"""P2 graph read-outs need not realize the auxiliary harmonic flow. The exact image/tangency proof is in TNFR_VARIATIONAL_PRINCIPLE.md section 3.7. These finite regressions exercise production readers, pressure refresh and the shared nodal integrator. They neither fit a phase law nor certify all graphs. """ import math import networkx as nx import numpy as np import pytest from tnfr.alias import get_attr from tnfr.constants.aliases import ALIAS_DNFR, ALIAS_EPI, ALIAS_THETA from tnfr.dynamics.dnfr import default_compute_delta_nfr from tnfr.dynamics.integrators import update_epi_via_nodal_equation from tnfr.physics.symplectic_substrate import ( evolve_substrate_flow, extract_phase_space_point, hamiltonian_vector_field, ) def _p2(*, phase=math.pi / 3, epi=(0.0, 1.0), capacity=(1.0, 1.0)): graph = nx.path_graph(2) graph.edges[0, 1].update(weight=1.0, length=1.0) graph.graph.update( DNFR_WEIGHTS={"phase": 0.0, "epi": 1.0, "vf": 0.0, "topo": 0.0}, GAMMA={"type": "none"}, use_extended_dynamics=False, DT_MIN=0.0, EPI_MIN=-2.0, EPI_MAX=2.0, CLIP_MODE="hard", ) for node in graph: graph.nodes[node].update( EPI=float(epi[node]), nu_f=float(capacity[node]), theta=0.0 if node == 0 else phase % math.tau, ) default_compute_delta_nfr(graph) return graph def _read(graph, aliases): return np.array([get_attr(graph.nodes[n], aliases, None) for n in graph]) def test_refreshed_epi_diffusion_is_not_the_extracted_harmonic_flow(): graph = _p2() initial = extract_phase_space_point(graph) phases = _read(graph, ALIAS_THETA).copy() np.testing.assert_allclose(initial.k_phi, [-math.pi / 3, math.pi / 3]) np.testing.assert_allclose(initial.j_phi, [math.sqrt(3) / 2, -math.sqrt(3) / 2]) np.testing.assert_allclose(_read(graph, ALIAS_DNFR), [1.0, -1.0]) harmonic_velocity = hamiltonian_vector_field(initial).reshape(2, 4) np.testing.assert_allclose(harmonic_velocity[:, 0], initial.j_phi) np.testing.assert_allclose(harmonic_velocity[:, 1], -initial.k_phi) # A held-pressure Euler segment, refreshed explicitly at every boundary. # Binary-exact dt is a numerical fixture, not an added physical parameter. dt = 1.0 / 8.0 for step in range(3): before = _read(graph, ALIAS_EPI) pressure = _read(graph, ALIAS_DNFR) update_epi_via_nodal_equation(graph, dt=dt, t=step * dt, method="euler") np.testing.assert_allclose(_read(graph, ALIAS_EPI), before + dt * pressure) np.testing.assert_array_equal(_read(graph, ALIAS_THETA), phases) default_compute_delta_nfr(graph) point = extract_phase_space_point(graph) np.testing.assert_array_equal(point.k_phi, initial.k_phi) np.testing.assert_array_equal(point.j_phi, initial.j_phi) difference = (1 - 2 * dt) ** (step + 1) np.testing.assert_allclose(_read(graph, ALIAS_DNFR), [difference, -difference]) np.testing.assert_allclose(point.phi_s, [-difference, difference]) np.testing.assert_allclose(point.j_dnfr, 2 * point.phi_s) harmonic = evolve_substrate_flow(initial, 3 * dt) assert not np.allclose(harmonic.k_phi, point.k_phi) assert not np.allclose(harmonic.j_phi, point.j_phi) assert not np.allclose(harmonic.j_phi + np.sin(harmonic.k_phi), 0.0) @pytest.mark.parametrize( "phase", [-2.5, -math.pi / 2, -math.pi / 3, math.pi / 3, math.pi / 2, 2.5] ) def test_harmonic_velocity_is_not_tangent_to_nonzero_p2_geometric_image(phase): # Read-only snapshots do not request a U3-gated coupling operation. point = extract_phase_space_point(_p2(phase=phase)) k, j = point.k_phi, point.j_phi np.testing.assert_allclose(j + np.sin(k), 0.0, atol=1e-14) velocity = hamiltonian_vector_field(point).reshape(2, 4) constraint_rate = velocity[:, 1] + np.cos(k) * velocity[:, 0] np.testing.assert_allclose(constraint_rate, -k - np.sin(k) * np.cos(k)) assert np.all(np.abs(constraint_rate) > 0.1) assert np.all(constraint_rate * k < 0.0) def test_synchronized_pressure_disagreement_still_obstructs_potential_flow(): point = extract_phase_space_point(_p2(phase=0.0)) np.testing.assert_allclose(point.k_phi, 0.0, atol=1e-14) np.testing.assert_allclose(point.j_phi, 0.0, atol=1e-14) np.testing.assert_allclose(point.phi_s, [-1.0, 1.0]) np.testing.assert_allclose(point.j_dnfr, [-2.0, 2.0]) velocity = hamiltonian_vector_field(point).reshape(2, 4) constraint_rate = velocity[:, 3] - 2 * velocity[:, 2] np.testing.assert_allclose(constraint_rate, -5 * point.phi_s) @pytest.mark.parametrize("capacity", [(1.0, 1.0), (0.5, 2.0), (2.0, 0.5)]) def test_derived_potential_decay_rate_is_the_sum_of_nodal_capacities(capacity): graph = _p2(capacity=capacity) before = extract_phase_space_point(graph) dt = 1.0 / 8.0 update_epi_via_nodal_equation(graph, dt=dt, t=0.0, method="euler") default_compute_delta_nfr(graph) after = extract_phase_space_point(graph) rate = sum(capacity) np.testing.assert_allclose((after.phi_s - before.phi_s) / dt, -rate * before.phi_s) np.testing.assert_allclose( (after.j_dnfr - before.j_dnfr) / dt, -rate * before.j_dnfr ) np.testing.assert_array_equal(after.k_phi, before.k_phi) np.testing.assert_array_equal(after.j_phi, before.j_phi) def test_zero_pressure_synchronized_control_is_a_common_fixed_point(): graph = _p2(phase=0.0, epi=(0.5, 0.5)) point = extract_phase_space_point(graph) np.testing.assert_allclose(point.to_vector(), 0.0, atol=1e-14) np.testing.assert_allclose(hamiltonian_vector_field(point), 0.0, atol=1e-14) update_epi_via_nodal_equation(graph, dt=0.125, t=0.0, method="euler") default_compute_delta_nfr(graph) np.testing.assert_allclose(_read(graph, ALIAS_EPI), [0.5, 0.5]) np.testing.assert_allclose(extract_phase_space_point(graph).to_vector(), 0.0) def test_isolated_harmonic_endpoint_can_return_to_geometric_image(): point = extract_phase_space_point(_p2()) half_turn = evolve_substrate_flow(point, math.pi) opposite = extract_phase_space_point(_p2(phase=-math.pi / 3)) np.testing.assert_allclose(half_turn.k_phi, opposite.k_phi, atol=1e-14) np.testing.assert_allclose(half_turn.j_phi, opposite.j_phi, atol=1e-14) quarter_turn = evolve_substrate_flow(point, math.pi / 2) assert not np.allclose(quarter_turn.j_phi + np.sin(quarter_turn.k_phi), 0.0) # Endpoint coincidence concerns this sector, not an executed graph event.