"""Necessary geometry/gain/mean-clock constraints from four finite boxcars. Exact quadratic moments reconstruct a constant-mean comparison history. Structural derivative bounds are applied separately on either side of the phase event; no observed-clock third derivative or point sensor is assumed. """ from __future__ import annotations from dataclasses import dataclass from fractions import Fraction as Q from .._exact_time import exact_or_represented_real from ..mathematics._rational_interval import INTERVAL_METHOD, I from .relational_observations import _ordered from .relational_sine_curvature_inference import ( SineCurvatureInference, infer_sine_geometry_gain_clock_curvature, ) from .relational_sine_two_port_inference import ( _BULK_DOMAIN, _GAMMA_UPPER, _RECEIVER_DOMAIN, _primitive_bounds, ) __all__ = ("SineApertureInference", "infer_sine_geometry_gain_clock_aperture") _RECONSTRUCTION = ( (Q(11, 6), Q(-7, 6), Q(1, 3), Q(0)), (Q(-1, 24), Q(13, 12), Q(-1, 24), Q(0)), (Q(1, 3), Q(-7, 6), Q(11, 6), Q(0)), (Q(-1, 3), Q(7, 6), Q(-11, 6), Q(2)), ) @dataclass(frozen=True) class SineApertureInference: """Necessary marginals for normalized boxcar observations of one history. The four apertures are [0,H/3], [H/3,2H/3], [2H/3,H], [H,2H]. A single positive gain and held offset apply to all averages; each has one additive error bounded by the original sensor allowance. The clock is positive C1 with supplied global rate and derivative bounds. ``reference_envelope`` consumes virtual noiseless point bands for a constant first-window-mean clock. Its zero sensor allowance does not remove the original four errors: their complete linear images already widen those bands. Marginal interval propagation may discard their correlations and does not establish a joint realization. """ bulk_angle_bounds: tuple[Q, Q] receiver_short_angle_bounds: tuple[Q, Q] form_radius: Q phase_radius: Q phase_increments: tuple[Q, Q] probe_duration: Q averaged_reading_bounds: tuple[tuple[Q, Q], ...] readout_error_bound: Q readout_gain_bounds: tuple[Q, Q] clock_rate_bounds: tuple[Q, Q] clock_rate_derivative_bound: Q reference_envelope: SineCurvatureInference aperture_windows: tuple[tuple[Q, Q], ...] virtual_observation_times: tuple[Q, Q, Q, Q] reconstruction_matrix: tuple[tuple[Q, ...], ...] averaged_reading_midpoints: tuple[Q, ...] averaged_reading_radii: tuple[Q, ...] structural_duration_upper_bound: Q whole_window_form_norm_candidate: Q whole_window_form_norm_upper_bound: Q | None structural_readout_speed_candidate: Q structural_readout_speed_upper_bound: Q | None second_derivative_bound_candidate: Q second_derivative_bound_upper_bound: Q | None third_derivative_bound_candidate: Q third_derivative_bound_upper_bound: Q | None averaged_exposure_discrepancy_bounds: tuple[Q, ...] averaged_clock_discrepancy_candidates: tuple[Q, ...] averaged_clock_discrepancy_upper_bounds: tuple[Q, ...] | None projected_numerical_radii: tuple[Q, ...] projected_sensor_error_radii: tuple[Q, ...] projected_clock_discrepancy_candidates: tuple[Q, ...] projected_clock_discrepancy_upper_bounds: tuple[Q, ...] | None reconstruction_error_candidates: tuple[Q, ...] reconstruction_error_upper_bounds: tuple[Q, ...] | None virtual_reading_midpoints: tuple[Q, ...] point_reference_reading_bounds: tuple[tuple[Q, Q], ...] original_curvature_average_coefficients: tuple[Q, Q, Q, Q] embedded_inverse_average_coefficients: tuple[tuple[I, ...], ...] | None nominal_bulk_angle_outer_bounds: I | None actual_long_arc_mean_outer_bounds: I | None effective_gain_outer_bounds: I | None readout_gain_outer_bounds: I | None first_window_mean_clock_rate_outer_bounds: I | None source_admitted: bool clock_drift_transfer_certified: bool aperture_reconstruction_certified: bool finite_curvature_bound_certified: bool rank_deficient: bool rank_certified: bool inverse_enclosure_available: bool status: str unavailable_reasons: tuple[str, ...] incompatibility_reasons: tuple[str, ...] arithmetic_method: str = INTERVAL_METHOD clock: str = "tau(s)=integral_0^s rho(u) du; positive C1 rho with supplied bounds" inferred_clock_statistic: str = "rho_bar_1=(1/H)*integral_0^H rho(s) ds" effective_gain_relation: str = "J=G*rho_bar_1" complete_observed_rows: tuple[str, str] = ( "dx/ds=rho(s)*(-A*x+gamma*f(theta))", "dtheta/ds=rho(s)*gamma*A*x", ) scope: tuple[str, ...] = ( "four_fixed_normalized_boxcar_averages_are_the_original_observations", "one_held_positive_gain_and_offset_and_four_scalar_sensor_errors", "global_positive_C1_clock_rate_and_derivative_bounds_are_supplied_premises", "original_complete_source_and_phase_events_at_zero_and_H_are_preserved", "form_is_continuous_at_H_but_derivative_bounds_are_applied_on_each_side", "no_prehistory_posthorizon_data_or_observed_clock_third_derivative", "constant_first_window_mean_reference_has_the_same_complete_event_states", "quadratic_moments_reconstruct_first_three_points_with_cubic_remainders", "last_point_uses_second_window_endpoint_identity_with_quadratic_remainder", "virtual_point_bands_already_include_all_original_sensor_errors", "reference_zero_sensor_allowance_refers_to_noiseless_comparison_points", "explicit_error_coefficient_maps_do_not_restore_discarded_joint_correlations", "reference_envelope_is_a_necessary_constraint_not_an_observed_point_trajectory", "first_window_mean_clock_rate_is_not_an_instantaneous_rate", "actual_long_arc_mean_retains_original_phase_radius_over_eight", "marginals_do_not_certify_joint_state_sensor_or_clock_profile_realizability", "no_response_producer_cached_report_or_physical_calibration_input", ) def to_dict(self): from ..sdk.relational_reports import _project return {"schema": "tnfr.sine-aperture-inference.v1", "report": _project(self)} def infer_sine_geometry_gain_clock_aperture( *, bulk_angle_bounds, receiver_short_angle_bounds, form_radius, phase_radius, phase_increments, probe_duration, averaged_reading_bounds, readout_error_bound, readout_gain_bounds, clock_rate_bounds, clock_rate_derivative_bound, ) -> SineApertureInference: """Infer necessary marginals from fixed finite-aperture observations. All eleven inputs are mandatory primitives. Domains match the bounded clock-drift inverse except that four averaged reading pairs replace its point readings. Each supplied interval encloses a recorded normalized average over the corresponding fixed aperture; additive sensor error is separate. Require H>0 and rho_plus*H<=1/2. Exact rational moments and comparison allowances produce four virtual point bands. One fresh curvature inverse consumes these with zero new sensor error. Its rate output refers to the actual first-window mean. Source-independent arithmetic candidates are certified only after that child re-admits the original phase chart and source norm budgets. """ b = _primitive_bounds(bulk_angle_bounds, "bulk_angle_bounds") receiver = _primitive_bounds( receiver_short_angle_bounds, "receiver_short_angle_bounds" ) amplitudes = _primitive_bounds(phase_increments, "phase_increments") gain = _primitive_bounds(readout_gain_bounds, "readout_gain_bounds") rates = _primitive_bounds(clock_rate_bounds, "clock_rate_bounds") raw = _ordered(averaged_reading_bounds, "averaged_reading_bounds", limit=5) if len(raw) != 4: raise ValueError( "averaged_reading_bounds must contain exactly four endpoint pairs" ) readings = tuple( _primitive_bounds(pair, f"averaged_reading_bounds[{index}]") for index, pair in enumerate(raw) ) x, y, horizon, noise, drift = tuple( exact_or_represented_real(value, label) for value, label in ( (form_radius, "form_radius"), (phase_radius, "phase_radius"), (probe_duration, "probe_duration"), (readout_error_bound, "readout_error_bound"), (clock_rate_derivative_bound, "clock_rate_derivative_bound"), ) ) if not _BULK_DOMAIN[0] <= b[0] <= b[1] <= _BULK_DOMAIN[1]: raise ValueError("bulk_angle_bounds must lie within [11/8,3/2] radians") if not _RECEIVER_DOMAIN[0] <= receiver[0] <= receiver[1] <= _RECEIVER_DOMAIN[1]: raise ValueError("receiver_short_angle_bounds must lie within [2/3,1] radians") if min(x, y, noise, drift) < 0: raise ValueError( "form_radius, phase_radius, readout_error_bound and clock_rate_derivative_bound must be nonnegative" ) if not 0 < amplitudes[0] <= amplitudes[1] <= 1: raise ValueError("cumulative phase_increments must satisfy 0 Q(1, 2): raise ValueError( "require positive probe_duration and clock_upper*duration<=1/2" ) hstar, g = rates[1] * horizon, _GAMMA_UPPER form_bound = x + 14 * g * hstar speed = 2 * form_bound + 7 * g second = 4 * (1 + g * g) * form_bound + 14 * g third = ( 8 * (1 + 2 * g * g) * form_bound + 28 * g * (1 + g * g) + 8 * g**3 * form_bound**2 ) rate_range = rates[1] - rates[0] exposure = tuple( min(coefficient * drift * horizon**2, 2 * coefficient * rate_range * horizon) for coefficient in (Q(7, 108), Q(13, 108), Q(7, 108)) ) + ( min(5 * drift * horizon**2 / 12, rate_range * horizon / 2), ) clock_average = tuple(gain[1] * speed * radius for radius in exposure) midpoints = tuple((lo + hi) / 2 for lo, hi in readings) radii = tuple((hi - lo) / 2 for lo, hi in readings) virtual = tuple( sum(w * c for w, c in zip(row, midpoints)) for row in _RECONSTRUCTION ) def project_radii(values): return tuple( sum(abs(w) * value for w, value in zip(row, values)) for row in _RECONSTRUCTION ) numerical = project_radii(radii) sensor = project_radii((noise,) * 4) clock = project_radii(clock_average) endpoint = gain[1] * third * hstar**3 / 108 reconstruction = ( endpoint, gain[1] * third * hstar**3 / 2304, endpoint, endpoint + gain[1] * second * hstar**2 / 6, ) point_radii = tuple( sum(parts) for parts in zip(numerical, sensor, clock, reconstruction) ) comparison = tuple( (c - radius, c + radius) for c, radius in zip(virtual, point_radii) ) reference = infer_sine_geometry_gain_clock_curvature( bulk_angle_bounds=b, receiver_short_angle_bounds=receiver, form_radius=x, phase_radius=y, phase_increments=amplitudes, probe_duration=horizon, recorded_reading_bounds=comparison, readout_error_bound=Q(0), readout_gain_bounds=gain, clock_rate_bounds=rates, ) embedded = None if reference.embedded_inverse_reading_coefficients is not None: embedded = tuple( tuple( sum((row[k] * _RECONSTRUCTION[k][j] for k in range(4)), I(0)) for j in range(4) ) for row in reference.embedded_inverse_reading_coefficients ) admitted = reference.source_admitted return SineApertureInference( bulk_angle_bounds=b, receiver_short_angle_bounds=receiver, form_radius=x, phase_radius=y, phase_increments=amplitudes, probe_duration=horizon, averaged_reading_bounds=readings, readout_error_bound=noise, readout_gain_bounds=gain, clock_rate_bounds=rates, clock_rate_derivative_bound=drift, reference_envelope=reference, aperture_windows=( (Q(0), horizon / 3), (horizon / 3, 2 * horizon / 3), (2 * horizon / 3, horizon), (horizon, 2 * horizon), ), virtual_observation_times=(Q(0), horizon / 2, horizon, 2 * horizon), reconstruction_matrix=_RECONSTRUCTION, averaged_reading_midpoints=midpoints, averaged_reading_radii=radii, structural_duration_upper_bound=2 * hstar, whole_window_form_norm_candidate=form_bound, whole_window_form_norm_upper_bound=form_bound if admitted else None, structural_readout_speed_candidate=speed, structural_readout_speed_upper_bound=speed if admitted else None, second_derivative_bound_candidate=second, second_derivative_bound_upper_bound=second if admitted else None, third_derivative_bound_candidate=third, third_derivative_bound_upper_bound=third if admitted else None, averaged_exposure_discrepancy_bounds=exposure, averaged_clock_discrepancy_candidates=clock_average, averaged_clock_discrepancy_upper_bounds=clock_average if admitted else None, projected_numerical_radii=numerical, projected_sensor_error_radii=sensor, projected_clock_discrepancy_candidates=clock, projected_clock_discrepancy_upper_bounds=clock if admitted else None, reconstruction_error_candidates=reconstruction, reconstruction_error_upper_bounds=reconstruction if admitted else None, virtual_reading_midpoints=virtual, point_reference_reading_bounds=comparison, original_curvature_average_coefficients=(Q(9, 4), Q(-9, 2), Q(9, 4), Q(0)), embedded_inverse_average_coefficients=embedded, nominal_bulk_angle_outer_bounds=reference.nominal_bulk_angle_outer_bounds, actual_long_arc_mean_outer_bounds=reference.actual_long_arc_mean_outer_bounds, effective_gain_outer_bounds=reference.effective_gain_outer_bounds, readout_gain_outer_bounds=reference.readout_gain_outer_bounds, first_window_mean_clock_rate_outer_bounds=reference.clock_rate_outer_bounds, source_admitted=admitted, clock_drift_transfer_certified=admitted, aperture_reconstruction_certified=admitted, finite_curvature_bound_certified=reference.finite_curvature_bound_certified, rank_deficient=reference.clock_envelope.rank_deficient, rank_certified=reference.clock_envelope.rank_certified, inverse_enclosure_available=reference.inverse_enclosure_available, status=reference.status, unavailable_reasons=reference.unavailable_reasons, incompatibility_reasons=reference.incompatibility_reasons, )