Datasets:

PureOne
/

Orythmea-Private-Predicate-Covers

{"check_name": "conditional_private_coarsening_geometry", "record_id": "orythmea-conditional_private_coarsening_geometry", "recorded_status": "passed", "results_json": "{\"actual_cap_overflow_fallbacks_on_bad_transcript\": 12, \"arithmetic\": \"exact fractions\", \"bad_transcript_fallback_exercised\": true, \"counts\": {\"greedy_threshold_boundary_checks\": 51, \"histogram_transcripts\": 4344, \"initial_predicate_checks\": 33224, \"noisy_distance_certificate_checks\": 84664, \"nonadjacent_valid_gaps\": 412, \"nonzero_initial_errors\": 1590, \"pruned_predicate_checks\": 66448, \"pruned_transcripts\": 8688, \"rejected_gap_certificates\": 2340, \"tree_law_accuracy_cases\": 682, \"valid_level_certificates\": 1086}, \"maximum_good_transcript_pruned_pool_including_empty\": 18, \"maximum_initial_error_over_tau\": \"3/40\", \"maximum_pruned_error_over_tau\": \"1/2\", \"status\": \"passed\", \"threshold_boundary_pool_sizes_exact_positive_negative_noise\": [2, 18, 2], \"trees\": [\"singleton\", \"chain_internal_mass\", \"binary_internal_mass\", \"irregular_terminated_branches\", \"unequal_branch_depths\"]}", "scope": "Finite checks supplement the proofs. They do not implement the imported private interior-point primitive, establish theorem-wide privacy by testing, or resolve the universal PAC conjecture.", "source_path": "research/verify_orythmea_results.json", "suite": "orythmea", "verification_script": "research/verify_orythmea.py"}
{"check_name": "finite_fixed_range_exponential_mechanism", "record_id": "orythmea-finite_fixed_range_exponential_mechanism", "recorded_status": "passed", "results_json": "{\"absolute_log_ratio_tolerance\": 1e-12, \"configurations\": [{\"domain_size\": 3, \"input_size\": 2, \"maximum_observed_log_likelihood_ratio\": 0.7041824712382778, \"ordered_neighbor_pairs\": 36, \"output_candidates\": 9, \"queries\": 8, \"synthetic_list_size\": 2}, {\"domain_size\": 3, \"input_size\": 3, \"maximum_observed_log_likelihood_ratio\": 0.6594210239679559, \"ordered_neighbor_pairs\": 162, \"output_candidates\": 9, \"queries\": 8, \"synthetic_list_size\": 2}, {\"domain_size\": 4, \"input_size\": 2, \"maximum_observed_log_likelihood_ratio\": 0.6819761814589245, \"ordered_neighbor_pairs\": 96, \"output_candidates\": 16, \"queries\": 16, \"synthetic_list_size\": 2}], \"counts\": {\"epsilon_configurations\": 9, \"exact_score_sensitivity_checks\": 3318, \"input_lists\": 52, \"numeric_singleton_likelihood_checks\": 9954, \"ordered_neighbor_pairs\": 294}, \"epsilon_values\": [0.1, 0.7, 1.0], \"likelihood_arithmetic\": \"IEEE-754 double precision math.exp/math.log\", \"maximum_log_ratio_divided_by_epsilon\": 0.7206491075766541, \"maximum_log_ratio_minus_epsilon\": -0.027935089242334593, \"scope\": \"Finite fixed-range exponential mechanism only; all ordered replacement neighbors and singleton outputs in the listed cases. Singleton inequalities imply all output-event inequalities for these finite cases.\", \"score_sensitivity_arithmetic\": \"exact fractions\", \"status\": \"passed\"}", "scope": "Finite checks supplement the proofs. They do not implement the imported private interior-point primitive, establish theorem-wide privacy by testing, or resolve the universal PAC conjecture.", "source_path": "research/verify_orythmea_results.json", "suite": "orythmea", "verification_script": "research/verify_orythmea.py"}
{"check_name": "gate_replacement_and_correlations", "record_id": "orythmea-gate_replacement_and_correlations", "recorded_status": "passed", "results_json": "{\"arithmetic\": \"exact fractions\", \"counts\": {\"correlated_joint_laws\": 35, \"expectation_gate_checks\": 45360, \"nonproduct_joint_laws\": 18, \"pointwise_gate_pairs\": 16656}, \"same_component_marginals\": [\"1/2\", \"1/2\"], \"same_marginals_different_joint_witnesses\": {\"AND\": {\"antidiagonal_law_mean\": \"0\", \"diagonal_law_mean\": \"1/2\"}, \"OR\": {\"antidiagonal_law_mean\": \"1\", \"diagonal_law_mean\": \"1/2\"}, \"XOR\": {\"antidiagonal_law_mean\": \"1\", \"diagonal_law_mean\": \"0\"}}, \"status\": \"passed\"}", "scope": "Finite checks supplement the proofs. They do not implement the imported private interior-point primitive, establish theorem-wide privacy by testing, or resolve the universal PAC conjecture.", "source_path": "research/verify_orythmea_results.json", "suite": "orythmea", "verification_script": "research/verify_orythmea.py"}
{"check_name": "laminar_packing_bound", "record_id": "orythmea-laminar_packing_bound", "recorded_status": "passed", "results_json": "{\"arithmetic\": \"exact fractions\", \"counts\": {\"candidate_families\": 107520, \"distributions\": 210, \"separated_families\": 6926}, \"law_denominator\": 4, \"status\": \"passed\", \"tree_vertices\": 7}", "scope": "Finite checks supplement the proofs. They do not implement the imported private interior-point primitive, establish theorem-wide privacy by testing, or resolve the universal PAC conjecture.", "source_path": "research/verify_orythmea_results.json", "suite": "orythmea", "verification_script": "research/verify_orythmea.py"}
{"check_name": "product_atom_exactness", "record_id": "orythmea-product_atom_exactness", "recorded_status": "passed", "results_json": "{\"arithmetic\": \"exact Boolean evaluation\", \"counts\": {\"artificial_tuple_gate_checks\": 64, \"pool_pairs\": 64, \"product_atom_gate_checks\": 123904, \"raw_vs_atom_gate_checks\": 230400}, \"status\": \"passed\", \"unrealizable_but_valid_synthetic_tuples_in_example\": 2}", "scope": "Finite checks supplement the proofs. They do not implement the imported private interior-point primitive, establish theorem-wide privacy by testing, or resolve the universal PAC conjecture.", "source_path": "research/verify_orythmea_results.json", "suite": "orythmea", "verification_script": "research/verify_orythmea.py"}
{"check_name": "collision_reconstruction", "record_id": "collision-collision_reconstruction", "recorded_status": "PASS", "results_json": "{\"dominant_recoveries\": 52, \"instances\": 73, \"intermediate_reconstructions\": 136, \"internal_record_partition_counterexample\": {\"ancestor_mass\": \"1\", \"conclusion\": \"Equality fails without padding; inequality suffices and both algorithms pass.\", \"deeper_descendant_mass_sum\": \"0\"}, \"targeted_cdf_error\": \"9999/50000000\", \"targeted_omitted_collision_mass\": \"9999/50000000\", \"worst_exact_error\": \"637/71600\"}", "scope": "Exact finite checks of deterministic lemmas; no numerical DP claim.", "source_path": "research/verify_collision_base_results.json", "suite": "collision_base", "verification_script": "research/verify_collision_base.py"}
{"check_name": "scalar_bin_transfer", "record_id": "collision-scalar_bin_transfer", "recorded_status": "PASS", "results_json": "{\"adversarial_all_errors_boundary_score\": \"166501/500000\", \"omitted_low_deviation_cases\": 4284, \"promised_coordinates_checked\": 7200, \"strict_pigeonhole_boundary\": {\"R_40k_all_counts_can_equal_threshold\": true, \"R_40k_plus_one_forces_a_count_strictly_below_threshold\": true, \"interpretation\": \"The extra representative gives strict slack; it is not necessary for a non-strict transfer bound.\"}, \"worst_exact_representative_minority\": \"49/100\"}", "scope": "Exact finite checks of deterministic lemmas; no numerical DP claim.", "source_path": "research/verify_collision_base_results.json", "suite": "collision_base", "verification_script": "research/verify_collision_base.py"}
{"check_name": "corrupted_prefix_extraction", "record_id": "collision-corrupted_prefix_extraction", "recorded_status": "PASS", "results_json": "{\"corrupted_matrices_exhaustively_checked\": 8476, \"inclusive_diagonal_extractions\": 7271, \"off_diagonal_only_counterexample\": {\"conclusion\": \"Equal-diagonal filtering is necessary for this extraction argument.\", \"rows\": [[1, 0], [1, 0]]}, \"strict_diagonal_extractions\": 1205}", "scope": "Exact finite checks of deterministic lemmas; no numerical DP claim.", "source_path": "research/verify_collision_base_results.json", "suite": "collision_base", "verification_script": "research/verify_collision_base.py"}
{"check_name": "fixed_rank_slice_adjacency", "record_id": "collision-fixed_rank_slice_adjacency", "recorded_status": "PASS", "results_json": "{\"maximum_multiset_replacement_distance\": 1, \"neighbor_window_pairs_checked\": 66432, \"scope\": \"Adjacency preprocessing only; imported IP privacy is not numerically tested.\"}", "scope": "Exact finite checks of deterministic lemmas; no numerical DP claim.", "source_path": "research/verify_collision_base_results.json", "suite": "collision_base", "verification_script": "research/verify_collision_base.py"}

	{"check_name": "conditional_private_coarsening_geometry", "record_id": "orythmea-conditional_private_coarsening_geometry", "recorded_status": "passed", "results_json": "{\"actual_cap_overflow_fallbacks_on_bad_transcript\": 12, \"arithmetic\": \"exact fractions\", \"bad_transcript_fallback_exercised\": true, \"counts\": {\"greedy_threshold_boundary_checks\": 51, \"histogram_transcripts\": 4344, \"initial_predicate_checks\": 33224, \"noisy_distance_certificate_checks\": 84664, \"nonadjacent_valid_gaps\": 412, \"nonzero_initial_errors\": 1590, \"pruned_predicate_checks\": 66448, \"pruned_transcripts\": 8688, \"rejected_gap_certificates\": 2340, \"tree_law_accuracy_cases\": 682, \"valid_level_certificates\": 1086}, \"maximum_good_transcript_pruned_pool_including_empty\": 18, \"maximum_initial_error_over_tau\": \"3/40\", \"maximum_pruned_error_over_tau\": \"1/2\", \"status\": \"passed\", \"threshold_boundary_pool_sizes_exact_positive_negative_noise\": [2, 18, 2], \"trees\": [\"singleton\", \"chain_internal_mass\", \"binary_internal_mass\", \"irregular_terminated_branches\", \"unequal_branch_depths\"]}", "scope": "Finite checks supplement the proofs. They do not implement the imported private interior-point primitive, establish theorem-wide privacy by testing, or resolve the universal PAC conjecture.", "source_path": "research/verify_orythmea_results.json", "suite": "orythmea", "verification_script": "research/verify_orythmea.py"}
	{"check_name": "finite_fixed_range_exponential_mechanism", "record_id": "orythmea-finite_fixed_range_exponential_mechanism", "recorded_status": "passed", "results_json": "{\"absolute_log_ratio_tolerance\": 1e-12, \"configurations\": [{\"domain_size\": 3, \"input_size\": 2, \"maximum_observed_log_likelihood_ratio\": 0.7041824712382778, \"ordered_neighbor_pairs\": 36, \"output_candidates\": 9, \"queries\": 8, \"synthetic_list_size\": 2}, {\"domain_size\": 3, \"input_size\": 3, \"maximum_observed_log_likelihood_ratio\": 0.6594210239679559, \"ordered_neighbor_pairs\": 162, \"output_candidates\": 9, \"queries\": 8, \"synthetic_list_size\": 2}, {\"domain_size\": 4, \"input_size\": 2, \"maximum_observed_log_likelihood_ratio\": 0.6819761814589245, \"ordered_neighbor_pairs\": 96, \"output_candidates\": 16, \"queries\": 16, \"synthetic_list_size\": 2}], \"counts\": {\"epsilon_configurations\": 9, \"exact_score_sensitivity_checks\": 3318, \"input_lists\": 52, \"numeric_singleton_likelihood_checks\": 9954, \"ordered_neighbor_pairs\": 294}, \"epsilon_values\": [0.1, 0.7, 1.0], \"likelihood_arithmetic\": \"IEEE-754 double precision math.exp/math.log\", \"maximum_log_ratio_divided_by_epsilon\": 0.7206491075766541, \"maximum_log_ratio_minus_epsilon\": -0.027935089242334593, \"scope\": \"Finite fixed-range exponential mechanism only; all ordered replacement neighbors and singleton outputs in the listed cases. Singleton inequalities imply all output-event inequalities for these finite cases.\", \"score_sensitivity_arithmetic\": \"exact fractions\", \"status\": \"passed\"}", "scope": "Finite checks supplement the proofs. They do not implement the imported private interior-point primitive, establish theorem-wide privacy by testing, or resolve the universal PAC conjecture.", "source_path": "research/verify_orythmea_results.json", "suite": "orythmea", "verification_script": "research/verify_orythmea.py"}
	{"check_name": "gate_replacement_and_correlations", "record_id": "orythmea-gate_replacement_and_correlations", "recorded_status": "passed", "results_json": "{\"arithmetic\": \"exact fractions\", \"counts\": {\"correlated_joint_laws\": 35, \"expectation_gate_checks\": 45360, \"nonproduct_joint_laws\": 18, \"pointwise_gate_pairs\": 16656}, \"same_component_marginals\": [\"1/2\", \"1/2\"], \"same_marginals_different_joint_witnesses\": {\"AND\": {\"antidiagonal_law_mean\": \"0\", \"diagonal_law_mean\": \"1/2\"}, \"OR\": {\"antidiagonal_law_mean\": \"1\", \"diagonal_law_mean\": \"1/2\"}, \"XOR\": {\"antidiagonal_law_mean\": \"1\", \"diagonal_law_mean\": \"0\"}}, \"status\": \"passed\"}", "scope": "Finite checks supplement the proofs. They do not implement the imported private interior-point primitive, establish theorem-wide privacy by testing, or resolve the universal PAC conjecture.", "source_path": "research/verify_orythmea_results.json", "suite": "orythmea", "verification_script": "research/verify_orythmea.py"}
	{"check_name": "laminar_packing_bound", "record_id": "orythmea-laminar_packing_bound", "recorded_status": "passed", "results_json": "{\"arithmetic\": \"exact fractions\", \"counts\": {\"candidate_families\": 107520, \"distributions\": 210, \"separated_families\": 6926}, \"law_denominator\": 4, \"status\": \"passed\", \"tree_vertices\": 7}", "scope": "Finite checks supplement the proofs. They do not implement the imported private interior-point primitive, establish theorem-wide privacy by testing, or resolve the universal PAC conjecture.", "source_path": "research/verify_orythmea_results.json", "suite": "orythmea", "verification_script": "research/verify_orythmea.py"}
	{"check_name": "product_atom_exactness", "record_id": "orythmea-product_atom_exactness", "recorded_status": "passed", "results_json": "{\"arithmetic\": \"exact Boolean evaluation\", \"counts\": {\"artificial_tuple_gate_checks\": 64, \"pool_pairs\": 64, \"product_atom_gate_checks\": 123904, \"raw_vs_atom_gate_checks\": 230400}, \"status\": \"passed\", \"unrealizable_but_valid_synthetic_tuples_in_example\": 2}", "scope": "Finite checks supplement the proofs. They do not implement the imported private interior-point primitive, establish theorem-wide privacy by testing, or resolve the universal PAC conjecture.", "source_path": "research/verify_orythmea_results.json", "suite": "orythmea", "verification_script": "research/verify_orythmea.py"}
	{"check_name": "collision_reconstruction", "record_id": "collision-collision_reconstruction", "recorded_status": "PASS", "results_json": "{\"dominant_recoveries\": 52, \"instances\": 73, \"intermediate_reconstructions\": 136, \"internal_record_partition_counterexample\": {\"ancestor_mass\": \"1\", \"conclusion\": \"Equality fails without padding; inequality suffices and both algorithms pass.\", \"deeper_descendant_mass_sum\": \"0\"}, \"targeted_cdf_error\": \"9999/50000000\", \"targeted_omitted_collision_mass\": \"9999/50000000\", \"worst_exact_error\": \"637/71600\"}", "scope": "Exact finite checks of deterministic lemmas; no numerical DP claim.", "source_path": "research/verify_collision_base_results.json", "suite": "collision_base", "verification_script": "research/verify_collision_base.py"}
	{"check_name": "scalar_bin_transfer", "record_id": "collision-scalar_bin_transfer", "recorded_status": "PASS", "results_json": "{\"adversarial_all_errors_boundary_score\": \"166501/500000\", \"omitted_low_deviation_cases\": 4284, \"promised_coordinates_checked\": 7200, \"strict_pigeonhole_boundary\": {\"R_40k_all_counts_can_equal_threshold\": true, \"R_40k_plus_one_forces_a_count_strictly_below_threshold\": true, \"interpretation\": \"The extra representative gives strict slack; it is not necessary for a non-strict transfer bound.\"}, \"worst_exact_representative_minority\": \"49/100\"}", "scope": "Exact finite checks of deterministic lemmas; no numerical DP claim.", "source_path": "research/verify_collision_base_results.json", "suite": "collision_base", "verification_script": "research/verify_collision_base.py"}
	{"check_name": "corrupted_prefix_extraction", "record_id": "collision-corrupted_prefix_extraction", "recorded_status": "PASS", "results_json": "{\"corrupted_matrices_exhaustively_checked\": 8476, \"inclusive_diagonal_extractions\": 7271, \"off_diagonal_only_counterexample\": {\"conclusion\": \"Equal-diagonal filtering is necessary for this extraction argument.\", \"rows\": [[1, 0], [1, 0]]}, \"strict_diagonal_extractions\": 1205}", "scope": "Exact finite checks of deterministic lemmas; no numerical DP claim.", "source_path": "research/verify_collision_base_results.json", "suite": "collision_base", "verification_script": "research/verify_collision_base.py"}
	{"check_name": "fixed_rank_slice_adjacency", "record_id": "collision-fixed_rank_slice_adjacency", "recorded_status": "PASS", "results_json": "{\"maximum_multiset_replacement_distance\": 1, \"neighbor_window_pairs_checked\": 66432, \"scope\": \"Adjacency preprocessing only; imported IP privacy is not numerically tested.\"}", "scope": "Exact finite checks of deterministic lemmas; no numerical DP claim.", "source_path": "research/verify_collision_base_results.json", "suite": "collision_base", "verification_script": "research/verify_collision_base.py"}