"""Own-law recovery and supplied three-C9 contact of actual acquired sources. Every call rebuilds primitive class-one acquisition under the supplied member of the matched-potential family. Fixed analytic recovery bounds then retain the actual state and its original mean constraints through contact and four form-input branches. No trajectory, reset, report admission or event execution occurs. Conditional branch arithmetic is not certified when handoff fails. Proof: theory/nodal/ORGANIZED_PATTERN_CONSTITUTIVE_FREEDOM.md #organized-pattern-carried-handoff. """ from __future__ import annotations from dataclasses import dataclass from fractions import Fraction as Q from ..mathematics._rational_interval import INTERVAL_METHOD from ._sine_class_constitutive_acquisition import _ConstitutiveFormedClassPair from ._sine_constitutive_recovery import ( _DECAY_POWER, _DWELL, _ENDPOINT_RADIUS, _FORMATION_TIME, _RADIUS, _assess_constitutive_recovery, ) _AMPLITUDE = Q(7, 10000) _JOINED_BARRIER = Q(1, 486000) @dataclass(frozen=True) class _ConstitutiveHandoffBranch: """Conditional carried-state work and identity for one prescribed input.""" name: str donor_amplitude: Q receiver_amplitude: Q input_work_bounds: tuple[Q, Q] relative_norm_squared_upper_bound: Q excess_storage_upper_bound: Q radius_margin: Q storage_margin: Q form_mean_bounds: tuple[Q, Q] phase_mean_bounds: tuple[Q, Q] identity_certified: bool @dataclass(frozen=True) class _ConstitutiveHandoff: """Fixed class-one preparation, own-law dwell and supplied contact bounds. The source's first class is consumed; its second class is not a premise. Norm and event bounds cover each actually reached preparation member. Prospective contact/branch fields retain their formulas on unavailable reports, but their premise is the separately reported certified handoff. """ source: _ConstitutiveFormedClassPair deformation: Q form_error_bound: Q phase_error_bound: Q transformed_stiffness_lower_bound: Q | None transformed_stiffness_upper_bound: Q lyapunov_position_lower_coefficient: Q | None lyapunov_position_upper_coefficient: Q lyapunov_initial_upper_bound: Q lyapunov_decay_rate: Q | None decay_exponent: Q | None 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 handoff_certified: bool attachment_work_bounds: tuple[Q, Q] joined_excess_storage_upper_bound: Q joined_form_mean_bounds: tuple[Q, Q] joined_phase_mean_bounds: tuple[Q, Q] branches: tuple[_ConstitutiveHandoffBranch, ...] status: str unresolved_conditions: tuple[str, ...] formation_time: Q = _FORMATION_TIME relaxation_duration: Q = _DWELL scaled_handoff_time: Q = _FORMATION_TIME + _DWELL original_handoff_time: Q = (_FORMATION_TIME + _DWELL) * Q(1024, 1023) radius: Q = _RADIUS endpoint_radius: Q = _ENDPOINT_RADIUS decay_power: int = _DECAY_POWER joined_storage_barrier: Q = _JOINED_BARRIER target_windings: tuple[int, int, int] = (1, 1, 1) bridges: tuple[tuple[int, int], ...] = ((4, 13), (13, 22)) central_degrees: tuple[int, int, int] = (3, 4, 3) degree_sum: int = 58 clock: str = "tau=e*t; e=1023/1024" arithmetic_method: str = INTERVAL_METHOD scope: tuple[str, ...] = ( "fresh_own_law_class_one_source_and_original_zero_sum_errors", "all_three_actual_components_keep_their_full_form_and_phase_state", "own_potential_Hessian_bounds_in_complete_nonlinear_modified_energy", "fixed_unforced_dwell_and_exact_decay_below_the_interval_grid", "endpoint_radius_bounds_reached_state_not_a_new_source_or_reset", "supplied_attachment_changes_degrees_without_changing_state", "own_law_attachment_work_and_actual_pre_input_form_work", "all_four_inputs_share_one_actual_pre_input_state_within_each_law", "retained_weighted_means_and_whole_future_joined_identity", "unavailable_is_not_failed_recovery_or_an_obstruction", "no_trajectory_event_occurrence_finite_response_or_physical_identity_claim", ) def _assess_constitutive_handoff( *, deformation, form_error_bound, phase_error_bound ) -> _ConstitutiveHandoff: """Rebuild fixed own-law acquisition, uninterrupted dwell and contact. All raw scalars are admitted before source or interval construction. Negative/nonfinite/Boolean inputs reject. Valid coefficients outside the proved family [0,1], absent capture, insufficient recovery and nonpositive identity margins yield explicit unavailability rather than a reset. """ recovery = _assess_constitutive_recovery( deformation=deformation, form_error_bound=form_error_bound, phase_error_bound=phase_error_bound, ) source, handoff = recovery.source, recovery.recovery_certified eps, u = _ENDPOINT_RADIUS, source.phase_hessian_upper_bound contact_work = Q(0), 4 * (1 + u) * eps**2 joined_excess = 10 * (1 + u) * eps**2 mean = -4 * eps / 58, 4 * eps / 58 branches = [] for name, a, b in ( ("neither", Q(0), Q(0)), ("donor", _AMPLITUDE, Q(0)), ("receiver", Q(0), _AMPLITUDE), ("both", _AMPLITUDE, _AMPLITUDE), ): nominal_work, work_error = Q(3, 2) * (a**2 + b**2), 6 * (a + b) * eps work = nominal_work - work_error, nominal_work + work_error norm = 6 * eps**2 + 2 * (a + b) * eps + a**2 + b**2 - (a + b) ** 2 / 27 excess = joined_excess + work[1] radius_margin, storage_margin = _RADIUS**2 - norm, _JOINED_BARRIER - excess branches.append( _ConstitutiveHandoffBranch( name=name, donor_amplitude=a, receiver_amplitude=b, input_work_bounds=work, relative_norm_squared_upper_bound=norm, excess_storage_upper_bound=excess, radius_margin=radius_margin, storage_margin=storage_margin, form_mean_bounds=tuple(value + 3 * (a + b) / 58 for value in mean), phase_mean_bounds=mean, identity_certified=handoff and radius_margin > 0 and storage_margin > 0, ) ) unresolved = list(recovery.unresolved_conditions) if not all(branch.identity_certified for branch in branches): unresolved.append("joined_four_branch_identity_not_certified") return _ConstitutiveHandoff( source=source, deformation=recovery.deformation, form_error_bound=recovery.form_error_bound, phase_error_bound=recovery.phase_error_bound, transformed_stiffness_lower_bound=recovery.transformed_stiffness_lower_bound, transformed_stiffness_upper_bound=recovery.transformed_stiffness_upper_bound, lyapunov_position_lower_coefficient=recovery.lyapunov_position_lower_coefficient, lyapunov_position_upper_coefficient=recovery.lyapunov_position_upper_coefficient, lyapunov_initial_upper_bound=recovery.lyapunov_initial_upper_bound, lyapunov_decay_rate=recovery.lyapunov_decay_rate, decay_exponent=recovery.decay_exponent, exact_decay_upper_bound=recovery.exact_decay_upper_bound, returned_lyapunov_upper_bound=recovery.returned_lyapunov_upper_bound, endpoint_form_norm_squared_upper_bound=recovery.endpoint_form_norm_squared_upper_bound, endpoint_phase_norm_squared_upper_bound=recovery.endpoint_phase_norm_squared_upper_bound, endpoint_form_margin=recovery.endpoint_form_margin, endpoint_phase_margin=recovery.endpoint_phase_margin, source_certified=recovery.source_certified, handoff_certified=handoff, attachment_work_bounds=contact_work, joined_excess_storage_upper_bound=joined_excess, joined_form_mean_bounds=mean, joined_phase_mean_bounds=mean, branches=tuple(branches), status="certified_constitutive_handoff" if not unresolved else "unavailable", unresolved_conditions=tuple(unresolved), )