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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_dynamics.py

grammar_dynamics.py

Grammar-Aware Dynamics: Proactive U1-U6 enforcement in operator selection.

Bridges the grammar validation system (U1-U6) with the dynamic operator selection layer. Provides incremental grammar checking for step-by-step dynamics, where operators are selected one at a time per node.

Physics basis

Grammar rules derive from the nodal equation ∂EPI/∂t = νf · ΔNFR(t). Proactive enforcement prevents grammar violations before they corrupt graph state, rather than detecting them reactively after the damage is done.

Incremental rule applicability

  • U1a (Initiation): Checked when EPI ≈ 0 and history is empty.
  • U2 (Convergence): Tracked via a destabilizer/stabilizer debt counter over a sliding window of recent history.
  • U3 (Resonant Coupling): Phase compatibility required for UM/RA candidates.
  • U4a (Bifurcation triggers): OZ/ZHIR require handlers in recent context.
  • U4b (Transformer context): ZHIR/THOL need a recent destabilizer (and prior IL for ZHIR).
  • U1b (Closure) and U5/U6 are whole-sequence or telemetry checks and cannot be fully enforced incrementally; they are advisory here.

References

  • AGENTS.md §Unified Grammar (U1-U6)
  • UNIFIED_GRAMMAR_RULES.md — complete derivations
  • grammar_core.py — batch validator (full sequences)

Source Code

python
"""Grammar-Aware Dynamics: Proactive U1-U6 enforcement in operator selection.

Bridges the grammar validation system (U1-U6) with the dynamic operator
selection layer.  Provides **incremental** grammar checking for step-by-step
dynamics, where operators are selected one at a time per node.

Physics basis
-------------
Grammar rules derive from the nodal equation ∂EPI/∂t = νf · ΔNFR(t).
Proactive enforcement prevents grammar violations *before* they corrupt graph
state, rather than detecting them reactively after the damage is done.

Incremental rule applicability
------------------------------
- **U1a** (Initiation): Checked when EPI ≈ 0 and history is empty.
- **U2**  (Convergence): Tracked via a destabilizer/stabilizer debt counter
  over a sliding window of recent history.
- **U3**  (Resonant Coupling): Phase compatibility required for UM/RA candidates.
- **U4a** (Bifurcation triggers): OZ/ZHIR require handlers in recent context.
- **U4b** (Transformer context): ZHIR/THOL need a recent destabilizer (and
  prior IL for ZHIR).
- **U1b** (Closure) and **U5/U6** are whole-sequence or telemetry checks and
  cannot be fully enforced incrementally; they are advisory here.

References
----------
- AGENTS.md §Unified Grammar (U1-U6)
- UNIFIED_GRAMMAR_RULES.md — complete derivations
- grammar_core.py — batch validator (full sequences)
"""

from __future__ import annotations

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

from ..types import Glyph
from .grammar_types import (
    BIFURCATION_HANDLERS,
    BIFURCATION_TRIGGERS,
    CLOSURES,
    COUPLING_RESONANCE,
    DESTABILIZERS,
    GENERATORS,
    GLYPH_TO_FUNCTION,
    STABILIZERS,
    TRANSFORMERS,
)
from ..config.operator_names import BIFURCATION_WINDOW, U2_DEBT_CAPACITY

# ── glyph code ↔ canonical function name helpers ──────────────────────────

# Build fast lookup from glyph code string ("IL") → canonical name ("coherence")
_CODE_TO_NAME: dict[str, str] = {g.value: name for g, name in GLYPH_TO_FUNCTION.items()}
# Reverse: canonical name → glyph code string
_NAME_TO_CODE: dict[str, str] = {name: g.value for g, name in GLYPH_TO_FUNCTION.items()}

# Sets of *glyph codes* (uppercase) for fast membership tests
_DESTABILIZER_CODES = frozenset(
    _NAME_TO_CODE[n] for n in DESTABILIZERS if n in _NAME_TO_CODE
)
_STABILIZER_CODES = frozenset(
    _NAME_TO_CODE[n] for n in STABILIZERS if n in _NAME_TO_CODE
)
_COUPLING_CODES = frozenset(
    _NAME_TO_CODE[n] for n in COUPLING_RESONANCE if n in _NAME_TO_CODE
)
_GENERATOR_CODES = frozenset(_NAME_TO_CODE[n] for n in GENERATORS if n in _NAME_TO_CODE)
_BIFURCATION_TRIGGER_CODES = frozenset(
    _NAME_TO_CODE[n] for n in BIFURCATION_TRIGGERS if n in _NAME_TO_CODE
)
_HANDLER_CODES = frozenset(
    _NAME_TO_CODE[n] for n in BIFURCATION_HANDLERS if n in _NAME_TO_CODE
)
_TRANSFORMER_CODES = frozenset(
    _NAME_TO_CODE[n] for n in TRANSFORMERS if n in _NAME_TO_CODE
)
_CLOSURE_CODES = frozenset(_NAME_TO_CODE[n] for n in CLOSURES if n in _NAME_TO_CODE)

# Canonical fallback when all else fails — IL (Coherence) is always safe
_FALLBACK_CODE = "IL"

# How many recent glyphs to consider for incremental grammar context
_DEFAULT_WINDOW = 6

# ── data structures ───────────────────────────────────────────────────────


@dataclass(slots=True)
class GrammarViolation:
    """A single incremental grammar rule violation."""

    rule: str  # e.g. "U2", "U4b"
    message: str  # human-readable explanation
    severity: str  # "error" (must fix) or "warning" (advisory)


@dataclass(slots=True)
class CandidateResult:
    """Result of validating a single candidate glyph against recent history."""

    candidate: str
    allowed: bool
    violations: list[GrammarViolation] = field(default_factory=list)
    suggested_alternative: str | None = None


# ── core incremental checks ──────────────────────────────────────────────


def _to_code(glyph: Any) -> str:
    """Normalize a glyph to its uppercase code string (e.g. 'IL')."""
    if isinstance(glyph, Glyph):
        return glyph.value
    s = str(glyph).strip()
    # Handle "Glyph.AL" format
    if "." in s:
        s = s.rsplit(".", 1)[-1]
    upper = s.upper()
    if upper in _CODE_TO_NAME:
        return upper
    # Try canonical name → code
    lower = s.lower()
    if lower in _NAME_TO_CODE:
        return _NAME_TO_CODE[lower]
    return upper  # best effort


def _recent_codes(G: Any, node: Any, window: int = _DEFAULT_WINDOW) -> list[str]:
    """Extract the last *window* glyph codes from the node's history."""
    nd = G.nodes[node]
    raw = nd.get("glyph_history")
    if not raw:
        return []
    items = list(raw)[-window:]
    return [_to_code(g) for g in items]


def _check_u1a(
    candidate: str,
    history: list[str],
    epi: float,
) -> GrammarViolation | None:
    """U1a: If EPI ≈ 0 and history is empty, first glyph must be a generator."""
    if history or epi > 0.0:
        return None  # not applicable
    if candidate not in _GENERATOR_CODES:
        return GrammarViolation(
            rule="U1a",
            message=(
                f"EPI=0 with empty history requires a generator "
                f"({sorted(_GENERATOR_CODES)}), got '{candidate}'."
            ),
            severity="error",
        )
    return None


def _check_u2(
    candidate: str,
    history: list[str],
) -> GrammarViolation | None:
    """U2: Convergence — destabilizer debt must not grow unbounded.

    Counts destabilizers vs stabilizers in recent history + candidate.
    If adding the candidate would leave >2 uncompensated destabilizers,
    flag a violation.
    """
    full = history + [candidate]
    destab = sum(1 for g in full if g in _DESTABILIZER_CODES)
    stab = sum(1 for g in full if g in _STABILIZER_CODES)
    debt = destab - stab
    if debt > U2_DEBT_CAPACITY:
        return GrammarViolation(
            rule="U2",
            message=(
                f"Convergence violation: {destab} destabilizers vs "
                f"{stab} stabilizers in recent window (debt={debt}). "
                f"Add a stabilizer (IL/THOL) before more destabilizers."
            ),
            severity="error",
        )
    return None


def _check_u3(
    candidate: str,
    G: Any,
    node: Any,
) -> GrammarViolation | None:
    """U3: Coupling/resonance candidates require phase-compatible neighbours."""
    if candidate not in _COUPLING_CODES:
        return None
    try:
        from ..alias import get_attr
        from ..constants.aliases import ALIAS_THETA
        from ..constants.canonical import DELTA_PHI_MAX

        theta_i = float(get_attr(G.nodes[node], ALIAS_THETA, 0.0))
        delta_phi_max = float(G.graph.get("DELTA_PHI_MAX", DELTA_PHI_MAX))
        for nb in G.neighbors(node):
            theta_j = float(get_attr(G.nodes[nb], ALIAS_THETA, 0.0))
            diff = abs(theta_i - theta_j)
            # Wrap to [0, π]
            import math

            diff = min(diff, 2 * math.pi - diff)
            if diff <= delta_phi_max:
                return None  # at least one compatible neighbour
        return GrammarViolation(
            rule="U3",
            message=(
                f"No phase-compatible neighbour for {candidate} "
                f"(all |φᵢ - φⱼ| > Δφ_max={delta_phi_max:.2f})."
            ),
            severity="warning",
        )
    except Exception:
        return None  # graceful degradation


def _check_u4a(
    candidate: str,
    history: list[str],
) -> GrammarViolation | None:
    """U4a: Bifurcation triggers need handlers in nearby context."""
    if candidate not in _BIFURCATION_TRIGGER_CODES:
        return None
    # Check if there's a handler anywhere in recent history or candidate itself
    full = history + [candidate]
    has_handler = any(g in _HANDLER_CODES for g in full)
    if not has_handler:
        return GrammarViolation(
            rule="U4a",
            message=(
                f"Bifurcation trigger '{candidate}' has no handler "
                f"({sorted(_HANDLER_CODES)}) in recent context."
            ),
            severity="error",
        )
    return None


def _check_u4b(
    candidate: str,
    history: list[str],
) -> GrammarViolation | None:
    """U4b: Transformers need recent destabilizer context.

    ZHIR also requires a prior IL (stable base).
    """
    if candidate not in _TRANSFORMER_CODES:
        return None
    # Look for a destabilizer within the emergent relaxation window: the
    # structure stays plastic until the |ΔNFR| perturbation relaxes into the
    # coherence band (BIFURCATION_WINDOW, derived from the pulse, = 3).
    w = BIFURCATION_WINDOW
    recent = history[-w:] if len(history) >= w else history
    has_destab = any(g in _DESTABILIZER_CODES for g in recent)
    if not has_destab:
        return GrammarViolation(
            rule="U4b",
            message=(
                f"Transformer '{candidate}' requires a recent destabilizer "
                f"(within ~{w} ops). Recent: {recent}."
            ),
            severity="error",
        )
    # ZHIR additionally requires prior IL
    if candidate == "ZHIR":
        has_il = "IL" in history
        if not has_il:
            return GrammarViolation(
                rule="U4b",
                message=(
                    "ZHIR (Mutation) requires prior IL (Coherence) "
                    "for a stable base before phase transformation."
                ),
                severity="error",
            )
    return None


# ── public API ────────────────────────────────────────────────────────────


def _check_violations(
    G: Any,
    node: Any,
    code: str,
    window: int = _DEFAULT_WINDOW,
) -> tuple[bool, list[GrammarViolation]]:
    """Core validation logic without alternative suggestion (avoids recursion)."""
    history = _recent_codes(G, node, window)

    # Read EPI for U1a
    try:
        from ..alias import get_attr
        from ..constants.aliases import ALIAS_EPI

        epi = float(get_attr(G.nodes[node], ALIAS_EPI, 1.0))
    except Exception:
        epi = 1.0  # assume initialized

    violations: list[GrammarViolation] = []
    for checker in (_check_u1a, _check_u2, _check_u4a, _check_u4b):
        v = checker(code, history, epi) if checker is _check_u1a else checker(code, history)  # type: ignore[call-arg]
        if v is not None:
            violations.append(v)

    # U3 needs the graph
    v3 = _check_u3(code, G, node)
    if v3 is not None:
        violations.append(v3)

    errors = [v for v in violations if v.severity == "error"]
    allowed = len(errors) == 0
    return allowed, violations


def validate_candidate(
    G: Any,
    node: Any,
    candidate: str | Glyph,
    *,
    window: int = _DEFAULT_WINDOW,
) -> CandidateResult:
    """Check whether *candidate* is grammar-valid given the node's recent history.

    Runs incremental checks for U1a, U2, U3, U4a, U4b.  Returns a
    :class:`CandidateResult` with ``allowed=True`` if no errors are found.

    Parameters
    ----------
    G : TNFRGraph
        Graph containing the node.
    node : NodeId
        Target node.
    candidate : str | Glyph
        Candidate glyph code (e.g. ``"OZ"``) or :class:`Glyph` enum.
    window : int, optional
        How many recent history entries to consider (default 6).

    Returns
    -------
    CandidateResult
        Validation result with violations and suggested alternative.
    """
    code = _to_code(candidate)
    allowed, violations = _check_violations(G, node, code, window)

    alt: str | None = None
    if not allowed:
        alt = suggest_alternative(G, node, code, window=window)

    return CandidateResult(
        candidate=code,
        allowed=allowed,
        violations=violations,
        suggested_alternative=alt,
    )


def filter_candidates(
    G: Any,
    node: Any,
    candidates: Sequence[str | Glyph],
    *,
    window: int = _DEFAULT_WINDOW,
) -> list[str]:
    """Return only grammar-valid candidates from the given list.

    Parameters
    ----------
    G : TNFRGraph
        Graph containing the node.
    node : NodeId
        Target node.
    candidates : sequence of str | Glyph
        Candidate glyph codes to evaluate.
    window : int, optional
        Recent history context size.

    Returns
    -------
    list[str]
        Codes that pass incremental grammar checks (errors only; warnings pass).
    """
    result: list[str] = []
    for c in candidates:
        cr = validate_candidate(G, node, c, window=window)
        if cr.allowed:
            result.append(cr.candidate)
    return result


_PRIORITY_ORDER = ["IL", "THOL", "EN", "SHA", "RA", "NAV", "AL"]
"""Fallback priority: stabilizers first, then neutral, then generators."""


def suggest_alternative(
    G: Any,
    node: Any,
    rejected: str,
    *,
    window: int = _DEFAULT_WINDOW,
) -> str:
    """Suggest the best grammar-safe alternative when *rejected* is invalid.

    Iterates a priority-ordered list of safe candidates and returns the first
    that passes incremental grammar checks.  Falls back to ``IL`` (always safe).

    Parameters
    ----------
    G : TNFRGraph
        Graph containing the node.
    node : NodeId
        Target node.
    rejected : str
        The glyph code that was rejected.
    window : int, optional
        Recent history context size.

    Returns
    -------
    str
        A grammar-safe glyph code.
    """
    for alt in _PRIORITY_ORDER:
        if alt == rejected:
            continue
        allowed, _ = _check_violations(G, node, alt, window)
        if allowed:
            return alt
    return _FALLBACK_CODE


def enforce_grammar_on_glyph(
    G: Any,
    node: Any,
    candidate: str | Glyph,
    *,
    window: int = _DEFAULT_WINDOW,
) -> str:
    """Validate *candidate* and replace it with a safe alternative if invalid.

    Single source of truth for incremental grammar enforcement (U1-U6).
    ``enforce_canonical_grammar()`` delegates here; all application paths
    converge through this function exactly once before executing the operator.

    Parameters
    ----------
    G : TNFRGraph
        Graph containing the node.
    node : NodeId
        Target node.
    candidate : str | Glyph
        Proposed glyph.
    window : int, optional
        Recent history context size.

    Returns
    -------
    str
        The validated (or replaced) glyph code.
    """
    cr = validate_candidate(G, node, candidate, window=window)
    if cr.allowed:
        return cr.candidate
    return cr.suggested_alternative or _FALLBACK_CODE


def validate_sequence_incremental(
    G: Any,
    node: Any,
    sequence: Sequence[str | Glyph],
    *,
    window: int = _DEFAULT_WINDOW,
) -> list[CandidateResult]:
    """Validate a full operator sequence step-by-step against a node's live history.

    Unlike :func:`grammar_core.validate_sequence` (which checks the sequence
    in isolation), this function considers the **actual glyph history** stored
    on the node, simulating how the sequence would be applied incrementally.

    It appends each accepted glyph to a *shadow* history copy so that later
    steps in the sequence see the effect of earlier ones.

    Parameters
    ----------
    G : TNFRGraph
        Graph containing the node.
    node : NodeId
        Target node.
    sequence : sequence of str | Glyph
        Ordered glyphs to validate.
    window : int, optional
        Recent history context size.

    Returns
    -------
    list[CandidateResult]
        One result per step.  All ``allowed=True`` means the sequence is
        grammar-safe for this node in its current state.
    """
    nd = G.nodes[node]
    raw = nd.get("glyph_history")
    shadow: list[str] = [_to_code(g) for g in (list(raw) if raw else [])]

    results: list[CandidateResult] = []
    for step in sequence:
        code = _to_code(step)
        # Temporarily set shadow history on the node for the check
        original_history = nd.get("glyph_history")
        nd["glyph_history"] = shadow[-window:] if shadow else []
        try:
            cr = validate_candidate(G, node, code, window=window)
        finally:
            # Restore original history
            if original_history is not None:
                nd["glyph_history"] = original_history
            else:
                nd.pop("glyph_history", None)
        results.append(cr)
        # Accepted glyphs extend the shadow for subsequent steps
        shadow.append(code)

    return results


__all__ = [
    "GrammarViolation",
    "CandidateResult",
    "validate_candidate",
    "filter_candidates",
    "suggest_alternative",
    "enforce_grammar_on_glyph",
    "validate_sequence_incremental",
]