"""Response-free sufficient resolution budgets for the fixed aperture model. Only declared source, sensor, numerical and clock-drift budgets are consumed. The exact rational corollary does not run an inverse, select a response or certify the outward arithmetic of an eventual numerical inverse. """ from __future__ import annotations from dataclasses import dataclass from fractions import Fraction as Q from .._exact_time import exact_or_represented_real from .relational_sine_two_port_inference import ( _BULK_DOMAIN, _GAMMA_UPPER, _RECEIVER_DOMAIN, ) __all__ = ("SineApertureBudget", "assess_sine_aperture_budget") @dataclass(frozen=True) class SineApertureBudget: """Conditional ideal width bounds, independent of any observed response. A common half-width t bounds each supplied recorded-average enclosure, including propagated source uncertainty and numerical enclosure error. It is a supplied bound, not a separately proved solver-error estimate; the four additive sensor errors bounded by delta remain distinct. The fixed chart, pulse pair, gain/rate priors and targets are explicit model/policy choices. Positive source and quotient margins admit the sufficient corollary; passing its targets does not supply an observation or guarantee executable inverse availability at finite precision. """ probe_duration: Q form_radius: Q phase_radius: Q readout_error_bound: Q averaged_reading_halfwidth_bound: Q clock_rate_derivative_bound: Q combined_average_error_bound: Q source_phase_margin: Q whole_window_form_norm_bound: Q structural_readout_speed_bound: Q second_derivative_bound: Q third_derivative_bound: Q clock_average_error_scale: Q endpoint_reconstruction_error_bound: Q midpoint_reconstruction_error_bound: Q second_window_reconstruction_error_bound: Q virtual_numerical_error_radii: tuple[Q, ...] virtual_sensor_error_radii: tuple[Q, ...] virtual_clock_error_radii: tuple[Q, ...] virtual_reconstruction_error_radii: tuple[Q, ...] virtual_point_error_radii: tuple[Q, ...] specialized_form_norm_bound: Q finite_response_error_bound: Q transformed_error_radius: Q transformed_radius_margin: Q specialized_sine_norm_bound: Q specialized_third_derivative_bound: Q initial_curvature_error_bound: Q normalized_curvature_error_bound: Q curvature_observation_error_term: Q curvature_clock_drift_term: Q curvature_reconstruction_term: Q curvature_numerator_diameter_bound: Q curvature_numerator_lower_candidate: Q corrected_curvature_numerator_margin: Q effective_gain_width_candidate: Q nominal_angle_width_candidate: Q | None actual_angle_width_candidate: Q | None mean_clock_width_candidate: Q | None readout_gain_width_candidate: Q | None effective_gain_width_upper_bound: Q | None nominal_angle_width_upper_bound: Q | None actual_angle_width_upper_bound: Q | None mean_clock_width_upper_bound: Q | None readout_gain_width_upper_bound: Q | None noise_overlap_sensor_error_threshold: Q noise_overlap_witness_admitted: bool source_chart_eligible: bool transformed_radius_eligible: bool curvature_quotients_eligible: bool sufficient_bound_eligible: bool sufficient_resolution_certified: bool status: str ineligibility_reasons: tuple[str, ...] unmet_resolution_targets: tuple[str, ...] bulk_angle_bounds: tuple[Q, Q] = _BULK_DOMAIN receiver_short_angle_bounds: tuple[Q, Q] = _RECEIVER_DOMAIN phase_increments: tuple[Q, Q] = (Q(1, 4), Q(3, 4)) readout_gain_bounds: tuple[Q, Q] = (Q(1), Q(2)) clock_rate_bounds: tuple[Q, Q] = (Q(1, 2), Q(2)) source_phase_margin_lower_bound: Q = Q(1, 256) natural_curvature_coefficient_lower_bound: Q = Q(1, 18000) actual_angle_width_target: Q = Q(1, 1024) effective_gain_width_target: Q = Q(1, 2048) readout_gain_width_target: Q = Q(1, 16) mean_clock_width_target: Q = Q(1, 64) noise_overlap_gain_rate_pairs: tuple[tuple[Q, Q], ...] = ( (Q(3, 2), Q(1)), (Q(1), Q(3, 2)), ) noise_overlap_common_effective_gain: Q = Q(3, 2) noise_overlap_required_gain_and_mean_clock_width: Q = Q(1, 2) arithmetic_method: str = ( "exact_rational_sufficient_aperture_resolution_corollary_v1" ) inferred_clock_statistic: str = "rho_bar_1=(1/H)*integral_0^H rho(s) ds" effective_gain_relation: str = "J=G*rho_bar_1" scope: tuple[str, ...] = ( "fixed_complete_two_port_law_chart_pulse_pair_and_gain_rate_priors", "fixed_normalized_boxcars_over_first_thirds_and_full_second_window", "only_declared_source_sensor_numerical_and_C1_clock_drift_budgets", "common_numerical_halfwidth_and_sensor_error_are_separate_primitives", "source_chart_guard_uses_pi_less_than_355_over_113_and_Y_less_than_1_over_256", "ideal_exact_arithmetic_conditional_width_bounds_without_readings", "positive_source_chart_transformed_radius_and_curvature_quotient_margins_are_required", "passing_targets_does_not_prove_compatible_data_or_joint_realizability", "eventual_outward_inverse_availability_and_width_need_separate_checks", "failed_sufficient_certificate_is_not_nonidentifiability_or_impossibility", "separate_noise_overlap_witness_is_existential_for_some_admissible_common_record", "witness_uses_zero_source_residuals_constant_clocks_same_geometry_and_held_offset", "witness_compares_only_physical_sensor_error_not_numerical_halfwidth", "witness_gain_and_mean_rate_pair_diameter_does_not_apply_to_every_record", "zero_residual_witness_does_not_require_certification_of_the_entire_source_ball", "no_response_fitting_horizon_search_producer_inverse_or_cached_report_input", "no_sensor_calibration_source_acquisition_or_physical_clock_identification", ) def to_dict(self): from ..sdk.relational_reports import _project return {"schema": "tnfr.sine-aperture-budget.v1", "report": _project(self)} def assess_sine_aperture_budget( *, probe_duration, form_radius, phase_radius, readout_error_bound, averaged_reading_halfwidth_bound, clock_rate_derivative_bound, ) -> SineApertureBudget: """Evaluate a fixed-model sufficient budget without selecting observations. All six primitives are mandatory. Require 01/226>1/256, using pi<355/113; all other edge margins are larger. Further strict radius and quotient guards precede certified width fields. Failed guards or resolution targets are explicit abstentions of this sufficient method, not lower bounds on achievable inference error. The separate noise-overlap witness uses zero residuals within every admitted nonnegative source budget, including balls that fail the sufficient chart guard. Its threshold consumes sensor error alone. """ h, x, y, noise, numerical, drift = tuple( exact_or_represented_real(value, label) for value, label in ( (probe_duration, "probe_duration"), (form_radius, "form_radius"), (phase_radius, "phase_radius"), (readout_error_bound, "readout_error_bound"), (averaged_reading_halfwidth_bound, "averaged_reading_halfwidth_bound"), (clock_rate_derivative_bound, "clock_rate_derivative_bound"), ) ) if not 0 < h <= Q(1, 4): raise ValueError("probe_duration must lie in (0,1/4]") if min(x, y, noise, numerical, drift) < 0: raise ValueError( "source radii and sensor, numerical and clock-drift bounds must be nonnegative" ) g, epsilon = _GAMMA_UPPER, noise + numerical source_margin = Q(1, 256) - y q0 = x + 28 * g * h speed = 2 * q0 + 7 * g m2 = 4 * (1 + g * g) * q0 + 14 * g m3 = 8 * (1 + 2 * g * g) * q0 + 28 * g * (1 + g * g) + 8 * g**3 * q0**2 clock = 2 * speed * drift * h * h endpoint = 4 * m3 * h**3 / 27 midpoint = m3 * h**3 / 144 last = 4 * m2 * h * h / 3 row_norms = (Q(10, 3), Q(7, 6), Q(10, 3), Q(16, 3)) numerical_radii = tuple(value * numerical for value in row_norms) sensor_radii = tuple(value * noise for value in row_norms) clock_radii = tuple( value * clock for value in (Q(91, 324), Q(11, 81), Q(91, 324), Q(361, 324)) ) reconstruction = (endpoint, midpoint, endpoint, endpoint + last) radii = tuple( sum(values) for values in zip(numerical_radii, sensor_radii, clock_radii, reconstruction) ) qs = (x + 4 * g * h * (7 + 2 * y)) / (1 - 64 * g * g * h * h) finite_error = 4 * h * qs + 4 * g * h * y + 32 * g * g * h * h * qs radius = 18000 * (2 * finite_error + radii[2] + radii[3]) / h radius_margin = Q(1, 8) - radius sine_bound = min(Q(7), 5 + 2 * y + 16 * g * h * qs) special_m3 = ( 8 * (1 + 2 * g * g) * qs + 4 * g * (1 + g * g) * sine_bound + 8 * g**3 * qs**2 ) initial_error = 4 * (1 + g * g) * x + 4 * g * y curvature_error = 2 * initial_error + 2 * h * special_m3 observation_term = 72 * epsilon / (h * h) drift_term = Q(40, 3) * speed * drift reconstruction_term = Q(67, 27) * m3 * h diameter = observation_term + drift_term + reconstruction_term k0 = Q(1, 18000) numerator_lower = (k0 / 2 - curvature_error) / 2 - diameter corrected_margin = numerator_lower / 4 - curvature_error wj = 4 * radius wb = actual = wrate = wgain = None if radius_margin > 0: wb = 2 * radius / (Q(1, 4) - 2 * radius) actual = wb + y / 4 relative = 11 * g * wb / (8 * k0) product = 2 * wj + relative + 2 * wj * relative wrate = ( 2 * diameter / k0 + (2 + curvature_error / k0) * product + 2 * curvature_error / k0 ) wgain = 2 * wj + 4 * wrate source_ok, radius_ok = source_margin > 0, radius_margin > 0 quotient_ok = numerator_lower > 0 and corrected_margin > 0 eligible = source_ok and radius_ok and quotient_ok ineligible = tuple( label for valid, label in ( (source_ok, "source_phase_radius_not_below_fixed_chart_margin"), (radius_ok, "transformed_error_radius_not_below_one_eighth"), (numerator_lower > 0, "curvature_numerator_lower_bound_not_positive"), (corrected_margin > 0, "corrected_curvature_numerator_margin_not_positive"), ) if not valid ) targets = ( ("actual_angle", actual, Q(1, 1024)), ("effective_gain", wj, Q(1, 2048)), ("readout_gain", wgain, Q(1, 16)), ("mean_clock", wrate, Q(1, 64)), ) unmet = tuple( name for name, value, target in targets if value is None or value >= target ) certified = eligible and not unmet overlap_threshold = Q(245, 8) * g * h**2 + Q(1365, 32) * g**3 * h**3 return SineApertureBudget( probe_duration=h, form_radius=x, phase_radius=y, readout_error_bound=noise, averaged_reading_halfwidth_bound=numerical, clock_rate_derivative_bound=drift, combined_average_error_bound=epsilon, source_phase_margin=source_margin, whole_window_form_norm_bound=q0, structural_readout_speed_bound=speed, second_derivative_bound=m2, third_derivative_bound=m3, clock_average_error_scale=clock, endpoint_reconstruction_error_bound=endpoint, midpoint_reconstruction_error_bound=midpoint, second_window_reconstruction_error_bound=last, virtual_numerical_error_radii=numerical_radii, virtual_sensor_error_radii=sensor_radii, virtual_clock_error_radii=clock_radii, virtual_reconstruction_error_radii=reconstruction, virtual_point_error_radii=radii, specialized_form_norm_bound=qs, finite_response_error_bound=finite_error, transformed_error_radius=radius, transformed_radius_margin=radius_margin, specialized_sine_norm_bound=sine_bound, specialized_third_derivative_bound=special_m3, initial_curvature_error_bound=initial_error, normalized_curvature_error_bound=curvature_error, curvature_observation_error_term=observation_term, curvature_clock_drift_term=drift_term, curvature_reconstruction_term=reconstruction_term, curvature_numerator_diameter_bound=diameter, curvature_numerator_lower_candidate=numerator_lower, corrected_curvature_numerator_margin=corrected_margin, effective_gain_width_candidate=wj, nominal_angle_width_candidate=wb, actual_angle_width_candidate=actual, mean_clock_width_candidate=wrate, readout_gain_width_candidate=wgain, effective_gain_width_upper_bound=wj if eligible else None, nominal_angle_width_upper_bound=wb if eligible else None, actual_angle_width_upper_bound=actual if eligible else None, mean_clock_width_upper_bound=wrate if eligible else None, readout_gain_width_upper_bound=wgain if eligible else None, noise_overlap_sensor_error_threshold=overlap_threshold, noise_overlap_witness_admitted=noise >= overlap_threshold, source_chart_eligible=source_ok, transformed_radius_eligible=radius_ok, curvature_quotients_eligible=quotient_ok, sufficient_bound_eligible=eligible, sufficient_resolution_certified=certified, status="certified_sufficient_budget" if certified else "not_certified", ineligibility_reasons=ineligible, unmet_resolution_targets=unmet, )