"""Prospective endpoint information budgets for a small phase preparation. Proof: ORGANIZED_SMALL_RESOURCE_INFORMATION.md#organized-small-resource-information. The fixed two-C9 complete law and nominal preparation are supplied. This instrument evaluates neither candidate response nor an observed reading. """ 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 INTERVAL_METHOD, I from ._organized_free_phase_probe import ( _CHILD_SIZE, _CONTACT_DENOMINATOR, _FINE_DECAY_DENOMINATOR, _FINE_ENERGY_LIMIT, _fine_energy_upper_bound, _free_probe_current_bounds, ) from .relational_sine_port_composition import _parameters @dataclass(frozen=True) class _OrganizedSmallResourceInformationBound: """Conditional information limits for one raw relative mean-form reading. Preparation bounds apply separately to each candidate law: they need not describe common nuisance values. Fine form/phase bounds are Euclidean norms of the eighteen separately child-centered residuals. The initial mean contrast has magnitude at most its error bound; relative phase differs from ``phase_offset`` by at most the registration error. The observation is Y=(1+g)*r(1+e_s)+e_read, with each signed nuisance bounded by its supplied magnitude. Timing uses the independently declared clock s=a*tau/2, not an unknown clock rate. A guaranteed separation is prospective; it identifies neither an observed law nor a physical sensor. ``current_coefficients`` records the lambda=1 endpoint used for the uniform current majorants; both endpoint laws remain candidates. Nonidentifiability uses a common nominal reading witness from reading noise alone, not overlap of conservative response enclosures. """ phase_offset: Q form_error_bound: Q phase_error_bound: Q initial_form_contrast_error_bound: Q phase_registration_error_bound: Q endpoint_reading_error_bound: Q exposure_time_error_bound: Q relative_gain_error_bound: Q current_coefficients: tuple[tuple[int, Q], ...] current_derivative_bounds: tuple[Q, Q, Q] gamma_bounds: I contact_conductance_bounds: I nominal_horizon_bounds: I exposure_window: tuple[Q, Q] fine_decay_rate_in_scaled_clock: Q fine_energy_upper_bound: Q fine_energy_margin: Q fine_current_defect_upper_bound: Q nominal_gap_lower_bound: Q nominal_gap_upper_bound: Q phase_comparison_seed_upper_bound: Q endpoint_phase_error_upper_bound: Q window_phase_error_upper_bound: Q endpoint_preparation_error_upper_bound: Q window_form_upper_bound: Q window_form_rate_upper_bound: Q exposure_error_upper_bound: Q gain_error_upper_bound: Q observation_error_upper_bound: Q separation_margin: Q nominal_reading_overlap_margin: Q nominal_attachment_work_lower_bound: Q nominal_attachment_work_upper_bound: Q attachment_work_upper_bound: Q status: str nominal_gap_orientation: str = "sine_endpoint_minus_alternative_endpoint_positive" interval_method: str = INTERVAL_METHOD conditional_on_preparation_and_observation_bounds: bool = True scope: tuple[str, ...] = ( "two_supplied_marked_winding_one_C9_children_with_nine_matching_contacts", "fixed_gamma_matching_weight_and_both_uniform_quarter_rows", "held_unit_capacities_no_input_jumps_or_later_support_changes", "nominal_child_mean_forms_zero_and_relative_phase_offset_positive", "fine_norm_bounds_retain_all_child_centered_form_and_phase_residuals", "each_candidate_has_its_own_allowed_preparation_and_observation_nuisances", "clock_is_s_equals_a_tau_over_two_without_unknown_rate_calibration", "one_raw_relative_mean_form_reading_at_nominal_s_equals_one", "multiplicative_gain_uncertainty_changes_readout_not_the_evolution_law", "supplied_bounds_do_not_authenticate_source_identity_or_sensor_capability", "guaranteed_separation_is_prospective_not_a_selected_observed_law", "nonidentifiability_uses_a_nominal_midpoint_reading_noise_witness", "not_certified_is_neither_separation_nor_a_proved_ambiguity_regime", "attachment_work_is_separate_from_source_formation_and_physical_cost", "no_trajectory_source_replay_response_evaluation_or_physical_admission", ) def _bound_organized_small_resource_information( *, phase_offset, form_error_bound, phase_error_bound, initial_form_contrast_error_bound, phase_registration_error_bound, endpoint_reading_error_bound, exposure_time_error_bound, relative_gain_error_bound, ) -> _OrganizedSmallResourceInformationBound: """Bound distinguishability without calculating either endpoint response. Every input is a required finite exact or represented real. The nominal phase lies in (0,1/100], all error bounds are nonnegative, and exposure jitter is at most 1/2 in s units. Gain uncertainty may be arbitrarily large; it can simply make separation uncertifiable. The shared sufficient fine energy must be strictly below 1/40000. Rejection at that boundary means this theorem is unavailable, not that the child identities are lost. Both nominal candidate endpoints are negative, with sine minus alternative bounded between gamma*d**3/20 and gamma*d**3/6. Preparation error is bounded for each law separately. A strict positive gap after both observation allowances guarantees nonoverlap. Reading noise of at least half the nominal gap upper bound admits their actual midpoint under both laws. No report, cached verdict or observed response replaces these primitives. """ names_and_values = ( ("phase_offset", phase_offset), ("form_error_bound", form_error_bound), ("phase_error_bound", phase_error_bound), ("initial_form_contrast_error_bound", initial_form_contrast_error_bound), ("phase_registration_error_bound", phase_registration_error_bound), ("endpoint_reading_error_bound", endpoint_reading_error_bound), ("exposure_time_error_bound", exposure_time_error_bound), ("relative_gain_error_bound", relative_gain_error_bound), ) d, rho_x, rho_theta, eps_r, eps_delta, eps_read, eta, gain = ( _exact(value, name) for name, value in names_and_values ) if not 0 < d <= Q(1, 100): raise ValueError("phase_offset requires the proved interval (0,1/100]") if min(rho_x, rho_theta, eps_r, eps_delta, eps_read, eta, gain) < 0: raise ValueError("preparation and observation error bounds must be nonnegative") if eta > Q(1, 2): raise ValueError("exposure_time_error_bound must be at most 1/2 in s units") gamma, _ = _parameters(()) gu, g_squared = gamma.hi, gamma.hi**2 coefficients, derivative_bounds = _free_probe_current_bounds(Q(1)) _, j1, j2 = derivative_bounds contact = gamma**2 / _CONTACT_DENOMINATOR decay = 2 * _CONTACT_DENOMINATOR / _FINE_DECAY_DENOMINATOR fine = _fine_energy_upper_bound(gu, rho_x, rho_theta) if fine >= _FINE_ENERGY_LIMIT: raise ValueError("fine error budget requires F0_upper < 1/40000") denominator_endpoint = 1 - g_squared * j1 denominator_window = 1 - g_squared * j1 * (1 + eta) if denominator_window <= 0: raise ArithmeticError("fixed-model phase comparison bound is unresolved") fine_current = 4 * j2 * fine / _CHILD_SIZE phase_initial = eps_delta + gu * eps_r + g_squared * fine_current / decay phase_endpoint = phase_initial / denominator_endpoint phase_window = phase_initial / denominator_window preparation = ( Q(2, 5) * eps_r + Q(2, 3) * gu * j1 * phase_endpoint + Q(2, 5) * gu * fine_current / (decay - 1) ) form_upper = eps_r + gu * j1 * (d + phase_window) + gu * fine_current / decay form_rate = ( eps_r + 2 * gu * j1 * (d + phase_window) + gu * fine_current * (1 + 1 / decay) ) exposure_error, gain_error = eta * form_rate, gain * form_upper observation_error = preparation + exposure_error + gain_error + eps_read gap_lower, gap_upper = gamma.lo * d**3 / 20, gu * d**3 / 6 margin, overlap_margin = gap_lower - 2 * observation_error, 2 * eps_read - gap_upper if margin > 0: status = "guaranteed_separation" elif overlap_margin >= 0: status = "observation_class_nonidentifiable" else: status = "not_certified" work_upper = contact.hi * ( Q(_CHILD_SIZE, 2) * (eps_r**2 + j1 * (d + eps_delta) ** 2) + rho_x**2 + j1 * rho_theta**2 ) return _OrganizedSmallResourceInformationBound( phase_offset=d, form_error_bound=rho_x, phase_error_bound=rho_theta, initial_form_contrast_error_bound=eps_r, phase_registration_error_bound=eps_delta, endpoint_reading_error_bound=eps_read, exposure_time_error_bound=eta, relative_gain_error_bound=gain, current_coefficients=coefficients, current_derivative_bounds=derivative_bounds, gamma_bounds=gamma, contact_conductance_bounds=contact, nominal_horizon_bounds=2 / contact, exposure_window=(1 - eta, 1 + eta), fine_decay_rate_in_scaled_clock=decay, fine_energy_upper_bound=fine, fine_energy_margin=_FINE_ENERGY_LIMIT - fine, fine_current_defect_upper_bound=fine_current, nominal_gap_lower_bound=gap_lower, nominal_gap_upper_bound=gap_upper, phase_comparison_seed_upper_bound=phase_initial, endpoint_phase_error_upper_bound=phase_endpoint, window_phase_error_upper_bound=phase_window, endpoint_preparation_error_upper_bound=preparation, window_form_upper_bound=form_upper, window_form_rate_upper_bound=form_rate, exposure_error_upper_bound=exposure_error, gain_error_upper_bound=gain_error, observation_error_upper_bound=observation_error, separation_margin=margin, nominal_reading_overlap_margin=overlap_margin, nominal_attachment_work_lower_bound=4 * contact.lo * d**2, nominal_attachment_work_upper_bound=5 * contact.hi * d**2, attachment_work_upper_bound=work_upper, status=status, )