"""Own-class-one recovery resources for freshly admitted isolated C9 sources. This analytical consumer retains the actual acquired state and its full relative preparation. The quarter-law dwell rescales both half-law rows; no reached state, supplied source report or cached verdict is accepted. Proof: theory/nodal/ORGANIZED_JOINT_RESOURCES.md. """ from __future__ import annotations from dataclasses import dataclass from fractions import Fraction as Q from .._exact_time import exact_or_represented_real as _exact from ..mathematics._rational_interval import INTERVAL_METHOD, I, cos, pi_interval, sqrt from ._sine_class_constitutive_acquisition import ( _assess_constitutive_class_pair, _ConstitutiveFormedClassPair, ) from ._sine_lyapunov import ( _sine_lyapunov_coefficients, _sine_lyapunov_initial_upper, _sine_lyapunov_return_squared, ) _FORMATION_TIME = Q(100) _RADIUS = Q(1, 12) _GAP, _RATE = Q(1, 5), Q(2) _MAX_DECAY_POWER = 4096 @dataclass(frozen=True) class _SineRecoveryResources: """Conditional source, contraction and actual endpoint radius evidence. Failed sufficient margins retain unavailability, not a necessary time obstruction. Neither support attachment nor observation is certified. The power cap bounds integer arithmetic, not physically permitted time. """ source: _ConstitutiveFormedClassPair form_error_bound: Q phase_error_bound: Q quarter_dwell: Q half_law_dwell: Q quarter_handoff_time: Q original_handoff_time: Q endpoint_radius: Q decay_power: int class_one_radius_angle_bounds: I class_one_phase_hessian_lower_bound: Q transformed_stiffness_lower_bound: Q transformed_stiffness_upper_bound: Q lyapunov_position_lower_coefficient: Q lyapunov_position_upper_coefficient: Q lyapunov_initial_upper_bound: Q lyapunov_decay_rate: Q decay_exponent: Q decay_exponent_margin: Q exact_decay_upper_bound: Q | None returned_lyapunov_upper_bound: Q | None endpoint_form_norm_squared_upper_bound: Q | None endpoint_phase_norm_squared_upper_bound: Q | None endpoint_form_margin: Q | None endpoint_phase_margin: Q | None source_certified: bool decay_certified: bool recovery_certified: bool status: str unresolved_conditions: tuple[str, ...] quarter_formation_time: Q = 2 * _FORMATION_TIME radius: Q = _RADIUS class_one_phase_hessian_upper_bound: Q = Q(1) target_winding: int = 1 clock: str = "tau=e*t; e=1023/1024; isolated quarter-law half-time=tau/2" arithmetic_method: str = INTERVAL_METHOD scope: tuple[str, ...] = ( "fresh_original_class_one_ramp_and_all_zero_sum_preparation_errors", "sine_law_acquisition_precedes_own_class_one_curvature_bound", "uninterrupted_quarter_law_dwell_transforms_both_half_law_rows", "exact_rational_power_certificate_without_exponential_grid_loss", "endpoint_radius_bounds_reached_state_not_a_new_source_or_reset", "unavailable_sufficient_bound_is_not_a_necessary_resource_obstruction", "no_contact_observation_trajectory_event_occurrence_or_physical_bridge", ) def _assess_sine_recovery_resources( *, form_error_bound, phase_error_bound, quarter_dwell, endpoint_radius, decay_power ) -> _SineRecoveryResources: """Certify a declared recovery budget after fresh primitive acquisition. All scalars are admitted before constructing a source or interval. Preparation allowances and quarter-law dwell are nonnegative; the endpoint radius is positive. ``decay_power`` is an exact integer in [1, 4096]. Its bound is an arithmetic policy, not a limit on the dwell or on the decay exponent. Only class-one capture is consumed. """ rx = _exact(form_error_bound, "form_error_bound") rt = _exact(phase_error_bound, "phase_error_bound") dwell = _exact(quarter_dwell, "quarter_dwell") q = _exact(endpoint_radius, "endpoint_radius") power = _exact(decay_power, "decay_power") if min(rx, rt, dwell) < 0: raise ValueError("preparation allowances and quarter dwell must be nonnegative") if q <= 0: raise ValueError("endpoint_radius must be strictly positive") if power.denominator != 1 or not 1 <= power <= _MAX_DECAY_POWER: raise ValueError("decay_power must be an exact integer in [1, 4096]") power = int(power) source = _assess_constitutive_class_pair( deformation=Q(0), scaled_time=_FORMATION_TIME, form_error_bound=rx, phase_error_bound=rt, radius=_RADIUS, ) angle = 2 * pi_interval() / 9 + sqrt(I(2)) * _RADIUS curvature = cos(angle).lo eta = source.eta_bounds mu, maximum, lower, upper, rate = _sine_lyapunov_coefficients( eta_lower=eta.lo, eta_upper=eta.hi, cosine_lower=curvature, gap_lower=_GAP, rate_upper=_RATE, phase_hessian_upper=Q(1), ) initial = _sine_lyapunov_initial_upper( eta_upper=eta.hi, rate_upper=_RATE, gap_lower=_GAP, position_upper=upper, form_norm_upper=source.endpoint_form_norm_upper_bounds[0], phase_norm_upper=source.endpoint_target_phase_norm_upper_bounds[0], ) source_ok = ( source.initial_zero_winding_certified and source.formation_certified_by_class[0] and source.source_budget_certified_by_class[0] ) exponent = rate * dwell / 2 exponent_margin = exponent - power decay_ok = exponent_margin >= 0 decay = Q(1, 2**power) if decay_ok else None returned = x2 = y2 = form_margin = phase_margin = None if decay is not None: returned, x2, y2 = _sine_lyapunov_return_squared( initial_upper=initial, decay_upper=decay, eta_lower=eta.lo, gap_lower=_GAP, rate_upper=_RATE, position_lower=lower, ) form_margin, phase_margin = q**2 - x2, q**2 - y2 unresolved = tuple( name for condition, name in ( (source_ok, "original_class_one_source_not_certified"), (decay_ok, "declared_dwell_decay_not_certified"), ( form_margin is not None and form_margin > 0, "actual_form_handoff_radius_not_certified", ), ( phase_margin is not None and phase_margin > 0, "actual_phase_handoff_radius_not_certified", ), ) if not condition ) return _SineRecoveryResources( source=source, form_error_bound=rx, phase_error_bound=rt, quarter_dwell=dwell, half_law_dwell=dwell / 2, quarter_handoff_time=2 * _FORMATION_TIME + dwell, original_handoff_time=(2 * _FORMATION_TIME + dwell) * Q(1024, 1023), endpoint_radius=q, decay_power=power, class_one_radius_angle_bounds=angle, class_one_phase_hessian_lower_bound=curvature, transformed_stiffness_lower_bound=mu, transformed_stiffness_upper_bound=maximum, lyapunov_position_lower_coefficient=lower, lyapunov_position_upper_coefficient=upper, lyapunov_initial_upper_bound=initial, lyapunov_decay_rate=rate, decay_exponent=exponent, decay_exponent_margin=exponent_margin, exact_decay_upper_bound=decay, returned_lyapunov_upper_bound=returned, endpoint_form_norm_squared_upper_bound=x2, endpoint_phase_norm_squared_upper_bound=y2, endpoint_form_margin=form_margin, endpoint_phase_margin=phase_margin, source_certified=source_ok, decay_certified=decay_ok, recovery_certified=not unresolved, status="certified_sine_recovery_resources" if not unresolved else "unavailable", unresolved_conditions=unresolved, )