"""Analytic contact of actual formed C9 families under one supplied sine law. Uninterrupted isolated recovery precedes a supplied unit bridge. A correlated fourth-order receiver comparison and a full-support barrier retain all source uncertainty. No ideal reset, trajectory solver or phase-probe report is used. """ 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, cos, pi_interval, sin from ._sine_formed_contact import _joined_contact_bounds, _unprobed_handoff from .relational_sine_formed_classes import SineFormedClassPair __all__ = ("SineFormedClassContact", "assess_sine_formed_class_contact") @dataclass(frozen=True) class SineFormedClassContact: """Conditional receiver contrast and identity after a supplied contact. The receiver is class one; donor cases follow the fresh pair's order. Endpoint budgets bound the actual unprobed source images. Ideal targets enter only the analytic comparison. Unavailable handoffs leave actual response, event and retention bounds unavailable, not zero or passing. """ formation_certificate: SineFormedClassPair relaxation_duration: Q contact_time: Q original_contact_time: Q phase_origin_difference: Q contact_duration: Q endpoint_radius: Q readout_error_bound: Q work_allowance: Q decay_power: int lyapunov_decay_rate: Q | None decay_exponent: Q | None exact_decay_upper_bound: Q | None initial_lyapunov_upper_bounds: tuple[Q, Q] endpoint_form_norm_squared_upper_bounds: tuple[Q, Q] | None endpoint_phase_norm_squared_upper_bounds: tuple[Q, Q] | None handoff_certified_by_class: tuple[bool, bool] ideal_fourth_derivative_contrast_bounds: I ideal_leading_contrast_bounds: I semigroup_tail_upper_bound: Q nonlinear_remainder_upper_bound: Q preparation_response_error_upper_bound: Q | None recorded_contrast_bounds: I | None disconnected_recorded_contrast_bounds: I | None joined_radius_squared_upper_bound: Q | None joined_excess_storage_upper_bound: Q | None joined_barrier_lower_bound: Q joined_radius_margin_bounds: I | None joined_storage_margin_bounds: I | None bridge_work_bounds: I | None work_margin_bounds: I | None joined_form_mean_bounds: I | None joined_phase_mean_bounds: I | None response_certified: bool identity_certified: bool work_within_allowance: bool status: str unavailable_reasons: tuple[str, ...] receiver_class: str = "winding_one" bridge: tuple[int, int] = (4, 13) receiver_node: int = 13 nodes: tuple[int, ...] = tuple(range(18)) edges: tuple[tuple[int, int], ...] = tuple( sorted( ((4, 13),) + tuple( (min(s + j, s + (j + 1) % 9), max(s + j, s + (j + 1) % 9)) for s in (0, 9) for j in range(9) ) ) ) joined_degrees: tuple[int, ...] = tuple(3 if j in (4, 13) else 2 for j in range(18)) joined_gap_lower_bound: Q = Q(2, 81) joined_cosine_lower_bound: Q = Q(1, 20) clock: str = "tau=e*t; e=1023/1024" interval_method: str = INTERVAL_METHOD scope: tuple[str, ...] = ( "actual_unprobed_original_source_families_with_separate_exact_zero_sums", "receiver_phase_origin_declared_from_preparation_not_a_contact_reset", "fresh_formation_and_uninterrupted_nonlinear_recovery_no_incoming_report", "unit_central_bridge_changes_degrees_and_memberwise_weighted_means", "same_interface_and_receiver_preparation_for_both_donor_classes", "correlated_fourth_order_ideal_comparison_with_full_nonlinear_remainder", "whole_actual_family_error_and_independent_readout_errors_retained", "full_support_barrier_retains_both_windings_and_gives_later_recovery", "disconnected_receiver_history_independent_of_donor_under_the_same_law", "supplied_contact_work_not_inferred_from_continuous_loss", "no_trajectory_solver_ideal_reset_parameter_search_or_physical_identification", ) def to_dict(self): from ..sdk.relational_reports import _project return {"schema": "tnfr.sine-formed-class-contact.v1", "report": _project(self)} def assess_sine_formed_class_contact( *, formation_time, relaxation_duration, phase_origin_difference, contact_duration, form_error_bound, phase_error_bound, endpoint_radius, readout_error_bound, radius, work_allowance, decay_power, ) -> SineFormedClassContact: """Rebuild a fixed-family contact certificate from explicit primitives. All times use the scaled structural clock. The phase origin is receiver minus donor, fixed from initial preparation. Require 0<=phase<=1, 0<=contact_duration<=1/4, 0 1 or v["contact_duration"] > Q(1, 4): raise ValueError( "require phase_origin_difference <= 1 and contact_duration <= 1/4" ) if type(decay_power) is not int or not 0 <= decay_power <= 4096: raise ValueError("decay_power must be an integer between zero and4096") handoff = _unprobed_handoff( formation_time=v["formation_time"], relaxation_duration=v["relaxation_duration"], form_error_bound=v["form_error_bound"], phase_error_bound=v["phase_error_bound"], radius=v["radius"], endpoint_radius=v["endpoint_radius"], decay_power=decay_power, ) fresh = handoff.formation_certificate gamma, eta = fresh.gamma_bounds, fresh.eta_bounds rate = handoff.lyapunov_decay_rate exponent = handoff.decay_exponent decay = handoff.exact_decay_upper_bound initial = handoff.initial_lyapunov_upper_bounds xs = handoff.endpoint_form_norm_squared_upper_bounds ys = handoff.endpoint_phase_norm_squared_upper_bounds flags = handoff.handoff_certified_by_class eps = v["endpoint_radius"] phi, h = v["phase_origin_difference"], v["contact_duration"] pi = pi_interval() dc, sine = cos(2 * pi / 9) - cos(4 * pi / 9), sin(I(phi)) if not (dc.lo > 0 and gamma.hi < Q(1, 3000) and eta.hi * h**2 <= Q(3, 4)): raise ArithmeticError("fixed contact response theorem constants failed") fourth = Q(11, 81) * gamma**3 * sine * dc leading = fourth * (h**4 / 24) tail = gamma.hi**3 * dc.hi * 4 * sine.abs_max * h**5 / (45 * (1 - h / 2)) nonlinear = Q(8, 15) * sine.abs_max * gamma.hi**5 * h**5 barrier = Q(1, 1620) * v["radius"] ** 2 prep = contrast = disconnected = z2 = energy = radius_margin = storage_margin = None work = work_margin = mean_x = mean_phase = None response = identity = allowed = False if all(flags): prep = 2 * eps / (1 - 3 * h) error = tail + nonlinear + prep + 2 * v["readout_error_bound"] contrast = leading + I(-error, error) null_error = prep + 2 * v["readout_error_bound"] disconnected = I(-null_error, null_error) response = contrast.lo > 0 joined = _joined_contact_bounds( endpoint_radius=eps, phase_origin_difference=phi, radius=v["radius"], work_allowance=v["work_allowance"], ) z2 = joined.joined_radius_squared_upper_bound energy = joined.joined_excess_storage_upper_bound radius_margin = joined.joined_radius_margin_bounds storage_margin = joined.joined_storage_margin_bounds work = joined.bridge_work_bounds work_margin = joined.work_margin_bounds mean_x = joined.joined_form_mean_bounds mean_phase = joined.joined_phase_mean_bounds identity = joined.identity_certified allowed = joined.work_within_allowance reasons = tuple( reason for condition, reason in ( (fresh.status == "certified_two_formed_classes", "formation_unavailable"), (all(flags), "unprobed_endpoint_budget_not_certified"), (identity, "whole_joined_identity_not_certified"), (allowed, "supplied_contact_work_allowance_not_certified"), (response, "recorded_receiver_contrast_not_strictly_positive"), ) if not condition ) contact_time = v["formation_time"] + v["relaxation_duration"] return SineFormedClassContact( formation_certificate=fresh, relaxation_duration=v["relaxation_duration"], contact_time=contact_time, original_contact_time=contact_time / fresh.form_loss, phase_origin_difference=phi, contact_duration=h, endpoint_radius=eps, readout_error_bound=v["readout_error_bound"], work_allowance=v["work_allowance"], decay_power=decay_power, lyapunov_decay_rate=rate, decay_exponent=exponent, exact_decay_upper_bound=decay, initial_lyapunov_upper_bounds=initial, endpoint_form_norm_squared_upper_bounds=xs, endpoint_phase_norm_squared_upper_bounds=ys, handoff_certified_by_class=flags, ideal_fourth_derivative_contrast_bounds=fourth, ideal_leading_contrast_bounds=leading, semigroup_tail_upper_bound=tail, nonlinear_remainder_upper_bound=nonlinear, preparation_response_error_upper_bound=prep, recorded_contrast_bounds=contrast, disconnected_recorded_contrast_bounds=disconnected, joined_radius_squared_upper_bound=z2, joined_excess_storage_upper_bound=energy, joined_barrier_lower_bound=barrier, joined_radius_margin_bounds=radius_margin, joined_storage_margin_bounds=storage_margin, bridge_work_bounds=work, work_margin_bounds=work_margin, joined_form_mean_bounds=mean_x, joined_phase_mean_bounds=mean_phase, response_certified=response, identity_certified=identity, work_within_allowance=allowed, status="certified_formed_class_contact" if not reasons else "unavailable", unavailable_reasons=reasons, )