"""Cancellation-aware all-time form bounds for the same reduced C9 network. The fixed-reference heat filters retain the fast/slow cancellation before taking norms. Neither commuting operators nor a derivative of the unknown forcing is assumed. Original preparations and phase bounds are rebuilt. """ from __future__ import annotations from dataclasses import dataclass from fractions import Fraction as Q from ..mathematics._rational_interval import INTERVAL_METHOD, I, sqrt from .relational_sine_port_relaxation import ( SinePortRelaxation, assess_sine_port_relaxation, ) __all__ = ("SinePortFormTracking", "assess_sine_port_form_tracking") @dataclass(frozen=True) class _HeatFormBounds: """Rational filter gains on one admitted centered parity subspace.""" gap_lower_bound: Q spectral_lower_bound: Q spectral_upper_bound: Q spectral_ratio_upper_bound: Q dyadic_band_count: int heat_integral_upper_bound: Q derivative_filter_gain_upper_bound: Q initial_norm_upper_bound: Q forcing_upper_bound: Q loop_gain_upper_bound: Q loop_margin: Q initial_form_contribution_upper_bound: Q initial_joint_contribution_upper_bound: Q forced_contribution_upper_bound: Q form_norm_upper_bound: Q | None certified: bool def _heat_form_bounds(*, gap, initial_norm, forcing, gamma_upper): """Use admitted rational spectral and forcing bounds, without a report. For mu<=B0<=M on the mean-free subspace, integral ||B0 exp(-B0 t)|| is at most 1+log(M/mu)/exp(1). The exact dyadic count, log(2)<7/10 and 1/exp(1)<3/8 give the rational bound below. The form-scale gamma cancels symbolically before interval endpoints are substituted. """ lower, upper = gap / 6, Q(2) ratio = upper / lower bands = max(0, ratio.numerator.bit_length() - ratio.denominator.bit_length()) if Q(2**bands) < ratio: bands += 1 heat = 1 + Q(21, 80) * bands gain = 1 + heat loop = gamma_upper**2 * upper * gain / gap margin = 1 - loop initial_joint = gamma_upper * upper * (1 + gamma_upper) * initial_norm / gap forced = gamma_upper * gain * forcing / gap form = (initial_norm + initial_joint + forced) / margin if margin > 0 else None return _HeatFormBounds( gap_lower_bound=gap, spectral_lower_bound=lower, spectral_upper_bound=upper, spectral_ratio_upper_bound=ratio, dyadic_band_count=bands, heat_integral_upper_bound=heat, derivative_filter_gain_upper_bound=gain, initial_norm_upper_bound=initial_norm, forcing_upper_bound=forcing, loop_gain_upper_bound=loop, loop_margin=margin, initial_form_contribution_upper_bound=initial_norm, initial_joint_contribution_upper_bound=initial_joint, forced_contribution_upper_bound=forced, form_norm_upper_bound=form, certified=margin > 0, ) @dataclass(frozen=True) class SinePortFormTracking: """Same-source phase evidence and a separate cancellation-aware form bound. The nested baseline is freshly reconstructed from all fourteen primitives. Its previous form envelope and verdict remain explicit. Mathematical channel flags are separate from the supplied-work policy required by overall status. No incoming baseline report or cached trajectory is accepted. """ baseline_certificate: SinePortRelaxation bridge_hessian_variation_upper_bound: Q | None even_bridge_forcing_upper_bound: Q | None odd_heat_bounds: _HeatFormBounds | None even_heat_bounds: _HeatFormBounds | None form_mean_error_floor: Q | None phase_mean_error_floor: Q | None all_time_form_error_upper_bound: Q | None all_time_phase_error_upper_bound: Q | None form_resolution_margin_bounds: I | None phase_resolution_margin_bounds: I | None all_time_envelopes_certified: bool form_resolution_certified: bool phase_resolution_certified: bool joint_resolution_certified: bool status: str unavailable_reasons: tuple[str, ...] resolution_limitations: tuple[str, ...] interval_method: str = INTERVAL_METHOD method: str = ( "fixed_reference_heat_filter_total_variation_and_finite_supremum_small_gain" ) scope: tuple[str, ...] = ( "same_complete_law_support_surrogate_source_and_resolution_primitives", "fresh_baseline_phase_parity_bounds_not_incoming_report_premises", "fixed_reference_phase_hessian_internal_cosines_and_unit_bridge_weights", "noncommuting_diffusion_and_phase_operators_keep_convolution_order", "time_varying_bridge_hessian_retained_as_explicit_even_forcing", "bounded_forcing_no_time_derivative_or_commuting_mode_assumption", "initial_form_and_joint_coordinate_exchange_retained", "uniform_all_time_fine_coordinate_envelopes_with_conserved_mean_floors", "declared_resolution_policy_not_observed_error_or_physical_sensor", "no_trajectory_solver_ideal_reset_probe_or_support_occurrence_rule", ) def to_dict(self): from ..sdk.relational_reports import _project return {"schema": "tnfr.sine-port-form-tracking.v1", "report": _project(self)} def assess_sine_port_form_tracking( *, classes, contacts, phase_origins, formation_time, relaxation_duration, form_error_bound, phase_error_bound, endpoint_radius, radius, decay_power, work_allowance, normalized_gap_lower_bound, phase_resolution_fraction, form_resolution_fraction, ) -> SinePortFormTracking: """Rebuild the source and refine its all-time form comparison bound. All mandatory primitive domains and work caps are owned by assess_sine_port_relaxation and are applied before any new arithmetic. The same phase envelope and declared origin-span allowances are retained. New form gains require positive finite-supremum loop margins on both parities; missing hypotheses return unavailable rather than an inferred small error. """ baseline = assess_sine_port_relaxation( classes=classes, contacts=contacts, phase_origins=phase_origins, formation_time=formation_time, relaxation_duration=relaxation_duration, form_error_bound=form_error_bound, phase_error_bound=phase_error_bound, endpoint_radius=endpoint_radius, radius=radius, decay_power=decay_power, work_allowance=work_allowance, normalized_gap_lower_bound=normalized_gap_lower_bound, phase_resolution_fraction=phase_resolution_fraction, form_resolution_fraction=form_resolution_fraction, ) bridge_variation = bridge_forcing = odd = even = error = margin = None envelopes = form_resolved = False if baseline.all_time_envelopes_certified: # Odd port values vanish. Only the even comparison sees the change # from the exact bridge Hessian to its fixed unit-weight reference. bridge_variation = baseline.edge_disagreement_norm_squared_upper_bound bridge_forcing = bridge_variation * baseline.even_bounds.phase_norm_upper_bound odd = _heat_form_bounds( gap=baseline.odd_bounds.gap_lower_bound, initial_norm=baseline.odd_bounds.initial_norm_upper_bound, forcing=baseline.odd_bounds.forcing_upper_bound, gamma_upper=baseline.gamma_bounds.hi, ) even = _heat_form_bounds( gap=baseline.even_bounds.gap_lower_bound, initial_norm=baseline.even_bounds.initial_norm_upper_bound, forcing=baseline.even_bounds.forcing_upper_bound + bridge_forcing, gamma_upper=baseline.gamma_bounds.hi, ) if odd.certified and even.certified: error = ( sqrt(I(odd.form_norm_upper_bound**2 + even.form_norm_upper_bound**2)).hi / sqrt(I(2)).lo + baseline.form_mean_error_floor ) margin = baseline.form_allowance_bounds - error envelopes = True form_resolved = margin.lo > 0 phase_resolved = baseline.phase_resolution_certified reasons = baseline.unavailable_reasons + ( () if envelopes else ("heat_form_envelopes_not_certified",) ) limitations = tuple( reason for condition, reason in ( (phase_resolved, "phase_resolution_not_certified"), (form_resolved, "form_resolution_not_certified"), ) if not condition ) status = "unavailable" if not reasons: status = ( "full" if phase_resolved and form_resolved else ( "phase_only" if phase_resolved else "form_only" if form_resolved else "envelopes_only" ) ) return SinePortFormTracking( baseline_certificate=baseline, bridge_hessian_variation_upper_bound=bridge_variation, even_bridge_forcing_upper_bound=bridge_forcing, odd_heat_bounds=odd, even_heat_bounds=even, form_mean_error_floor=baseline.form_mean_error_floor, phase_mean_error_floor=baseline.phase_mean_error_floor, all_time_form_error_upper_bound=error, all_time_phase_error_upper_bound=baseline.all_time_phase_error_upper_bound, form_resolution_margin_bounds=margin, phase_resolution_margin_bounds=baseline.phase_resolution_margin_bounds, all_time_envelopes_certified=envelopes, form_resolution_certified=form_resolved, phase_resolution_certified=phase_resolved, joint_resolution_certified=phase_resolved and form_resolved, status=status, unavailable_reasons=reasons, resolution_limitations=limitations, )