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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
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tetrad_evaluator.py
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FILE: src/tnfr/operators/emission.py

emission.py

TNFR Operator: Emission

Emission structural operator (AL) - Foundational activation of nodal resonance.

Physics: See AGENTS.md § Emission Grammar: UNIFIED_GRAMMAR_RULES.md

Source Code

python
"""TNFR Operator: Emission

Emission structural operator (AL) - Foundational activation of nodal resonance.

**Physics**: See AGENTS.md § Emission
**Grammar**: UNIFIED_GRAMMAR_RULES.md
"""  # flake8: noqa

from __future__ import annotations

import warnings
from typing import Any, ClassVar

from ..alias import get_attr
from ..config.operator_names import EMISSION
from ..constants.aliases import ALIAS_EPI
from ..dynamics.feedback import StructuralFeedbackLoop
from ..types import Glyph, TNFRGraph
from .definitions_base import Operator


class Emission(Operator):
    """Emission structural operator (AL).

    Foundational activation of nodal resonance.

    Activates structural symbol ``AL`` to initialise outward resonance around a
    nascent node, initiating the first phase of structural reorganization.

    TNFR Context
    ------------
    In the Resonant Fractal Nature paradigm, Emission (AL) represents
    the moment when a latent Primary Information Structure (EPI) begins
    to emit coherence toward its surrounding network. This is not passive
    information broadcast but active structural reorganization that boosts
    the node's EPI (the form) from its latent state. Per the canonical
    contract the EPI channel is the direct effect; νf settles at its basal
    ν₀⁺ and ΔNFR/phase are left untouched.

    **Key Elements:**
        - **Coherent Emergence**: Node exists because it resonates;
            AL starts resonance
    - **Form Activation**: Raises EPI (Primary Information Structure)
    - **Structural Frequency**: νf settles at its basal ν₀⁺ (not driven by AL)
    - **Network Coupling**: Prepares node for phase alignment
    - **Nodal Equation**: Drives ∂EPI/∂t ≥ 0 directly on the EPI channel

    **Structural Irreversibility (TNFR.pdf §2.2.1):**
    AL is inherently irreversible - once activated, it leaves a persistent
    structural trace that cannot be undone. Each emission marks "time
    zero" for the node and
    establishes genealogical traceability:

    - **emission_timestamp**: ISO 8601 UTC timestamp of first activation
    - **_emission_activated**: Immutable boolean flag
    - **_emission_origin**: Preserved original timestamp (never overwritten)
    - **_structural_lineage**: Genealogical record with:
      - ``origin``: First emission timestamp
      - ``activation_count``: Number of AL applications
      - ``derived_nodes``: list for tracking EPI emergence (future use)
      - ``parent_emission``: Reference to parent node (future use)

    Re-activation increments ``activation_count`` while preserving the
    original timestamp.

    Use Cases
    ---------
    **Biomedical**: HRV coherence training, neural activation, therapy start
    **Cognitive**: Idea germination, learning initiation, creative spark
    **Social**: Team activation, community emergence, ritual initiation

    Typical Sequences
    -----------------
    **AL → EN → IL → SHA**: Basic activation with stabilization and silence
    **AL → RA**: Emission with immediate propagation
    **AL → NAV → IL**: Phased activation with transition

    Preconditions
    -------------
    - EPI < 0.8 (activation threshold)
    - Node in latent or low-activation state
    - Sufficient network coupling potential

    Structural Effects
    ------------------
    **EPI**: Increments (form activation) — the direct AL channel
    **νf**: Untouched (settles at basal ν₀⁺)
    **ΔNFR**: Untouched (AL does not impose reorganization pressure)
    **θ**: Untouched

    Examples
    --------
    >>> from tnfr.constants import DNFR_PRIMARY, EPI_PRIMARY, VF_PRIMARY
    >>> from tnfr.dynamics import set_delta_nfr_hook
    >>> from tnfr.structural import create_nfr, run_sequence
    >>> from tnfr.operators.definitions import (
    ...     Emission, Reception, Coherence, Silence
    ... )
    >>> G, node = create_nfr("seed", epi=0.18, vf=1.0)
    >>> run_sequence(
    ...     G,
    ...     node,
    ...     [Emission(), Reception(), Coherence(), Silence()]
    ... )
    >>> # Verify irreversibility
    >>> assert G.nodes[node]["_emission_activated"] is True
    >>> assert "emission_timestamp" in G.nodes[node]
    >>> print(
    ...     f"Activated at: {G.nodes[node]['emission_timestamp']}"
    ... )  # doctest: +SKIP
    Activated at: 2025-11-07T15:47:10.209731+00:00

    See Also
    --------
    Coherence : Stabilizes emitted structures
    Resonance : Propagates emitted coherence
    Reception : Receives external emissions
    """

    __slots__ = ()
    name: ClassVar[str] = EMISSION
    glyph: ClassVar[Glyph] = Glyph.AL

    def __call__(self, G: TNFRGraph, node: Any, **kw: Any) -> None:
        """Apply AL with structural irreversibility tracking.

        Marks temporal irreversibility before delegating to grammar execution.
        This ensures every emission leaves a persistent structural trace as
        required by TNFR.pdf §2.2.1 (AL - Foundational emission).

        Parameters
        ----------
        G : TNFRGraph
            Graph storing TNFR nodes and structural operator history.
        node : Any
            Identifier or object representing the target node within ``G``.
        **kw : Any
            Additional keyword arguments forwarded to the grammar layer.
        """
        # Check and clear latency state if reactivating from silence
        self._check_reactivation(G, node)

        # Mark structural irreversibility BEFORE grammar execution
        self._mark_irreversibility(G, node)

        # Delegate to parent __call__ which applies grammar
        super().__call__(G, node, **kw)

    def _check_reactivation(self, G: TNFRGraph, node: Any) -> None:
        """Check and clear latency state when reactivating from silence.

        When AL (Emission) is applied to a node in latent state (from SHA),
        this validates the reactivation and clears the latency attributes.

        Parameters
        ----------
        G : TNFRGraph
            Graph containing the node.
        node : Any
            Target node being reactivated.

        Warnings
        --------
        - Warns if node is reactivated after extended silence (duration check)
        - Warns if EPI has drifted from preserved value during silence
        """
        if G.nodes[node].get("latent", False):
            # Node is in latent state, reactivating from silence
            silence_duration = G.nodes[node].get("silence_duration", 0.0)

            # Get max silence duration threshold from graph config
            max_silence = G.graph.get("MAX_SILENCE_DURATION", float("inf"))

            # Validate reactivation timing
            if silence_duration > max_silence:
                warnings.warn(
                    f"Node {node} reactivating after extended silence "
                    f"(duration: {silence_duration:.2f}, "
                    f"max: {max_silence:.2f})",
                    stacklevel=3,
                )

            # Check EPI preservation integrity
            preserved_epi = G.nodes[node].get("preserved_epi")
            if preserved_epi is not None:
                # get_attr already imported at module top

                current_epi = float(get_attr(G.nodes[node], ALIAS_EPI, 0.0))
                epi_drift = abs(current_epi - preserved_epi)

                # Enhanced tolerance for initial nodes and dynamic networks
                # For initial nodes (preserved_epi ≈ 0), use absolute threshold
                # For established nodes, use relative threshold
                if abs(preserved_epi) < 1e-6:  # Initial node
                    # Tolerance is an operational value (not derived)
                    # EPI_THRESHOLD ≈ 0.330 (operational tolerance)
                    # This respects TNFR nodal dynamics: ∂EPI/∂t = νf · ΔNFR
                    # Initial nodes can evolve according to canonical limits
                    tolerance = StructuralFeedbackLoop.EPI_THRESHOLD  # ≈ 0.330
                    should_warn = epi_drift > tolerance
                else:  # Established node
                    # Use 1% relative tolerance for established nodes
                    tolerance = 0.01 * abs(preserved_epi)
                    should_warn = epi_drift > tolerance

                if should_warn:
                    # Different message based on node type
                    node_type = (
                        "initial" if abs(preserved_epi) < 1e-6 else "established"
                    )
                    warnings.warn(
                        f"Node {node} ({node_type}) EPI drifted during silence "
                        f"(preserved: {preserved_epi:.3f}, "
                        f"current: {current_epi:.3f}, "
                        f"drift: {epi_drift:.3f}, tolerance: {tolerance:.3f})",
                        stacklevel=3,
                    )

            # Clear latency state
            del G.nodes[node]["latent"]
            if "latency_start_time" in G.nodes[node]:
                del G.nodes[node]["latency_start_time"]
            if "preserved_epi" in G.nodes[node]:
                del G.nodes[node]["preserved_epi"]
            if "silence_duration" in G.nodes[node]:
                del G.nodes[node]["silence_duration"]
            if "was_initial_on_silence" in G.nodes[node]:
                del G.nodes[node]["was_initial_on_silence"]

    def _mark_irreversibility(self, G: TNFRGraph, node: Any) -> None:
        """Mark structural irreversibility for AL operator.

        According to TNFR.pdf §2.2.1, AL (Emission) is structurally
        irreversible:
        "Una vez activado, AL reorganiza el campo. No puede deshacerse."

        This method establishes:
        - Temporal marker: ISO timestamp of first emission
        - Activation flag: Persistent boolean indicating AL was activated
        - Structural lineage: Genealogical record for EPI traceability

        Parameters
        ----------
        G : TNFRGraph
            Graph containing the node.
        node : Any
            Target node for emission marking.

        Notes
        -----
        On first activation:
        - Sets emission_timestamp (ISO format)
        - Sets _emission_activated = True (immutable)
        - Sets _emission_origin (timestamp copy for preservation)
        - Initializes _structural_lineage dict

        On re-activation:
        - Preserves original timestamp
        - Increments activation_count in lineage
        """
        from datetime import datetime, timezone

        from ..alias import set_attr_str
        from ..constants.aliases import ALIAS_EMISSION_TIMESTAMP

        # Check if this is first activation
        if "_emission_activated" not in G.nodes[node]:
            # Generate UTC timestamp in ISO format
            emission_timestamp = datetime.now(timezone.utc).isoformat()

            # set canonical timestamp using alias system (string values)
            set_attr_str(G.nodes[node], ALIAS_EMISSION_TIMESTAMP, emission_timestamp)

            # set persistent activation flag (immutable marker)
            G.nodes[node]["_emission_activated"] = True

            # Preserve origin timestamp (never overwritten)
            G.nodes[node]["_emission_origin"] = emission_timestamp

            # Initialize structural lineage for genealogical traceability
            G.nodes[node]["_structural_lineage"] = {
                "origin": emission_timestamp,
                "activation_count": 1,
                "derived_nodes": [],  # Nodes that emerge from this emission
                "parent_emission": None,  # If derived from another node
            }
        else:
            # Re-activation: increment counter, keep original timestamp
            if "_structural_lineage" in G.nodes[node]:
                G.nodes[node]["_structural_lineage"]["activation_count"] += 1

    def _validate_preconditions(self, G: TNFRGraph, node: Any) -> None:
        """Validate AL-specific preconditions with strict canonical checks.

        Implements TNFR.pdf §2.2.1 precondition validation:
        1. EPI < latent threshold (node in nascent/latent state)
        2. νf > basal threshold (sufficient structural frequency)
        3. Network connectivity check (warning for isolated nodes)

        Raises
        ------
        ValueError
            If EPI too high or νf too low for emission
        """
        from .preconditions.emission import validate_emission_strict

        validate_emission_strict(G, node)

    def _collect_metrics(
        self, G: TNFRGraph, node: Any, state_before: dict[str, Any]
    ) -> dict[str, Any]:
        """Collect AL-specific metrics."""
        from .metrics import emission_metrics

        return emission_metrics(
            G,
            node,
            state_before["epi"],
            state_before["vf"],
        )