"""Full-state capture of three acquired C9 objects under two fixed contacts. ACQUIRED_ORGANIZED_NETWORK_CAPTURE.md owns the conditional proof. This detached certificate rebuilds original preparation and recovery; it neither integrates a response nor resets a reached state to its registered target. """ 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 from ._organized_network_capture import ( _CELL_GAP, _TARGET_GAP, _derive_organized_triangle_capture, ) from ._organized_network_compatibility import _EQUAL_CONTROL as _EQUAL from ._organized_network_compatibility import _UNEQUAL_CONTROL as _UNEQUAL from ._organized_network_compatibility import _mixings, _OrganizedTriangle from ._sine_constitutive_recovery import ( _assess_constitutive_recovery, _ConstitutiveRecovery, ) @dataclass(frozen=True) class _AcquiredOrganizedTriangleCapture: """Conditional full-law certificate; unsupported sources remain unavailable. Tiny source/work corrections are exact rationals kept separately from interval-rounded nominal quantities. Only a certified source makes these conditional bounds statements about the actual acquired trajectories. """ recovery: _ConstitutiveRecovery geometry: _OrganizedTriangle target_root_bounds: I | None target_root_endpoint_sign_bounds: tuple[I, I] | None target_root_derivative_lower_bound: Q | None target_phase_origins_bounds: tuple[I, ...] target_contact_gaps_bounds: tuple[I, ...] target_fine_gap_bounds: tuple[I, ...] target_hessian_lower_bound: Q laplacian_gap_lower_bound: Q edge_effective_resistances: tuple[Q, ...] bregman_coefficient_bounds: I nominal_excess_bounds: I source_excess_upper_bound: Q initial_excess_upper_bound: Q boundary_energy_lower_bound: Q capture_margin: Q attachment_work_bounds: I attachment_residual_work_bounds: tuple[Q, Q] joint_error_squared_upper_bound: Q | None source_certified: bool target_certified: bool barrier_certified: bool capture_certified: bool winding_retained: bool converges_to_target: bool status: str unresolved_conditions: tuple[str, ...] cell_edge_gap_bound: Q = _CELL_GAP target_edge_gap_bound: Q = _TARGET_GAP target_windings: tuple[int, ...] = (1, 1, 1) scope: tuple[str, ...] = ( "three_actual_independently_recovered_class_one_C9_sources", "fixed_equal_or_unequal_oriented_contacts_and_full_54_coordinate_flow", "held_unit_capacity_degree_four_sine_law_and_structural_clock", "registered_lifts_and_conserved_global_zero_means", "target_acute_but_trapping_cell_need_not_be_acute_or_convex_in_energy", "supplied_positive_attachment_work_is_separate_from_continuous_loss", "no_reset_trajectory_campaign_contact_selection_or_physical_identification", ) def _assess_acquired_organized_triangle( *, mixing, form_error_bound, phase_error_bound ) -> _AcquiredOrganizedTriangleCapture: """Admit primitives, rebuild source and certify both fixed contact controls. Other mixtures require a separate target/source theorem, rather than a rounded target, transferred pair constants or an incoming cached report. """ 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, _UNEQUAL): raise ValueError("capture requires one of the two fixed contact controls") recovery = _assess_constitutive_recovery( deformation=Q(0), form_error_bound=rx, phase_error_bound=rt ) capture_geometry = _derive_organized_triangle_capture(mixing=weights) geometry = capture_geometry.geometry excess = capture_geometry.nominal_excess_bounds barrier = capture_geometry.boundary_energy_lower_bound target_ok = capture_geometry.target_certified barrier_ok = capture_geometry.barrier_certified alpha = 2 * pi_interval() / 9 epsilon = recovery.endpoint_radius source_excess = 24 * epsilon**2 initial = excess.hi + source_excess margin = barrier - initial source_ok = recovery.recovery_certified entry_ok = alpha.hi + 2 * epsilon < _CELL_GAP unresolved = [] for condition, admitted in ( ("original_source_recovery_not_certified", source_ok), ("joined_target_not_certified", target_ok), ("full_state_boundary_not_certified", barrier_ok), ("source_not_inside_registered_cell", entry_ok), ("source_energy_not_below_boundary", margin > 0), ): if not admitted: unresolved.append(condition) capture = not unresolved work_residual = (Q(0), 12 * epsilon**2) return _AcquiredOrganizedTriangleCapture( recovery=recovery, geometry=geometry, target_root_bounds=capture_geometry.target_root_bounds, target_root_endpoint_sign_bounds=capture_geometry.target_root_endpoint_sign_bounds, target_root_derivative_lower_bound=capture_geometry.target_root_derivative_lower_bound, target_phase_origins_bounds=capture_geometry.target_phase_origins_bounds, target_contact_gaps_bounds=capture_geometry.target_contact_gaps_bounds, target_fine_gap_bounds=capture_geometry.target_fine_gap_bounds, target_hessian_lower_bound=capture_geometry.target_hessian_lower_bound, laplacian_gap_lower_bound=capture_geometry.laplacian_gap_lower_bound, edge_effective_resistances=capture_geometry.edge_effective_resistances, bregman_coefficient_bounds=capture_geometry.bregman_coefficient_bounds, nominal_excess_bounds=excess, source_excess_upper_bound=source_excess, initial_excess_upper_bound=initial, boundary_energy_lower_bound=barrier, capture_margin=margin, attachment_work_bounds=geometry.aligned_attachment_work_bounds + I(*work_residual), attachment_residual_work_bounds=work_residual, joint_error_squared_upper_bound=( initial / capture_geometry.joint_coercivity_lower_bound if capture else None ), source_certified=source_ok, target_certified=target_ok, barrier_certified=barrier_ok, capture_certified=capture, winding_retained=capture, converges_to_target=capture, status=( "certified_acquired_organized_triangle_capture" if capture else "unavailable" ), unresolved_conditions=tuple(unresolved), )