"""Detached mean and form budgets for finite ideal organized-source words. The prescribed word is Reception, Coherence, Silence on targets zero and one. The budget assumes the separately justified passive primary maps and reciprocal positive-capacity continuation. It executes no events or flow and does not establish grammar, the Silence capacity floor, occurrence or backend errors. """ from __future__ import annotations from dataclasses import dataclass from fractions import Fraction as Q from .._exact_time import exact_or_represented_real as _exact from ..mathematics._rational_interval import I, sqrt from ..operators.factor_contracts import validate_glyph_factor from ._organized_source_port import ( _derive_organized_source_port, _source_emission_geometry, ) _MAX_WORD_COUNT = 4096 _ENERGY_CEILING = Q(1, 100) @dataclass(frozen=True) class _OrganizedSourceReuseBudget: """Conditional bounds, not a receipt or permission to invoke an operator.""" reception_mix: Q silence_capacity_factor: Q initial_mean_bound: Q energy_budget: Q word_count: int initial_pair_capacity: Q final_pair_capacity: Q support_diameter: int target_degree: int reception_step: Q reception_mean_loss_coefficient: Q inverse_mean_denominator_squared_sum_bounds: I pair_weight_increment: Q form_range_bounds: I reception_mean_drift_bounds: I silence_mean_drift_bounds: I final_mean_absolute_upper_bound: Q form_absolute_upper_bound: Q reception_pressure_absolute_upper_bound: Q unit_form_rails_certified: bool scope: tuple[str, ...] = ( "fixed_45_node_90_unit_edge_support_and_targets_zero_one", "exact_positive_pair_capacity_initial_v_times_kappa_power_j_others_one", "initial_acute_cell_and_actual_excess_strictly_below_one_hundredth", "energy_budget_bounds_initial_excess_and_all_intermediate_excess", "reception_exact_unclipped_simultaneous_pair_map_with_declared_mix", "coherence_holds_forms_and_is_separately_proved_storage_nonincreasing", "silence_holds_forms_phases_support_and_multiplies_pair_capacity", "exact_reciprocal_shared_capacity_continuation_between_complete_words", "arbitrary_finite_waits_and_final_future_flow_with_capacity_held", "finite_word_count_is_a_work_budget_not_capacity_or_grammar_admission", "sum_defined_exactly_by_admitted_v_kappa_count_enclosed_on_dyadic_grid", "no_events_flows_runtime_roundoff_or_autonomous_selection_are_certified", ) def _support_diameter(geometry): """Derive distances from the shared support, without a second edge catalog.""" adjacency = {node: set() for node in geometry.node_order} for left, right, _ in geometry.weighted_edges: adjacency[left].add(right) adjacency[right].add(left) diameter = 0 for origin in geometry.node_order: distances = {origin: 0} frontier = [origin] for node in frontier: for neighbor in adjacency[node]: if neighbor not in distances: distances[neighbor] = distances[node] + 1 frontier.append(neighbor) if len(distances) != len(adjacency): raise ValueError("organized-source support must be connected") diameter = max(diameter, max(distances.values())) return diameter def _assess_organized_source_reuse_budget( *, reception_mix, silence_capacity_factor, initial_mean_bound, energy_budget, word_count, initial_pair_capacity=Q(1), ): """Bound mean drift and form rails under the declared finite composition. All non-target capacities are one; the two targets start at ``v`` and have capacity ``v*kappa**j`` before word ``j``. The exact finite sum is ``sum((43*v*kappa**j + 2)**-2 for j in range(word_count))``. Its defining primitives are retained; outward dyadic accumulation avoids constructing the enormous common denominator of a collapsed rational sum. For ``a=beta/5`` and ``Q=q[0]+q[1]``, the Reception mean shift is ``-a*Q/(43*v+2)``. Its loss has the exact correlated component ``a*(1-2*a)*Q**2/2``. Cauchy's inequality bounds all Reception mean shifts using their *joint* loss budget, not a fresh copy per event. Silence changes only the weighting of the same forms. Those pair-weight increments telescope, bounding total mean drift by their net increment times the common form-range bound. ``energy_budget`` may equal 1/100 as an upper bound, but actual states must satisfy the strict acute-cell excess hypothesis. Geometric retention, passivity of Coherence, live policies and represented defects are separate obligations. A failed sufficient rail check does not prove a rail exit. """ if type(word_count) is not int or not 0 <= word_count <= _MAX_WORD_COUNT: raise ValueError("word_count must be an integer between zero and 4096") values = { name: _exact(value, name) for name, value in ( ("reception_mix", reception_mix), ("silence_capacity_factor", silence_capacity_factor), ("initial_mean_bound", initial_mean_bound), ("energy_budget", energy_budget), ("initial_pair_capacity", initial_pair_capacity), ) } beta = values["reception_mix"] kappa = values["silence_capacity_factor"] mean = values["initial_mean_bound"] energy = values["energy_budget"] initial_capacity = values["initial_pair_capacity"] for name, key in ( ("reception_mix", "EN_mix"), ("silence_capacity_factor", "SHA_vf_factor"), ): if Q(validate_glyph_factor(key, values[name])) != values[name]: raise ValueError(f"{name} must be the exact represented runtime factor") if kappa <= 0 or initial_capacity <= 0: raise ValueError("continued pair capacities must be strictly positive") if mean < 0: raise ValueError("initial_mean_bound must be nonnegative") if not 0 <= energy <= _ENERGY_CEILING: raise ValueError("energy_budget must lie between zero and one hundredth") geometry = _derive_organized_source_port() valid, *_ = _source_emission_geometry(geometry) if not valid: raise ValueError("the organized-source support contract is required") diameter = _support_diameter(geometry) if diameter != 7 or geometry.support_degrees[:2] != (5, 5): raise ValueError("the diameter-seven, degree-five target support is required") a = beta / 5 coefficient = 2 * a / (1 - 2 * a) denominator_sum = I(0) capacity_bounds = I(initial_capacity) for _ in range(word_count): denominator_sum += 1 / (43 * capacity_bounds + 2) ** 2 capacity_bounds *= kappa final_capacity = initial_capacity * kappa**word_count pair_weight_increment = 2 / (43 * final_capacity + 2) - 2 / ( 43 * initial_capacity + 2 ) form_range = sqrt(I(2 * diameter * energy)) reception_drift = sqrt(energy * coefficient * denominator_sum) silence_drift = pair_weight_increment * form_range mean_bound = mean + reception_drift.hi + silence_drift.hi form_bound = mean_bound + form_range.hi degree = geometry.support_degrees[0] pressure_bound = (sqrt(I(2 * degree * energy)) + degree * geometry.gamma_bounds) / 4 return _OrganizedSourceReuseBudget( reception_mix=beta, silence_capacity_factor=kappa, initial_mean_bound=mean, energy_budget=energy, word_count=word_count, initial_pair_capacity=initial_capacity, final_pair_capacity=final_capacity, support_diameter=diameter, target_degree=degree, reception_step=a, reception_mean_loss_coefficient=coefficient, inverse_mean_denominator_squared_sum_bounds=denominator_sum, pair_weight_increment=pair_weight_increment, form_range_bounds=form_range, reception_mean_drift_bounds=reception_drift, silence_mean_drift_bounds=silence_drift, final_mean_absolute_upper_bound=mean_bound, form_absolute_upper_bound=form_bound, reception_pressure_absolute_upper_bound=pressure_bound.hi, unit_form_rails_certified=form_bound < 1, )