"""Finite class-mediated transmission between three acquired C9 patterns. The two full-law comparisons differ only in the mediator's acquired class. Each receiver response subtracts its own unprobed continuation from the same reached state. Exact walk algebra and explicit nonlinear/family remainders do not replace that baseline, replay a trajectory or reset a formation image. """ from __future__ import annotations from dataclasses import dataclass from fractions import Fraction as Q from .._exact_time import exact_or_represented_real from ..mathematics._exact_linear_algebra import exact_matrix_product from ..mathematics._rational_interval import INTERVAL_METHOD, I from ._sine_formed_contact import _unprobed_handoff, _UnprobedHandoff from ._sine_port_bounds import _joined_port_bounds, _JoinedPortBounds from ._sine_port_geometry import ( _central_port_geometry, _component_interior_matrix, _PortGeometry, ) from .relational_sine_port_composition import _parameters __all__ = ("SineClassMediation", "assess_sine_class_mediation") _CLASSES = ((1, 1, 1), (1, 2, 1)) _CONTACTS = ((0, 1), (1, 2)) _NODES = tuple(range(27)) _EDGES = tuple( (9 * component + j, 9 * component + (j + 1) % 9) for component in range(3) for j in range(9) ) + ((4, 13), (13, 22)) def _mediation_walks(geometry): """Rebuild central-donor to central-receiver walks on the shared quotient.""" form = geometry.normalized_form_matrix mediator = _component_interior_matrix(geometry, 1) square = exact_matrix_product(form, form) transmitted = exact_matrix_product(exact_matrix_product(form, mediator), form) return square[10][0], transmitted[10][0] @dataclass(frozen=True) class _MediationReferenceBounds: """Shared ideal-reference algebra; callers admit the physical primitives.""" gamma: I cosines: tuple[I, I] eta: I difference: I common: Q walk: Q leading: I tail: Q denominator: Q nonlinear: Q ideal: I def _mediation_reference_bounds(geometry, a, h): """Retain the established outward operation order of the ideal contrast.""" common, walk = _mediation_walks(geometry) gamma, cosines = _parameters((1, 2)) eta = gamma**2 difference = cosines[0] - cosines[1] leading = a * eta * difference * h**3 * walk / 6 tail = 9 * a * eta.hi * difference.hi * h**4 / (1 - 3 * h / 4) denominator = 1 - 2 * eta.hi * h**2 nonlinear = 16 * gamma.hi**3 * a**2 * h**3 / (3 * denominator**2 * (1 - 3 * h)) ideal = leading + I(-tail - nonlinear, tail + nonlinear) return _MediationReferenceBounds( gamma, cosines, eta, difference, common, walk, leading, tail, denominator, nonlinear, ideal, ) @dataclass(frozen=True) class SineClassMediation: """Conditional response, identity and event-work certificates. Source errors are componentwise original-preparation budgets with exact separate zero sums. The freshly rebuilt handoff bounds every component's reached Euclidean form/phase errors by endpoint_radius. Each actual response uses its same-state unprobed baseline. Readout error bounds one scalar reading; four readings enter the oriented class contrast. A phase-blind alternative retains both rows, support, clock and kick but removes phase-to-form feedback. Its ideal class contrast is zero; its actual-family enclosure retains preparation and readout errors. Identity, supplied-work policy and response separation have distinct flags. """ formation_time: Q relaxation_duration: Q contact_duration: Q probe_amplitude: Q form_error_bound: Q phase_error_bound: Q endpoint_radius: Q radius: Q decay_power: int readout_error_bound: Q contact_work_allowance: Q probe_work_allowance: Q geometry: _PortGeometry source_handoff: _UnprobedHandoff joined_bounds: _JoinedPortBounds gamma_bounds: I eta_bounds: I mediator_cosine_bounds: tuple[I, I] mediator_cosine_difference_bounds: I common_diffusion_walk_coefficient: Q common_second_derivative_per_amplitude_bounds: I mediator_walk_coefficient: Q leading_contrast_bounds: I linear_tail_upper_bound: Q nonlinear_contrast_error_upper_bound: Q nonlinear_bootstrap_margin: Q ideal_nonlinear_contrast_bounds: I preparation_contrast_error_upper_bound: Q | None readout_contrast_error_upper_bound: Q | None actual_contrast_bounds: I | None recorded_contrast_bounds: I | None phase_blind_recorded_contrast_bounds: I | None phase_blind_exclusion_margin_bounds: I | None contact_work_bounds: I | None probe_work_bounds: I | None probe_work_margin: Q | None post_probe_radius_squared_upper_bound: Q | None post_probe_excess_storage_upper_bound: Q | None post_probe_radius_margin: Q | None post_probe_storage_margin: Q | None post_probe_form_mean_bounds: I | None post_probe_phase_mean_bounds: I | None source_handoff_certified: bool response_certified: bool phase_blind_alternative_excluded: bool baseline_identity_certified: bool probe_identity_certified: bool identity_certified: bool contact_work_within_allowance: bool probe_work_within_allowance: bool work_within_allowances: bool status: str unavailable_reasons: tuple[str, ...] classes: tuple[tuple[int, ...], ...] = _CLASSES contacts: tuple[tuple[int, int], ...] = _CONTACTS phase_origins: tuple[Q, ...] = (Q(0),) * 3 nodes: tuple[int, ...] = _NODES edges: tuple[tuple[int, int], ...] = _EDGES donor_node: int = 4 mediator_node: int = 13 receiver_node: int = 22 held_capacities: tuple[Q, ...] = (Q(1),) * 27 first_class_dependent_derivative_order: int = 3 scaled_generator_norm_upper_bound: Q = Q(3) probe_form_mean_shift: Q = Q(0) form_loss: Q = Q(1023, 1024) exchange_weight: Q = Q(1, 1024) phase_exchange_beta: Q = Q(1) law: str = "x'=-KLx+gamma*KS(theta); theta'=gamma*KLx" clock: str = "tau=e*t; e=1023/1024" response_definition: str = "R_k=x_probe[22](h)-x_unprobed[22](h); contrast=R_1-R_2" phase_blind_law: str = "x'=-KLx; theta'=gamma*KLx" interval_method: str = INTERVAL_METHOD scope: tuple[str, ...] = ( "same_complete_law_support_capacity_clock_probe_and_receiver_for_both_classes", "fresh_original_preparation_and_unprobed_dwell_no_cached_report_admission", "aligned_origins_are_original_preparation_choices_not_handoff_resets", "three_independent_component_errors_with_original_separate_zero_sums", "full_27_node_form_and_phase_state_retained_by_the_family_comparison", "reflection_even_quotient_used_only_for_ideal_tangent_walk_algebra", "actual_probe_and_unprobed_baseline_start_at_the_same_reached_state", "strict_positive_oriented_contrast_with_nonlinear_and_preparation_errors", "four_scalar_reading_errors_have_total_bound_four_delta", "phase_blind_complete_alternative_keeps_actual_source_error_allowance", "contact_and_form_jump_work_have_separate_supplied_allowances", "identity_and_recovery_are_on_the_actual_post_event_conserved_mean_leaf", "response_identity_and_work_flags_are_independent_obligations", "no_trajectory_solver_source_reset_autonomous_contact_or_physical_identification", ) def to_dict(self): from ..sdk.relational_reports import _project return {"schema": "tnfr.sine-class-mediation.v1", "report": _project(self)} def assess_sine_class_mediation( *, formation_time, relaxation_duration, contact_duration, probe_amplitude, form_error_bound, phase_error_bound, endpoint_radius, radius, decay_power, readout_error_bound, contact_work_allowance, probe_work_allowance, ) -> SineClassMediation: """Rebuild an acquired-family transmission certificate from twelve primitives. All scalar inputs use shared exact-or-represented-real admission. Require nonnegative times, errors, amplitude and allowances, 0 Q(1, 4): raise ValueError("contact_duration must not exceed1/4") if v["formation_time"] > 20480: raise ValueError("formation_time/5 must not exceed4096") if type(decay_power) is not int or not 0 <= decay_power <= 4096: raise ValueError("decay_power must be an ordinary integer zero through4096") a, h, eps, r = ( v[key] for key in ("probe_amplitude", "contact_duration", "endpoint_radius", "radius") ) geometry = _central_port_geometry(3, _CONTACTS) reference = _mediation_reference_bounds(geometry, a, h) handoff = _unprobed_handoff( **{ key: v[key] for key in ( "formation_time", "relaxation_duration", "form_error_bound", "phase_error_bound", "endpoint_radius", "radius", ) }, decay_power=decay_power, ) source = all(handoff.handoff_certified_by_class) joined = _joined_port_bounds( geometry=geometry, phase_origins=(Q(0),) * 3, endpoint_radius=eps, radius=r, work_allowance=v["contact_work_allowance"], handoff_available=source, ) preparation = readout = actual = recorded = blind = blind_margin = None contact_work = probe_work = work_margin = z2 = energy = z_margin = e_margin = None form_mean = phase_mean = None response = excluded = identity_probe = allowed_probe = False shift = Q(3, 58) * a if source: preparation = 4 * eps / (1 - 3 * h) readout = 4 * v["readout_error_bound"] actual = reference.ideal + I(-preparation, preparation) recorded = actual + I(-readout, readout) blind = I(-preparation - readout, preparation + readout) blind_margin = recorded - blind.hi response = bool(a > 0 and h > 0 and recorded.lo > 0) excluded = bool(response and blind_margin.lo > 0) contact_work = I(0, joined.contact_work_upper_bound) probe_center, probe_error = Q(3, 2) * a**2, 6 * a * eps probe_work = I(probe_center - probe_error, probe_center + probe_error) work_margin = v["probe_work_allowance"] - probe_center - probe_error allowed_probe = work_margin >= 0 z2 = 6 * eps**2 + 2 * a * eps + Q(26, 27) * a**2 energy = 22 * eps**2 + 6 * a * eps + Q(3, 2) * a**2 z_margin = r**2 - z2 if joined.joined_barrier_lower_bound is not None: e_margin = joined.joined_barrier_lower_bound - energy identity_probe = z_margin > 0 and e_margin > 0 mean_error = Q(4, 58) * eps form_mean = I(shift - mean_error, shift + mean_error) phase_mean = I(-mean_error, mean_error) identity = bool(joined.identity_certified and identity_probe) allowed = bool(joined.work_within_allowance and allowed_probe) reasons = tuple( label for passed, label in ( (source, "actual_source_handoff_not_certified"), (response, "strict_positive_class_contrast_not_certified"), (excluded, "phase_blind_alternative_not_excluded"), (identity, "baseline_and_probe_identity_not_certified"), (allowed, "contact_and_probe_work_not_within_allowances"), ) if not passed ) status = "certified_class_mediation" if not reasons else "unavailable" return SineClassMediation( **v, decay_power=decay_power, geometry=geometry, source_handoff=handoff, joined_bounds=joined, gamma_bounds=reference.gamma, eta_bounds=reference.eta, mediator_cosine_bounds=reference.cosines, mediator_cosine_difference_bounds=reference.difference, common_diffusion_walk_coefficient=reference.common, common_second_derivative_per_amplitude_bounds=(1 - reference.eta) * reference.common, mediator_walk_coefficient=reference.walk, leading_contrast_bounds=reference.leading, linear_tail_upper_bound=reference.tail, nonlinear_contrast_error_upper_bound=reference.nonlinear, nonlinear_bootstrap_margin=reference.denominator, ideal_nonlinear_contrast_bounds=reference.ideal, preparation_contrast_error_upper_bound=preparation, readout_contrast_error_upper_bound=readout, actual_contrast_bounds=actual, recorded_contrast_bounds=recorded, phase_blind_recorded_contrast_bounds=blind, phase_blind_exclusion_margin_bounds=blind_margin, contact_work_bounds=contact_work, probe_work_bounds=probe_work, probe_work_margin=work_margin, post_probe_radius_squared_upper_bound=z2, post_probe_excess_storage_upper_bound=energy, post_probe_radius_margin=z_margin, post_probe_storage_margin=e_margin, post_probe_form_mean_bounds=form_mean, post_probe_phase_mean_bounds=phase_mean, source_handoff_certified=source, response_certified=response, phase_blind_alternative_excluded=excluded, baseline_identity_certified=joined.identity_certified, probe_identity_certified=identity_probe, identity_certified=identity, contact_work_within_allowance=joined.work_within_allowance, probe_work_within_allowance=allowed_probe, work_within_allowances=allowed, status=status, unavailable_reasons=reasons, probe_form_mean_shift=shift, )