Aggregate Checker Results
Generated: 2026-08-23T07:48:40.495014+00:00
All scripts use Python's standard library only.
1. tree_context_baseline_check.py — PASS
Elapsed: 0.039 seconds
PASS tree-context finite corroboration
{'sharpness_family': [{'states': 2, 'first_separation_depth': 0}, {'states': 3, 'first_separation_depth': 1}, {'states': 4, 'first_separation_depth': 2}, {'states': 5, 'first_separation_depth': 3}, {'states': 6, 'first_separation_depth': 4}, {'states': 7, 'first_separation_depth': 5}, {'states': 8, 'first_separation_depth': 6}, {'states': 9, 'first_separation_depth': 7}, {'states': 10, 'first_separation_depth': 8}, {'states': 11, 'first_separation_depth': 9}, {'states': 12, 'first_separation_depth': 10}], 'unreachable_parameter_counterexample': {'reachable_parameter_relation': 'p equivalent q', 'all_state_parameter_relation': 'p and q first separate at depth 1', 'distinguishing_polynomial': 'f(hole,r)'}, 'scope': 'finite regression evidence only; general statements use written proofs'}2. sat_residual_obdd_check.py — PASS
Elapsed: 0.161 seconds
PASS SAT residual/OBDD finite corroboration
{'family': 'AND_i (x_i OR z OR w)', 'order': 'x_1,...,x_m,z,w', 'results': [{'m': 1, 'raw_x_prefix_tree_nodes': 3, 'obdd_nonterminals': 3, 'obdd_nodes_with_terminals': 5, 'distinct_x_prefix_obdd_roots': 3, 'final_x_cut': {'x_prefix_length': 1, 'raw_histories': 2, 'semantic_residuals': 2, 'obdd_cut_states': 2, 'origin_labelled_residual_cnfs': 2, 'duplicate_multiset_residual_cnfs': 2, 'duplicate_deleted_residual_cnfs': 2}}, {'m': 2, 'raw_x_prefix_tree_nodes': 7, 'obdd_nonterminals': 4, 'obdd_nodes_with_terminals': 6, 'distinct_x_prefix_obdd_roots': 4, 'final_x_cut': {'x_prefix_length': 2, 'raw_histories': 4, 'semantic_residuals': 2, 'obdd_cut_states': 2, 'origin_labelled_residual_cnfs': 4, 'duplicate_multiset_residual_cnfs': 3, 'duplicate_deleted_residual_cnfs': 2}}, {'m': 3, 'raw_x_prefix_tree_nodes': 15, 'obdd_nonterminals': 5, 'obdd_nodes_with_terminals': 7, 'distinct_x_prefix_obdd_roots': 5, 'final_x_cut': {'x_prefix_length': 3, 'raw_histories': 8, 'semantic_residuals': 2, 'obdd_cut_states': 2, 'origin_labelled_residual_cnfs': 8, 'duplicate_multiset_residual_cnfs': 4, 'duplicate_deleted_residual_cnfs': 2}}, {'m': 4, 'raw_x_prefix_tree_nodes': 31, 'obdd_nonterminals': 6, 'obdd_nodes_with_terminals': 8, 'distinct_x_prefix_obdd_roots': 6, 'final_x_cut': {'x_prefix_length': 4, 'raw_histories': 16, 'semantic_residuals': 2, 'obdd_cut_states': 2, 'origin_labelled_residual_cnfs': 16, 'duplicate_multiset_residual_cnfs': 5, 'duplicate_deleted_residual_cnfs': 2}}, {'m': 5, 'raw_x_prefix_tree_nodes': 63, 'obdd_nonterminals': 7, 'obdd_nodes_with_terminals': 9, 'distinct_x_prefix_obdd_roots': 7, 'final_x_cut': {'x_prefix_length': 5, 'raw_histories': 32, 'semantic_residuals': 2, 'obdd_cut_states': 2, 'origin_labelled_residual_cnfs': 32, 'duplicate_multiset_residual_cnfs': 6, 'duplicate_deleted_residual_cnfs': 2}}, {'m': 6, 'raw_x_prefix_tree_nodes': 127, 'obdd_nonterminals': 8, 'obdd_nodes_with_terminals': 10, 'distinct_x_prefix_obdd_roots': 8, 'final_x_cut': {'x_prefix_length': 6, 'raw_histories': 64, 'semantic_residuals': 2, 'obdd_cut_states': 2, 'origin_labelled_residual_cnfs': 64, 'duplicate_multiset_residual_cnfs': 7, 'duplicate_deleted_residual_cnfs': 2}}, {'m': 7, 'raw_x_prefix_tree_nodes': 255, 'obdd_nonterminals': 9, 'obdd_nodes_with_terminals': 11, 'distinct_x_prefix_obdd_roots': 9, 'final_x_cut': {'x_prefix_length': 7, 'raw_histories': 128, 'semantic_residuals': 2, 'obdd_cut_states': 2, 'origin_labelled_residual_cnfs': 128, 'duplicate_multiset_residual_cnfs': 8, 'duplicate_deleted_residual_cnfs': 2}}, {'m': 8, 'raw_x_prefix_tree_nodes': 511, 'obdd_nonterminals': 10, 'obdd_nodes_with_terminals': 12, 'distinct_x_prefix_obdd_roots': 10, 'final_x_cut': {'x_prefix_length': 8, 'raw_histories': 256, 'semantic_residuals': 2, 'obdd_cut_states': 2, 'origin_labelled_residual_cnfs': 256, 'duplicate_multiset_residual_cnfs': 9, 'duplicate_deleted_residual_cnfs': 2}}, {'m': 9, 'raw_x_prefix_tree_nodes': 1023, 'obdd_nonterminals': 11, 'obdd_nodes_with_terminals': 13, 'distinct_x_prefix_obdd_roots': 11, 'final_x_cut': {'x_prefix_length': 9, 'raw_histories': 512, 'semantic_residuals': 2, 'obdd_cut_states': 2, 'origin_labelled_residual_cnfs': 512, 'duplicate_multiset_residual_cnfs': 10, 'duplicate_deleted_residual_cnfs': 2}}, {'m': 10, 'raw_x_prefix_tree_nodes': 2047, 'obdd_nonterminals': 12, 'obdd_nodes_with_terminals': 14, 'distinct_x_prefix_obdd_roots': 12, 'final_x_cut': {'x_prefix_length': 10, 'raw_histories': 1024, 'semantic_residuals': 2, 'obdd_cut_states': 2, 'origin_labelled_residual_cnfs': 1024, 'duplicate_multiset_residual_cnfs': 11, 'duplicate_deleted_residual_cnfs': 2}}], 'scope': 'finite regression evidence only; all-size claims use written proofs'}3. sat_graded_congruence_check.py — PASS
Elapsed: 9.751 seconds
PASS graded SAT-prefix finite corroboration
{'boolean_functions_checked': 65812, 'by_arity': {1: 4, 2: 16, 3: 256, 4: 65536}, 'recursive_pair_checks': 5576020, 'compatible_extension_checks': 3905720, 'hostile_witnesses': ['grade-erased lifted residual equality is not append-compatible', 'ROBDD node alone does not determine a uniform next-bit update'], 'scope': 'finite corroboration only; the general theorem is written'}4. streaming_position_quotient_check.py — PASS
Elapsed: 0.149 seconds
j= 1 states= 3 refinement_rounds= 1 max_distinguishing_depth= 0
j= 2 states= 4 refinement_rounds= 2 max_distinguishing_depth= 1
j= 3 states= 5 refinement_rounds= 3 max_distinguishing_depth= 2
j= 4 states= 6 refinement_rounds= 4 max_distinguishing_depth= 3
j= 5 states= 7 refinement_rounds= 5 max_distinguishing_depth= 4
j= 6 states= 8 refinement_rounds= 6 max_distinguishing_depth= 5
j= 7 states= 9 refinement_rounds= 7 max_distinguishing_depth= 6
j= 8 states=10 refinement_rounds= 8 max_distinguishing_depth= 7
j= 9 states=11 refinement_rounds= 9 max_distinguishing_depth= 8
j=10 states=12 refinement_rounds=10 max_distinguishing_depth= 9
j=11 states=13 refinement_rounds=11 max_distinguishing_depth=10
j=12 states=14 refinement_rounds=12 max_distinguishing_depth=11
j=13 states=15 refinement_rounds=13 max_distinguishing_depth=12
j=14 states=16 refinement_rounds=14 max_distinguishing_depth=13
j=15 states=17 refinement_rounds=15 max_distinguishing_depth=14
j=16 states=18 refinement_rounds=16 max_distinguishing_depth=15
j=17 states=19 refinement_rounds=17 max_distinguishing_depth=16
j=18 states=20 refinement_rounds=18 max_distinguishing_depth=17
j=19 states=21 refinement_rounds=19 max_distinguishing_depth=18
j=20 states=22 refinement_rounds=20 max_distinguishing_depth=19
j=21 states=23 refinement_rounds=21 max_distinguishing_depth=20
j=22 states=24 refinement_rounds=22 max_distinguishing_depth=21
j=23 states=25 refinement_rounds=23 max_distinguishing_depth=22
j=24 states=26 refinement_rounds=24 max_distinguishing_depth=23
j=25 states=27 refinement_rounds=25 max_distinguishing_depth=24
j=26 states=28 refinement_rounds=26 max_distinguishing_depth=25
j=27 states=29 refinement_rounds=27 max_distinguishing_depth=26
j=28 states=30 refinement_rounds=28 max_distinguishing_depth=27
j=29 states=31 refinement_rounds=29 max_distinguishing_depth=28
j=30 states=32 refinement_rounds=30 max_distinguishing_depth=29
j=31 states=33 refinement_rounds=31 max_distinguishing_depth=30
j=32 states=34 refinement_rounds=32 max_distinguishing_depth=31
j=33 states=35 refinement_rounds=33 max_distinguishing_depth=32
j=34 states=36 refinement_rounds=34 max_distinguishing_depth=33
j=35 states=37 refinement_rounds=35 max_distinguishing_depth=34
j=36 states=38 refinement_rounds=36 max_distinguishing_depth=35
j=37 states=39 refinement_rounds=37 max_distinguishing_depth=36
j=38 states=40 refinement_rounds=38 max_distinguishing_depth=37
j=39 states=41 refinement_rounds=39 max_distinguishing_depth=38
j=40 states=42 refinement_rounds=40 max_distinguishing_depth=39
j=41 states=43 refinement_rounds=41 max_distinguishing_depth=40
j=42 states=44 refinement_rounds=42 max_distinguishing_depth=41
j=43 states=45 refinement_rounds=43 max_distinguishing_depth=42
j=44 states=46 refinement_rounds=44 max_distinguishing_depth=43
j=45 states=47 refinement_rounds=45 max_distinguishing_depth=44
j=46 states=48 refinement_rounds=46 max_distinguishing_depth=45
j=47 states=49 refinement_rounds=47 max_distinguishing_depth=46
j=48 states=50 refinement_rounds=48 max_distinguishing_depth=47
j=49 states=51 refinement_rounds=49 max_distinguishing_depth=48
j=50 states=52 refinement_rounds=50 max_distinguishing_depth=49
j=51 states=53 refinement_rounds=51 max_distinguishing_depth=50
j=52 states=54 refinement_rounds=52 max_distinguishing_depth=51
j=53 states=55 refinement_rounds=53 max_distinguishing_depth=52
j=54 states=56 refinement_rounds=54 max_distinguishing_depth=53
j=55 states=57 refinement_rounds=55 max_distinguishing_depth=54
j=56 states=58 refinement_rounds=56 max_distinguishing_depth=55
j=57 states=59 refinement_rounds=57 max_distinguishing_depth=56
j=58 states=60 refinement_rounds=58 max_distinguishing_depth=57
j=59 states=61 refinement_rounds=59 max_distinguishing_depth=58
j=60 states=62 refinement_rounds=60 max_distinguishing_depth=59
j=61 states=63 refinement_rounds=61 max_distinguishing_depth=60
j=62 states=64 refinement_rounds=62 max_distinguishing_depth=61
j=63 states=65 refinement_rounds=63 max_distinguishing_depth=62
j=64 states=66 refinement_rounds=64 max_distinguishing_depth=63
PASS j=1..64; audited unordered state pairs=479045. rewriting_disjoint_square_check.py — PASS
Elapsed: 1.964 seconds
PASS unary rewriting disjoint-square corroboration
{'system': ['aa -> a'], 'results': [{'n': 1, 'raw_histories': 1, 'disjoint_square_classes': 1, 'expected_catalan': 1, 'disjoint_square_edges': 0, 'overlap_edges': 0, 'augmented_history_edges': 0, 'tree_rotation_edges': 0, 'classes_after_overlap_cell': 1}, {'n': 2, 'raw_histories': 1, 'disjoint_square_classes': 1, 'expected_catalan': 1, 'disjoint_square_edges': 0, 'overlap_edges': 0, 'augmented_history_edges': 0, 'tree_rotation_edges': 0, 'classes_after_overlap_cell': 1}, {'n': 3, 'raw_histories': 2, 'disjoint_square_classes': 2, 'expected_catalan': 2, 'disjoint_square_edges': 0, 'overlap_edges': 1, 'augmented_history_edges': 1, 'tree_rotation_edges': 1, 'classes_after_overlap_cell': 1}, {'n': 4, 'raw_histories': 6, 'disjoint_square_classes': 5, 'expected_catalan': 5, 'disjoint_square_edges': 1, 'overlap_edges': 5, 'augmented_history_edges': 6, 'tree_rotation_edges': 5, 'classes_after_overlap_cell': 1}, {'n': 5, 'raw_histories': 24, 'disjoint_square_classes': 14, 'expected_catalan': 14, 'disjoint_square_edges': 10, 'overlap_edges': 26, 'augmented_history_edges': 36, 'tree_rotation_edges': 21, 'classes_after_overlap_cell': 1}, {'n': 6, 'raw_histories': 120, 'disjoint_square_classes': 42, 'expected_catalan': 42, 'disjoint_square_edges': 86, 'overlap_edges': 154, 'augmented_history_edges': 240, 'tree_rotation_edges': 84, 'classes_after_overlap_cell': 1}, {'n': 7, 'raw_histories': 720, 'disjoint_square_classes': 132, 'expected_catalan': 132, 'disjoint_square_edges': 756, 'overlap_edges': 1044, 'augmented_history_edges': 1800, 'tree_rotation_edges': 330, 'classes_after_overlap_cell': 1}, {'n': 8, 'raw_histories': 5040, 'disjoint_square_classes': 429, 'expected_catalan': 429, 'disjoint_square_edges': 7092, 'overlap_edges': 8028, 'augmented_history_edges': 15120, 'tree_rotation_edges': 1287, 'classes_after_overlap_cell': 1}, {'n': 9, 'raw_histories': 40320, 'disjoint_square_classes': 1430, 'expected_catalan': 1430, 'disjoint_square_edges': 71856, 'overlap_edges': 69264, 'augmented_history_edges': 141120, 'tree_rotation_edges': 5005, 'classes_after_overlap_cell': 1}], 'total_histories_checked': 46234, 'smallest_overlap_obstruction': 'a^3', 'scope': 'finite corroboration only; all-n claims use written proofs'}6. rewriting_pentagon_coherence_check.py — PASS
Elapsed: 0.061 seconds
PASS unary rewriting a^4 pentagon corroboration
{'raw_history_graph': {'vertices': 6, 'edges': 6, 'disjoint_edges': 1, 'overlap_edges': 5, 'shape': 'C6', 'first_betti_number': 1}, 'small_rotation_graphs': [{'leaves': 1, 'vertices': 1, 'edges': 0, 'components': 1, 'cycle_rank': 0}, {'leaves': 2, 'vertices': 1, 'edges': 0, 'components': 1, 'cycle_rank': 0}, {'leaves': 3, 'vertices': 2, 'edges': 1, 'components': 1, 'cycle_rank': 0}, {'leaves': 4, 'vertices': 5, 'edges': 5, 'components': 1, 'cycle_rank': 1}], 'pentagon_cycle': ['(((ab)c)d)', '((ab)(cd))', '(a(b(cd)))', '(a((bc)d))', '((a(bc))d)'], 'edge_support_sizes': [3, 3, 4, 4, 4], 'independent_interchange_pairs': 0, 'nondegenerate_commuting_rotation_squares': 0, 'unquotiented_a4_histories': 6, 'a4_tree_fibre_sizes': [1, 1, 1, 1, 2], 'hostile_a5_rotation_vertices': 14, 'hostile_a5_commuting_squares': 3, 'hostile_a5_disjoint_leaf_pairs': 0, 'right_rotation_paths': [['(((ab)c)d)', '((a(bc))d)', '(a((bc)d))', '(a(b(cd)))'], ['(((ab)c)d)', '((ab)(cd))', '(a(b(cd)))']], 'right_rotation_path_lengths': [2, 3], 'H1_rank_before_filling': 1, 'H1_rank_after_one_primitive_pentagon_filling': 0, 'rank_boundary_1': 4, 'rank_boundary_2': 1, 'scope': 'finite corroboration only; homotopy claims use the written proof'}7. rewriting_a5_cell_complex_check.py — PASS
Elapsed: 0.052 seconds
PASS unary rewriting a^5 cell-complex corroboration
{'vertices': 14, 'rotation_edges': 21, 'pentagon_faces': 6, 'square_faces': 3, 'face_intervals': {'pentagons': [(1, 2), (2, 3), (3, 4), (4, 5), (1, 4), (2, 5)], 'squares': [(1, 3), (2, 4), (3, 5)]}, 'edge_face_incidence': 'every edge lies in exactly two faces', 'euler_characteristic': 2, 'rank_boundary_1': 13, 'rank_boundary_2': 8, 'H1_rank': 0, 'H2_rank': 1, 'omitted_face': (1, 2), 'face_collapse_order': ((1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)), 'remaining_graph': {'vertices': 14, 'edges': 13, 'components': 1, 'shape': 'tree'}, 'collapse_certificate': [{'face': (1, 3), 'free_edge': ['((((AB)C)D)E)', '(((AB)C)(DE))']}, {'face': (1, 4), 'free_edge': ['((((AB)C)D)E)', '(((A(BC))D)E)']}, {'face': (2, 3), 'free_edge': ['(((A(BC))D)E)', '((A((BC)D))E)']}, {'face': (2, 4), 'free_edge': ['((A((BC)D))E)', '((A(B(CD)))E)']}, {'face': (2, 5), 'free_edge': ['(A(((BC)D)E))', '(A((B(CD))E))']}, {'face': (3, 4), 'free_edge': ['(((AB)(CD))E)', '((A(B(CD)))E)']}, {'face': (3, 5), 'free_edge': ['((AB)((CD)E))', '((AB)(C(DE)))']}, {'face': (4, 5), 'free_edge': ['(((AB)C)(DE))', '((A(BC))(DE))']}], 'scope': 'finite corroboration; completeness and collapse use written proof'}8. tree_automaton_disjoint_update_check.py — PASS
Elapsed: 0.189 seconds
PASS deterministic bottom-up disjoint-update corroboration
{'exhaustive_semantic_cache_cases': 6144, 'structural_leaf_pairs_checked': 43435, 'largest_checked_sequential_to_batch_ratio': (1.8, (8, 'LLLLLLLL', 'LLLLLLLR', 18, 10)), 'state_dependent_disjoint_counterexample': {'U_then_V': {'L': 0, 'R': 1}, 'V_then_U': {'L': 1, 'R': 1}}, 'overlapping_fixed_counterexample': {'U_then_V': (0, 1), 'V_then_U': (1, 1)}, 'scope': 'finite corroboration only; the general theorem uses the written proof'}9. tree_automaton_early_stop_order_check.py — PASS
Elapsed: 0.036 seconds
PASS deterministic tree-automaton early-stop order audit
{'states': 2, 'merge_table_00_01_10_11': (0, 1, 0, 0), 'smallest_witness': {'h': 1, 'tree_depth': 2, 'left_then_right_work': 4, 'right_then_left_work': 6, 'gap': 2, 'root_observation_traces': {'left_then_right': [0, 0], 'right_then_left': [0, 0]}}, 'largest_checked_h': {'h': 128, 'left_then_right': 4, 'right_then_left': 260, 'gap': 256, 'ratio': 65.0}, 'boolean_transition_corner_cases': 576, 'maximum_gap_by_h_0_through_8': {0: 0, 1: 2, 2: 4, 3: 6, 4: 8, 5: 10, 6: 12, 7: 14, 8: 16}, 'maximal_h1_boolean_witnesses': 16, 'scope': 'finite corroboration; all-h sharpness uses the written proof'}10. tree_automaton_unary_chain_flatness_check.py — PASS
Elapsed: 1.158 seconds
PASS unary-chain early-stopping flatness corroboration
{'partition_lattice_size': 15, 'multichains_checked': 5384, 'flat_multichains': 1724, 'counts_by_height': {1: 15, 2: 60, 3: 154, 4: 315, 5: 561, 6: 910, 7: 1380, 8: 1989}, 'maximum_gap_by_height': {1: 2, 2: 4, 3: 6, 4: 8, 5: 10, 6: 12, 7: 14, 8: 16}, 'verified_properties': ['ultrapseudometric strong triangle inequality', 'no sign cancellation across nested levels', 'total flatness iff levelwise flatness', 'levelwise flatness iff endpoint-class membership balance', 'sharp absolute gap 2h'], 'scope': 'finite four-corner corroboration; general theorem is written'}11. tree_automaton_lca_composition_check.py — PASS
Elapsed: 10.482 seconds
PASS Run 11 LCA-composition audit
{'cases': 2182400, 'branch_summaries': 20, 'boolean_lca_transitions': 16, 'common_chain_heights': '0..4', 'maximum_gaps_by_height': {0: 0, 1: 2, 2: 4, 3: 6, 4: 8}, 'arrival_only_obstruction': 'XOR gap 0 versus (not-left AND right) gap 2'}12. tree_automaton_persistent_dag_alias_check.py — PASS
Elapsed: 8.034 seconds
PASS persistent-DAG occurrence-alias audit
{'exhaustive_leaf_update_cases': 320768, 'cases_with_identical_target_node': 160384, 'aggregate_leaf_identity_reductions': 25024, 'verified': ['path-copy unfolding equals occurrence substitution', 'incomparable fixed occurrence updates commute', 'fresh allocation is exactly depth(u)+depth(v)', 'shared and unshared transition-evaluation counts agree', 'destructive node-identity updates need not commute', 'global canonical reuse can defeat exact allocation counts'], 'scope': 'Boolean leaves, binary trees through five leaves; general alias-transparency theorem is proved separately'}13. tree_automaton_hashcons_allocation_check.py — PASS
Elapsed: 0.119 seconds
PASS retained hash-cons allocation-order audit
{'exhaustive_cases': 20865, 'genuine_two_update_cases': 9248, 'allocation_asymmetric_cases': 4624, 'enriched_endpoint_mismatches': 6936, 'flat_but_enriched_mismatches': 2312, 'minimum_nullary_payload_table_nodes': 4, 'first_minimum_nullary_payload_witness': {'children': 2, 'table': [(0, 0), (1, 0)], 'updates': (0, 1, 0, 1), 'UV': 1, 'VU': 2}, 'general_acyclic_compound_payload_witness_nodes': 3, 'verified': ['general two-order allocation formulas', 'membership-balance iff allocation-flatness for genuine updates', 'sharp absolute allocation gap one', 'no-op updates are allocation-flat', 'enriched table endpoints agree iff both intermediates pre-exist', 'allocation-flat paths can retain different equal-size tables', 'four-node initial witness is minimal with nullary payloads', 'three-node compound-payload witness is valid and asymmetric'], 'scope': 'one ordered binary root, one through three retained child identities, all canonical root-key subsets containing the current root; proof is separate'}14. tree_automaton_hashcons_height_two_check.py — PASS
Elapsed: 0.406 seconds
PASS height-two retained hash-cons allocation audit
{'abstract_cases': 118458, 'flat_cases': 81354, 'asymmetric_cases': 37104, 'endpoint_mismatches': 41820, 'flat_but_endpoint_mismatches': 4716, 'initial_membership_false_predictions': 37392, 'maximum_gap': 1, 'concrete_acyclic_collision_witness': {'initial_nodes': 4, 'UV': 2, 'VU': 3, 'both_exclusive_roots_initially_absent': True, 'cross_level_collision': 'r10 == q1'}, 'verified': ['exact common-set allocation formulas', 'coverage-balance iff allocation-flatness', 'sharp absolute gap one', 'exact enriched-table endpoint criterion', 'initial-H membership alone is insufficient with collisions'], 'scope': 'all equality patterns on five candidate roles over identity universes of size one through five and every initial subset'}15. tree_automaton_hashcons_spine_rank_check.py — PASS
Elapsed: 0.070 seconds
PASS arbitrary-height retained hash-cons spine-rank audit
{'by_exclusive_spine_length': {1: {'cases': 6, 'maximum_gap': 1}, 2: {'cases': 30, 'maximum_gap': 2}, 3: {'cases': 140, 'maximum_gap': 3}, 4: {'cases': 630, 'maximum_gap': 4}}, 'total_downward_closed_quotient_cases': 806, 'partitions_with_cross_chain_identity': 94, 'flat_cost_but_distinct_final_tables': 200, 'sharp_acyclic_witnesses_UV_VU': {1: (1, 0), 2: (2, 0), 3: (3, 0), 4: (4, 0), 5: (5, 0), 6: (6, 0), 7: (7, 0), 8: (8, 0), 9: (9, 0), 10: (10, 0), 11: (11, 0), 12: (12, 0)}, 'height_three_cross_level_collision_witness': {'UV': 4, 'VU': 5, 'collision': 'x1 == q1'}, 'unrestricted_cancellation_obstruction': {'biases': [1, -1], 'total_gap': 0, 'invalidity': 'x2 covered while required descendant x1 is uncovered'}, 'verified': ['common-set rank formulas', 'covered-prefix characterization', 'no opposite normalized level biases under descendant closure', 'flatness iff equal covered-prefix lengths', 'sharp gap equals exclusive spine length m', 'flat allocation need not imply equal retained tables']}16. tree_automaton_hashcons_dependency_poset_check.py — PASS
Elapsed: 2.785 seconds
PASS dependency-poset allocation and native-path audit
{'by_size': {1: {'naturally_labelled_transitive_posets': 1, 'chains': 1, 'nonchains': 0, 'ordered_equal_rank_cancelling_ideal_pairs': 0}, 2: {'naturally_labelled_transitive_posets': 2, 'chains': 1, 'nonchains': 1, 'ordered_equal_rank_cancelling_ideal_pairs': 2}, 3: {'naturally_labelled_transitive_posets': 7, 'chains': 1, 'nonchains': 6, 'ordered_equal_rank_cancelling_ideal_pairs': 28}, 4: {'naturally_labelled_transitive_posets': 40, 'chains': 1, 'nonchains': 39, 'ordered_equal_rank_cancelling_ideal_pairs': 452}, 5: {'naturally_labelled_transitive_posets': 357, 'chains': 1, 'nonchains': 356, 'ordered_equal_rank_cancelling_ideal_pairs': 9764}, 6: {'naturally_labelled_transitive_posets': 4824, 'chains': 1, 'nonchains': 4823, 'ordered_equal_rank_cancelling_ideal_pairs': 291956}}, 'total_posets': 5231, 'total_ordered_ideal_pairs': 2174862, 'total_equal_rank_cancelling_pairs': 302202, 'minimum_cancellation_size': 2, 'smallest_structural_cancellation_witness': {'exclusive_poset': 'two-element antichain', 'costs': {'X': 1, 'Y': 1}, 'local_biases': [-1, 1], 'net_gap': 0, 'local_l1': 2, 'final_tables_equal': False}, 'native_single_occurrence_path_copy': {'maximum_address_depth': 6, 'incomparable_update_position_pairs': 7359, 'ordered_first-update_path_checks': 14718, 'forked_exclusive_regions_found': 0}, 'verified': ['exact ideal-rank allocation formula', 'opposite local biases iff coverage ideals are incomparable', 'universal no-cancellation iff dependency poset is a chain', 'every finite nonchain has equal-rank incomparable ideals', 'two-element antichain is the smallest cancellation poset', 'single-occurrence path-copy exclusive regions remain chains']}17. sat_learned_resolvent_separation_check.py — PASS
Elapsed: 5.047 seconds
PASS minimal strict-3CNF learned-resolvent separation
{'named_witness': {'base': ((1, 2, 3), (1, 2, -3)), 'learned_resolvent': (1, 2), 'prefix': {1: False}, 'base_UP': ('open', {1: False}), 'learned_UP': ('satisfied', {1: False, 2: True}), 'minimum_DPLL_decisions': (1, 0)}, 'exhaustive_audit': {3: {'strict_clauses': 8, 'one_clause_entailed_clause_cases': 8, 'one_clause_separations': 0, 'two_clause_entailed_clause_cases': 68, 'two_clause_separations': 24}, 4: {'strict_clauses': 32, 'one_clause_entailed_clause_cases': 32, 'one_clause_separations': 0, 'two_clause_entailed_clause_cases': 1328, 'two_clause_separations': 672}}, 'verified': ['semantic residual equality', 'one-step resolution derivability', 'root unit-propagation separation', 'exact one-decision saving', 'one source clause cannot realize the separation']}18. sat_product_additivity_check.py — PASS
Elapsed: 6.770 seconds
PASS SAT product additivity and cross-block boundary
{'local_receipt_subset_cases': 126, 'semantic_truth_table_comparisons': 8, 'maximum_blocks_decision_checked': 6, 'maximum_blocks_semantics_checked': 4, 'laws': {'local_subset_cost': 'k-|S|', 'all_local_receipts_cost': 0, 'cross_chain_cost': 1, 'resolution_closure_cross_block_clauses': 0}, 'verified': ['exact additive decision law for every local-receipt subset', 'semantic equality of base, locally learned, and cross-chain databases', 'cross-block entailed clauses collapse k decisions to one', 'ordinary resolution closure of a disjoint union remains component-local']}19. sat_connected_resolution_chain_check.py — PASS
Elapsed: 4.429 seconds
PASS connected pure-resolution propagation chain
{'local_receipt_subset_cases': 62, 'semantic_truth_table_comparisons': 4, 'maximum_chain_length_decision_checked': 5, 'strict_three_clause_formulas_searched_n_le_4': 5016, 'connected_formulas_searched_n_le_4': 5016, 'smaller_external_trigger_witnesses': 0, 'laws': {'receipt_subset_cost': 'k-|S|', 'fully_learned_cost': 0, 'source_clauses': '2k+1', 'source_variables': '2k+3'}}20. sat_receipt_amortization_check.py — PASS
Elapsed: 0.188 seconds
PASS SAT receipt acquisition and amortization
{'episode_counts_checked': 50, 'learning_time_policies_checked': 1275, 'weighted_break_even_cases_checked': 9000, 'maximum_episodes': 50, 'resource_vectors': {'never_learn': '(r,0,0)', 'learn_immediately_and_retain': '(1,1,1)', 'learn_at_t_and_retain': '(t,1,1)', 'learn_then_forget_each_episode': '(r,r,0)'}, 'break_even': '(r-1)*decision_weight >= conflict_weight + storage_weight'}21. sat_receipt_coverage_check.py — PASS
Elapsed: 0.596 seconds
PASS SAT receipt demand coverage
{'coverage_table': [(False, False, True, 1, 0, 1), (False, True, False, 1, 1, 2), (True, False, False, 1, 1, 2), (True, True, False, 1, 1, 2)], 'sequences_exhaustively_checked': 21844, 'acquisition_time_policies_checked': 145636, 'maximum_sequence_length': 7, 'weighted_break_even_cases_checked': 229500, 'laws': {'never_learn': '(r,0,0)', 'optimal_acquire_when_H_ge_1': '(r-H+1,1,1)', 'decision_saving': 'H-1', 'weighted_break_even': '(H-1)*d >= c+s'}}22. sat_proof_fiber_obdd_check.py — PASS
Elapsed: 2.932 seconds
PASS SAT proof-state fiber versus semantic OBDD width
{'proof_states_checked': 8190, 'exact_dpll_states_checked': 62, 'semantic_truth_table_families': 4, 'fixed_order_cut_profiles_checked': 80, 'maximum_k_proof_fiber': 12, 'maximum_k_exact_dpll': 5, 'maximum_k_cut_profile': 8, 'laws': {'exact_proof_states': '2^k', 'minimum_decision_classes': 'k+1', 'class_multiplicity_at_cost_q': 'binomial(k,q)', 'semantic_roots_over_learning_histories': 1, 'reduced_obdd_nonterminal_width': 1, 'semantic_cut_width_including_false_terminal': 2}}23. sat_propagation_demand_information_check.py — PASS
Elapsed: 0.435 seconds
PASS SAT propagation-demand information theorem
{'proof_states_checked': 2046, 'up_demands_checked': 18434, 'projection_quotients_checked': 2046, 'projection_state_pairs_checked': 1398100, 'semantic_truth_table_families': 4, 'largest_native_up_k': 10, 'largest_information_law_k': 32, 'laws': {'full_demand_vector': 'chi_S', 'exact_full_demand_states': '2^k', 'exact_full_demand_bits': 'k', 'restricted_T_states': '2^|T|', 'restricted_T_bits': '|T|', 'scalar_cost_states': 'k+1', 'semantic_states': 1}}24. sat_second_order_branching_separation_check.py — PASS
Elapsed: 0.476 seconds
PASS minimal second-order SAT branching separation
{'named_base_models': 12, 'named_base_trace_decisions_conflicts': (3, 0), 'named_augmented_trace_decisions_conflicts': (2, 0), 'satisfiable_three_variable_formulas': 255, 'nontrivial_three_variable_entailments': 0, 'four_variable_one_clause_entailments': 0, 'connected_two_clause_entailed_additions': 192, 'same_singleton_signature_additions': 192, 'fixed_policy_separations': 8}25. sat_arbitrary_width_interaction_depth_check.py — PASS
Elapsed: 0.237 seconds
PASS arbitrary-width SAT interaction-depth theorem
{'widths_checked': 10, 'width_range': [3, 12], 'truth_assignments_checked': 16368, 'low_order_seeds_checked_through_width_8': 16980, 'rup_checks': 10, 'laws': {'variables': 'r+1', 'source_clauses': 2, 'agreement_depth': 'r-2', 'first_separation_depth': 'r-1', 'base_decisions': 'r', 'augmented_decisions': 'r-1', 'conflicts_on_successful_trace': 0, 'models': '2^(r+1)-4'}}26. sat_fixed_width_absorption_check.py — PASS
Elapsed: 10.268 seconds
PASS fixed-width absorption and completeness theorem
{'three_variable_census': {'variables': 3, 'configurations': 106301, 'shallow_equal': 8856, 'absorbed_sets': 8856, 'entailed_trace_checks': 8856}, 'four_variable_census': {'variables': 4, 'configurations': 4096, 'shallow_equal': 240, 'absorbed_sets': 240, 'entailed_trace_checks': 240}, 'sharp_widths_checked': 6, 'theorem': 'sigma_(w-1) equality iff every added width<=w clause is absorbed; then all-seed UP signatures agree', 'fixed_order_corollary': 'entailed absorbed additions preserve the complete DPLL trace'}27. sat_first_uip_reason_compression_check.py — PASS
Elapsed: 2.444 seconds
PASS UP-equivalent first-UIP reason-compression family
{'all_seed_instances': 88533, 'UP_closures_compared': 177066, 'semantic_truth_rows': 16368, 'deterministic_conflict_traces': 128, 'pure_resolution_derivation_steps_checked': 2080, 'largest_chain': 64, 'base_first_UIP_steps': 'm+1', 'augmented_first_UIP_steps': 1, 'learned_clause': 'x or y', 'maximum_analysis_width': 3}28. sat_first_uip_schedule_minimum_check.py — PASS
Elapsed: 8.983 seconds
PASS priority-independent minimum first-UIP law
{'chain_lengths': '1..8', 'complete_reason_traces': 176800, 'base_cost_set': '{m+1}', 'augmented_cost_set': '{1,m+1}', 'minimum_gap': 'm', 'common_learned_clause': 'x or y', 'base_width_set': '{3} at m=1; {3,4} for m>=2', 'augmented_width_set': '{3}', 'rows': [{'m': 1, 'base_traces': 8, 'augmented_traces': 8, 'base_costs': [2], 'augmented_costs': [1, 2]}, {'m': 2, 'base_traces': 32, 'augmented_traces': 16, 'base_costs': [3], 'augmented_costs': [1, 3]}, {'m': 3, 'base_traces': 128, 'augmented_traces': 32, 'base_costs': [4], 'augmented_costs': [1, 4]}, {'m': 4, 'base_traces': 512, 'augmented_traces': 64, 'base_costs': [5], 'augmented_costs': [1, 5]}, {'m': 5, 'base_traces': 2048, 'augmented_traces': 128, 'base_costs': [6], 'augmented_costs': [1, 6]}, {'m': 6, 'base_traces': 8192, 'augmented_traces': 256, 'base_costs': [7], 'augmented_costs': [1, 7]}, {'m': 7, 'base_traces': 32768, 'augmented_traces': 512, 'base_costs': [8], 'augmented_costs': [1, 8]}, {'m': 8, 'base_traces': 131072, 'augmented_traces': 1024, 'base_costs': [9], 'augmented_costs': [1, 9]}]}Aggregate
PASS: 28/28 scripts in 78.276 seconds.