"""Independent loss, weighted-mean and finite-sum checks without events or flow.""" from dataclasses import replace from fractions import Fraction as Q import mpmath import networkx as nx import pytest from tnfr.operators.factor_contracts import canonical_glyph_factor_defaults from tnfr.physics import _organized_source_reuse_budget as owner from tnfr.physics._organized_source_port import _derive_organized_source_port @pytest.fixture(scope="module") def factors(): source = canonical_glyph_factor_defaults() return { "reception_mix": Q(source["EN_mix"]), "silence_capacity_factor": Q(source["SHA_vf_factor"]), } def _budget(factors, **overrides): parameters = dict( **factors, initial_mean_bound=Q(1, 30), energy_budget=Q(1, 100), word_count=56, ) parameters.update(overrides) return owner._assess_organized_source_reuse_budget(**parameters) def _mean(form, capacity): weights = (1 / capacity, 1 / capacity) + (Q(1),) * 43 return sum((weight * x for weight, x in zip(weights, form)), Q(0)) / sum( weights, Q(0) ) def test_support_diameter_from_independent_shortest_paths(factors): geometry = _derive_organized_source_port() graph = nx.Graph() graph.add_edges_from((a, b) for a, b, _ in geometry.weighted_edges) report = _budget(factors) assert nx.diameter(graph) == report.support_diameter == 7 assert graph.degree(0) == graph.degree(1) == report.target_degree == 5 def test_exact_finite_sum_is_enclosed_without_a_collapsed_report_denominator(factors): report = _budget(factors) kappa = report.silence_capacity_factor exact_sum = sum((1 / (43 * kappa**j + 2) ** 2 for j in range(56)), Q(0)) assert report.inverse_mean_denominator_squared_sum_bounds.contains(exact_sum) assert report.inverse_mean_denominator_squared_sum_bounds.width < Q(1, 10**32) assert report.final_pair_capacity == kappa**56 assert report.pair_weight_increment == 2 / (43 * kappa**56 + 2) - Q(2, 45) assert report.reception_mean_loss_coefficient == ( 2 * report.reception_step / (1 - 2 * report.reception_step) ) def _mp(value): return mpmath.mpf(value.numerator) / value.denominator def test_high_precision_oracle_and_coarse_56_word_domain(factors): report = _budget(factors) with mpmath.workdps(80): beta, kappa = map(_mp, (report.reception_mix, report.silence_capacity_factor)) a, energy = beta / 5, _mp(report.energy_budget) summed = mpmath.fsum(1 / (43 * kappa**j + 2) ** 2 for j in range(56)) radius = mpmath.sqrt(14 * energy) en = mpmath.sqrt(energy * 2 * a / (1 - 2 * a) * summed) sha = (2 / (43 * kappa**56 + 2) - mpmath.mpf(2) / 45) * radius total = _mp(report.initial_mean_bound) + en + sha + radius pressure = (mpmath.sqrt(10 * energy) + 5 / (1023 * mpmath.pi)) / 4 assert _mp(report.form_absolute_upper_bound) >= total assert _mp(report.form_absolute_upper_bound) - total < mpmath.mpf("1e-33") assert _mp(report.reception_pressure_absolute_upper_bound) >= pressure assert report.form_absolute_upper_bound < Q(107, 120) < Q(9, 10) assert report.reception_pressure_absolute_upper_bound < Q(81, 1000) assert report.unit_form_rails_certified @pytest.mark.parametrize("capacity", (Q(1), Q(1, 7), Q(3))) def test_exact_pair_mean_jumps_and_correlated_event_loss(factors, capacity): geometry = _derive_organized_source_port() form = tuple(Q((7 * node) % 17 - 8, 128) for node in range(45)) gradient = [Q(0)] * 45 for a, b, _ in geometry.weighted_edges: gradient[a] += form[a] - form[b] gradient[b] += form[b] - form[a] a = factors["reception_mix"] / 5 successor = list(form) for node in (0, 1): successor[node] -= a * gradient[node] q_sum, q_difference = gradient[0] + gradient[1], gradient[0] - gradient[1] before = sum( ((form[b] - form[a_]) ** 2 / 2 for a_, b, _ in geometry.weighted_edges), Q(0), ) after = sum( ( (successor[b] - successor[a_]) ** 2 / 2 for a_, b, _ in geometry.weighted_edges ), Q(0), ) loss = a * ((1 - 2 * a) * q_sum**2 + (1 - 3 * a) * q_difference**2) / 2 assert before - after == loss > 0 assert _mean(successor, capacity) - _mean(form, capacity) == ( -a * q_sum / (43 * capacity + 2) ) next_capacity = capacity * factors["silence_capacity_factor"] pair_mean = (successor[0] + successor[1]) / 2 other_mean = sum(successor[2:], Q(0)) / 43 weight_change = 2 / (43 * next_capacity + 2) - 2 / (43 * capacity + 2) assert _mean(successor, next_capacity) - _mean(successor, capacity) == ( weight_change * (pair_mean - other_mean) ) def test_joint_cauchy_loss_budget_and_telescope_not_per_event_energy(factors): report = _budget( factors, initial_pair_capacity=Q(1, 2), word_count=4, energy_budget=Q(1, 1000) ) a, kappa = report.reception_step, report.silence_capacity_factor # Independent signed gradient sums; the same joint event losses pay for # these four shifts. No extra copy of the energy budget is used per word. sums = (Q(1, 100), Q(-1, 200), Q(1, 300), Q(-1, 400)) losses = tuple(a * (1 - 2 * a) * value**2 / 2 for value in sums) exact_drift = sum( ( abs(a * value / (43 * Q(1, 2) * kappa**j + 2)) for j, value in enumerate(sums) ), Q(0), ) assert sum(losses, Q(0)) < report.energy_budget assert exact_drift <= report.reception_mean_drift_bounds.hi increments = tuple( 2 / (43 * Q(1, 2) * kappa ** (j + 1) + 2) - 2 / (43 * Q(1, 2) * kappa**j + 2) for j in range(4) ) assert all(increment > 0 for increment in increments) assert sum(increments, Q(0)) == report.pair_weight_increment def test_zero_words_and_zero_energy_have_no_invented_event_drift(factors): no_words = _budget(factors, word_count=0, initial_pair_capacity=Q(1, 3)) assert no_words.inverse_mean_denominator_squared_sum_bounds.contains(0) assert no_words.reception_mean_drift_bounds.hi == 0 assert no_words.silence_mean_drift_bounds.hi == 0 assert no_words.pair_weight_increment == 0 assert no_words.final_pair_capacity == Q(1, 3) zero_energy = _budget(factors, energy_budget=0) assert zero_energy.form_absolute_upper_bound == zero_energy.initial_mean_bound assert zero_energy.reception_mean_drift_bounds.hi == 0 assert zero_energy.silence_mean_drift_bounds.hi == 0 def test_large_finite_budget_and_tiny_capacity_remain_outward_and_available(factors): report = _budget( factors, silence_capacity_factor=Q(1, 2), initial_pair_capacity=Q(1, 2**1100), word_count=4096, ) assert report.final_pair_capacity == Q(1, 2**5196) assert report.inverse_mean_denominator_squared_sum_bounds.hi <= 1024 assert report.inverse_mean_denominator_squared_sum_bounds.lo > Q(1023) assert not report.unit_form_rails_certified assert report.reception_pressure_absolute_upper_bound < Q(81, 1000) assert "finite_word_count_is_a_work_budget_not_capacity_or_grammar_admission" in ( report.scope ) @pytest.mark.parametrize("name", ("reception_mix", "silence_capacity_factor")) def test_exact_factor_association_rejects_unrepresented_fraction(factors, name): with pytest.raises(ValueError, match="exact represented runtime factor"): _budget(factors, **{name: Q(1, 3)}) @pytest.mark.parametrize( "name,value", ( ("word_count", True), ("word_count", Q(1)), ("word_count", -1), ("word_count", 4097), ("initial_mean_bound", -1), ("energy_budget", Q(-1, 100)), ("energy_budget", Q(11, 1000)), ("initial_pair_capacity", 0), ("initial_pair_capacity", -1), ("silence_capacity_factor", 0), ("silence_capacity_factor", 1), ("reception_mix", 0), ("reception_mix", 2), ), ) def test_domain_rejections(factors, name, value): with pytest.raises((TypeError, ValueError)): _budget(factors, **{name: value}) @pytest.mark.parametrize( "name", ( "initial_mean_bound", "energy_budget", "initial_pair_capacity", "silence_capacity_factor", "reception_mix", ), ) @pytest.mark.parametrize("value", (True, float("nan"), float("inf"))) def test_scalar_admission_before_geometry(factors, monkeypatch, name, value): def forbidden(): pytest.fail("invalid primitives reached geometry") monkeypatch.setattr(owner, "_derive_organized_source_port", forbidden) with pytest.raises((TypeError, ValueError)): _budget(factors, **{name: value}) def test_changed_support_cannot_reuse_diameter_or_coefficients(factors, monkeypatch): geometry = _derive_organized_source_port() changed = replace(geometry, weighted_edges=geometry.weighted_edges[:-1]) monkeypatch.setattr(owner, "_derive_organized_source_port", lambda: changed) with pytest.raises(ValueError, match="support contract"): _budget(factors)