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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: src/tnfr/validation/aggregator.py

aggregator.py

Enhanced structural validation aggregator (Phase 3).

Combines grammar validation (U1-U4 primary + optional U6 confinement telemetry) with canonical structural field thresholds (Φ_s, |∇φ|, K_φ, ξ_C). Produces a unified report object for downstream tooling (health checks, telemetry enrichment, CI guards).

Design Principles

  1. Read-only: Never mutates graph state; all computations are telemetry.
  2. Non-invasive: Wraps existing grammar error factory without altering its behaviour or the validator core.
  3. Extensible: Thresholds overrideable; adding new canonical fields or rules only requires updating constants / mapping.
  4. Bounded Overhead: Single-pass field computations; avoids recompute.

Threshold Defaults (Canonical / Safety)

|Φ_s|_max : 0.771 (empirical per-node threshold, U6 confinement) |∇φ|_max : 0.38 (stable operation upper bound) |K_φ|_flag : 2.8274 (local confinement / fault zone flag) ξ_C_crit_mult : 1.0 (ξ_C > system_diameter signals critical approach) ξ_C_watch_mult: 3.1416 (ξ_C > 3× mean_node_distance watch condition)

Report Semantics

status : "valid" | "invalid" (grammar only) risk_level: "low" | "elevated" | "critical" (fields + grammar) grammar_errors: list[ExtendedGrammarError] field_metrics : raw field snapshots + aggregates thresholds_exceeded: dict[name, bool]

Usage

from tnfr.validation.aggregator import run_structural_validation report = run_structural_validation(G, sequence=["AL","UM","IL"]) if report.status == "invalid": ... for err in report.grammar_errors: print(err.message) if report.risk_level != "low": ... print("Structural risk detected", report.thresholds_exceeded)

Physics Traceability

Grammar rules reference nodal equation boundedness and coupling conditions (U1-U4). Field thresholds derive from empirical validation summarised in AGENTS.md and docs/XI_C_CANONICAL_PROMOTION.md.

Source Code

python
"""Enhanced structural validation aggregator (Phase 3).

Combines grammar validation (U1-U4 primary + optional U6 confinement
telemetry) with canonical structural field thresholds (Φ_s, |∇φ|, K_φ,
ξ_C). Produces a unified report object for downstream tooling (health
checks, telemetry enrichment, CI guards).

Design Principles
-----------------
1. Read-only: Never mutates graph state; all computations are telemetry.
2. Non-invasive: Wraps existing grammar error factory without altering
   its behaviour or the validator core.
3. Extensible: Thresholds overrideable; adding new canonical fields or
   rules only requires updating constants / mapping.
4. Bounded Overhead: Single-pass field computations; avoids recompute.

Threshold Defaults (Canonical / Safety)
--------------------------------------
|Φ_s|_max      : 0.771  (empirical per-node threshold, U6 confinement)
|∇φ|_max      : 0.38   (stable operation upper bound)
|K_φ|_flag    : 2.8274    (local confinement / fault zone flag)
ξ_C_crit_mult : 1.0    (ξ_C > system_diameter signals critical approach)
ξ_C_watch_mult: 3.1416    (ξ_C > 3× mean_node_distance watch condition)

Report Semantics
----------------
status    : "valid" | "invalid" (grammar only)
risk_level: "low" | "elevated" | "critical" (fields + grammar)
grammar_errors: list[ExtendedGrammarError]
field_metrics : raw field snapshots + aggregates
thresholds_exceeded: dict[name, bool]

Usage
-----
>>> from tnfr.validation.aggregator import run_structural_validation
>>> report = run_structural_validation(G, sequence=["AL","UM","IL"])
>>> if report.status == "invalid":
...     for err in report.grammar_errors: print(err.message)
>>> if report.risk_level != "low":
...     print("Structural risk detected", report.thresholds_exceeded)

Physics Traceability
--------------------
Grammar rules reference nodal equation boundedness and coupling
conditions (U1-U4). Field thresholds derive from empirical validation
summarised in AGENTS.md and docs/XI_C_CANONICAL_PROMOTION.md.
"""

from __future__ import annotations

from dataclasses import dataclass
from typing import Any, Iterable, Sequence

from ..constants.canonical import K_PHI_CANONICAL_THRESHOLD

try:  # Graph dependency (NetworkX-like interface)
    import networkx as nx  # type: ignore
except ImportError:  # pragma: no cover
    nx = None  # type: ignore

from ..operators.grammar_error_factory import (
    ExtendedGrammarError,
    collect_grammar_errors,
)
from ..performance.guardrails import PerformanceRegistry
from ..physics.fields import (
    compute_phase_curvature,
    compute_phase_gradient,
    compute_structural_potential,
    estimate_coherence_length,
)

__all__ = [
    "ValidationReport",
    "run_structural_validation",
]


@dataclass(slots=True)
class ValidationReport:
    """Unified structural validation result.

    Attributes
    ----------
    status : str
        "valid" if no grammar errors else "invalid".
    risk_level : str
        "low", "elevated", or "critical" based on field thresholds & grammar.
    grammar_errors : list[ExtendedGrammarError]
        Enriched grammar error payloads (possibly empty).
    field_metrics : dict[str, Any]
        Raw & aggregate field telemetry (per-node maps + summary stats).
    thresholds_exceeded : dict[str, bool]
        Boolean flags per monitored threshold.
    sequence : tuple[str, ...]
        Operator glyph sequence validated.
    notes : list[str]
        Informational annotations (e.g. which conditions set risk level).
    """

    status: str
    risk_level: str
    grammar_errors: list[ExtendedGrammarError]
    field_metrics: dict[str, Any]
    thresholds_exceeded: dict[str, bool]
    sequence: tuple[str, ...]
    notes: list[str]

    def to_dict(self) -> dict[str, Any]:  # noqa: D401
        return {
            "status": self.status,
            "risk_level": self.risk_level,
            "grammar_errors": [e.to_payload() for e in self.grammar_errors],
            "field_metrics": self.field_metrics,
            "thresholds_exceeded": self.thresholds_exceeded,
            "sequence": self.sequence,
            "notes": self.notes,
        }


def _mean(values: Iterable[float]) -> float:
    vals = list(values)
    return sum(vals) / max(len(vals), 1)


def run_structural_validation(
    G: Any,
    *,
    sequence: Sequence[str] | None = None,
    # Threshold overrides
    max_delta_phi_s: float = PHI,
    max_phase_gradient: float = 0.38,
    k_phi_flag_threshold: float = K_PHI_CANONICAL_THRESHOLD,
    xi_c_critical_multiplier: float = 1.0,
    xi_c_watch_multiplier: float = 3.0,
    # Optional baselines for drift calculations
    baseline_structural_potential: dict[Any, float] | None = None,
    # Performance instrumentation (opt-in)
    perf_registry: PerformanceRegistry | None = None,
) -> ValidationReport:
    """Run enhanced structural validation aggregating grammar + field safety.

    Parameters
    ----------
    G : Graph
        TNFR network (NetworkX-like) with required node attributes
        for ΔNFR & phase where available.
        where available.
    sequence : Sequence[str] | None
        Operator glyphs applied. If provided, grammar errors collected.
        If None, grammar validation skipped (status remains 'valid'
        unless field risk escalates).
    max_delta_phi_s : float
        Confinement escape threshold (ΔΦ_s). Evaluated against mean
        absolute drift if baseline provided; otherwise potential
        reported without drift flagging.
    max_phase_gradient : float
        Stable operation threshold for |∇φ|.
    k_phi_flag_threshold : float
        Local confinement / fault zone threshold for |K_φ| magnitudes.
    xi_c_critical_multiplier : float
        Critical approach when ξ_C > system_diameter * multiplier.
    xi_c_watch_multiplier : float
        Watch condition when ξ_C > mean_node_distance * multiplier.
    baseline_structural_potential : dict | None
        Optional prior Φ_s snapshot to compute drift; if omitted
        ΔΦ_s not computed.
    perf_registry : PerformanceRegistry | None
        Optional registry for timing measurements (opt-in overhead).

    Returns
    -------
    ValidationReport
        Unified structural validation result.
    """

    notes: list[str] = []

    # Performance start (if instrumentation active)
    start_time = None
    if perf_registry is not None:
        try:
            import time as _t

            start_time = _t.perf_counter()
        except Exception:  # pragma: no cover
            start_time = None

    # Grammar errors (read-only enrichment)
    grammar_errors: list[ExtendedGrammarError] = []
    if sequence is not None:
        grammar_errors = collect_grammar_errors(sequence)
    status = "valid" if not grammar_errors else "invalid"

    # Field computations (canonical tetrad)
    phi_s_map = compute_structural_potential(G)
    grad_map = compute_phase_gradient(G)
    curvature_map = compute_phase_curvature(G)
    xi_c = estimate_coherence_length(G)

    # Aggregates
    mean_phi_s = _mean(phi_s_map.values())
    mean_grad = _mean(grad_map.values())
    max_grad = max(grad_map.values()) if grad_map else 0.0
    max_k_phi = max(abs(v) for v in curvature_map.values()) if curvature_map else 0.0

    # Drift (optional baseline)
    delta_phi_s = None
    if baseline_structural_potential is not None:
        # Mean absolute difference
        diffs = []
        for n, val in phi_s_map.items():
            prev = baseline_structural_potential.get(n)
            if prev is not None:
                diffs.append(abs(val - prev))
        delta_phi_s = _mean(diffs) if diffs else 0.0

    # System geometry approximation (unweighted)
    if nx is not None:
        try:
            # Use fast diameter approximation (46-111× speedup)
            try:
                from ..utils.fast_diameter import (
                    approximate_diameter_2sweep,
                    compute_eccentricity_cached,
                )

                system_diameter = approximate_diameter_2sweep(G)
            except (ImportError, Exception):
                # Fallback to exact (slow) diameter
                system_diameter = nx.diameter(G)  # type: ignore
                compute_eccentricity_cached = None  # type: ignore
        except Exception:  # pragma: no cover - fallback path
            system_diameter = 0
            compute_eccentricity_cached = None  # type: ignore
        # Mean node distance (cached eccentricity, ~2.3s → 0.000s)
        try:
            if compute_eccentricity_cached is not None:
                ecc = compute_eccentricity_cached(G)
            else:
                ecc = nx.eccentricity(G)  # type: ignore
            mean_node_distance = _mean(ecc.values())
        except Exception:  # pragma: no cover
            mean_node_distance = 0.0
    else:  # pragma: no cover
        system_diameter = 0
        mean_node_distance = 0.0

    # Threshold evaluations
    thresholds_exceeded: dict[str, bool] = {}

    if delta_phi_s is not None:
        exceeded = delta_phi_s >= max_delta_phi_s
        thresholds_exceeded["delta_phi_s"] = exceeded
        if exceeded:
            notes.append(
                (
                    f"ΔΦ_s drift {delta_phi_s:.3f} ≥ "
                    f"{max_delta_phi_s:.3f} (escape threshold)"
                )
            )

    # Phase gradient (mean & max considered; max is more sensitive to spikes)
    grad_exceeded = max_grad >= max_phase_gradient
    thresholds_exceeded["phase_gradient_max"] = grad_exceeded
    if grad_exceeded:
        notes.append(
            (
                f"max |∇φ| {max_grad:.3f} ≥ "
                f"{max_phase_gradient:.3f} (stress threshold)"
            )
        )

    # Curvature confinement pockets
    k_phi_flag = max_k_phi >= k_phi_flag_threshold
    thresholds_exceeded["k_phi_flag"] = k_phi_flag
    if k_phi_flag:
        notes.append(
            (
                f"|K_φ| max {max_k_phi:.3f} ≥ "
                f"{k_phi_flag_threshold:.3f} (fault zone flag)"
            )
        )

    # Coherence length critical / watch thresholds
    xi_c_critical = (
        system_diameter > 0 and xi_c > system_diameter * xi_c_critical_multiplier
    )
    xi_c_watch = (
        mean_node_distance > 0 and xi_c > mean_node_distance * xi_c_watch_multiplier
    )
    thresholds_exceeded["xi_c_critical"] = bool(xi_c_critical)
    thresholds_exceeded["xi_c_watch"] = bool(xi_c_watch)
    if xi_c_critical:
        notes.append(
            (
                f"ξ_C {xi_c:.1f} > diameter {system_diameter} * "
                f"{xi_c_critical_multiplier} (critical approach)"
            )
        )
    elif xi_c_watch:
        notes.append(
            (
                f"ξ_C {xi_c:.1f} > mean_dist {mean_node_distance:.1f} * "
                f"{xi_c_watch_multiplier} (watch)"
            )
        )

    # Risk level derivation
    if status == "invalid":
        risk_level = "critical"
        notes.append("Grammar invalid (U1-U4).")
    else:
        if thresholds_exceeded.get("xi_c_critical") or thresholds_exceeded.get(
            "delta_phi_s"
        ):
            risk_level = "critical"
        elif (
            thresholds_exceeded.get("phase_gradient_max")
            or thresholds_exceeded.get("k_phi_flag")
            or thresholds_exceeded.get("xi_c_watch")
        ):
            risk_level = "elevated"
        else:
            risk_level = "low"

    field_metrics: dict[str, Any] = {
        "phi_s": phi_s_map,
        "phase_gradient": grad_map,
        "phase_curvature": curvature_map,
        "xi_c": xi_c,
        "mean_structural_potential": mean_phi_s,
        "mean_phase_gradient": mean_grad,
        "max_phase_gradient": max_grad,
        "max_k_phi": max_k_phi,
        "delta_phi_s": delta_phi_s,
        "system_diameter": system_diameter,
        "mean_node_distance": mean_node_distance,
    }

    report = ValidationReport(
        status=status,
        risk_level=risk_level,
        grammar_errors=grammar_errors,
        field_metrics=field_metrics,
        thresholds_exceeded=thresholds_exceeded,
        sequence=tuple(sequence or []),
        notes=notes,
    )

    if perf_registry is not None and start_time is not None:
        try:
            import time as _t

            perf_registry.record(
                "validation",
                _t.perf_counter() - start_time,
                meta={
                    "nodes": (
                        G.number_of_nodes() if hasattr(G, "number_of_nodes") else None
                    ),
                    "edges": (
                        G.number_of_edges() if hasattr(G, "number_of_edges") else None
                    ),
                    "sequence_len": (len(sequence) if sequence is not None else 0),
                    "status": status,
                },
            )
        except Exception:  # pragma: no cover
            pass

    return report