"""Finite supplied-probe response of the two acquired outer organizations. ORGANIZED_OUTER_RESPONSE.md owns the frozen protocol and full nonlinear argument. Every assessment rebuilds the original acquisition, including its actual nonstationary zero-form control. No trajectory, source reset, runtime operator or autonomous event selector is installed. """ from __future__ import annotations from dataclasses import dataclass from fractions import Fraction as Q from ..mathematics._rational_interval import I, cos, pi_interval, sin from ._organized_outer_winding import ( _assess_organized_outer_winding, _OrganizedOuterWinding, ) from ._repeated_organized_composition import _vector from ._sine_preparation import _prepared_degree_four_probe_remainder _EPSILON = Q(1, 1000) _DELAY = Q(1, 100) _ALLOWANCE = Q(1, 10**10) _RAW_ERROR = Q(1, 10**12) _MINIMUM_CONTRAST = Q(1, 10**10) _WORK_BUDGET = Q(1, 1000) _PHASE_JUMP = tuple(_EPSILON * (int(node // 9 == 0) - Q(1, 5)) for node in range(45)) def _apply_outer_response_probe(*, form, phase_offsets): """Apply the declared detached jump after admitting both complete rows. Signed forms, every internal phase gap and the global lifted-phase mean are preserved. Admission of the source, signed work, sector and later evolution belongs to the assessor, not to this algebraic intervention. """ values = _vector(form, "form", 45) offsets = _vector(phase_offsets, "phase_offsets", 45) return values, tuple(value + jump for value, jump in zip(offsets, _PHASE_JUMP)) def _outer_response_event_work_bounds(*, opening_gap_bounds, closing_gap_bounds): """Enclose signed work on all eighteen changed outer edges. The supplied actual gap intervals apply to every slot of the marked opening 0->1 and closing 4->0 interfaces. The trigonometric identity retains the cancellation between interfaces before interval evaluation. It admits neither source provenance nor occurrence of the supplied jump. """ opening = I.coerce(opening_gap_bounds) closing = I.coerce(closing_gap_bounds) return 9 * ( (1 - cos(I(_EPSILON))) * (cos(opening) + cos(closing)) + sin(I(_EPSILON)) * (sin(closing) - sin(opening)) ) def _outer_response_finite_remainder(*, gamma_upper, initial_form_upper_bound): """Bound the fixed finite increment after the caller admits the full law. The proof uses all degree-four rows, heat contraction, the global sine derivative bound and the declared jump. Both background motion and nonlinear probe feedback are retained. This is not an ODE approximation or a bound transferred from a tangent model. """ return _prepared_degree_four_probe_remainder( gamma_upper=gamma_upper, initial_form_upper_bound=initial_form_upper_bound, phase_jump_upper_bound=_EPSILON, elapsed_time=_DELAY, ) @dataclass(frozen=True) class _OrganizedOuterResponse: """Actual-source finite response with separate work and identity decisions.""" form_error_bounds: tuple[Q, ...] phase_error_bounds: tuple[Q, ...] acquisition: _OrganizedOuterWinding source_full_form_error_upper_bound: Q source_full_phase_error_upper_bound: Q source_outer_gap_bounds: tuple[tuple[I, ...], tuple[I, ...]] probed_outer_gap_bounds: tuple[tuple[I, ...], tuple[I, ...]] outer_one_source_form_upper_bound: Q outer_zero_source_form_upper_bound: Q outer_one_event_work_bounds: I outer_zero_event_work_bounds: I outer_one_event_work_absolute_upper_bound: Q outer_zero_event_work_absolute_upper_bound: Q outer_one_post_probe_excess_upper_bound: Q outer_zero_post_probe_excess_upper_bound: Q outer_one_post_probe_capture_margin: Q outer_zero_post_probe_capture_margin: Q outer_one_response_slope_bounds: I outer_zero_response_slope_bounds: I outer_one_finite_remainder_upper_bound: Q outer_zero_finite_remainder_upper_bound: Q outer_one_response_bounds: I outer_zero_response_bounds: I contrast_bounds: I observed_contrast_bounds: I response_contrast_margin: Q internal_positive_gap_margin: Q internal_acute_gap_margin: Q outer_one_post_probe_acute_margin: Q outer_zero_post_probe_acute_margin: Q finite_comparison_domain_margin: Q sufficient_margins: tuple[tuple[str, Q], ...] source_certified: bool conditional_response_certified: bool work_certified: bool child_identities_retained: bool outer_identities_retained: bool finite_response_certified: bool contrast_certified: bool post_probe_capture_certified: bool subsequent_maintenance_certified: bool admitted: bool status: str unresolved_conditions: tuple[str, ...] source_organization_order: tuple[int, int] = (1, 0) receiver_child: int = 1 probe_phase_increments: tuple[Q, ...] = _PHASE_JUMP probe_amplitude: Q = _EPSILON source_scaled_time: Q = Q(200) elapsed_probe_scaled_time: Q = _DELAY elapsed_probe_original_time: Q = _DELAY * Q(1024, 1023) raw_readout_error_upper_bound: Q = _RAW_ERROR raw_readout_error_contributions: tuple[Q, ...] = (_RAW_ERROR,) * 4 increment_readout_error_upper_bound: Q = 2 * _RAW_ERROR contrast_readout_error_upper_bound: Q = 4 * _RAW_ERROR minimum_observed_contrast: Q = _MINIMUM_CONTRAST probe_work_budget: Q = _WORK_BUDGET protocol_revision: str = "50ce12a5" clock: str = "tau=(1023/1024)*t; h=tau-200" scope: tuple[str, ...] = ( "all_ten_original_allowances_admitted_before_fresh_source_rebuilding", "actual_outer_one_and_zero_sources_at_two_hundred_not_limiting_targets", "same_original_isolated_errors_not_identical_later_reached_fine_states", "control_fine_errors_transported_to_readout_not_assumed_stationary", "all_ninety_continuous_rows_and_eighty_original_relative_directions", "zero_total_child_uniform_phase_jump_with_exact_unchanged_forms_and_support", "signed_work_of_both_changed_interfaces_without_credit_for_previous_loss", "source_preserving_probed_minus_unprobed_comparison_for_each_organization", "finite_nonlinear_increment_retains_background_motion_and_probe_feedback", "four_arbitrary_raw_readout_errors_without_independence_assumption", "all_five_internal_and_nine_respective_outer_windings_retained", "complete_post_jump_storage_gives_separate_all_future_maintenance", "organization_contrast_does_not_identify_winding_as_a_sufficient_state", "no_trajectory_frozen_producer_operator_selection_or_physical_identification", "no_arbitrary_scale_fractality_or_resonance_spectrum_claim", ) def _assess_organized_outer_response(*, form_error_bounds, phase_error_bounds): """Assess the fixed probe on freshly rebuilt original source families. Smaller primitive allowances select subsets of the frozen source family. A failed sufficient condition remains unavailable and does not establish failure of response, formation or identity. No caller report or tunable amplitude, delay, work budget or resolution replaces this protocol. """ rx = _vector(form_error_bounds, "form_error_bounds", 5) rt = _vector(phase_error_bounds, "phase_error_bounds", 5) if min(*rx, *rt) < 0: raise ValueError("original preparation errors must be nonnegative") if max(*rx, *rt) > _ALLOWANCE: raise ValueError("original preparation errors must not exceed frozen 1e-10") acquisition = _assess_organized_outer_winding( form_error_bounds=rx, phase_error_bounds=rt ) source_ok = ( acquisition.admitted and acquisition.capture_certified and acquisition.control.capture_certified and acquisition.fine_error_certified ) gamma = acquisition.geometry.gamma_bounds form_error = acquisition.full_form_error_upper_bound phase_error = acquisition.full_phase_error_upper_bound one_gaps = acquisition.endpoint_oriented_outer_phase_gap_bounds # The same initial full-norm allowances and global heat comparison apply # around the stationary nominal control. Its actual residuals still move. zero_gaps = (I(-2 * phase_error, 2 * phase_error),) * 45 changes = tuple( _PHASE_JUMP[b] - _PHASE_JUMP[a] for a, b, _ in acquisition.geometry.outer_edges ) one_probed = tuple(gap + change for gap, change in zip(one_gaps, changes)) zero_probed = tuple(gap + change for gap, change in zip(zero_gaps, changes)) one_work = _outer_response_event_work_bounds( opening_gap_bounds=one_gaps[0], closing_gap_bounds=one_gaps[4] ) zero_work = _outer_response_event_work_bounds( opening_gap_bounds=zero_gaps[0], closing_gap_bounds=zero_gaps[4] ) one_excess = acquisition.endpoint_excess_upper_bound + one_work.hi zero_excess = acquisition.control.initial_excess_upper_bound + zero_work.hi one_capture = acquisition.boundary_energy_lower_bound - one_excess zero_capture = acquisition.control.boundary_energy_lower_bound - zero_excess pi = pi_interval() inner = acquisition.transit_internal_phase_gap_bounds inner_positive = inner.lo inner_acute = pi.lo / 2 - inner.hi one_acute = pi.lo / 2 - max(box.abs_max for box in one_probed) zero_acute = pi.lo / 2 - max(box.abs_max for box in zero_probed) one_x = ( max(box.abs_max for box in acquisition.primitive_entry.endpoint_form_bounds) + form_error ) zero_x = form_error finite_domain = Q(1, 2) - 2 * gamma.hi**2 * _DELAY**2 # Receiver one has one changed incident gap. The shared identity avoids # subtracting two interval sine values with the same uncertain argument. def slope(opening): return gamma * sin(I(_EPSILON / 2)) * cos(opening - _EPSILON / 2) / 2 one_slope, zero_slope = slope(one_gaps[0]), slope(zero_gaps[0]) one_remainder = _outer_response_finite_remainder( gamma_upper=gamma.hi, initial_form_upper_bound=one_x ) zero_remainder = _outer_response_finite_remainder( gamma_upper=gamma.hi, initial_form_upper_bound=zero_x ) one_response = _DELAY * one_slope + I(-one_remainder, one_remainder) zero_response = _DELAY * zero_slope + I(-zero_remainder, zero_remainder) contrast = zero_response - one_response observed = contrast + I(-4 * _RAW_ERROR, 4 * _RAW_ERROR) contrast_margin = observed.lo - _MINIMUM_CONTRAST work_margins = ( ("outer_one_absolute_probe_work", _WORK_BUDGET - one_work.abs_max), ("outer_zero_absolute_probe_work", _WORK_BUDGET - zero_work.abs_max), ) identity_margins = ( ("internal_positive_gap", inner_positive), ("internal_acute_gap", inner_acute), ("outer_one_post_probe_acute_cell", one_acute), ("outer_zero_post_probe_acute_cell", zero_acute), ("outer_one_complete_post_probe_capture", one_capture), ("outer_zero_complete_post_probe_capture", zero_capture), ) margins = ( work_margins + identity_margins + ( ("finite_nonlinear_comparison_domain", finite_domain), ("resolved_observed_finite_response_contrast", contrast_margin), ) ) work_ok = all(value > 0 for _, value in work_margins) identity_ok = all(value > 0 for _, value in identity_margins) conditional = all(value > 0 for _, value in margins) source_conditions = ( ("original_outer_source_not_admitted", acquisition.admitted), ("actual_outer_one_capture_not_certified", acquisition.capture_certified), ( "actual_outer_zero_capture_not_certified", acquisition.control.capture_certified, ), ("both_actual_source_errors_not_certified", acquisition.fine_error_certified), ) unresolved = tuple( name for name, passed in source_conditions if not passed ) + tuple(name for name, value in margins if value <= 0) admitted = source_ok and conditional return _OrganizedOuterResponse( form_error_bounds=rx, phase_error_bounds=rt, acquisition=acquisition, source_full_form_error_upper_bound=form_error, source_full_phase_error_upper_bound=phase_error, source_outer_gap_bounds=(one_gaps, zero_gaps), probed_outer_gap_bounds=(one_probed, zero_probed), outer_one_source_form_upper_bound=one_x, outer_zero_source_form_upper_bound=zero_x, outer_one_event_work_bounds=one_work, outer_zero_event_work_bounds=zero_work, outer_one_event_work_absolute_upper_bound=one_work.abs_max, outer_zero_event_work_absolute_upper_bound=zero_work.abs_max, outer_one_post_probe_excess_upper_bound=one_excess, outer_zero_post_probe_excess_upper_bound=zero_excess, outer_one_post_probe_capture_margin=one_capture, outer_zero_post_probe_capture_margin=zero_capture, outer_one_response_slope_bounds=one_slope, outer_zero_response_slope_bounds=zero_slope, outer_one_finite_remainder_upper_bound=one_remainder, outer_zero_finite_remainder_upper_bound=zero_remainder, outer_one_response_bounds=one_response, outer_zero_response_bounds=zero_response, contrast_bounds=contrast, observed_contrast_bounds=observed, response_contrast_margin=contrast_margin, internal_positive_gap_margin=inner_positive, internal_acute_gap_margin=inner_acute, outer_one_post_probe_acute_margin=one_acute, outer_zero_post_probe_acute_margin=zero_acute, finite_comparison_domain_margin=finite_domain, sufficient_margins=margins, source_certified=source_ok, conditional_response_certified=conditional, work_certified=source_ok and work_ok, child_identities_retained=source_ok and identity_ok, outer_identities_retained=source_ok and identity_ok, finite_response_certified=source_ok and finite_domain > 0, contrast_certified=source_ok and finite_domain > 0 and contrast_margin > 0, post_probe_capture_certified=source_ok and identity_ok, subsequent_maintenance_certified=source_ok and identity_ok, admitted=admitted, status="certified_organized_outer_response" if admitted else "unavailable", unresolved_conditions=unresolved, )