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: examples/10_applications/91_breast_cancer_phase_gate_demo.py

91_breast_cancer_phase_gate_demo.py

Example 91 — Biomedical Phase-Gate Audit on WDBC data.

This example uses the real Wisconsin Diagnostic Breast Cancer dataset bundled with scikit-learn. It builds a k-nearest-neighbour graph from tumor morphology measurements, encodes the diagnosis as a binary phase signal, and asks a very concrete non-financial question:

text
Which cases sit in a local morphology neighbourhood that disagrees with
their diagnostic phase?

Scope

This is a structural audit / model-review example, not clinical decision support. It demonstrates that TNFR phase-gate telemetry localizes graph-local diagnostic boundary cases that global class balance and topology-only baselines cannot localize.

Run: python examples/10_applications/91_breast_cancer_phase_gate_demo.py

Source Code

python
#!/usr/bin/env python3
"""Example 91 — Biomedical Phase-Gate Audit on WDBC data.

This example uses the real Wisconsin Diagnostic Breast Cancer dataset bundled
with scikit-learn.  It builds a k-nearest-neighbour graph from tumor morphology
measurements, encodes the diagnosis as a binary phase signal, and asks a very
concrete non-financial question:

    Which cases sit in a local morphology neighbourhood that disagrees with
    their diagnostic phase?

Scope
-----
This is a structural audit / model-review example, not clinical decision
support.  It demonstrates that TNFR phase-gate telemetry localizes graph-local
diagnostic boundary cases that global class balance and topology-only baselines
cannot localize.

Run:
    python examples/10_applications/91_breast_cancer_phase_gate_demo.py
"""
from __future__ import annotations

import html
import json
import math
import sys
import warnings
from pathlib import Path
from typing import Any, Mapping

ROOT = Path(__file__).resolve().parents[1]
SRC = ROOT / "src"
sys.path.insert(0, str(SRC))

loaded_tnfr = sys.modules.get("tnfr")
loaded_path = str(getattr(loaded_tnfr, "__file__", "")) if loaded_tnfr else ""
if loaded_tnfr is not None and not loaded_path.startswith(str(SRC)):
    for name in list(sys.modules):
        if name == "tnfr" or name.startswith("tnfr."):
            del sys.modules[name]

import networkx as nx  # noqa: E402
from sklearn.datasets import load_breast_cancer  # noqa: E402
from sklearn.neighbors import NearestNeighbors  # noqa: E402
from sklearn.preprocessing import StandardScaler  # noqa: E402

from tnfr.validation.phase_gate import (  # noqa: E402
    DEFAULT_PHASE_GATE,
    analyze_phase_gate,
    rank_phase_stress_hotspots,
)


def build_wdbc_knn_graph(k: int = 8) -> tuple[nx.Graph, Any]:
    """Build a morphology kNN graph for the real WDBC dataset."""
    data = load_breast_cancer()
    X = StandardScaler().fit_transform(data.data)
    y = data.target

    neighbours = NearestNeighbors(n_neighbors=int(k) + 1)
    neighbours.fit(X)
    distances, indices = neighbours.kneighbors(X)

    G = nx.Graph()
    for node, target in enumerate(y):
        diagnosis = str(data.target_names[int(target)])
        # scikit-learn encoding: 0=malignant, 1=benign.
        phase = 0.0 if diagnosis == "benign" else math.pi
        G.add_node(
            node,
            phase=phase,
            theta=phase,
            EPI=1.0,
            diagnosis=diagnosis,
            mean_radius=float(data.data[node][0]),
            mean_texture=float(data.data[node][1]),
            mean_concavity=float(data.data[node][6]),
            glyph_history=[],
        )

    for node in range(len(y)):
        for distance, neighbour in zip(distances[node][1:], indices[node][1:]):
            G.add_edge(node, int(neighbour), morphology_distance=float(distance))

    # Attach local structural pressure from diagnostic disagreement with
    # morphology neighbours.  This keeps Φ_s tied to graph-local conflict.
    for node in G.nodes():
        degree = G.degree[node]
        conflicts = sum(
            1
            for neighbour in G.neighbors(node)
            if G.nodes[neighbour]["diagnosis"] != G.nodes[node]["diagnosis"]
        )
        conflict_rate = conflicts / degree if degree else 0.0
        G.nodes[node]["incident_diagnostic_conflicts"] = conflicts
        G.nodes[node]["delta_nfr"] = conflict_rate
        G.nodes[node]["dnfr"] = conflict_rate
        G.nodes[node]["coherence"] = 1.0 / (1.0 + conflict_rate)

    return G, data


def _binary_auc(labels: Mapping[int, bool], scores: Mapping[int, float]) -> float:
    positives = [scores[node] for node, label in labels.items() if label]
    negatives = [scores[node] for node, label in labels.items() if not label]
    if not positives or not negatives:
        return 0.5

    wins = 0.0
    ties = 0.0
    for positive in positives:
        for negative in negatives:
            if positive > negative:
                wins += 1.0
            elif positive == negative:
                ties += 1.0
    return (wins + 0.5 * ties) / (len(positives) * len(negatives))


def _precision_at_review_count(
    labels: Mapping[int, bool],
    scores: Mapping[int, float],
) -> float:
    review_count = sum(labels.values())
    if review_count <= 0:
        return 0.0
    ranked = sorted(scores, key=scores.get, reverse=True)[:review_count]
    return sum(1 for node in ranked if labels[node]) / review_count


def _mean_neighbour_distance(G: nx.Graph, node: int) -> float:
    distances = [
        float(G.edges[node, neighbour].get("morphology_distance", 0.0))
        for neighbour in G.neighbors(node)
    ]
    return sum(distances) / len(distances) if distances else 0.0


def _markdown_table(headers: list[str], rows: list[list[Any]]) -> str:
    header = "| " + " | ".join(headers) + " |"
    sep = "| " + " | ".join("---" for _ in headers) + " |"
    body = ["| " + " | ".join(str(cell) for cell in row) + " |" for row in rows]
    return "\n".join([header, sep, *body])


def run_demo(
    *,
    k: int = 8,
    review_conflict_threshold: int = 3,
    top_n: int = 10,
    output_dir: Path | None = None,
) -> dict[str, Any]:
    """Run the WDBC phase-gate audit and optionally export reports."""
    G, data = build_wdbc_knn_graph(k=k)

    # Structural potential may emit harmless divide warnings on degenerate
    # graph-distance internals; suppress them for report readability.
    with warnings.catch_warnings():
        warnings.filterwarnings("ignore", category=RuntimeWarning)
        report = analyze_phase_gate(G, gate=DEFAULT_PHASE_GATE, top_n=top_n)
        all_hotspots = rank_phase_stress_hotspots(
            G,
            gate=DEFAULT_PHASE_GATE,
            top_n=None,
        )

    hotspot_scores = {int(item.node): float(item.stress_score) for item in all_hotspots}
    degree_scores = {int(node): float(G.degree[node]) for node in G.nodes()}
    distance_scores = {
        int(node): _mean_neighbour_distance(G, int(node)) for node in G.nodes()
    }
    constant_scores = {int(node): 1.0 for node in G.nodes()}
    review_labels = {
        int(node): int(G.nodes[node]["incident_diagnostic_conflicts"])
        >= int(review_conflict_threshold)
        for node in G.nodes()
    }

    score_rows = [
        (
            "TNFR phase-stress hotspot",
            hotspot_scores,
            "phase gate + |∇φ| + |Kφ| + incident excess",
        ),
        (
            "Mean morphology-neighbour distance",
            distance_scores,
            "feature-space distance only",
        ),
        ("Topology degree", degree_scores, "topology only"),
        ("Global constant baseline", constant_scores, "no localization signal"),
    ]
    comparison = [
        {
            "score": name,
            "basis": basis,
            "auc": _binary_auc(review_labels, scores),
            "precision_at_review_count": _precision_at_review_count(
                review_labels,
                scores,
            ),
        }
        for name, scores, basis in score_rows
    ]

    prescriptions_by_target = {
        prescription.target: prescription.sequence
        for prescription in report.operator_prescriptions
        if prescription.scope == "node"
    }
    top_hotspots = []
    for hotspot in report.hotspots:
        node = int(hotspot.node)
        top_hotspots.append(
            {
                "sample_id": node,
                "diagnosis": G.nodes[node]["diagnosis"],
                "incident_diagnostic_conflicts": int(
                    G.nodes[node]["incident_diagnostic_conflicts"]
                ),
                "stress_score": float(hotspot.stress_score),
                "mean_radius": G.nodes[node]["mean_radius"],
                "mean_texture": G.nodes[node]["mean_texture"],
                "mean_concavity": G.nodes[node]["mean_concavity"],
                "prescription": list(
                    prescriptions_by_target.get(node, ("IL", "OZ", "THOL", "SHA"))
                ),
            }
        )

    summary = {
        "dataset": {
            "name": "Wisconsin Diagnostic Breast Cancer (scikit-learn bundled)",
            "sector": "biomedical / diagnostic morphology",
            "samples": int(G.number_of_nodes()),
            "features": int(len(data.feature_names)),
            "target_counts": {
                str(data.target_names[value]): int((data.target == value).sum())
                for value in sorted(set(data.target))
            },
        },
        "graph": {
            "construction": f"Standardized morphology {k}-NN graph",
            "nodes": int(G.number_of_nodes()),
            "edges": int(G.number_of_edges()),
            "k": int(k),
        },
        "phase_gate": {
            "gate": DEFAULT_PHASE_GATE,
            "edge_compliance": report.compliance.compliance_ratio,
            "violations": report.compliance.violation_count,
            "global_order_r": report.baseline_summary["global_order_r"],
            "phase_histogram_entropy": report.baseline_summary[
                "phase_histogram_entropy"
            ],
            "recommendation": report.recommendation,
        },
        "review_definition": {
            "meaning": "case has at least N morphology-neighbours with opposite diagnosis",
            "threshold": int(review_conflict_threshold),
            "review_node_count": int(sum(review_labels.values())),
        },
        "score_comparison": comparison,
        "top_hotspots": top_hotspots,
        "honest_interpretation": (
            "This example does not claim clinical validity. It shows that TNFR "
            "phase-gated local telemetry can prioritize real biomedical samples "
            "whose morphology-neighbourhood conflicts with their diagnostic phase. "
            "Global class balance and topology-only baselines do not provide that "
            "node-level localization."
        ),
    }

    if output_dir is not None:
        output_dir.mkdir(parents=True, exist_ok=True)
        (output_dir / "wdbc_phase_gate_demo.json").write_text(
            json.dumps(summary, indent=2) + "\n",
            encoding="utf-8",
        )
        markdown = render_markdown(summary)
        (output_dir / "wdbc_phase_gate_demo.md").write_text(
            markdown,
            encoding="utf-8",
        )
        (output_dir / "wdbc_phase_gate_demo.html").write_text(
            render_html(markdown),
            encoding="utf-8",
        )

    return summary


def render_markdown(summary: Mapping[str, Any]) -> str:
    """Render the WDBC audit summary as Markdown."""
    comparison_rows = [
        [
            row["score"],
            row["basis"],
            f"{row['auc']:.3f}",
            f"{row['precision_at_review_count']:.3f}",
        ]
        for row in summary["score_comparison"]
    ]
    hotspot_rows = [
        [
            item["sample_id"],
            item["diagnosis"],
            item["incident_diagnostic_conflicts"],
            f"{item['stress_score']:.3f}",
            f"{item['mean_radius']:.2f}",
            f"{item['mean_texture']:.2f}",
            f"{item['mean_concavity']:.5f}",
            " → ".join(item["prescription"]),
        ]
        for item in summary["top_hotspots"]
    ]
    return (
        "\n\n".join(
            [
                "# TNFR WDBC Biomedical Phase-Gate Audit",
                "## Dataset",
                (
                    f"Name: {summary['dataset']['name']}  \n"
                    f"Sector: {summary['dataset']['sector']}  \n"
                    f"Samples: {summary['dataset']['samples']}  \n"
                    f"Features: {summary['dataset']['features']}  \n"
                    f"Target counts: {summary['dataset']['target_counts']}"
                ),
                "## Graph and phase-gate state",
                (
                    f"Graph: {summary['graph']['construction']}  \n"
                    f"Nodes: {summary['graph']['nodes']}  \n"
                    f"Edges: {summary['graph']['edges']}  \n"
                    f"Edge compliance: {summary['phase_gate']['edge_compliance']:.4f}  \n"
                    f"Violations: {summary['phase_gate']['violations']}  \n"
                    f"Global order R: {summary['phase_gate']['global_order_r']:.4f}  \n"
                    f"Recommendation: {summary['phase_gate']['recommendation']}"
                ),
                "## Node-level review task",
                (
                    f"Definition: {summary['review_definition']['meaning']}  \n"
                    f"Threshold: {summary['review_definition']['threshold']}  \n"
                    f"Review nodes: {summary['review_definition']['review_node_count']}"
                ),
                "## Score comparison",
                _markdown_table(
                    ["Score", "Basis", "AUC", "Precision@review_count"],
                    comparison_rows,
                ),
                "## Top TNFR hotspots",
                _markdown_table(
                    [
                        "Sample",
                        "Diagnosis",
                        "Conflicts",
                        "Stress",
                        "Mean radius",
                        "Mean texture",
                        "Mean concavity",
                        "TNFR prescription",
                    ],
                    hotspot_rows,
                ),
                "## Honest interpretation",
                str(summary["honest_interpretation"]),
            ]
        )
        + "\n"
    )


def render_html(markdown: str) -> str:
    """Render a small standalone HTML report from the Markdown summary."""
    body: list[str] = []
    table_rows: list[str] = []
    in_table = False

    def flush_table() -> None:
        nonlocal in_table, table_rows
        if not in_table:
            return
        body.append("<table>")
        for index, raw in enumerate(table_rows):
            if index == 1:
                continue
            cells = [cell.strip() for cell in raw.strip("|").split("|")]
            tag = "th" if index == 0 else "td"
            body.append(
                "<tr>"
                + "".join(f"<{tag}>{html.escape(cell)}</{tag}>" for cell in cells)
                + "</tr>"
            )
        body.append("</table>")
        table_rows = []
        in_table = False

    for line in markdown.splitlines():
        if line.startswith("| "):
            in_table = True
            table_rows.append(line)
            continue
        flush_table()
        if line.startswith("# "):
            body.append(f"<h1>{html.escape(line[2:])}</h1>")
        elif line.startswith("## "):
            body.append(f"<h2>{html.escape(line[3:])}</h2>")
        elif line.strip():
            body.append(f"<p>{html.escape(line)}</p>")
    flush_table()

    return """<!DOCTYPE html>
<html lang=\"en\">
<head>
<meta charset=\"utf-8\">
<title>TNFR WDBC Biomedical Phase-Gate Audit</title>
<style>
body {{ font-family: Arial, sans-serif; margin: 2rem; line-height: 1.45; }}
table {{ border-collapse: collapse; width: 100%; margin: 1rem 0; }}
th, td {{ border: 1px solid #ccc; padding: 0.35rem 0.5rem; text-align: left; }}
th {{ background: #f3f5f7; }}
</style>
</head>
<body>
{body}
</body>
</html>
""".format(
        body="\n".join(body)
    )


def main() -> None:
    output_dir = ROOT / "results" / "reports"
    summary = run_demo(output_dir=output_dir)

    print("TNFR WDBC Biomedical Phase-Gate Audit")
    print("Real dataset: Wisconsin Diagnostic Breast Cancer")
    print(f"Samples: {summary['dataset']['samples']}")
    print(f"Graph edges: {summary['graph']['edges']}")
    print(f"Phase-gate compliance: {summary['phase_gate']['edge_compliance']:.4f}")
    print(f"Gate violations: {summary['phase_gate']['violations']}")
    print(
        "Review nodes (>= "
        f"{summary['review_definition']['threshold']} opposite-diagnosis neighbours): "
        f"{summary['review_definition']['review_node_count']}"
    )
    print("\nScore comparison:")
    for row in summary["score_comparison"]:
        print(
            f"  {row['score']:<38} "
            f"AUC={row['auc']:.3f} "
            f"P@N={row['precision_at_review_count']:.3f}"
        )
    print("\nTop TNFR hotspots:")
    for item in summary["top_hotspots"][:5]:
        print(
            f"  sample={item['sample_id']:>3} "
            f"diagnosis={item['diagnosis']:<9} "
            f"conflicts={item['incident_diagnostic_conflicts']:<2} "
            f"stress={item['stress_score']:.3f} "
            f"sequence={' -> '.join(item['prescription'])}"
        )
    print(f"\nReports written to: {output_dir}")


if __name__ == "__main__":
    main()