"""Conditional quantitative forgetting of organized-source child asymmetry. The shared complete source law and its retained acute energy domain imply a common quadratic decay bound even while the sine secant stiffness changes. This reader evaluates that inequality from primitive state, not a response, and bounds the instantaneous error of discarding the hidden coordinates. """ 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 from ._organized_source_capture import ( _derive_organized_source_capture_barrier, _organized_source_offset_edge_angles, _OrganizedSourceCaptureBarrier, ) from ._organized_source_child_orbit import ( _encode_organized_source_child_orbit, _observe_organized_source_child_orbit, _OrganizedSourceChildOrbitObservation, ) from ._repeated_organized_composition import _vector from ._sine_lyapunov import ( _sine_common_quadratic_coefficients, _sine_common_quadratic_initial_upper, ) from .reversible_eigenmode_reference import _MAX_RATIONAL_EXPONENT, _negative_exp_bounds _ENERGY_CEILING = Q(1, 100) _COSINE_LOWER = Q(1, 2) _HIDDEN_GAP_LOWER = Q(2) @dataclass(frozen=True) class _OrganizedSourceChildRelaxationBound: """Primitive evidence and an optional conditional squared-norm allowance. Initial metric bounds and exponential endpoints remain exact rational pairs, preserving nonzero quantities below the interval grid. Initial derivative intervals come from both complete fine rows at the supplied state. The decayed fields are absent when geometric or work admission fails. A certified allowance is not an evaluated hidden trajectory. Projected defects compare the full law projected at its current state with the same law at that state's symmetric projection. They do not compare two separately evolved solutions. The Coherence field bounds the difference of the target resultant arguments; multiplying by an independently admitted phase coefficient gives its increment defect. """ form: tuple[Q, ...] phase_offsets: tuple[Q, ...] capacities: tuple[Q, ...] elapsed_time: Q orbit: _OrganizedSourceChildOrbitObservation barrier: _OrganizedSourceCaptureBarrier edge_angle_bounds: tuple[I, ...] excess_bounds: I energy_ceiling: Q geometry_certified: bool in_acute_cell: bool below_energy_ceiling: bool boundary_ceiling_margin: Q collar_angle_upper: Q collar_margin: Q carrier_cosine_lower_bound: Q gamma_bounds: I cosine_lower_bound: Q hidden_gap_lower_bound: Q paired_capacity_lower: Q paired_capacity_upper: Q capacity_upper: Q initial_hidden_norm_squared: Q initial_weighted_square: Q initial_weighted_cross: Q initial_metric_bounds: tuple[Q, Q] | None initial_metric_upper: Q | None initial_metric_derivative_bounds: I initial_euclidean_squared_derivative_bounds: I metric_lower: Q | None metric_upper: Q | None decay_rate_lower: Q | None exponent: Q | None domain_certified: bool exponential_work_admitted: bool certified: bool decay_bounds: tuple[Q, Q] | None metric_upper_bound: Q | None hidden_norm_squared_upper_bound: Q | None projected_form_defect_upper_bound: Q | None projected_phase_defect_upper_bound: Q | None coherence_argument_defect_upper_bound: Q | None unavailable_reasons: tuple[str, ...] scope: tuple[str, ...] = ( "all_primitive_state_and_elapsed_time_admitted_before_geometry", "same_complete_quarter_rate_reciprocal_law_with_Gamma_absent", "positive_held_capacities_equal_on_the_two_exchanged_children", "raw_carrier_offset_cell_and_energy_excess_below_one_hundredth", "common_quadratic_metric_does_not_freeze_the_time_varying_secant_stiffness", "exact_rational_source_scaling_and_shared_negative_exponential_bounds", "initial_derivatives_retain_both_complete_fine_rows", "instantaneous_projected_law_defect_not_separately_evolved_core_error", "coherence_argument_defect_uses_the_conditional_resultant_floor_four", "a_separately_admitted_marked_word_keeps_hidden_state_and_paired_capacity", "no_live_word_admission_context_authentication_or_occurrence_selector", "no_trajectory_finite_time_symmetry_acquisition_or_guard_time_certificate", ) def _bound_organized_source_child_relaxation( *, form, phase_offsets, capacities, elapsed_time ): """Bound hidden relaxation on the admitted all-future acute sublevel. With V the fixed paired capacity, H=L_C9+2I and H/2<=K(t)<=H, W=a^T V^-1 a+b^T V^-1 b+2*gamma*a^T V^-1 b satisfies W'<=-r*W, r=nu_min*gamma^2/[4*(1+gamma)]. No derivative of K is required. The low-energy edge collar proves these stiffness bounds, and the shared capture barrier supplies their uninterrupted retention. A marked ideal word may be covered only with its separate admission, unchanged a,b,V and retained domain. The supplied elapsed time then counts continuous structural time; no event is executed by this reader. """ values = _vector(form, "form", 45) offsets = _vector(phase_offsets, "phase_offsets", 45) mobilities = _vector(capacities, "capacities", 45) duration = _exact(elapsed_time, "elapsed_time") if duration < 0: raise ValueError("elapsed_time must be nonnegative") state = _encode_organized_source_child_orbit( form=values, phase_offsets=offsets, capacities=mobilities ) orbit = _observe_organized_source_child_orbit( form_coordinates=state.form_coordinates, phase_offset_coordinates=state.phase_offset_coordinates, capacity_coordinates=state.capacity_coordinates, hidden_gram=state.hidden_gram, ) barrier = _derive_organized_source_capture_barrier() geometry = state.geometry.fine_geometry geometry_ok = ( geometry == orbit.state.geometry.fine_geometry and geometry == orbit.fine.unit_capacity_reference.geometry and geometry == barrier.geometry ) angles = _organized_source_offset_edge_angles(geometry, offsets) acute = all(angle.abs_max < barrier.cell_edge_gap_bounds.lo for angle in angles) excess = orbit.joint_storage_bounds - barrier.target_storage_bounds below = excess.hi < _ENERGY_CEILING boundary_margin = barrier.boundary_energy_lower_bound - _ENERGY_CEILING carrier_cosine = 1 - barrier.cycle_storage_minimum_bounds.hi / 9 # The existing cycle Taylor bound gives sum_e u_e^2 <= 4E < 1/25. # The entire child-exchange chord therefore lies below this same collar. collar = geometry.alpha_bounds.hi + Q(1, 5) collar_margin = 2 * barrier.cell_edge_gap_bounds.lo / 3 - collar gamma = geometry.gamma_bounds gamma_ok = 0 < gamma.lo <= gamma.hi <= Q(1, 2) paired = tuple( state.capacities[block[0]] for block in state.geometry.blocks if len(block) == 2 ) capacity_lower, capacity_upper = min(paired), max(paired) maximum_capacity = max(mobilities) a, b = state.hidden_coordinates[:9], state.hidden_coordinates[9:] da, db = orbit.hidden_tau_rate_bounds[:9], orbit.hidden_tau_rate_bounds[9:] squared = sum((x * x + y * y for x, y in zip(a, b)), Q(0)) weighted_square = sum( ((x * x + y * y) / nu for x, y, nu in zip(a, b, paired)), Q(0) ) weighted_cross = sum((x * y / nu for x, y, nu in zip(a, b, paired)), Q(0)) euclidean_derivative = 2 * sum( (x * dx + y * dy for x, y, dx, dy in zip(a, b, da, db)), I(0) ) metric_derivative = 2 * sum( ( (x / nu + gamma * (y / nu)) * dx + (y / nu + gamma * (x / nu)) * dy for x, y, dx, dy, nu in zip(a, b, da, db, paired) ), I(0), ) metric_lower = metric_upper = rate = initial_upper = initial_bounds = None if gamma_ok: metric_lower, metric_upper, rate = _sine_common_quadratic_coefficients( gamma_lower=gamma.lo, gamma_upper=gamma.hi, cosine_lower=_COSINE_LOWER, gap_lower=_HIDDEN_GAP_LOWER, capacity_lower=capacity_lower, capacity_upper=capacity_upper, ) initial_upper = _sine_common_quadratic_initial_upper( gamma_lower=gamma.lo, gamma_upper=gamma.hi, weighted_square=weighted_square, weighted_cross=weighted_cross, ) opposite_upper = _sine_common_quadratic_initial_upper( gamma_lower=gamma.lo, gamma_upper=gamma.hi, weighted_square=weighted_square, weighted_cross=-weighted_cross, ) initial_bounds = (2 * weighted_square - opposite_upper, initial_upper) conditions = ( (geometry_ok, "shared_geometry_unavailable"), (barrier.barrier_certified, "acute_boundary_barrier_unavailable"), (acute, "state_not_certified_in_fixed_branch_acute_cell"), (below, "state_excess_not_strictly_below_fixed_ceiling"), (boundary_margin > 0, "fixed_ceiling_not_below_acute_boundary"), (carrier_cosine > Q(3, 4), "carrier_cosine_taylor_bound_unavailable"), (collar_margin > 0, "half_stiffness_edge_collar_unavailable"), (gamma_ok, "positive_gamma_at_most_one_half_unavailable"), ) reasons = [reason for passed, reason in conditions if not passed] domain = not reasons exponent = rate * duration if rate is not None else None work_ok = exponent is not None and exponent <= _MAX_RATIONAL_EXPONENT if not work_ok: reasons.append("negative_exponential_work_limit_unavailable") certified = domain and work_ok decay = returned_metric = returned_squared = form_defect = None phase_defect = argument_defect = None if certified: decay = _negative_exp_bounds(exponent) # Keep source scaling outside dyadic interval arithmetic: exact # symmetry remains zero and arbitrarily small asymmetry stays small. returned_metric = initial_upper * decay[1] returned_squared = returned_metric / metric_lower form_defect = 5 * gamma.hi * maximum_capacity * returned_squared / 4 phase_defect = Q(0) argument_defect = returned_squared / 4 return _OrganizedSourceChildRelaxationBound( form=values, phase_offsets=offsets, capacities=mobilities, elapsed_time=duration, orbit=orbit, barrier=barrier, edge_angle_bounds=angles, excess_bounds=excess, energy_ceiling=_ENERGY_CEILING, geometry_certified=geometry_ok, in_acute_cell=acute, below_energy_ceiling=below, boundary_ceiling_margin=boundary_margin, collar_angle_upper=collar, collar_margin=collar_margin, carrier_cosine_lower_bound=carrier_cosine, gamma_bounds=gamma, cosine_lower_bound=_COSINE_LOWER, hidden_gap_lower_bound=_HIDDEN_GAP_LOWER, paired_capacity_lower=capacity_lower, paired_capacity_upper=capacity_upper, capacity_upper=maximum_capacity, initial_hidden_norm_squared=squared, initial_weighted_square=weighted_square, initial_weighted_cross=weighted_cross, initial_metric_bounds=initial_bounds, initial_metric_upper=initial_upper, initial_metric_derivative_bounds=metric_derivative, initial_euclidean_squared_derivative_bounds=euclidean_derivative, metric_lower=metric_lower, metric_upper=metric_upper, decay_rate_lower=rate, exponent=exponent, domain_certified=domain, exponential_work_admitted=work_ok, certified=certified, decay_bounds=decay, metric_upper_bound=returned_metric, hidden_norm_squared_upper_bound=returned_squared, projected_form_defect_upper_bound=form_defect, projected_phase_defect_upper_bound=phase_defect, coherence_argument_defect_upper_bound=argument_defect, unavailable_reasons=tuple(reasons), )