{ "groups": { "smoke": [ "add_zero_right" ], "broader": [ "mul_add_distrib_right", "add_mul_distrib_left", "and_all_repeat_true", "sum_slow_append_slow", "map_double_slow_append_slow", "tree_leaves_mirror", "rev_slow_append_slow" ], "heldout": [ "six_shift_eq_six_mul_add_one", "seven_add_eq_self_sum", "plus_slow_assoc", "mul_slow_add_left", "length_slow_map_succ_slow", "length_slow_rev_slow", "tree_size_mirror_sum_twice" ], "combined": [ "mul_add_distrib_right", "add_mul_distrib_left", "and_all_repeat_true", "sum_slow_append_slow", "map_double_slow_append_slow", "tree_leaves_mirror", "rev_slow_append_slow", "six_shift_eq_six_mul_add_one", "seven_add_eq_self_sum", "plus_slow_assoc", "mul_slow_add_left", "length_slow_map_succ_slow", "length_slow_rev_slow", "tree_size_mirror_sum_twice" ], "negative_controls": [ "mul_add_distrib_right", "add_mul_distrib_left", "mul_assoc_builtin", "mul_comm_builtin", "add_left_cancel_builtin", "filter_length_le_builtin" ], "challenge_v2_no_helper": [ "challenge_v2_length_rev_no_helper", "challenge_v2_sum_rev_no_helper", "challenge_v2_map_succ_rev_no_helper" ], "challenge_v3_generalization": [ "challenge_v3_rev_acc_generalization", "challenge_v3_sum_acc_generalization", "challenge_v3_tree_flatten_mirror", "challenge_v3_map_rev_append_combined" ], "challenge_transfer": [ "challenge_v2_length_rev_no_helper", "challenge_v2_sum_rev_no_helper", "challenge_v2_map_succ_rev_no_helper", "challenge_v3_rev_acc_generalization", "challenge_v3_sum_acc_generalization", "challenge_v3_tree_flatten_mirror", "challenge_v3_map_rev_append_combined" ], "challenge_v4_count": [ "challenge_v4_count_acc_generalization", "challenge_v4_count_rev_slow", "challenge_v4_count_flatten_mirror", "challenge_v4_count_mapSucc_rev" ], "challenge_v5_attribution": [ "challenge_v5_tally_acc_pair", "challenge_v5_partition_count_length", "challenge_v5_filter_rev_count_combo", "challenge_v5_tree_tally_mirror" ], "challenge_v5_tree_tally": [ "challenge_v5_tree_tally_mirror" ], "challenge_v13_decomposition_order": [ "challenge_v13_partition_side_bundle_no_stats_flatten_mirror", "challenge_v13_partition_reordered_metrics_flatten_mirror", "challenge_v13_raw_count_length_sum_flatten_mirror", "challenge_v13_keep_drop_triple_metrics_append", "challenge_v13_partition_metrics_with_append_hyps_flatten_mirror", "challenge_v13_partition_metrics_from_side_hyps" ], "challenge_v14_metric_order_permutations": [ "challenge_v14_order_count_length_sum_flatten_mirror", "challenge_v14_order_count_sum_length_flatten_mirror", "challenge_v14_order_length_count_sum_flatten_mirror", "challenge_v14_order_length_sum_count_flatten_mirror", "challenge_v14_order_sum_count_length_flatten_mirror", "challenge_v14_order_sum_length_count_flatten_mirror" ], "challenge_extended_transfer": [ "challenge_v2_length_rev_no_helper", "challenge_v2_sum_rev_no_helper", "challenge_v2_map_succ_rev_no_helper", "challenge_v3_rev_acc_generalization", "challenge_v3_sum_acc_generalization", "challenge_v3_tree_flatten_mirror", "challenge_v3_map_rev_append_combined", "challenge_v4_count_acc_generalization", "challenge_v4_count_rev_slow", "challenge_v4_count_flatten_mirror", "challenge_v4_count_mapSucc_rev", "challenge_v5_tally_acc_pair", "challenge_v5_partition_count_length", "challenge_v5_filter_rev_count_combo", "challenge_v5_tree_tally_mirror", "challenge_v6_stats_acc_rev", "challenge_v6_tree_partition_mirror", "challenge_v6_mapSucc_rev_count_sum", "challenge_v6_mutual_depth_stats_mirror", "challenge_v7_partition_stats_acc_mirror", "challenge_v7_mutual_values_stats_acc_mirror", "challenge_v7_partition_reassemble_stats_acc_mirror", "challenge_v7_tree_mapSucc_stats_acc_mirror", "challenge_v8_stats_acc_flatten_mirror", "challenge_v8_keep_stats_acc_flatten_mirror", "challenge_v8_drop_stats_acc_flatten_mirror", "challenge_v8_partition_reassemble_stats_acc_list", "challenge_v9_keep_length_flatten_mirror", "challenge_v9_keep_sum_flatten_mirror", "challenge_v9_keep_length_sum_flatten_mirror", "challenge_v9_drop_length_flatten_mirror", "challenge_v9_drop_sum_flatten_mirror", "challenge_v9_drop_length_sum_flatten_mirror", "challenge_v10_stats_acc_reify_list", "challenge_v10_stats_acc_extensional_from_metrics", "challenge_v10_keep_count_flatten_mirror", "challenge_v10_drop_count_flatten_mirror", "challenge_v10_keep_stats_acc_from_metric_hyps", "challenge_v10_drop_stats_acc_from_metric_hyps", "challenge_v11_keep_metric_bundle_flatten_mirror", "challenge_v11_drop_metric_bundle_flatten_mirror", "challenge_v11_keep_stats_acc_from_metric_bundle", "challenge_v11_drop_stats_acc_from_metric_bundle", "challenge_v11_partition_metric_bundles_flatten_mirror", "challenge_v11_partition_stats_from_metric_bundles", "challenge_v12_partition_count_metrics_flatten_mirror", "challenge_v12_partition_length_metrics_flatten_mirror", "challenge_v12_partition_sum_metrics_flatten_mirror", "challenge_v12_partition_count_length_metrics_flatten_mirror", "challenge_v12_partition_count_sum_metrics_flatten_mirror", "challenge_v12_partition_length_sum_metrics_flatten_mirror", "challenge_v12_partition_count_length_sum_metrics_flatten_mirror", "challenge_v13_partition_side_bundle_no_stats_flatten_mirror", "challenge_v13_partition_reordered_metrics_flatten_mirror", "challenge_v13_raw_count_length_sum_flatten_mirror", "challenge_v13_keep_drop_triple_metrics_append", "challenge_v13_partition_metrics_with_append_hyps_flatten_mirror", "challenge_v13_partition_metrics_from_side_hyps", "challenge_v14_order_count_length_sum_flatten_mirror", "challenge_v14_order_count_sum_length_flatten_mirror", "challenge_v14_order_length_count_sum_flatten_mirror", "challenge_v14_order_length_sum_count_flatten_mirror", "challenge_v14_order_sum_count_length_flatten_mirror", "challenge_v14_order_sum_length_count_flatten_mirror", "challenge_v15_order_length_count_sum_from_metric_hyps", "challenge_v15_order_length_count_sum_from_side_hyps", "challenge_v15_order_length_count_sum_with_append_hyps", "challenge_v15_order_length_count_sum_with_append_and_reassembly_hyp", "challenge_v16_order_length_count_sum_with_top_level_packer", "challenge_v16_order_length_count_sum_with_pair_and_top_packers", "challenge_v16_order_length_count_sum_with_nat_scalar_packer", "challenge_v16_order_length_count_sum_with_named_metric_packers", "challenge_v17_pair_top_packers_with_coarse_plan_hints", "challenge_v17_pair_top_packers_with_detailed_plan_hints", "challenge_v17_named_metric_packers_with_coarse_plan_hints", "challenge_v17_named_metric_packers_with_detailed_plan_hints", "challenge_v18_pair_top_packers_clean", "challenge_v18_named_metric_packers_clean" ], "challenge_v6_frontier": [ "challenge_v6_stats_acc_rev", "challenge_v6_tree_partition_mirror", "challenge_v6_mapSucc_rev_count_sum", "challenge_v6_mutual_depth_stats_mirror" ], "challenge_v7_frontier": [ "challenge_v7_partition_stats_acc_mirror", "challenge_v7_mutual_values_stats_acc_mirror", "challenge_v7_partition_reassemble_stats_acc_mirror", "challenge_v7_tree_mapSucc_stats_acc_mirror" ], "challenge_v8_diagnostics": [ "challenge_v8_stats_acc_flatten_mirror", "challenge_v8_keep_stats_acc_flatten_mirror", "challenge_v8_drop_stats_acc_flatten_mirror", "challenge_v8_partition_reassemble_stats_acc_list" ], "challenge_v9_composition_gradient": [ "challenge_v9_keep_length_flatten_mirror", "challenge_v9_keep_sum_flatten_mirror", "challenge_v9_keep_length_sum_flatten_mirror", "challenge_v9_drop_length_flatten_mirror", "challenge_v9_drop_sum_flatten_mirror", "challenge_v9_drop_length_sum_flatten_mirror" ], "challenge_v10_stats_reification": [ "challenge_v10_stats_acc_reify_list", "challenge_v10_stats_acc_extensional_from_metrics", "challenge_v10_keep_count_flatten_mirror", "challenge_v10_drop_count_flatten_mirror", "challenge_v10_keep_stats_acc_from_metric_hyps", "challenge_v10_drop_stats_acc_from_metric_hyps" ], "challenge_v11_metric_composition": [ "challenge_v11_keep_metric_bundle_flatten_mirror", "challenge_v11_drop_metric_bundle_flatten_mirror", "challenge_v11_keep_stats_acc_from_metric_bundle", "challenge_v11_drop_stats_acc_from_metric_bundle", "challenge_v11_partition_metric_bundles_flatten_mirror", "challenge_v11_partition_stats_from_metric_bundles" ], "challenge_v12_simultaneous_metrics": [ "challenge_v12_partition_count_metrics_flatten_mirror", "challenge_v12_partition_length_metrics_flatten_mirror", "challenge_v12_partition_sum_metrics_flatten_mirror", "challenge_v12_partition_count_length_metrics_flatten_mirror", "challenge_v12_partition_count_sum_metrics_flatten_mirror", "challenge_v12_partition_length_sum_metrics_flatten_mirror", "challenge_v12_partition_count_length_sum_metrics_flatten_mirror" ], "challenge_v15_proof_shape_hints": [ "challenge_v15_order_length_count_sum_from_metric_hyps", "challenge_v15_order_length_count_sum_from_side_hyps", "challenge_v15_order_length_count_sum_with_append_hyps", "challenge_v15_order_length_count_sum_with_append_and_reassembly_hyp" ], "challenge_v16_compact_reassembly_hints": [ "challenge_v16_order_length_count_sum_with_top_level_packer", "challenge_v16_order_length_count_sum_with_pair_and_top_packers", "challenge_v16_order_length_count_sum_with_nat_scalar_packer", "challenge_v16_order_length_count_sum_with_named_metric_packers" ], "challenge_v17_proof_plan_hints": [ "challenge_v17_pair_top_packers_with_coarse_plan_hints", "challenge_v17_pair_top_packers_with_detailed_plan_hints", "challenge_v17_named_metric_packers_with_coarse_plan_hints", "challenge_v17_named_metric_packers_with_detailed_plan_hints" ], "challenge_v18_prompt_only_skeleton_hints": [ "challenge_v18_pair_top_packers_clean", "challenge_v18_named_metric_packers_clean" ], "challenge_v19_bare_skeleton_names": [ "challenge_v18_pair_top_packers_clean", "challenge_v18_named_metric_packers_clean" ], "challenge_v20_description_only_skeleton": [ "challenge_v18_pair_top_packers_clean", "challenge_v18_named_metric_packers_clean" ], "challenge_v21_neutral_anchor_skeleton": [ "challenge_v18_pair_top_packers_clean", "challenge_v18_named_metric_packers_clean" ], "challenge_v22_code_like_anchor_skeleton": [ "challenge_v18_pair_top_packers_clean", "challenge_v18_named_metric_packers_clean" ], "challenge_v23_exact_labels_without_plan_prefix": [ "challenge_v18_pair_top_packers_clean", "challenge_v18_named_metric_packers_clean" ], "challenge_v24_plan_prefix_generic_labels": [ "challenge_v18_pair_top_packers_clean", "challenge_v18_named_metric_packers_clean" ], "challenge_v25_step_prefix_exact_labels": [ "challenge_v18_pair_top_packers_clean", "challenge_v18_named_metric_packers_clean" ] }, "descriptions": { "smoke": "One quick theorem for setup and smoke checks.", "broader": "Seven broader fixtures covering Nat distribution, Bool/List recursion, list helpers, tree helpers, and reverse/append.", "heldout": "Seven original held-out transfer fixtures.", "combined": "The broader group followed by the heldout group.", "negative_controls": "Six fixtures where generic Nat/List hint candidates should fail Lean before fallback.", "challenge_v2_no_helper": "Three no-expected-proof challenge fixtures requiring local append/map helper lemma discovery.", "challenge_v3_generalization": "Four no-expected-proof theorem-generalization fixtures requiring accumulator generalization and multi-helper proof plans.", "challenge_transfer": "All v2/v3 challenge fixtures for proof-transfer experiments; no expected proofs are bundled.", "challenge_v4_count": "Four no-expected-proof count/list/tree fixtures covering occurrence counting, reverse preservation, tree mirror/flatten, and successor-map-after-reverse.", "challenge_v5_attribution": "Four no-expected-proof fixtures designed to separate seeded, unseeded, and direct repair on simultaneous invariants and multi-helper composition.", "challenge_v5_tree_tally": "The hardest v5 tree/tally mirror fixture for repeated attribution controls.", "challenge_extended_transfer": "All v2/v3/v4/v5/v6/v7/v8/v9/v10/v11/v12/v13/v14/v15/v16/v17/v18 challenge fixtures; no expected proofs are bundled.", "challenge_v6_frontier": "Four no-expected-proof frontier fixtures covering multi-accumulator reverse invariants, nested tree partition stats, successor-map reverse count/sum, and mutually recursive tree depth statistics.", "challenge_v7_frontier": "Four no-expected-proof frontier-plus fixtures combining nested tree partition/filter composition, stats accumulator generalization, mutually recursive traversals, and shifted successor-map statistics.", "challenge_v8_diagnostics": "Four no-expected-proof diagnostic fixtures isolating the v7 partition-heavy accumulator frontier into raw tree stats, keep-side mirror stats, drop-side mirror stats, and list-only partition reassembly.", "challenge_v9_composition_gradient": "Six no-expected-proof composition-gradient fixtures splitting keep/drop partition-through-mirror into scalar length/sum obligations and paired length+sum obligations.", "challenge_v10_stats_reification": "Six no-expected-proof statsAcc-reification fixtures isolating accumulator tuple normalization, metric extensionality, count metrics, and keep/drop stats equality from metric hypotheses.", "challenge_v11_metric_composition": "Six no-expected-proof metric-composition fixtures combining keep/drop metric bundles with statsAcc extensionality boundaries, stopping short of proving the full v7/v8 theorem outright.", "challenge_v12_simultaneous_metrics": "Seven no-expected-proof simultaneous-metric fixtures isolating keep/drop count-only, length-only, sum-only, pair, and triple metric bundles through tree mirror.", "challenge_v13_decomposition_order": "Six no-expected-proof decomposition/order fixtures isolating full-triple metric grouping, append/filter sub-lemmas, raw tree metrics, and conjunction reassembly.", "challenge_v14_metric_order_permutations": "Six no-expected-proof metric-order fixtures covering all count/length/sum permutations in the full simultaneous keep/drop tree-mirror theorem.", "challenge_v15_proof_shape_hints": "Four no-expected-proof proof-shape hint fixtures exposing metric-bundle, side-bundle, append/filter, and final reassembly hypotheses for the hardest length/count/sum order.", "challenge_v16_compact_reassembly_hints": "Four no-expected-proof compact reassembly-hint fixtures replacing the large v15 higher-order reassembly hypothesis with smaller generic or named first-order packers.", "challenge_v17_proof_plan_hints": "Four no-expected-proof proof-plan hint fixtures adding harmless True-valued skeleton names to compact v16-style packer hypotheses.", "challenge_v18_prompt_only_skeleton_hints": "Two no-expected-proof fixtures reusing v16 compact packer theorem statements while supplying detailed proof-plan skeleton names only through the seeded playbook context.", "challenge_v19_bare_skeleton_names": "Ablation group reusing the two clean v18 compact-packer fixtures while supplying only bare skeleton-name bullets in the seeded playbook context.", "challenge_v20_description_only_skeleton": "Ablation group reusing the two clean v18 compact-packer fixtures while supplying compact natural-language skeleton descriptions without plan labels in the seeded playbook context.", "challenge_v21_neutral_anchor_skeleton": "Ablation group reusing the two clean v18 compact-packer fixtures while supplying neutral natural-language step anchors plus compact skeleton descriptions without plan labels in the seeded playbook context.", "challenge_v22_code_like_anchor_skeleton": "Ablation group reusing the two clean v18 compact-packer fixtures while supplying compact skeleton descriptions plus code-like snake_case step anchors without the v18 plan_ prefix.", "challenge_v23_exact_labels_without_plan_prefix": "Ablation group reusing the two clean v18 compact-packer fixtures while supplying the v18 detailed skeleton labels with only the detailed-plan prefix removed.", "challenge_v24_plan_prefix_generic_labels": "Ablation group reusing the two clean v18 compact-packer fixtures while supplying compact descriptions plus generic plan_ labels that differ from v18 exact labels.", "challenge_v25_step_prefix_exact_labels": "Ablation group reusing the two clean v18 compact-packer fixtures while supplying compact descriptions plus step_ prefixed exact v18 label roots." } }