"""One autonomous finite-storage extension of the acquired-parent model. ORGANIZED_PARENT_RESERVOIR_EXCHANGE.md owns the fixed joint law, preparation and finite response criterion. The auxiliary signed reservoir is supplied constitutive state, not an identified physical bath or an acquired NFR mode. """ 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_parent_acquisition import ( _assess_organized_parent_acquisition, _OrganizedParentAcquisition, ) from ._repeated_organized_composition import ( _observe_repeated_composition, _RepeatedCompositionObservation, _vector, ) from .reversible_eigenmode_reference import _negative_exp_bounds _CLOCK_FACTOR = Q(1023, 1024) _RESERVOIR_CENTER = Q(12, 5) _STORAGE_BUDGET = Q(3) def _port(value): if type(value) is not str or value not in ("connected", "disconnected"): raise ValueError("port must be 'connected' or 'disconnected'") return value @dataclass(frozen=True) class _ParentReservoirObservation: """Complete joint rows, signed exchange and storage in all three clocks.""" network: _RepeatedCompositionObservation reservoir_state: Q port: str coupling_bounds: tuple[I, ...] reservoir_decay_bounds: I port_output_tau_bounds: I network_input_tau_bounds: tuple[I, ...] network_input_slow_bounds: tuple[I, ...] network_input_original_bounds: tuple[I, ...] form_tau_rate_bounds: tuple[I, ...] form_slow_rate_bounds: tuple[I, ...] form_original_rate_bounds: tuple[I, ...] phase_tau_rate_bounds: tuple[I, ...] phase_slow_rate_bounds: tuple[I, ...] phase_original_rate_bounds: tuple[I, ...] reservoir_tau_rate_bounds: I reservoir_slow_rate_bounds: I reservoir_original_rate_bounds: I reservoir_pressure_tau_bounds: I reservoir_storage: Q joint_storage_bounds: I network_input_power_tau_bounds: I network_input_power_slow_bounds: I network_input_power_original_bounds: I network_storage_tau_rate_bounds: I reservoir_storage_tau_rate_bounds: I joint_storage_tau_rate_bounds: I joint_storage_slow_rate_bounds: I joint_storage_original_rate_bounds: I network_dissipation_tau: Q reservoir_dissipation_tau_bounds: I joint_dissipation_tau_bounds: I joint_storage_rate_from_rows_bounds: I balance_residual_bounds: I reservoir_capacity: Q = Q(1) clock: str = "tau=(1023/1024)*t; s=gamma^2*tau/2" pressure_law: str = "p_r_tau=-b^T*L*x-lambda*r; unit capacity in tau" scope: tuple[str, ...] = ( "signed_reservoir_and_all_network_primitives_admitted_before_observation", "fixed_matching_network_with_an_added_constitutive_exchange_channel", "reservoir_pressure_supplied_from_joint_state_not_reconstructed_from_response", "all_three_rows_inputs_and_power_retain_their_clock_transformations", "signed_network_work_is_paid_by_reservoir_storage_change_and_reservoir_loss", "zero_initial_reservoir_does_not_disconnect_the_coupled_dynamics", "joint_balance_does_not_certify_registration_response_or_source_history", "no_phase_coordinate_for_auxiliary_state_no_graph_mutation_or_trajectory", ) def _observe_parent_reservoir_exchange( *, form, phase_offsets, reservoir_state, port ) -> _ParentReservoirObservation: """Observe the fixed autonomous joint law or its disconnected control.""" selected = _port(port) values = _vector(form, "form", 36) offsets = _vector(phase_offsets, "phase_offsets", 36) reservoir = _exact(reservoir_state, "reservoir_state") return _observe_admitted_parent_reservoir_exchange( form=values, phase_offsets=offsets, reservoir_state=reservoir, port=selected, leakage="original", ) def _observe_admitted_parent_reservoir_exchange( *, form, phase_offsets, reservoir_state, port, leakage ): """Joint algebra for caller-admitted primitives and one declared leakage. The public-to-this-module adapters own scalar, vector and law admission. This shared kernel installs no law and certifies no trapping or source. """ values, offsets, reservoir, selected = form, phase_offsets, reservoir_state, port network = _observe_repeated_composition( interface="matching", form=values, phase_offsets=offsets ) gamma = network.geometry.gamma_bounds decay = gamma**2 / 2 if leakage == "original" else I(0) coupling = tuple( gamma * Q(2 * (node // 9 % 2) - 1, 12) if selected == "connected" else I(0) for node in range(36) ) output = sum((b * q for b, q in zip(coupling, network.form_gradient)), I(0)) forcing = tuple(b * reservoir for b in coupling) form_rate = tuple( rate + added for rate, added in zip(network.form_rate_bounds, forcing) ) phase_rate = network.phase_rate_bounds reservoir_rate = -output - decay * reservoir power = output * reservoir reservoir_storage = reservoir**2 / 2 network_loss = network.dissipation reservoir_loss = decay * reservoir**2 joint_loss = network_loss + reservoir_loss joint_rate = -joint_loss # Independent contraction of the complete rows retains both exchange signs. direct_rate = ( sum( ( q * dx - current * dt for q, current, dx, dt in zip( network.form_gradient, network.phase_current_bounds, form_rate, phase_rate, ) ), I(0), ) + reservoir * reservoir_rate ) slow_factor = 2 / gamma**2 return _ParentReservoirObservation( network=network, reservoir_state=reservoir, port=selected, coupling_bounds=coupling, reservoir_decay_bounds=decay, port_output_tau_bounds=output, network_input_tau_bounds=forcing, network_input_slow_bounds=tuple(slow_factor * value for value in forcing), network_input_original_bounds=tuple(_CLOCK_FACTOR * value for value in forcing), form_tau_rate_bounds=form_rate, form_slow_rate_bounds=tuple(slow_factor * value for value in form_rate), form_original_rate_bounds=tuple(_CLOCK_FACTOR * value for value in form_rate), phase_tau_rate_bounds=phase_rate, phase_slow_rate_bounds=tuple(slow_factor * value for value in phase_rate), phase_original_rate_bounds=tuple(_CLOCK_FACTOR * value for value in phase_rate), reservoir_tau_rate_bounds=reservoir_rate, reservoir_slow_rate_bounds=slow_factor * reservoir_rate, reservoir_original_rate_bounds=_CLOCK_FACTOR * reservoir_rate, reservoir_pressure_tau_bounds=reservoir_rate, reservoir_storage=reservoir_storage, joint_storage_bounds=network.storage_bounds + reservoir_storage, network_input_power_tau_bounds=power, network_input_power_slow_bounds=slow_factor * power, network_input_power_original_bounds=_CLOCK_FACTOR * power, network_storage_tau_rate_bounds=-network_loss + power, reservoir_storage_tau_rate_bounds=-power - reservoir_loss, joint_storage_tau_rate_bounds=joint_rate, joint_storage_slow_rate_bounds=slow_factor * joint_rate, joint_storage_original_rate_bounds=_CLOCK_FACTOR * joint_rate, network_dissipation_tau=network_loss, reservoir_dissipation_tau_bounds=reservoir_loss, joint_dissipation_tau_bounds=joint_loss, joint_storage_rate_from_rows_bounds=direct_rate, balance_residual_bounds=direct_rate - joint_rate, ) @dataclass(frozen=True) class _OrganizedParentReservoirExchange: """Finite response bounds and a separately admitted fixed-criterion result. Parent gap bounds are absolute lifted same-slot gaps. The nominal envelope fields enclose analytic supersolutions, not a sampled nominal trajectory. Registration at the deadline does not assert earlier loss or restoration. """ form_error_bounds: tuple[Q, ...] phase_error_bounds: tuple[Q, ...] reservoir_error_bound: Q acquisition: _OrganizedParentAcquisition reservoir_initial_bounds: I reservoir_initial_storage_upper_bound: Q network_input_work_upper_bound: Q initial_joint_error_energy_upper_bound: Q readout_joint_form_error_upper_bound: Q readout_joint_phase_error_upper_bound: Q readout_joint_reservoir_error_upper_bound: Q whole_joint_form_error_upper_bound: Q whole_joint_phase_error_upper_bound: Q whole_joint_reservoir_error_upper_bound: Q nominal_readout_envelope_bounds: I nominal_deadline_envelope_bounds: I connected_parent_gap_at_readout_upper_bound: Q connected_parent_gap_at_deadline_upper_bound: Q disconnected_parent_gap_upper_bound: Q child_positive_gap_margin: Q child_acute_gap_margin: Q registration_retention_margin: Q deadline_registration_margin: Q disconnected_registration_margin: Q storage_budget_margin: Q elapsed_scaled_readout_time_bounds: I elapsed_scaled_deadline_time_bounds: I elapsed_original_readout_time_bounds: I elapsed_original_deadline_time_bounds: I sufficient_margins: tuple[tuple[str, Q], ...] network_source_certified: bool reservoir_preparation_certified: bool source_certified: bool response_domain_certified: bool finite_work_certified: bool child_identities_retained: bool disconnected_registration_retained: bool registered_at_deadline: bool disruption_ruled_out: bool conditional_obstruction_certified: bool obstruction_certified: bool status: str unresolved_conditions: tuple[str, ...] disruption_certified: bool = False protocol_satisfied: bool = False source_slow_time: Q = Q(4) readout_elapsed_slow_time: Q = Q(1, 2) deadline_elapsed_slow_time: Q = Q(8) readout_slow_time: Q = Q(9, 2) deadline_slow_time: Q = Q(12) reservoir_initial_center: Q = _RESERVOIR_CENTER reservoir_storage_budget: Q = _STORAGE_BUDGET reservoir_capacity: Q = Q(1) parent_identity_gap: Q = Q(1, 4) protocol_revision: str = "9a0071de" clock: str = "tau=(1023/1024)*t; s=gamma^2*tau/2; h=s-4" scope: tuple[str, ...] = ( "all_nine_primitive_allowances_admitted_before_fresh_original_acquisition", "auxiliary_signed_form_pressure_storage_and_coupling_are_supplied_premises", "each_actual_reservoir_initial_value_indexes_its_own_nominal_reference", "reservoir_uncertainty_retained_in_the_entire_response_domain", "joint_error_energy_includes_reservoir_feedback_not_an_identical_input_assumption", "mean_zero_form_error_and_joint_storage_exchange_cancellation_are_required", "complete_joint_loss_pays_network_net_work_from_finite_initial_reservoir_storage", "network_work_upper_bound_is_not_positive_only_supply_or_actuator_bandwidth", "disconnected_control_changes_b_to_zero_not_initial_reservoir_to_zero", "child_winding_retained_in_both_branches_through_the_fixed_deadline", "certified_negative_result_concerns_only_the_fixed_half_unit_disruption_criterion", "registration_at_deadline_does_not_establish_a_preceding_disruption_or_restoration", "intermediate_parent_registration_and_other_reservoir_laws_are_unclassified", "no_trajectory_source_refinement_coefficient_scan_or_physical_reservoir_identification", ) def _assess_organized_parent_reservoir_exchange( *, form_error_bounds, phase_error_bounds, reservoir_error_bound ) -> _OrganizedParentReservoirExchange: """Assess the frozen reservoir mechanism without moving its response gate. Network acquisition is rebuilt from primitive allowances. The independent reservoir interval remains a parameter of the nominal proof, while the full network/reservoir separation uses a new joint-energy inequality. No preceding actuation or restoring-response verdict is consumed. """ rx = _vector(form_error_bounds, "form_error_bounds", 4) rt = _vector(phase_error_bounds, "phase_error_bounds", 4) radius = _exact(reservoir_error_bound, "reservoir_error_bound") if min(*rx, *rt, radius) < 0: raise ValueError("all preparation error allowances must be nonnegative") acquisition = _assess_organized_parent_acquisition( form_error_bounds=rx, phase_error_bounds=rt ) geometry = acquisition.geometry gamma, eta_upper = geometry.gamma_bounds, geometry.gamma_bounds.hi**2 initial_form = acquisition.full_form_error_upper_bound initial_phase = acquisition.full_phase_error_upper_bound # W=xi.L.xi/2+rho^2/2+4||zeta||^2; W_h<=8W. Reservoir differences # start at zero for each actual r0, but subsequent feedback is retained. initial_energy = 4 * (initial_form**2 + initial_phase**2) readout_phase = (initial_form + initial_phase) * 3**2 whole_phase = (initial_form + initial_phase) * 3**32 reservoir_lower = _RESERVOIR_CENTER - radius reservoir_upper = _RESERVOIR_CENTER + radius storage = reservoir_upper**2 / 2 storage_margin = _STORAGE_BUDGET - storage initial_cap, sector_cap, restoring_slope = Q(1, 64), Q(17, 64), Q(9, 10) readout_envelope = initial_cap + (1 - I(*_negative_exp_bounds(Q(2)))) / 4 deadline_envelope = I(*_negative_exp_bounds(Q(8, 5))) / 3 readout_gap = readout_envelope.hi + 2 * readout_phase deadline_gap = deadline_envelope.hi + 2 * whole_phase control_gap = initial_cap + 2 * whole_phase child_positive = geometry.alpha_bounds.lo - 2 * whole_phase child_acute = pi_interval().lo / 2 - geometry.alpha_bounds.hi - 2 * whole_phase registration_margin = acquisition.parent_identity_gap - readout_gap deadline_margin = acquisition.parent_identity_gap - deadline_gap control_margin = acquisition.parent_identity_gap - control_gap response_margins = ( ( "acquired_nominal_inner_positive", acquisition.nominal_inner_gap_at_entry_bounds.lo, ), ( "acquired_nominal_inner_gap", initial_cap - acquisition.nominal_inner_gap_at_entry_bounds.hi, ), ("cooperative_joint_rows", 1 - 16 * eta_upper), ("retained_initial_velocity_cone", 3 - 2 * eta_upper), ("restoring_sine_sector", 1 - sector_cap**2 / 6 - restoring_slope), ( "bounded_supersolution_curvature", Q(1, 3) - restoring_slope / 4 - 4 * eta_upper, ), ( "bounded_supersolution_initial_reservoir", restoring_slope * initial_cap + restoring_slope / 4 - (reservoir_upper - 2) / 3, ), ("decaying_supersolution_initial_phase", Q(1, 3) - initial_cap), ( "decaying_supersolution_initial_reservoir", Q(5, 2) - reservoir_upper - 6 * initial_cap, ), ("decaying_supersolution_residual", Q(1, 5)), ) network_conditions = ( ("original_children_not_certified", acquisition.sources_certified), ("original_parent_entry_not_certified", acquisition.entry_certified), ( "original_child_identities_not_certified", acquisition.child_identities_retained, ), ) network_ok = all(passed for _, passed in network_conditions) reservoir_ok = reservoir_lower >= 0 and storage_margin >= 0 source_ok = network_ok and reservoir_ok response_ok = all(value > 0 for _, value in response_margins) children_ok = min(child_positive, child_acute) > 0 non_disruption = response_ok and registration_margin > 0 control_ok = control_margin > 0 conditional = reservoir_ok and non_disruption and children_ok and control_ok obstruction = network_ok and conditional margins = response_margins + ( ("reservoir_nonnegative_preparation", reservoir_lower), ("finite_reservoir_storage_budget", storage_margin), ("retained_child_positive_gap", child_positive), ("retained_child_acute_gap", child_acute), ("connected_registration_retained_at_readout", registration_margin), ("connected_registration_at_deadline", deadline_margin), ("disconnected_registration_retained", control_margin), ) decisions = network_conditions + ( ("reservoir_preparation_not_certified", reservoir_ok), ("connected_response_domain_not_certified", response_ok), ("child_identities_not_certified", children_ok), ("connected_non_disruption_not_certified", non_disruption), ( "connected_deadline_registration_not_certified", response_ok and deadline_margin > 0, ), ("disconnected_registration_not_certified", control_ok), ) tau_readout, tau_deadline = 1 / gamma**2, 16 / gamma**2 return _OrganizedParentReservoirExchange( form_error_bounds=rx, phase_error_bounds=rt, reservoir_error_bound=radius, acquisition=acquisition, reservoir_initial_bounds=I(reservoir_lower, reservoir_upper), reservoir_initial_storage_upper_bound=storage, network_input_work_upper_bound=storage, initial_joint_error_energy_upper_bound=initial_energy, readout_joint_form_error_upper_bound=6 * readout_phase, readout_joint_phase_error_upper_bound=readout_phase, readout_joint_reservoir_error_upper_bound=4 * readout_phase, whole_joint_form_error_upper_bound=6 * whole_phase, whole_joint_phase_error_upper_bound=whole_phase, whole_joint_reservoir_error_upper_bound=4 * whole_phase, nominal_readout_envelope_bounds=readout_envelope, nominal_deadline_envelope_bounds=deadline_envelope, connected_parent_gap_at_readout_upper_bound=readout_gap, connected_parent_gap_at_deadline_upper_bound=deadline_gap, disconnected_parent_gap_upper_bound=control_gap, child_positive_gap_margin=child_positive, child_acute_gap_margin=child_acute, registration_retention_margin=registration_margin, deadline_registration_margin=deadline_margin, disconnected_registration_margin=control_margin, storage_budget_margin=storage_margin, elapsed_scaled_readout_time_bounds=tau_readout, elapsed_scaled_deadline_time_bounds=tau_deadline, elapsed_original_readout_time_bounds=tau_readout / _CLOCK_FACTOR, elapsed_original_deadline_time_bounds=tau_deadline / _CLOCK_FACTOR, sufficient_margins=margins, network_source_certified=network_ok, reservoir_preparation_certified=reservoir_ok, source_certified=source_ok, response_domain_certified=response_ok, finite_work_certified=source_ok, child_identities_retained=source_ok and children_ok, disconnected_registration_retained=source_ok and control_ok, registered_at_deadline=source_ok and response_ok and children_ok and deadline_margin > 0, disruption_ruled_out=source_ok and non_disruption, conditional_obstruction_certified=conditional, obstruction_certified=obstruction, status=( "certified_reservoir_disruption_obstruction" if obstruction else "unavailable" ), unresolved_conditions=tuple(name for name, passed in decisions if not passed), )