"""Independent analytic controls for a prescribed clock and state uncertainty. No research preparation, reserved response or model-specific trajectory is evaluated here. Time derivatives and same-time state derivatives differ. """ from fractions import Fraction as Q import mpmath as mp import pytest from tnfr.mathematics._rational_interval import I from tnfr.mathematics._validated_metric import validated_metric_taylor_step from tnfr.mathematics._validated_taylor import flow_jets, interval_jacobian def _everywhere(time, state): return (Q(1),) def test_time_jet_retains_nonzero_origin_and_all_polynomial_derivatives(): rows = flow_jets( (I(7),), 4, lambda time, state: (time**2 + 0 * state[0],), prescribed_time=Q(3, 2), ) # Integral of (3/2+s)^2, independently expanded in powers of s. expected = (Q(7), Q(9, 4), Q(3, 2), Q(1, 3), Q(0)) assert all(bound.contains(value) for bound, value in zip(rows[0], expected)) assert rows[0][-1] == I(0) def test_under_ordered_polynomial_retains_time_derivative_in_remainder(): start, duration, center = Q(2), Q(1, 8), Q(3) step, failed, reason = validated_metric_taylor_step( (center,), Q(0), ((Q(1),),), duration, lambda time, state: (time**2 + 0 * state[0],), _everywhere, growth_rate=Q(0), order=2, time=start, time_dependent=True, ) assert step is not None and failed is reason is None exact = center + ((start + duration) ** 3 - start**3) / 3 assert step.endpoint[0].contains(exact) assert step.local_remainder_bounds[0].contains(duration**3 / 3) assert step.local_remainder_bounds[0].lo > 0 assert step.prescribed_time_interval == I(start, start + duration) def test_large_clock_derivative_does_not_create_initial_clock_uncertainty(): start, duration, radius = Q(2), Q(1, 8), Q(1, 32) scale = Q(10**6) step, failed, reason = validated_metric_taylor_step( (Q(3),), radius, ((Q(1),),), duration, lambda time, state: (scale * time**2 + 0 * state[0],), _everywhere, growth_rate_bounds=(Q(0), Q(0)), order=4, time=start, time_dependent=True, ) assert step is not None and failed is reason is None assert step.growth_certificate.certified assert step.growth_certificate.jacobian_bounds == ((I(0),),) assert step.growth_certificate.prescribed_time_interval == I( start, start + duration ) assert step.propagated_initial_radius == radius assert radius <= step.endpoint_radius < radius + Q(1, 10**25) assert len(step.endpoint) == 1 shift = scale * ((start + duration) ** 3 - start**3) / 3 for initial in (3 - radius, Q(3), 3 + radius): assert step.endpoint[0].contains(initial + shift) def test_time_varying_state_growth_covers_the_whole_common_time_interval(): start, duration, radius = Q(3, 2), Q(1, 8), Q(1, 64) step, failed, reason = validated_metric_taylor_step( (Q(1),), radius, ((Q(1),),), duration, lambda time, state: (time * state[0],), _everywhere, growth_rate_bounds=(start + duration, start + duration), order=12, time=start, time_dependent=True, ) assert step is not None and failed is reason is None assert step.growth_certificate.jacobian_bounds == ((I(start, start + duration),),) ctx = mp.mp.clone() ctx.dps = 85 def real(value): return ctx.mpf(value.numerator) / value.denominator exponent = ((start + duration) ** 2 - start**2) / 2 for initial in (1 - radius, Q(1), 1 + radius): exact = real(initial) * ctx.exp(real(exponent)) assert real(step.endpoint[0].lo) <= exact <= real(step.endpoint[0].hi) assert step.growth_rate_upper_bound == start + duration def test_non_autonomous_nonlinear_solution_retains_initial_ball(): start, duration, radius = Q(1, 2), Q(1, 32), Q(1, 64) step, failed, reason = validated_metric_taylor_step( (Q(1),), radius, ((Q(1),),), duration, lambda time, state: (time * state[0] ** 2,), lambda time, state: (state[0].lo - Q(1, 2), 2 - state[0].hi), growth_rate=Q(3), order=8, time=start, time_dependent=True, ) assert step is not None and failed is reason is None integral = ((start + duration) ** 2 - start**2) / 2 for initial in (1 - radius, Q(1), 1 + radius): exact = initial / (1 - initial * integral) assert step.endpoint[0].contains(exact) assert abs(exact - step.endpoint_center[0]) <= step.endpoint_radius def test_state_jacobian_holds_time_fixed_but_encloses_all_times(): actual = interval_jacobian( (I(2, 3), I(4, 5)), lambda time, state: (time**2 * state[1], time * state[0] ** 2), prescribed_time=I(1, 2), ) assert actual == ((I(0), I(1, 4)), (I(4, 12), I(0))) def test_domain_reader_receives_the_entire_prescribed_time_interval(): seen = [] def domain(time, state): seen.append(time) return (2 - time.hi,) step, failed, reason = validated_metric_taylor_step( (Q(0),), Q(0), ((Q(1),),), Q(1, 4), lambda time, state: (time + 0 * state[0],), domain, growth_rate=Q(0), order=4, time=Q(15, 8), time_dependent=True, ) assert step is None and failed is not None assert reason == "whole_tube_domain_not_admitted" assert seen == [I(Q(15, 8), Q(17, 8))] def test_declared_switch_preserves_reached_state_and_radius(): center, radius, duration = Q(5), Q(1, 16), Q(1, 8) initial_radius = radius for index, sign in enumerate((1, -1)): step, failed, reason = validated_metric_taylor_step( (center,), radius, ((Q(1),),), duration, lambda time, state: (sign * time + 0 * state[0],), _everywhere, growth_rate=Q(0), order=3, time=index * duration, time_dependent=True, ) assert step is not None and failed is reason is None center, radius = step.endpoint_center[0], step.endpoint_radius assert center == 5 - Q(1, 64) assert radius == initial_radius assert step.endpoint[0] == I(center - radius, center + radius) @pytest.mark.parametrize("flag", (None, 0, 1, "true")) def test_prescribed_time_mode_requires_an_explicit_boolean(flag): with pytest.raises(TypeError, match="time_dependent"): validated_metric_taylor_step( (Q(0),), Q(0), ((Q(1),),), Q(1, 8), lambda state: state, lambda state: (Q(1),), growth_rate=Q(1), order=4, time_dependent=flag, )