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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: tests/sdk/test_simple_advanced.py

test_simple_advanced.py

Tests for the upgraded Simple SDK — tetrad, conservation, telemetry.

Validates that the advanced TNFR physics stack (Structural Field Tetrad, conservation laws, integrity monitoring, grammar-aware dynamics) is correctly exposed through the simplified Network API.

Source Code

python
"""Tests for the upgraded Simple SDK — tetrad, conservation, telemetry.

Validates that the advanced TNFR physics stack (Structural Field Tetrad,
conservation laws, integrity monitoring, grammar-aware dynamics) is
correctly exposed through the simplified Network API.
"""

from __future__ import annotations

import pytest

from tnfr.sdk.simple import (
    TNFR,
    ConservationReport,
    FactorizationReport,
    Network,
    NodalDynamicsReport,
    NodalStateReport,
    PrimalityReport,
    Results,
    TetradSnapshot,
)

# ---------------------------------------------------------------------------
# Fixtures
# ---------------------------------------------------------------------------


@pytest.fixture
def small_ring() -> Network:
    """5-node ring network — minimal connected topology."""
    return TNFR.create(5, name="ring5").ring()


@pytest.fixture
def medium_random() -> Network:
    """15-node random network — realistic density."""
    return TNFR.create(15, name="random15").random(0.3)


# ---------------------------------------------------------------------------
# TetradSnapshot dataclass
# ---------------------------------------------------------------------------


class TestTetradSnapshot:
    """TetradSnapshot creation and methods."""

    def test_empty_snapshot_summary(self):
        snap = TetradSnapshot()
        assert "empty" in snap.summary()

    def test_empty_snapshot_is_safe(self):
        snap = TetradSnapshot()
        safety = snap.is_safe()
        assert safety["overall"] is True

    def test_tetrad_from_network(self, small_ring: Network):
        snap = small_ring.tetrad()
        assert isinstance(snap, TetradSnapshot)
        assert len(snap.phi_s) == 5
        assert len(snap.grad_phi) == 5
        assert len(snap.k_phi) == 5
        assert isinstance(snap.xi_c, float)
        assert len(snap.j_phi) == 5
        assert len(snap.j_dnfr) == 5

    def test_tetrad_summary_nonempty(self, small_ring: Network):
        snap = small_ring.tetrad()
        summary = snap.summary()
        assert "Phi_s" in summary
        assert "N=5" in summary

    def test_tetrad_safety_returns_all_keys(self, small_ring: Network):
        safety = small_ring.tetrad().is_safe()
        for key in (
            "phi_s_safe",
            "grad_phi_safe",
            "k_phi_safe",
            "xi_c_safe",
            "overall",
        ):
            assert key in safety


# ---------------------------------------------------------------------------
# ConservationReport dataclass
# ---------------------------------------------------------------------------


class TestConservationReport:
    """ConservationReport creation and methods."""

    def test_default_report_stable(self):
        report = ConservationReport()
        assert report.lyapunov_stable is True
        assert "STABLE" in report.summary()

    def test_conservation_from_network(self, small_ring: Network):
        report = small_ring.conservation()
        assert isinstance(report, ConservationReport)
        assert isinstance(report.noether_charge, float)
        assert isinstance(report.energy, float)
        assert isinstance(report.lyapunov_stable, bool)


# ---------------------------------------------------------------------------
# Network.tetrad(), .fields(), .telemetry()
# ---------------------------------------------------------------------------


class TestNetworkFields:
    """Structural Field Tetrad integration in Network."""

    def test_tetrad_returns_correct_type(self, small_ring: Network):
        assert isinstance(small_ring.tetrad(), TetradSnapshot)

    def test_fields_returns_dict(self, small_ring: Network):
        f = small_ring.fields()
        assert isinstance(f, dict)
        assert "phi_s" in f
        assert "grad_phi" in f
        assert "k_phi" in f
        assert "xi_c" in f
        assert "j_phi" in f
        assert "j_dnfr" in f

    def test_telemetry_returns_dict(self, small_ring: Network):
        t = small_ring.telemetry()
        assert isinstance(t, dict)
        assert len(t) > 0

    def test_tensor_invariants(self, small_ring: Network):
        inv = small_ring.tensor_invariants()
        assert isinstance(inv, dict)
        assert "energy_density" in inv

    def test_emergent_fields(self, small_ring: Network):
        ef = small_ring.emergent_fields()
        assert isinstance(ef, dict)
        assert "chirality" in ef


# ---------------------------------------------------------------------------
# Network.conservation()
# ---------------------------------------------------------------------------


class TestNetworkConservation:
    """Conservation law integration in Network."""

    def test_conservation_report_keys(self, small_ring: Network):
        c = small_ring.conservation()
        assert hasattr(c, "noether_charge")
        assert hasattr(c, "energy")
        assert hasattr(c, "lyapunov_stable")

    def test_conservation_multiple_calls_track_snapshots(self, small_ring: Network):
        """Calling conservation() twice populates Lyapunov derivative."""
        c1 = small_ring.conservation()
        # Evolve to change state
        small_ring.evolve(1)
        c2 = small_ring.conservation()
        # Second call should have a real Lyapunov derivative
        assert isinstance(c2.lyapunov_derivative, float)


# ---------------------------------------------------------------------------
# Network.evolve_grammar_aware()
# ---------------------------------------------------------------------------


class TestGrammarAwareDynamics:
    """Grammar-aware evolution preserves coherence."""

    def test_evolve_grammar_aware_returns_self(self, small_ring: Network):
        result = small_ring.evolve_grammar_aware(steps=2)
        assert result is small_ring

    def test_evolve_grammar_aware_maintains_coherence(self, small_ring: Network):
        c_before = small_ring.coherence()
        small_ring.evolve_grammar_aware(steps=3)
        c_after = small_ring.coherence()
        # Should not catastrophically break (allow some tolerance)
        assert c_after >= c_before * 0.5


# ---------------------------------------------------------------------------
# Network.integrity_check()
# ---------------------------------------------------------------------------


class TestIntegrityMonitor:
    """Structural integrity monitoring."""

    def test_integrity_check_returns_dict(self, small_ring: Network):
        report = small_ring.integrity_check()
        assert isinstance(report, dict)
        if report:  # non-empty if module available
            assert "operator" in report
            assert "nodes_checked" in report
            assert "pass_rate" in report


# ---------------------------------------------------------------------------
# Results — full_summary, to_dict, is_coherent, is_stable
# ---------------------------------------------------------------------------


class TestResults:
    """Upgraded Results with tetrad and conservation."""

    def test_results_has_tetrad(self, small_ring: Network):
        r = small_ring.results()
        assert isinstance(r, Results)
        assert r.tetrad is not None
        assert isinstance(r.tetrad, TetradSnapshot)

    def test_results_has_conservation(self, small_ring: Network):
        r = small_ring.results()
        assert r.conservation is not None
        assert isinstance(r.conservation, ConservationReport)

    def test_results_has_unified_fields(self, small_ring: Network):
        r = small_ring.results()
        assert r.unified_fields is not None
        assert isinstance(r.unified_fields, dict)

    def test_full_summary_multiline(self, small_ring: Network):
        r = small_ring.results()
        summary = r.full_summary()
        assert "\n" in summary
        assert "Tetrad" in summary

    def test_to_dict_serializable(self, small_ring: Network):
        r = small_ring.results()
        d = r.to_dict()
        assert isinstance(d, dict)
        assert "coherence" in d
        assert isinstance(d["coherence"], float)

    def test_is_coherent_and_is_stable(self, small_ring: Network):
        r = small_ring.results()
        assert isinstance(r.is_coherent(), bool)
        assert isinstance(r.is_stable(), bool)


# ---------------------------------------------------------------------------
# TNFR.analyze() — one-shot comprehensive analysis
# ---------------------------------------------------------------------------


class TestTNFRAnalyze:
    """TNFR.analyze() one-shot comprehensive analysis."""

    def test_analyze_returns_complete_dict(self, small_ring: Network):
        analysis = TNFR.analyze(small_ring)
        assert isinstance(analysis, dict)
        assert "coherence" in analysis
        assert "tetrad" in analysis
        assert "conservation" in analysis
        assert "tensor_invariants" in analysis
        assert "emergent_fields" in analysis
        assert "features" in analysis

    def test_analyze_tetrad_type(self, small_ring: Network):
        analysis = TNFR.analyze(small_ring)
        assert isinstance(analysis["tetrad"], TetradSnapshot)


# ---------------------------------------------------------------------------
# TNFR.compare() — updated comparison
# ---------------------------------------------------------------------------


class TestTNFRCompare:
    """Updated compare with conservation data."""

    def test_compare_includes_conservation(self):
        n1 = TNFR.create(5).ring()
        n2 = TNFR.create(8).ring()
        comp = TNFR.compare(n1, n2)
        assert comp["count"] == 2
        # Should have conservation data in results
        for r in comp["results"]:
            assert "coherence" in r


# ---------------------------------------------------------------------------
# Network.info() — features dict
# ---------------------------------------------------------------------------


class TestNetworkInfo:
    """Network.info() includes feature availability."""

    def test_info_has_features(self, small_ring: Network):
        info = small_ring.info()
        assert "features" in info
        for key in (
            "fields",
            "conservation",
            "integrity",
            "grammar_dynamics",
            "optimization",
        ):
            assert key in info["features"]
            assert isinstance(info["features"][key], bool)


# ---------------------------------------------------------------------------
# SDK __init__.py exports
# ---------------------------------------------------------------------------


class TestSDKExports:
    """Verify new types are importable from tnfr.sdk."""

    def test_import_tetrad_snapshot(self):
        from tnfr.sdk import TetradSnapshot as TS

        assert TS is TetradSnapshot

    def test_import_conservation_report(self):
        from tnfr.sdk import ConservationReport as CR

        assert CR is ConservationReport

    def test_import_factorization_report(self):
        from tnfr.sdk import FactorizationReport as FR

        assert FR is FactorizationReport

    def test_import_primality_report(self):
        from tnfr.sdk import PrimalityReport as PR

        assert PR is PrimalityReport

    def test_import_nodal_state_report(self):
        from tnfr.sdk import NodalStateReport as NSR

        assert NSR is NodalStateReport

    def test_import_nodal_dynamics_report(self):
        from tnfr.sdk import NodalDynamicsReport as NDR

        assert NDR is NodalDynamicsReport


class TestNodalDynamicsBridge:
    """SDK nodal-dynamics diagnostics for TNFR equation study."""

    def test_nodal_state_returns_report(self, small_ring: Network):
        state = small_ring.nodal_state(0)
        assert isinstance(state, NodalStateReport)
        assert state.node == 0
        assert isinstance(state.expected_depi_dt, float)
        assert isinstance(state.d2epi_dt2, float)

    def test_nodal_scan_returns_report(self, small_ring: Network):
        report = small_ring.nodal_scan()
        assert isinstance(report, NodalDynamicsReport)
        assert len(report.nodes) == len(small_ring.G.nodes())
        top = report.top_pressure_nodes(3)
        assert len(top) <= 3

    def test_nodal_profile_returns_dict(self, small_ring: Network):
        profile = small_ring.nodal_profile(0)
        assert isinstance(profile, dict)
        assert "expected_depi_dt" in profile
        assert "delta_nfr" in profile

    def test_tnfr_analyze_includes_nodal_dynamics(self, small_ring: Network):
        analysis = TNFR.analyze(small_ring)
        assert "nodal_dynamics" in analysis
        assert isinstance(analysis["nodal_dynamics"], NodalDynamicsReport)


class TestSDKFactorizationBridge:
    """SDK bridge between canonical factorization and network telemetry."""

    def test_tnfr_factorize_returns_report(self):
        report = TNFR.factorize(91)
        assert isinstance(report, FactorizationReport)
        assert report.n == 91
        assert report.modulus > 0
        assert isinstance(report.candidate_factors, list)
        assert isinstance(report.telemetry, dict)
        assert "delta_nfr" in report.telemetry

    def test_network_factorize_includes_synergy(self, small_ring: Network):
        report = small_ring.factorize(91)
        assert isinstance(report, FactorizationReport)
        assert report.network_synergy is not None
        assert "synergy_index" in report.network_synergy
        assert "coherence_alignment" in report.network_synergy


class TestSDKPrimalityBridge:
    """SDK bridge between canonical primality module and network telemetry."""

    def test_tnfr_primality_returns_report(self):
        report = TNFR.primality(97)
        assert isinstance(report, PrimalityReport)
        assert report.n == 97
        assert report.is_prime is True
        assert abs(report.delta_nfr) <= report.tolerance
        assert isinstance(report.components, dict)
        assert isinstance(report.triad, dict)

    def test_network_primality_includes_synergy(self, small_ring: Network):
        report = small_ring.primality(91)
        assert isinstance(report, PrimalityReport)
        assert report.network_synergy is not None
        assert "synergy_index" in report.network_synergy
        assert "coherence_alignment" in report.network_synergy
        assert small_ring.is_prime(91) is False


class TestResearchFunctions:
    """New SDK research/teaching functions: trajectory, operators, explain."""

    def test_trajectory_records_per_operator(self, small_ring: Network):
        hist = small_ring.trajectory(cycles=2, sequence="basic_activation")
        assert len(hist) > 0
        assert len(hist) % 2 == 0  # two cycles
        for snap in hist:
            assert "step" in snap and "operator" in snap
            assert isinstance(snap["coherence"], float)
            assert isinstance(snap["sense_index"], float)
        assert [s["step"] for s in hist] == list(range(1, len(hist) + 1))

    def test_trajectory_unknown_sequence_raises(self, small_ring: Network):
        with pytest.raises(Exception):
            small_ring.trajectory(sequence="does_not_exist")

    def test_operators_catalog_has_13(self):
        catalog = TNFR.operators()
        assert isinstance(catalog, list)
        assert len(catalog) == 13
        names = {op["name"] for op in catalog}
        assert "Emission" in names
        assert "Mutation" in names

    def test_operators_single_emission(self):
        emi = TNFR.operators("emission")
        assert emi["name"] == "Emission"
        assert emi["glyph"] == "AL"
        assert emi["channel"] == "EPI"
        assert "generator" in emi["roles"]

    def test_operators_accepts_glyph(self):
        il = TNFR.operators("IL")
        assert il["name"] == "Coherence"
        assert "stabilizer" in il["roles"]

    def test_explain_sequence_valid(self):
        info = TNFR.explain_sequence(["emission", "coherence", "silence"])
        assert info["valid"] is True
        assert info["starts_with_generator"] is True
        assert info["ends_with_closure"] is True
        assert len(info["roles"]) == 3

    def test_explain_sequence_invalid_no_generator(self):
        info = TNFR.explain_sequence(["coherence", "resonance"])
        assert info["valid"] is False
        assert info["starts_with_generator"] is False

    def test_explain_sequence_accepts_glyphs(self):
        info = TNFR.explain_sequence(["AL", "OZ", "IL", "SHA"])
        assert info["operators"][0] == "Emission"
        assert info["has_destabilizer"] is True
        assert info["has_stabilizer"] is True


class TestEmergentOntologyAndNumberTheory:
    """Emergent ontology + number theory functions (unified dNFR=0 template)."""

    def test_primes_matches_known(self):
        result = TNFR.primes(30)
        assert result["primes"] == [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
        assert result["count"] == 10
        assert result["max_number"] == 30

    def test_magic_numbers_noble_gases(self):
        magic = TNFR.magic_numbers()
        assert magic[:6] == [2, 10, 18, 36, 54, 86]

    def test_element_noble_gas_zero_dnfr(self):
        neon = TNFR.element(10)
        assert neon["closed_shell"] is True
        assert neon["reactivity"] == 0.0
        assert neon["delta_nfr"] == 0.0

    def test_element_reactive_nonzero_dnfr(self):
        sodium = TNFR.element(11)
        assert sodium["closed_shell"] is False
        assert sodium["reactivity"] > 0.0

    def test_network_particle(self, small_ring: Network):
        p = small_ring.particle()
        assert "winding" in p
        assert "particle_class" in p
        assert isinstance(p["chirality"], int)

    def test_network_phase(self, small_ring: Network):
        ph = small_ring.phase()
        assert ph["phase"] in ("non_life", "critical", "life")
        assert isinstance(ph["is_life"], bool)
        assert "order_parameter" in ph

    def test_network_gauge(self):
        net = TNFR.create(8, seed=3).ring().evolve(4)
        g = net.gauge()
        assert "dominant_regime" in g
        assert isinstance(g["regime_distribution"], dict)

    def test_network_spectrum(self):
        net = TNFR.create(8, seed=3).ring().evolve(3)
        s = net.spectrum()
        assert s["spectral_gap"] >= 0.0
        assert len(s["relaxation_rates"]) >= 1
        assert s["structural_rank"] >= 1

    def test_symbolic_layer_reads_canonical_fixed_point(self):
        """Chemistry ΔNFR is read through the SAME equilibrium predicate."""
        from tnfr.metrics.common import is_structural_equilibrium

        assert is_structural_equilibrium(TNFR.element(10)["delta_nfr"])  # Ne
        assert not is_structural_equilibrium(TNFR.element(11)["delta_nfr"])  # Na


class TestStructuralEquilibriumPrimitive:
    """The single canonical fixed-point primitive shared by every domain.

    Particles read this fixed point directly (winding); numbers and elements
    read it symbolically. The coherence map and equilibrium predicate are one.
    """

    def test_structural_coherence_unity_at_equilibrium(self):
        from tnfr.metrics.common import structural_coherence

        assert structural_coherence(0.0) == 1.0
        assert structural_coherence(0.0, 0.0) == 1.0

    def test_structural_coherence_monotone(self):
        from tnfr.metrics.common import structural_coherence

        assert (
            structural_coherence(0.0)
            > structural_coherence(1.0)
            > structural_coherence(5.0)
        )

    def test_structural_coherence_includes_depi(self):
        from tnfr.metrics.common import structural_coherence

        assert structural_coherence(1.0, 1.0) == 1.0 / 3.0

    def test_is_structural_equilibrium_default_tolerance(self):
        from tnfr.metrics.common import is_structural_equilibrium

        assert is_structural_equilibrium(0.0)
        assert is_structural_equilibrium(1e-4)  # below 1e-3 default
        assert not is_structural_equilibrium(0.5)

    def test_is_structural_equilibrium_custom_eps(self):
        from tnfr.metrics.common import is_structural_equilibrium

        assert is_structural_equilibrium(1e-13, eps_dnfr=1e-12)
        assert not is_structural_equilibrium(1e-10, eps_dnfr=1e-12)

    def test_compute_coherence_uses_kernel(self):
        """compute_coherence delegates to the structural_coherence kernel."""
        from tnfr.metrics.common import compute_coherence, structural_coherence

        net = TNFR.create(6, seed=1).ring().evolve(3)
        c, dnfr_mean, depi_mean = compute_coherence(net.G, return_means=True)
        assert c == structural_coherence(dnfr_mean, depi_mean)

    def test_number_theory_local_coherence_delegates(self):
        """Arithmetic local coherence routes through the canonical kernel."""
        from tnfr.mathematics.number_theory import ArithmeticTNFRFormalism as F
        from tnfr.metrics.common import structural_coherence

        assert F.local_coherence(2.0) == structural_coherence(2.0)
        assert F.local_coherence(0.0) == 1.0


class TestFractalResonantNode:
    """NFR (Nodo Fractal Resonante) read-out: nodal topology + facets.

    Per TNFR.pdf section 1.4.1 the NFR has a nodal topology (radial/annular/
    multinodal) read from the canonical structural-potential geometry.
    """

    def test_classify_radial(self):
        import networkx as nx

        from tnfr.physics.fields import classify_nodal_topology

        r = classify_nodal_topology(nx.star_graph(9))
        assert r["topology"] == "radial"
        assert len(r["centers"]) == 1

    def test_classify_annular(self):
        import networkx as nx

        from tnfr.physics.fields import classify_nodal_topology

        assert classify_nodal_topology(nx.cycle_graph(10))["topology"] == "annular"
        assert classify_nodal_topology(nx.complete_graph(6))["topology"] == "annular"

    def test_classify_multinodal(self):
        import networkx as nx

        from tnfr.physics.fields import classify_nodal_topology

        r = classify_nodal_topology(nx.barbell_graph(5, 0))
        assert r["topology"] == "multinodal"
        assert len(r["centers"]) >= 2

    def test_network_nfr_ring_is_annular(self):
        net = TNFR.create(10, seed=2).ring().evolve(3)
        d = net.nfr()
        assert d["topology"] == "annular"
        assert set(d) >= {
            "topology",
            "centers",
            "concentration",
            "coherence",
            "equilibrium_fraction",
            "coherence_length",
            "triad",
            "n_nodes",
        }
        assert 0.0 <= d["equilibrium_fraction"] <= 1.0
        assert set(d["triad"]) == {"epi_mean", "vf_mean", "phase_sync"}

    def test_network_nfr_uniform_is_one_nfr(self):
        """A fully relaxed network is one uniform NFR at the attractor."""
        net = TNFR.create(8, seed=1).ring().evolve(6)
        d = net.nfr()
        assert d["equilibrium_fraction"] == 1.0
        assert d["coherence"] >= 0.7

    def test_nodal_state_exposes_coherence_facet(self):
        """The per-node micro-NFR exposes its constitutive coherence."""
        net = TNFR.create(6, seed=3).ring().evolve(4)
        n0 = list(net.G.nodes())[0]
        s = net.nodal_state(n0)
        assert hasattr(s, "coherence")
        assert 0.0 < s.coherence <= 1.0
        assert "coherence" in s.to_dict()

    def test_micro_and_macro_nfr_equilibrium_agree(self):
        """nodal_state (micro-NFR) and Network.nfr (macro-NFR) share the
        canonical equilibrium predicate and tolerance."""
        net = TNFR.create(8, seed=1).ring().evolve(6)
        scan = net.nodal_scan()
        micro = sum(1 for r in scan.nodes.values() if r.equilibrium) / len(scan.nodes)
        assert micro == net.nfr()["equilibrium_fraction"]
        assert scan.equilibrium_tolerance == pytest.approx(1e-3)

    def test_pulse_trajectory_records_rhythm_in_motion(self):
        """The pulse in motion: the rhythm forms as the NFR pulses resonate.

        Snapshots are time-blind; from a perturbed state the trajectory
        records the synchronization R(t) and the local-before-global cascade,
        and the collective pulse is computed once (evolution-invariant)."""
        import random

        from tnfr.alias import set_attr
        from tnfr.constants.aliases import ALIAS_THETA, ALIAS_VF

        net = TNFR.create(24, seed=0).ring()
        rng = random.Random(0)
        for n in net.G.nodes():
            set_attr(net.G.nodes[n], ALIAS_VF, rng.uniform(0.6, 1.4))
            set_attr(net.G.nodes[n], ALIAS_THETA, rng.uniform(0.0, 6.283))
        traj = net.pulse_trajectory(steps=8)
        assert traj["steps"] == 8
        for key in ("phase_coherence", "coherence", "local_resonance"):
            assert len(traj[key]) == 8
        assert all(0.0 <= r <= 1.0 for r in traj["phase_coherence"])
        assert all(0.0 <= x <= 1.0 for x in traj["local_resonance"])
        # the per-NFR pulses synchronize over the run (R rises)
        assert traj["synchronizing"] is True
        assert traj["delta_R"] > 0.0
        # local-before-global: per-NFR pulses lock with neighbours first, so
        # local resonance leads the global rhythm (robust margin)
        assert traj["local_resonance"][-1] > traj["phase_coherence"][-1]
        assert traj["local_leads_global"] is True
        assert isinstance(traj["collective_pulse"]["fundamental"], float)

    def test_pulse_trajectory_is_non_destructive(self):
        """The trajectory evolves a copy; the caller's network is untouched."""
        net = TNFR.create(12, seed=1).ring().evolve(2)
        before = net.coherence()
        first = net.pulse_trajectory(steps=4)
        second = net.pulse_trajectory(steps=4)
        # identical first sample => the network was not advanced in place
        assert first["phase_coherence"][0] == pytest.approx(
            second["phase_coherence"][0]
        )
        assert net.coherence() == pytest.approx(before)

    def test_evolve_record_populates_rhythm_history(self):
        """evolve(record=True) records the canonical pulse-in-motion series.

        The engine's own metrics step samples kuramoto_R / C_steps after each
        cycle, surfaced by history() -- the resonance forming, not a snapshot.
        """
        import random

        from tnfr.alias import set_attr
        from tnfr.constants.aliases import ALIAS_THETA, ALIAS_VF

        net = TNFR.create(24, seed=0).ring()
        rng = random.Random(0)
        for n in net.G.nodes():
            set_attr(net.G.nodes[n], ALIAS_VF, rng.uniform(0.6, 1.4))
            set_attr(net.G.nodes[n], ALIAS_THETA, rng.uniform(0.0, 6.283))
        net.evolve(5, record=True)
        hist = net.history()
        assert len(hist["kuramoto_R"]) == 5
        assert len(hist["C_steps"]) == 5
        assert all(0.0 <= r <= 1.0 for r in hist["kuramoto_R"])
        # the per-NFR pulses synchronize over the run (the rhythm forms)
        assert hist["kuramoto_R"][-1] > hist["kuramoto_R"][0]

    def test_evolve_without_record_keeps_fast_path(self):
        """The default path records no per-step rhythm series."""
        net = TNFR.create(8, seed=1).ring().evolve(3)
        assert net.history()["kuramoto_R"] == []