"""Joint C9 acquisition from the fixed ramps on preexisting fine support. ORGANIZED_JOINT_ACQUISITION.md owns this complete-law certificate. The structural deadline and whole-network preparation budget are fixed before assessment; no isolated acquisition or recovery verdict is consumed. """ 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_network_capture import ( _derive_organized_triangle_capture, _OrganizedTriangleCapture, ) from ._organized_network_compatibility import _EQUAL_CONTROL, _UNEQUAL_CONTROL, _mixings from ._sine_preparation import _prepared_form_costs, _prepared_transit_radii from .relational_sine_formed_classes import _SOURCE_SCALE from .reversible_eigenmode_reference import _negative_exp_bounds _TIME = Q(200) _BUDGET = Q(10**9) @dataclass(frozen=True) class _OrganizedJointAcquisition: """Fresh source, full-law transit and independently rebuilt capture geometry. Norm bounds concern the actual endpoint. Budget policy, initial winding, endpoint entry and formation are separate conditions. An unavailable sufficient bound is not a nonformation theorem. """ capture_geometry: _OrganizedTriangleCapture form_error_bound: Q phase_error_bound: Q relative_preparation_dimension: int nominal_initial_forms: tuple[Q, ...] nominal_initial_internal_form_storage: Q nominal_initial_contact_form_storage: Q nominal_initial_form_storage: Q initial_form_gradient_l1: Q initial_storage_correction_upper_bound: Q initial_storage_upper_bound: Q source_budget_margin: Q initial_form_error_norm_upper_bound: Q initial_phase_error_norm_upper_bound: Q scaled_initial_norm_upper_bound: Q semigroup_gap_lower_bound: Q exponential_decay_bounds: I forcing_norm_bounds: I proxy_target_distance_bounds: I endpoint_scaled_form_norm_upper_bound: Q endpoint_form_norm_upper_bound: Q endpoint_aligned_phase_norm_upper_bound: Q endpoint_linear_phase_storage_upper_bound: Q endpoint_form_storage_upper_bound: Q endpoint_quadratic_phase_storage_upper_bound: Q endpoint_excess_storage_upper_bound: Q initial_zero_winding_margin: Q endpoint_acute_margin: Q endpoint_cell_margin: Q capture_margin: Q source_budget_certified: bool initial_zero_winding_certified: bool entry_certified: bool formation_certified: bool winding_retained: bool converges_to_target: bool status: str unresolved_conditions: tuple[str, ...] acquisition_time: Q = _TIME original_acquisition_time: Q = _TIME * Q(1024, 1023) common_source_storage_budget: Q = _BUDGET nominal_source_scale: Q = _SOURCE_SCALE nominal_initial_phases: tuple[Q, ...] = (Q(0),) * 27 held_capacities: tuple[Q, ...] = (Q(1),) * 27 nominal_initial_windings: tuple[int, ...] = (0, 0, 0) target_windings: tuple[int, ...] = (1, 1, 1) joined_mean_leaf_dimension: int = 52 scope: tuple[str, ...] = ( "same_primitive_ramps_freshly_admitted_on_both_fixed_connected_supports", "complete_degree_four_reciprocal_sine_law_and_held_unit_capacity", "all_initial_contact_storage_included_no_later_input_or_event", "separate_initial_component_error_sums_zero_only_global_means_conserved", "all_54_coordinates_retained_through_full_law_semigroup_bounds", "phase_passage_before_deadline_allowed_target_cell_entered_only_at_deadline", "linear_phase_storage_term_retained_for_moving_component_means", "no_isolated_capture_recovery_or_tiny_endpoint_radius_transferred", "budget_policy_separate_from_mathematical_formation_and_capture", "no_trajectory_support_birth_autonomous_preparation_or_physical_identification", ) def _assess_organized_joint_acquisition( *, mixing, form_error_bound, phase_error_bound ) -> _OrganizedJointAcquisition: """Assess the frozen time and budget from primitive preparation allowances.""" weights = _mixings(mixing) 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") if weights not in (_EQUAL_CONTROL, _UNEQUAL_CONTROL): raise ValueError("joint acquisition requires one of the two fixed controls") capture = _derive_organized_triangle_capture(mixing=weights) geometry = capture.geometry forms = tuple(_SOURCE_SCALE * (node % 9 - 4) for node in geometry.nodes) costs, gradient = _prepared_form_costs( form=forms, weighted_edges=geometry.weighted_edges ) internal, contact = Q(0), Q(0) for (a, b, _), cost in zip(geometry.weighted_edges, costs): if a // 9 == b // 9: internal += cost else: contact += cost gradient_l1 = sum(abs(value) for value in gradient) correction = gradient_l1 * rx + 108 * (rx**2 + rt**2) source_storage = internal + contact + correction source_margin = _BUDGET - source_storage pi = pi_interval() gamma = geometry.gamma_bounds alpha = 2 * pi / 9 norm = sqrt(I(27)) ex, et = (norm * rx).hi, (norm * rt).hi initial_norm = gamma.hi * (sqrt(I(sum(value**2 for value in forms))).hi + ex) gap = capture.laplacian_gap_lower_bound * geometry.clock_factor decay = I(*_negative_exp_bounds(gap * _TIME)) scaled_form, phase_remainder = _prepared_transit_radii( time=_TIME, decay_upper=decay.hi, gap_lower=gap, initial_norm_upper=initial_norm, feedback_upper=(gamma**2).hi, forcing_upper=norm.hi, ) form_radius = (1 / gamma).hi * scaled_form proxy_distance = sqrt(I(180)) * abs(gamma * _SOURCE_SCALE - alpha) phase_radius = proxy_distance.hi + phase_remainder + gamma.hi * ex + et linear = capture.aligned_gradient_norm_bounds.hi * phase_radius form_storage = 4 * form_radius**2 quadratic = 4 * phase_radius**2 excess = capture.nominal_excess_bounds.hi + form_storage + linear + quadratic initial_margin = pi.lo - 2 * rt edge_gap_upper = alpha.hi + 2 * phase_radius acute_margin = pi.lo / 2 - edge_gap_upper cell_margin = capture.cell_edge_gap_bound - edge_gap_upper capture_margin = capture.boundary_energy_lower_bound - excess budget_ok = source_margin > 0 initial_ok = initial_margin > 0 entry = ( capture.target_certified and capture.barrier_certified and acute_margin > 0 and cell_margin > 0 and capture_margin > 0 ) formation = initial_ok and entry unresolved = tuple( reason for passed, reason in ( (budget_ok, "connected_preparation_budget_not_certified"), (initial_ok, "initial_zero_winding_not_certified"), (capture.target_certified, "joined_target_not_certified"), (capture.barrier_certified, "full_state_boundary_not_certified"), (acute_margin > 0, "endpoint_acute_winding_not_certified"), (cell_margin > 0, "endpoint_cell_entry_not_certified"), (capture_margin > 0, "endpoint_energy_entry_not_certified"), ) if not passed ) return _OrganizedJointAcquisition( capture_geometry=capture, form_error_bound=rx, phase_error_bound=rt, relative_preparation_dimension=24 * (int(rx > 0) + int(rt > 0)), nominal_initial_forms=forms, nominal_initial_internal_form_storage=internal, nominal_initial_contact_form_storage=contact, nominal_initial_form_storage=internal + contact, initial_form_gradient_l1=gradient_l1, initial_storage_correction_upper_bound=correction, initial_storage_upper_bound=source_storage, source_budget_margin=source_margin, initial_form_error_norm_upper_bound=ex, initial_phase_error_norm_upper_bound=et, scaled_initial_norm_upper_bound=initial_norm, semigroup_gap_lower_bound=gap, exponential_decay_bounds=decay, forcing_norm_bounds=norm, proxy_target_distance_bounds=proxy_distance, endpoint_scaled_form_norm_upper_bound=scaled_form, endpoint_form_norm_upper_bound=form_radius, endpoint_aligned_phase_norm_upper_bound=phase_radius, endpoint_linear_phase_storage_upper_bound=linear, endpoint_form_storage_upper_bound=form_storage, endpoint_quadratic_phase_storage_upper_bound=quadratic, endpoint_excess_storage_upper_bound=excess, initial_zero_winding_margin=initial_margin, endpoint_acute_margin=acute_margin, endpoint_cell_margin=cell_margin, capture_margin=capture_margin, source_budget_certified=budget_ok, initial_zero_winding_certified=initial_ok, entry_certified=entry, formation_certified=formation, winding_retained=entry, converges_to_target=entry, status=( "certified_organized_joint_acquisition" if not unresolved else "unavailable" ), unresolved_conditions=unresolved, )