"""Necessary two-pulse geometry and gain bounds with one uncertain clock rate. The known-clock inverse supplies an auxiliary constraint envelope, not a replacement trajectory. Full finite-time dependence remains in its error bound; only the leading response combines sensor gain and clock rate. """ 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_sine_two_port_inference import _primitive_bounds from .relational_sine_two_pulse_inference import ( SineTwoPulseInference, infer_sine_two_pulse_geometry_gain, ) __all__ = ("SineClockInference", "infer_sine_geometry_gain_clock") @dataclass(frozen=True) class SineClockInference: """Conditional outer marginals with ``tau=rho*s`` and fixed gamma. ``probe_duration`` is the observed duration H of each successive window. One positive clock rate rho and one sensor gain G are held throughout. ``constraint_envelope`` uses h*=rho_plus*H and auxiliary gain L=G*rho/rho_plus. Its gain fields refer to L, and its known-clock trajectory wording does not assert that the actual trajectory reaches h*. It is consumed only as a necessary algebraic constraint envelope. The effective gain is J=G*rho. Its bounds and the separate G/rho projections are necessary marginals, not a joint realization claim or an exact full-flow gain/clock symmetry. All geometry concerns the original source, including the Y/8 actual-mean expansion. """ 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 recorded_reading_bounds: tuple[tuple[Q, Q], ...] readout_error_bound: Q readout_gain_bounds: tuple[Q, Q] clock_rate_bounds: tuple[Q, Q] structural_probe_duration_bounds: tuple[Q, Q] auxiliary_gain_prior_bounds: tuple[Q, Q] effective_gain_prior_bounds: tuple[Q, Q] constraint_envelope: SineTwoPulseInference finite_remainder_over_clock_candidate: Q finite_remainder_over_clock_upper_bound: Q | 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 clock_rate_outer_bounds: I | None source_admitted: bool finite_response_certified: bool rank_deficient: bool rank_certified: bool whole_window_acute_certified: bool inverse_enclosure_available: bool status: str unavailable_reasons: tuple[str, ...] incompatibility_reasons: tuple[str, ...] arithmetic_method: str = INTERVAL_METHOD clock: str = "tau=rho*s; rho is one held positive rate" effective_gain_relation: str = "J=G*rho" complete_observed_rows: tuple[str, str] = ( "dx/ds=rho*(-A*x+gamma*f(theta))", "dtheta/ds=rho*gamma*A*x", ) scope: tuple[str, ...] = ( "fixed_gamma_and_complete_two_port_law_under_one_unknown_constant_clock_rate", "two_events_at_observed_times_zero_and_H_without_source_reset", "auxiliary_envelope_gain_is_L_equal_G_times_rho_over_rho_upper", "auxiliary_upper_duration_is_not_the_actual_unknown_trajectory_duration", "monotone_finite_remainder_over_clock_rate_retains_full_flow_dependence", "three_reading_errors_remain_in_sensor_units_without_clock_division", "effective_gain_J_is_G_times_rho_not_sensor_gain_alone", "separate_gain_and_clock_bounds_project_one_necessary_product_relation", "coordinate_product_need_not_be_jointly_realizable", "no_exact_full_flow_gain_clock_symmetry_or_separate_point_identification", "original_source_actual_arc_mean_retains_original_phase_radius_over_eight", "no_acquisition_calibration_trajectory_producer_or_physical_identification", ) def to_dict(self): from ..sdk.relational_reports import _project return {"schema": "tnfr.sine-clock-inference.v1", "report": _project(self)} def infer_sine_geometry_gain_clock( *, bulk_angle_bounds, receiver_short_angle_bounds, form_radius, phase_radius, phase_increments, probe_duration, recorded_reading_bounds, readout_error_bound, readout_gain_bounds, clock_rate_bounds, ) -> SineClockInference: """Project geometry, effective gain and separate gain/clock outer bounds. All ten inputs are mandatory primitives. Here ``probe_duration`` is H in observed time s. Require H>0, positive ordered gain and clock priors, and rho_upper*H<=1/2. The shared two-pulse inverse admits the original source, cumulative phase inputs and three reading pairs with unchanged domains. At h*=rho_upper*H, the auxiliary gain prior is [G_lower*rho_lower/rho_upper, G_upper]. Monotonicity of E(rho*H)/rho proves G*E(rho*H)<=L*E(h*), so its finite envelope covers every admitted clock. No recorded reading or sensor error is divided by a clock rate. Exact endpoint products/quotients precede outward interval projection. """ rates = _primitive_bounds(clock_rate_bounds, "clock_rate_bounds") gain = _primitive_bounds(readout_gain_bounds, "readout_gain_bounds") duration = exact_or_represented_real(probe_duration, "probe_duration") if rates[0] <= 0: raise ValueError("clock_rate_bounds must be strictly positive") if gain[0] <= 0: raise ValueError("readout_gain_bounds must be strictly positive") if duration <= 0 or rates[1] * duration > Q(1, 2): raise ValueError( "require positive probe_duration and clock_upper*duration<=1/2" ) structural = tuple(rate * duration for rate in rates) auxiliary_gain = (gain[0] * rates[0] / rates[1], gain[1]) effective_prior = (gain[0] * rates[0], gain[1] * rates[1]) envelope = infer_sine_two_pulse_geometry_gain( bulk_angle_bounds=bulk_angle_bounds, receiver_short_angle_bounds=receiver_short_angle_bounds, form_radius=form_radius, phase_radius=phase_radius, phase_increments=phase_increments, probe_duration=structural[1], recorded_reading_bounds=recorded_reading_bounds, readout_error_bound=readout_error_bound, readout_gain_bounds=auxiliary_gain, ) effective = inferred_gain = inferred_rate = None nominal = envelope.nominal_bulk_angle_outer_bounds actual = envelope.actual_long_arc_mean_outer_bounds status = envelope.status incompatible = envelope.incompatibility_reasons if envelope.inverse_enclosure_available: auxiliary = envelope.readout_gain_outer_bounds # Retain exact products while projecting the relation. Constructing a # tiny positive clock interval first could introduce a zero divisor. lo, hi = rates[1] * auxiliary.lo, rates[1] * auxiliary.hi gain_lo, gain_hi = max(gain[0], lo / rates[1]), min(gain[1], hi / rates[0]) rate_lo, rate_hi = max(rates[0], lo / gain[1]), min(rates[1], hi / gain[0]) if gain_lo > gain_hi or rate_lo > rate_hi: status = "incompatible" incompatible += ("effective_gain_excludes_the_supplied_gain_clock_product",) nominal = actual = None else: effective = I(lo, hi) inferred_gain = I(gain_lo, gain_hi) inferred_rate = I(rate_lo, rate_hi) error_over_clock = envelope.finite_remainder_candidate / rates[1] return SineClockInference( bulk_angle_bounds=envelope.bulk_angle_bounds, receiver_short_angle_bounds=envelope.receiver_short_angle_bounds, form_radius=envelope.form_radius, phase_radius=envelope.phase_radius, phase_increments=envelope.phase_increments, probe_duration=duration, recorded_reading_bounds=envelope.recorded_reading_bounds, readout_error_bound=envelope.readout_error_bound, readout_gain_bounds=gain, clock_rate_bounds=rates, structural_probe_duration_bounds=structural, auxiliary_gain_prior_bounds=auxiliary_gain, effective_gain_prior_bounds=effective_prior, constraint_envelope=envelope, finite_remainder_over_clock_candidate=error_over_clock, finite_remainder_over_clock_upper_bound=( error_over_clock if envelope.finite_response_certified else None ), nominal_bulk_angle_outer_bounds=nominal, actual_long_arc_mean_outer_bounds=actual, effective_gain_outer_bounds=effective, readout_gain_outer_bounds=inferred_gain, clock_rate_outer_bounds=inferred_rate, source_admitted=envelope.source_admitted, finite_response_certified=envelope.finite_response_certified, rank_deficient=envelope.rank_deficient, rank_certified=envelope.rank_certified, whole_window_acute_certified=envelope.whole_window_acute_certified, inverse_enclosure_available=status == "bounded_candidate", status=status, unavailable_reasons=envelope.unavailable_reasons, incompatibility_reasons=incompatible, )