"""Uniform full-law admission of the two-ramp receiver's slow phase motion. ORGANIZED_RECEIVER_SLOW_ADMISSION.md owns the exact phase/velocity closure, retained structural energy and all-future force-balance defect theorem. No reference trajectory, donor-retention corridor or joined entry is evaluated. """ 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 I, pi_interval, sqrt from ._organized_receiver_mechanism import ( _assess_organized_receiver_mechanism, _OrganizedReceiverMechanism, ) from ._sine_preparation import _prepared_transit_radii, _prepared_velocity_defect from .reversible_eigenmode_reference import _negative_exp_bounds _RELEASE_TIME = Q(400) _DEFECT_BUDGET = Q(11, 10**6) _RATE_FLOOR = Q(3, 20) _LIPSCHITZ = Q(2) @dataclass(frozen=True) class _OrganizedReceiverSlowAdmission: """Actual velocity control and its source-specific release conditions. The velocity discrepancy is uniformly bounded after release. It does not bound accumulated phase error without an admitted comparison tube. Phase-rate signs and windings refer only to the release instant. """ preparation: _OrganizedReceiverMechanism nominal_initial_slow_velocity_bounds: tuple[I, ...] nominal_form_gradient_norm_bounds: I initial_defect_norm_upper_bound: Q damping_lower_bound: Q defect_decay_bounds: I asymptotic_defect_upper_bound: Q uniform_velocity_defect_upper_bound: Q velocity_defect_margin: Q uniform_form_rate_norm_upper_bound: Q release_form_decay_bounds: I release_scaled_form_norm_upper_bound: Q release_form_norm_upper_bound: Q release_phase_error_norm_upper_bound: Q bridge_phase_error_norm_upper_bound: Q bridge_donor_acute_margin: Q release_donor_acute_margin: Q release_receiver_zero_winding_margin: Q release_phase_rate_bounds: tuple[I, ...] release_receiver_signed_rate_lower_bound: Q receiver_rate_margin: Q release_windings: tuple[int, int, int] | None uniform_defect_certified: bool donor_release_bridge_certified: bool receiver_phase_motion_certified: bool status: str unresolved_conditions: tuple[str, ...] release_time: Q = _RELEASE_TIME original_release_time: Q = _RELEASE_TIME * Q(1024, 1023) velocity_defect_budget: Q = _DEFECT_BUDGET receiver_signed_rate_floor: Q = _RATE_FLOOR global_phase_lipschitz_bound: Q = _LIPSCHITZ structural_energy_ratio: Q = Q(1, 4) phase_mean_leaf_dimension: int = 26 first_order_exact_closure: bool = False eventual_receiver_acquisition: str = "unresolved" eventual_donor_retention: str = "unresolved" joined_capture: str = "unresolved" slow_clock: str = "s=gamma**2*tau; tau=(1023/1024)*t" scope: tuple[str, ...] = ( "unchanged_two_ramp_source_rebuilt_from_primitive_error_allowances", "exact_second_order_phase_law_on_global_mean_zero_leaf", "initial_phase_velocity_retains_supplied_form_and_all_errors", "structural_inertial_storage_is_H_over_four_not_physical_mass", "uniform_velocity_defect_for_all_times_after_release", "actual_receiver_phase_rate_signs_only_at_release_not_a_future_monotonicity_claim", "phase_accumulation_requires_separate_tube_and_residual_control", "donor_history_and_complete_form_phase_capture_remain_unresolved", "no_reference_trajectory_or_reserved_response_evaluated", ) def _assess_organized_receiver_slow_admission( *, form_error_bound, phase_error_bound ) -> _OrganizedReceiverSlowAdmission: """Rebuild source and certify slow velocity without accepting cached reports.""" rx = _exact(form_error_bound, "form_error_bound") rt = _exact(phase_error_bound, "phase_error_bound") if rx < 0 or rt < 0: raise ValueError("preparation error bounds must be nonnegative") source = _assess_organized_receiver_mechanism( form_error_bound=rx, phase_error_bound=rt ) gamma = source.capture_geometry.geometry.gamma_bounds epsilon = source.slow_clock_factor_bounds gap = source.semigroup_gap_lower_bound norm = source.forcing_norm_bounds gradient_norm = sqrt( I(sum(value**2 for value in source.nominal_initial_form_gradient)) ) inverse_gamma = 1 / gamma initial_defect = ( gradient_norm.hi * inverse_gamma.hi / 4 + 2 * norm.hi * rx * inverse_gamma.hi + _LIPSCHITZ * norm.hi * rt ) damping, decay, floor, defect = _prepared_velocity_defect( time=_RELEASE_TIME, gap_lower=gap, feedback_upper=epsilon.hi, lipschitz_upper=_LIPSCHITZ, forcing_upper=norm.hi, initial_defect_upper=initial_defect, ) form_decay = I(*_negative_exp_bounds(gap * _RELEASE_TIME)) scaled_form, phase_remainder = _prepared_transit_radii( time=_RELEASE_TIME, decay_upper=form_decay.hi, gap_lower=gap, initial_norm_upper=source.scaled_initial_norm_upper_bound, feedback_upper=epsilon.hi, forcing_upper=norm.hi, ) phase_radius = ( source.proxy_reference_distance_bounds.hi + norm.hi * (rt + gamma.hi * rx) + phase_remainder ) bridge_radius = ( source.proxy_reference_distance_bounds.hi + norm.hi * (rt + gamma.hi * rx) + source.layer_scaled_form_norm_upper_bound + epsilon.hi * _RELEASE_TIME * norm.hi ) form_radius = inverse_gamma.hi * scaled_form phase_row_error = sqrt(I(2)).hi * phase_radius + defect rates = tuple( current / 4 + I(-phase_row_error, phase_row_error) for current in source.reference_current_bounds ) oriented = min( -rates[18 + j].hi if j < 4 else rates[18 + j].lo for j in range(9) if j != 4 ) pi = pi_interval() donor_margin = pi.lo / 2 - (2 * pi / 9).hi - sqrt(I(2)).hi * phase_radius bridge_margin = pi.lo / 2 - (2 * pi / 9).hi - sqrt(I(2)).hi * bridge_radius receiver_margin = pi.lo - sqrt(I(2)).hi * phase_radius defect_margin = _DEFECT_BUDGET - defect rate_margin = oriented - _RATE_FLOOR release_ok = donor_margin > 0 and receiver_margin > 0 defect_ok = defect_margin > 0 motion_ok = rate_margin > 0 bridge_ok = bridge_margin > 0 unresolved = tuple( reason for passed, reason in ( (release_ok, "release_donor_one_receiver_zero_not_certified"), (bridge_ok, "donor_identity_bridge_not_certified"), (defect_ok, "uniform_velocity_defect_budget_not_certified"), (motion_ok, "receiver_phase_motion_floor_not_certified"), ) if not passed ) return _OrganizedReceiverSlowAdmission( preparation=source, nominal_initial_slow_velocity_bounds=tuple( inverse_gamma * value / 4 for value in source.nominal_initial_form_gradient ), nominal_form_gradient_norm_bounds=gradient_norm, initial_defect_norm_upper_bound=initial_defect, damping_lower_bound=damping, defect_decay_bounds=decay, asymptotic_defect_upper_bound=floor, uniform_velocity_defect_upper_bound=defect, velocity_defect_margin=defect_margin, uniform_form_rate_norm_upper_bound=gamma.hi * defect, release_form_decay_bounds=form_decay, release_scaled_form_norm_upper_bound=scaled_form, release_form_norm_upper_bound=form_radius, release_phase_error_norm_upper_bound=phase_radius, bridge_phase_error_norm_upper_bound=bridge_radius, bridge_donor_acute_margin=bridge_margin, release_donor_acute_margin=donor_margin, release_receiver_zero_winding_margin=receiver_margin, release_phase_rate_bounds=rates, release_receiver_signed_rate_lower_bound=oriented, receiver_rate_margin=rate_margin, release_windings=(1, 1, 0) if release_ok else None, uniform_defect_certified=defect_ok, donor_release_bridge_certified=bridge_ok, receiver_phase_motion_certified=motion_ok, status="certified_uniform_slow_admission" if not unresolved else "unavailable", unresolved_conditions=unresolved, )