchmark:
        print(f"Running TNFR primality benchmark up to {args.benchmark:,}...")
        print("=" * 60)

        optimizer = OptimizedTNFRPrimality()
        results = optimizer.benchmark(args.benchmark)

        print("Benchmark Results:")
        print("-" * 30)
        print(f"Numbers tested: {results['total_numbers']:,}")
        print(f"Primes found: {results['primes_found']:,}")
        print(f"Composites found: {results['composites_found']:,}")
        print(f"Total time: {results['total_time_ms']:.2f} ms")
        print(f"Average time per number: {results['average_time_us']:.2f} μs")
        print(f"Processing rate: {results['numbers_per_second']:.0f} numbers/second")
        print(f"Cache hit rate: {results['cache_hit_rate']:.2%}")
        print(f"Optimization level: {results['optimization_effectiveness']}")

        return 0

    # Sieve mode
    if args.sieve:
        print(f"Generating primes up to {args.sieve:,} using TNFR-verified sieve...")

        optimizer = OptimizedTNFRPrimality()
        start_time = time.perf_counter()
        primes = optimizer.sieve_primes(args.sieve)
        elapsed = time.perf_counter() - start_time

        print(f"Found {len(primes):,} primes in {elapsed*1000:.2f} ms")

        if len(primes) <= 100:
            print("Primes found:", primes)
        else:
            print("First 20 primes:", primes[:20])
            print("Last 20 primes:", primes[-20:])

        return 0

    # Performance comparison mode
    if args.compare and args.numbers:
        print("Comparing basic vs optimized TNFR implementations...")
        print("=" * 60)

        results = performance_comparison(args.numbers)

        print("Performance Comparison Results:")
        print("-" * 35)
        print(f"Numbers tested: {results['numbers_tested']}")
        print(f"Basic implementation: {results['basic_time_ms']:.2f} ms")
        print(f"Optimized (1st pass): {results['optimized_time_ms']:.2f} ms")
        print(f"Optimized (cached): {results['optimized_cached_time_ms']:.2f} ms")
        print(f"Speedup (1st pass): {results['speedup_first_pass']:.2f}x")
        print(f"Speedup (cached): {results['speedup_cached_pass']:.2f}x")
        print(f"Cache effectiveness: {results['cache_effectiveness']:.2f}x")

        return 0

    # Regular testing mode
    if not args.numbers:
        print("Error: No numbers provided for testing")
        print("Use --help for usage information")
        return 1

    # Choose implementation
    if args.optimized or args.batch:
        optimizer = OptimizedTNFRPrimality()

        if args.batch:
            # Batch processing mode
            print("TNFR Batch Primality Testing (Optimized)")
            print("=" * 45)

            start_time = time.perf_counter()
            results = optimizer.batch_test(args.numbers)
            batch_time = time.perf_counter() - start_time

            # Display results
            if args.timing:
                print(
                    f"{'Number':>12}  {'Prime':>8}  {'ΔNFR':>14}  {'Individual(μs)':>15}"
                )
                print("-" * 65)
            else:
                print(f"{'Number':>12}  {'Prime':>8}  {'ΔNFR':>14}")
                print("-" * 40)

            for n, is_prime, delta_nfr in results:
                if args.timing:
                    # Individual timing approximation
                    individual_time = (batch_time / len(args.numbers)) * 1_000_000
                    print(
                        f"{n:12d}  {str(is_prime):>8}  {delta_nfr:14.6f}  {individual_time:15.2f}"
                    )
                else:
                    print(f"{n:12d}  {str(is_prime):>8}  {delta_nfr:14.6f}")

            print(f"\nBatch Summary:")
            print(f"Total numbers: {len(args.numbers)}")
            print(f"Batch time: {batch_time*1000:.2f} ms")
            print(
                f"Average per number: {(batch_time/len(args.numbers))*1_000_000:.2f} μs"
            )

            if args.stats:
                print("\nOptimizer Statistics:")
                print("-" * 25)
                stats = optimizer.get_statistics()
                for key, value in stats.items():
                    if isinstance(value, float):
                        print(f"{key}: {value:.4f}")
                    else:
                        print(f"{key}: {value}")

        else:
            # Individual optimized testing
            print("TNFR Primality Testing (Optimized)")
            print("=" * 38)

            if args.timing:
                header = f"{'Number':>12}  {'Prime':>8}  {'ΔNFR':>14}  {'Time(μs)':>10}"
            else:
                header = f"{'Number':>12}  {'Prime':>8}  {'ΔNFR':>14}"

            print(header)
            print("-" * len(header))

            for n in args.numbers:
                if args.timing:
                    start = time.perf_counter()

                is_prime, delta_nfr = optimizer.is_prime(n)

                if args.timing:
                    elapsed_us = (time.perf_counter() - start) * 1_000_000
                    print(
                        f"{n:12d}  {str(is_prime):>8}  {delta_nfr:14.6f}  {elapsed_us:10.2f}"
                    )
                else:
                    print(f"{n:12d}  {str(is_prime):>8}  {delta_nfr:14.6f}")

            if args.stats:
                print("\nOptimizer Statistics:")
                print("-" * 25)
                stats = optimizer.get_statistics()
                for key, value in stats.items():
                    if isinstance(value, float):
                        print(f"{key}: {value:.4f}")
                    else:
                        print(f"{key}: {value}")

    else:
        # Basic implementation mode
        print("TNFR Primality Testing (Basic)")
        print("=" * 32)

        if args.timing:
            header = f"{'Number':>12}  {'Prime':>8}  {'ΔNFR':>14}  {'Time(μs)':>10}"
        else:
            header = f"{'Number':>12}  {'Prime':>8}  {'ΔNFR':>14}"

        print(header)
        print("-" * len(header))

        total_time = 0
        for n in args.numbers:
            if args.timing:
                start = time.perf_counter()

            is_prime, delta_nfr = tnfr_is_prime(n)

            if args.timing:
                elapsed_us = (time.perf_counter() - start) * 1_000_000
                total_time += elapsed_us
                print(
                    f"{n:12d}  {str(is_prime):>8}  {delta_nfr:14.6f}  {elapsed_us:10.2f}"
                )
            else:
                print(f"{n:12d}  {str(is_prime):>8}  {delta_nfr:14.6f}")

        if args.timing and len(args.numbers) > 1:
            avg_time = total_time / len(args.numbers)
            print(f"\nAverage time per number: {avg_time:.2f} μs")

    return 0


if __name__ == "__main__":
    raise SystemExit(main())