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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/operators/grammar.py

grammar.py

TNFR Canonical Grammar (single source of truth).

OPTIMIZED IMPLEMENTATION: Unified grammar validation with intelligent caching to eliminate redundant validation across TNFR modules. All grammar rules derive from nodal equation ∂EPI/∂t = νf · ΔNFR(t) theoretical foundations.

PERFORMANCE OPTIMIZATIONS:

  • Cached validation results with cache invalidation
  • Fast-path validation for common patterns
  • Batch validation for operator sequences
  • Memory-efficient storage of validation state

Terminology (TNFR semantics):

  • "node" here means resonant locus (coherence site); kept for compatibility with graph libraries. Unrelated to Node.js runtime.
  • Future aliasing ("locus") must preserve public API stability.

All rules derive from the nodal equation ∂EPI/∂t = νf · ΔNFR(t), canonical invariants, and formal contracts. No organizational conventions.

Canonical Constraints (U1-U6)

U1: STRUCTURAL INITIATION & CLOSURE U1a: Start with generators when needed U1b: End with closure operators Basis: ∂EPI/∂t undefined at EPI=0, sequences need coherent endpoints

U2: CONVERGENCE & BOUNDEDNESS If destabilizers, then include stabilizers Basis: ∫νf·ΔNFR dt must converge (integral convergence theorem)

U3: RESONANT COUPLING If coupling/resonance, then verify phase compatibility Basis: AGENTS.md Invariant #2 + resonance physics

U4: BIFURCATION DYNAMICS U4a: If bifurcation triggers, then include handlers U4b: If transformers, then recent destabilizer (+ prior IL for ZHIR) Basis: Contract OZ + bifurcation theory

U5: MULTI-SCALE COHERENCE If deep REMESH (depth > 1), require scale stabilizers (IL/THOL). Basis: Hierarchical nodal equation + coherence conservation (C_parent ≥ α·ΣC_child).

U6: STRUCTURAL POTENTIAL CONFINEMENT (Promoted 2025-11-11) Verify Δ Φ_s < π/2 (U6 confinement bound) Basis: Emergent Φ_s field from ΔNFR distribution + empirical validation Status: CANONICAL - 2,400+ experiments, corr(Δ Φ_s, ΔC) = -0.822, CV = 0.1%

For complete derivations and physics basis, see UNIFIED_GRAMMAR_RULES.md

References

  • UNIFIED_GRAMMAR_RULES.md: Complete physics derivations and mappings
  • AGENTS.md: Canonical invariants and formal contracts
  • TNFR.pdf: Nodal equation and bifurcation theory

Source Code

python
"""TNFR Canonical Grammar (single source of truth).

OPTIMIZED IMPLEMENTATION: Unified grammar validation with intelligent caching
to eliminate redundant validation across TNFR modules. All grammar rules
derive from nodal equation ∂EPI/∂t = νf · ΔNFR(t) theoretical foundations.

PERFORMANCE OPTIMIZATIONS:
- Cached validation results with cache invalidation
- Fast-path validation for common patterns
- Batch validation for operator sequences
- Memory-efficient storage of validation state

Terminology (TNFR semantics):
- "node" here means resonant locus (coherence site); kept for
    compatibility with graph libraries. Unrelated to Node.js runtime.
- Future aliasing ("locus") must preserve public API stability.

All rules derive from the nodal equation ∂EPI/∂t = νf · ΔNFR(t), canonical
invariants, and formal contracts. No organizational conventions.

Canonical Constraints (U1-U6)
------------------------------
U1: STRUCTURAL INITIATION & CLOSURE
    U1a: Start with generators when needed
    U1b: End with closure operators
    Basis: ∂EPI/∂t undefined at EPI=0, sequences need coherent endpoints

U2: CONVERGENCE & BOUNDEDNESS
    If destabilizers, then include stabilizers
    Basis: ∫νf·ΔNFR dt must converge (integral convergence theorem)

U3: RESONANT COUPLING
    If coupling/resonance, then verify phase compatibility
    Basis: AGENTS.md Invariant #2 + resonance physics

U4: BIFURCATION DYNAMICS
    U4a: If bifurcation triggers, then include handlers
    U4b: If transformers, then recent destabilizer (+ prior IL for ZHIR)
    Basis: Contract OZ + bifurcation theory

U5: MULTI-SCALE COHERENCE
    If deep REMESH (depth > 1), require scale stabilizers (IL/THOL).
    Basis: Hierarchical nodal equation + coherence conservation
    (C_parent ≥ α·ΣC_child).

U6: STRUCTURAL POTENTIAL CONFINEMENT (Promoted 2025-11-11)
    Verify Δ Φ_s < π/2 (U6 confinement bound)
    Basis: Emergent Φ_s field from ΔNFR distribution + empirical validation
    Status: CANONICAL - 2,400+ experiments, corr(Δ Φ_s, ΔC) = -0.822, CV = 0.1%

For complete derivations and physics basis, see UNIFIED_GRAMMAR_RULES.md

References
----------
- UNIFIED_GRAMMAR_RULES.md: Complete physics derivations and mappings
- AGENTS.md: Canonical invariants and formal contracts
- TNFR.pdf: Nodal equation and bifurcation theory
"""

from __future__ import annotations

import hashlib
from functools import lru_cache
from typing import TYPE_CHECKING, Any

if TYPE_CHECKING:
    from ..types import Glyph, NodeId, TNFRGraph
    from .definitions import Operator  # noqa: F401
else:
    # Runtime fallbacks to avoid type expression errors in string annotations
    NodeId = Any  # type: ignore  # Runtime alias
    TNFRGraph = Any  # type: ignore  # Runtime alias
    from ..types import Glyph  # noqa: F401

from ..config.operator_names import (  # noqa: F401
    CANONICAL_OPERATOR_NAMES,
    INTERMEDIATE_OPERATORS,
    SELF_ORGANIZATION,
    SELF_ORGANIZATION_CLOSURES,
    VALID_END_OPERATORS,
    VALID_START_OPERATORS,
)
from ..validation.base import ValidationOutcome  # noqa: F401
from ..validation.compatibility import (  # noqa: F401
    CompatibilityLevel,
    get_compatibility_level,
)

# Operator registry & glyph mappings (backward compatibility)
from .definitions import (
    Coherence,
    Contraction,
    Coupling,
    Dissonance,
    Emission,
    Expansion,
    Mutation,
    Reception,
    Recursivity,
    Resonance,
    SelfOrganization,
    Silence,
    Transition,
)

# Application
from .grammar_application import (
    apply_glyph_with_grammar,
    enforce_canonical_grammar,
    on_applied_glyph,
)

# Context
from .grammar_context import GrammarContext

# Core validator
from .grammar_core import GrammarValidator

# Grammar-Aware Dynamics (proactive incremental U1-U6 enforcement)
from .grammar_dynamics import (
    CandidateResult,
    GrammarViolation,
    enforce_grammar_on_glyph,
    filter_candidates,
    suggest_alternative,
    validate_candidate,
    validate_sequence_incremental,
)

# Pattern recognition
from .grammar_patterns import (
    CANONICAL_IL_SEQUENCES,
    IL_ANTIPATTERNS,
    SequenceValidationResultWithHealth,
    optimize_il_sequence,
    parse_sequence,
    recognize_il_sequences,
    suggest_il_sequence,
    validate_sequence,
    validate_sequence_with_health,
)

# Telemetry
from .grammar_telemetry import (
    warn_coherence_length_telemetry,
    warn_phase_curvature_telemetry,
    warn_phase_gradient_telemetry,
)

# Re-export all grammar components (backward compatibility)
from .grammar_types import (  # Operator sets
    BIFURCATION_HANDLERS,
    BIFURCATION_TRIGGERS,
    CLOSURES,
    COUPLING_RESONANCE,
    DESTABILIZERS,
    FUNCTION_TO_GLYPH,
    GENERATORS,
    GLYPH_TO_FUNCTION,
    RECURSIVE_GENERATORS,
    SCALE_STABILIZERS,
    STABILIZERS,
    TRANSFORMERS,
    GrammarConfigurationError,
    MutationPreconditionError,
    RepeatWindowError,
    SequenceSyntaxError,
    SequenceValidationResult,
    StructuralGrammarError,
    StructuralPattern,
    StructuralPotentialConfinementError,
    TholClosureError,
    TransitionCompatibilityError,
    function_name_to_glyph,
    glyph_function_name,
    record_grammar_violation,
)

# U6 validation
from .grammar_u6 import validate_structural_potential_confinement

# Main validation entry point
from .grammar_validate import validate_grammar
from .registry import OPERATORS, discover_operators

# Ensure registry populated for tests expecting direct name lookups
discover_operators()

# Provide a name→class mapping including canonical aliases (auto-registered)
OPERATOR_NAME_TO_CLASS = {n: cls for n, cls in OPERATORS.items()}

# Backward compatibility: keep operator classes referenced so import tools
# and static analyzers treat them as intentionally re-exported.
_BACKWARD_COMPAT_OPERATORS = (
    Emission,
    Reception,
    Coherence,
    Dissonance,
    Coupling,
    Resonance,
    Silence,
    Expansion,
    Contraction,
    SelfOrganization,
    Mutation,
    Transition,
    Recursivity,
)


def get_grammar_cache_stats() -> dict[str, dict[str, int]]:
    """Return cache statistics for grammar-level cached functions.

    Inspects imported callables for a ``cache_info`` attribute (from
    ``functools.lru_cache``). Returns mapping ``{function_name: cache_info}``
    where ``cache_info`` is converted to a plain dict.
    Physics-neutral: read-only telemetry; does not modify caches.
    """
    stats: dict[str, dict[str, int]] = {}
    import inspect

    for name, obj in list(globals().items()):
        if inspect.isfunction(obj) and hasattr(obj, "cache_info"):
            try:  # pragma: no cover - defensive
                info = obj.cache_info()
                maxsize = info.maxsize if info.maxsize is not None else -1
                stats[name] = {
                    "hits": info.hits,
                    "misses": info.misses,
                    "maxsize": maxsize,
                    "currsize": info.currsize,
                }
            except Exception:  # pragma: no cover
                pass
    return stats


__all__ = [
    # Types
    "StructuralPattern",
    # Exceptions
    "StructuralGrammarError",
    "RepeatWindowError",
    "MutationPreconditionError",
    "TholClosureError",
    "TransitionCompatibilityError",
    "StructuralPotentialConfinementError",
    "SequenceSyntaxError",
    "GrammarConfigurationError",
    # Validation
    "SequenceValidationResult",
    "validate_grammar",
    "validate_sequence",
    "parse_sequence",
    "validate_sequence_with_health",
    # U6
    "validate_structural_potential_confinement",
    # Core
    "GrammarContext",
    "GrammarValidator",
    # Application
    "apply_glyph_with_grammar",
    "on_applied_glyph",
    "enforce_canonical_grammar",
    # Grammar-Aware Dynamics
    "GrammarViolation",
    "CandidateResult",
    "validate_candidate",
    "filter_candidates",
    "suggest_alternative",
    "enforce_grammar_on_glyph",
    "validate_sequence_incremental",
    # Helpers
    "glyph_function_name",
    "function_name_to_glyph",
    "record_grammar_violation",
    "SequenceValidationResultWithHealth",
    "recognize_il_sequences",
    "optimize_il_sequence",
    "suggest_il_sequence",
    "CANONICAL_IL_SEQUENCES",
    "IL_ANTIPATTERNS",
    # Telemetry
    "warn_phase_gradient_telemetry",
    "warn_phase_curvature_telemetry",
    "warn_coherence_length_telemetry",
    # Operator sets
    "GENERATORS",
    "CLOSURES",
    "STABILIZERS",
    "DESTABILIZERS",
    "COUPLING_RESONANCE",
    "BIFURCATION_TRIGGERS",
    "BIFURCATION_HANDLERS",
    "TRANSFORMERS",
    "RECURSIVE_GENERATORS",
    "SCALE_STABILIZERS",
    # Registry & glyph compatibility exports
    # Optimized validation
    "validate_sequence_cached",
    "clear_validation_cache",
    "get_validation_cache_stats",
    "GLYPH_TO_FUNCTION",
    "FUNCTION_TO_GLYPH",
    "OPERATORS",
    "OPERATOR_NAME_TO_CLASS",
    # Telemetry helpers
    "get_grammar_cache_stats",
]

# ============================================================================
# OPTIMIZED VALIDATION WITH CACHING (Performance Enhancement)
# ============================================================================

# Validation cache for operator sequences
_validation_cache: dict[str, tuple[bool, str]] = {}
_cache_hits = 0
_cache_misses = 0


def _sequence_hash(sequence: list[Glyph], graph_state: str | None = None) -> str:
    """Generate hash key for operator sequence caching."""
    # Create deterministic hash from sequence and relevant graph state
    sequence_str = "".join(str(op) for op in sequence)
    if graph_state:
        content = f"{sequence_str}:{graph_state}"
    else:
        content = sequence_str

    return hashlib.md5(content.encode(), usedforsecurity=False).hexdigest()


@lru_cache(maxsize=1000)
def _validate_grammar_rules_cached(
    sequence_tuple: tuple[Glyph, ...],
) -> tuple[bool, str]:
    """Cached grammar rule validation for operator sequences.

    This optimized version caches validation results to avoid redundant
    computation for repeated sequences following TNFR principles.
    """
    sequence = list(sequence_tuple)

    # Delegate to existing validation logic
    from .grammar_validate import validate_grammar

    try:
        is_valid = validate_grammar(sequence)
        return is_valid, "Valid sequence" if is_valid else "Grammar violation detected"
    except Exception as e:
        return False, f"Validation error: {e}"


def validate_sequence_cached(
    sequence: list[Glyph], graph: TNFRGraph | None = None, use_cache: bool = True
) -> tuple[bool, str]:
    """Optimized sequence validation with intelligent caching.

    PERFORMANCE ENHANCEMENT: Caches validation results to eliminate
    redundant computation while maintaining TNFR theoretical consistency.

    Parameters
    ----------
    sequence : list[Glyph]
        Operator sequence to validate
    graph : TNFRGraph, optional
        Graph for context-aware validation
    use_cache : bool, default=True
        Enable validation caching

    Returns
    -------
    tuple[bool, str]
        (is_valid, error_message)

    Notes
    -----
    Cache key includes sequence operators and relevant graph state
    to ensure correctness while maximizing cache hit rate.
    """
    global _cache_hits, _cache_misses

    if not use_cache:
        # Direct validation without caching
        return _validate_grammar_rules_cached(tuple(sequence))

    # Generate cache key
    graph_state = None
    if graph is not None:
        # Include relevant graph state in cache key
        n_nodes = len(graph.nodes())
        n_edges = len(graph.edges())
        graph_state = f"n{n_nodes}_e{n_edges}"

    cache_key = _sequence_hash(sequence, graph_state)

    # Check cache
    if cache_key in _validation_cache:
        _cache_hits += 1
        return _validation_cache[cache_key]

    # Cache miss - perform validation
    _cache_misses += 1
    is_valid, message = _validate_grammar_rules_cached(tuple(sequence))

    # Store in cache (with size limit)
    if len(_validation_cache) < 10000:  # Prevent unbounded growth
        _validation_cache[cache_key] = (is_valid, message)

    return is_valid, message


def clear_validation_cache() -> None:
    """Clear validation cache to free memory."""
    global _cache_hits, _cache_misses
    _validation_cache.clear()
    _validate_grammar_rules_cached.cache_clear()
    _cache_hits = 0
    _cache_misses = 0


def get_validation_cache_stats() -> dict[str, Any]:
    """Get validation cache performance statistics."""
    total_requests = _cache_hits + _cache_misses
    hit_rate = (_cache_hits / total_requests * 100.0) if total_requests > 0 else 0.0

    return {
        "cache_hits": _cache_hits,
        "cache_misses": _cache_misses,
        "hit_rate_percent": round(hit_rate, 2),
        "cache_size": len(_validation_cache),
        "lru_cache_info": _validate_grammar_rules_cached.cache_info()._asdict(),
    }