{ "id": "sample_000013", "task_type": "matrix_3x3", "focus": "3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_size). Per-T attribute change: all leaves share one size level and follow Distribute-three order (S -> M -> L), reverse. Horizontal relation E[r,c+1]=T^2(E[r,c]); vertical relation E[r+1,c]=T^1(E[r,c]). Effective stride detail: horizontal applies T^2 Distribute-three steps; vertical applies T^1 Distribute-three steps.", "target_position": [ 2, 2 ], "missing_positions": [ [ 2, 2 ] ], "empty_grid_positions": [ [ 2, 2 ] ], "grid_observation_mask": [ [ true, true, true ], [ true, true, true ], [ true, true, false ] ], "grid_paths": [ [ "sample_000013/grid_0_0.ply", "sample_000013/grid_0_1.ply", "sample_000013/grid_0_2.ply" ], [ "sample_000013/grid_1_0.ply", "sample_000013/grid_1_1.ply", "sample_000013/grid_1_2.ply" ], [ "sample_000013/grid_2_0.ply", "sample_000013/grid_2_1.ply", null ] ], "candidate_paths": [ "sample_000013/cand_0.ply", "sample_000013/cand_1.ply", "sample_000013/cand_2.ply", "sample_000013/cand_3.ply" ], "gt_index": 1, "gt_label": "B", "distractor_types": [ "analogical_wrong_relation", "gt", "perceptual_plausible", "irrelevant" ], "rule_template": "Distribute-three", "rule_params": { "template": "Distribute-three", "axis": "distribute_three_size", "leaf_idx": null, "leaf_indices": null, "direction": -1, "directions": null, "rot_axis": null, "source_indices": null }, "rule_params_vertical": { "template": "Distribute-three", "axis": "distribute_three_size", "leaf_idx": null, "leaf_indices": null, "direction": -1, "directions": null, "rot_axis": null, "source_indices": null }, "matrix_relation": { "formula": "E[r,c] = T^(r*k_v + c*k_h)(E[0,0])", "rule_instance": { "template": "Distribute-three", "axis": "distribute_three_size", "changed_attribute": "size_level", "description": "Distribute-three on size_level (direction=-1)", "direction": -1 }, "attribute_change_detail": { "template": "Distribute-three", "axis": "distribute_three_size", "per_T_change": { "attribute": "size_level(all_leaves)", "direction": -1, "distribution": "distribute-three" }, "horizontal_effective_change": { "applied_power": 2 }, "vertical_effective_change": { "applied_power": 1 } }, "horizontal_relation": { "step_power": 2, "formula": "E[r,c+1] = T^2(E[r,c])", "changed_attribute": "size_level", "description": "Distribute-three on size_level (direction=-1)" }, "vertical_relation": { "step_power": 1, "formula": "E[r+1,c] = T^1(E[r,c])", "changed_attribute": "size_level", "description": "Distribute-three on size_level (direction=-1)" } }, "k_h": 2, "k_v": 1, "K_max": 6, "matrix_level_config": { "size_levels": [ "XS", "M", "XL" ], "delta_levels": [ "VeryNear", "Near", "Mid", "Far", "VeryFar" ], "density_levels": [ 11264, 8192, 5120 ], "density_indices": [ 0, 2, 4 ], "slot_levels": [ -1, 0, 1 ], "color_levels": [ "red", "green", "blue" ] }, "n_points": 4096, "point_cloud_row_perturbation": { "enabled": true, "single_type_per_sample": true, "selected_type": "jitter", "apply_density_perturb_on_density_rules": true, "rows": { "index_0_row1": { "density_keep_ratio": 1.0, "jitter_std_ratio": 0.0, "quantize_step_ratio": 0.0, "outlier_replace_ratio": 0.0 }, "index_1_row2": { "density_keep_ratio": 0.75, "jitter_std_ratio": 0.003, "quantize_step_ratio": 0.005, "outlier_replace_ratio": 0.01 }, "index_2_row3": { "density_keep_ratio": 0.5, "jitter_std_ratio": 0.009, "quantize_step_ratio": 0.015, "outlier_replace_ratio": 0.04 } } }, "rule": { "template": "Distribute-three", "source_align": [ "R1-6", "R3-10" ], "params": { "template": "Distribute-three", "axis": "distribute_three_size", "leaf_idx": null, "leaf_indices": null, "direction": -1, "directions": null, "rot_axis": null, "source_indices": null }, "vertical_template": "Distribute-three", "vertical_params": { "template": "Distribute-three", "axis": "distribute_three_size", "leaf_idx": null, "leaf_indices": null, "direction": -1, "directions": null, "rot_axis": null, "source_indices": null } }, "entities": { "grid": [ [ { "csg": { "type": "op", "op": "union", "left": { "type": "op", "op": "union", "left": { "type": "leaf", "id": 0, "prim": "cylinder", "size": "M", "local_pose_deg": [ 120, 300, 0 ], "slot": -1, "delta_level": "Mid" }, "right": { "type": "leaf", "id": 1, "prim": "box", "size": "M", "local_pose_deg": [ 180, 0, 0 ], "slot": 0, "delta_level": "Mid" } }, "right": { "type": "leaf", "id": 2, "prim": "cylinder", "size": "M", "local_pose_deg": [ 180, 0, 120 ], "slot": 1, "delta_level": "Mid" } }, "obs": { "global_pose_deg": [ 300, 240, 60 ], "global_translation": [ 0.0, 0.0, 0.0 ], "sampling_mode": "surface", "n_points": 8192, "part_sampling_weights": null, "density_preset_idx": 2, "color_preset_idx": 2 }, "expr": "Union(Union(Cylinder,Box),Cylinder)" }, { "csg": { "type": "op", "op": "union", "left": { "type": "op", "op": "union", "left": { "type": "leaf", "id": 0, "prim": "cylinder", "size": "L", "local_pose_deg": [ 120, 300, 0 ], "slot": -1, "delta_level": "Mid" }, "right": { "type": "leaf", "id": 1, "prim": "box", "size": "L", "local_pose_deg": [ 180, 0, 0 ], "slot": 0, "delta_level": "Mid" } }, "right": { "type": "leaf", "id": 2, "prim": "cylinder", "size": "L", "local_pose_deg": [ 180, 0, 120 ], "slot": 1, "delta_level": "Mid" } }, "obs": { 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2, "color_preset_idx": 2 }, "expr": "Union(Union(Cylinder,Box),Cylinder)" }, { "csg": { "type": "op", "op": "union", "left": { "type": "op", "op": "union", "left": { "type": "leaf", "id": 0, "prim": "cylinder", "size": "S", "local_pose_deg": [ 120, 300, 0 ], "slot": -1, "delta_level": "Mid" }, "right": { "type": "leaf", "id": 1, "prim": "box", "size": "S", "local_pose_deg": [ 180, 0, 0 ], "slot": 0, "delta_level": "Mid" } }, "right": { "type": "leaf", "id": 2, "prim": "cylinder", "size": "S", "local_pose_deg": [ 180, 0, 120 ], "slot": 1, "delta_level": "Mid" } }, "obs": { "global_pose_deg": [ 300, 240, 60 ], "global_translation": [ 0.0, 0.0, 0.0 ], "sampling_mode": "surface", "n_points": 8192, "part_sampling_weights": null, "density_preset_idx": 2, "color_preset_idx": 2 }, "expr": "Union(Union(Cylinder,Box),Cylinder)" }, { "csg": { "type": "op", "op": "union", "left": { "type": "op", "op": "union", "left": { "type": "leaf", "id": 0, "prim": "cylinder", "size": "M", "local_pose_deg": [ 120, 300, 0 ], "slot": -1, "delta_level": "Mid" }, "right": { "type": "leaf", "id": 1, "prim": "box", "size": "M", "local_pose_deg": [ 180, 0, 0 ], "slot": 0, "delta_level": "Mid" } }, "right": { "type": "leaf", "id": 2, "prim": "cylinder", "size": "M", "local_pose_deg": [ 180, 0, 120 ], "slot": 1, "delta_level": "Mid" } }, "obs": { "global_pose_deg": [ 300, 240, 60 ], "global_translation": [ 0.0, 0.0, 0.0 ], "sampling_mode": "surface", "n_points": 8192, "part_sampling_weights": null, "density_preset_idx": 2, "color_preset_idx": 2 }, "expr": "Union(Union(Cylinder,Box),Cylinder)" } ] ], "candidates": [ { "csg": { "type": "op", "op": "union", "left": { "type": "op", "op": "union", "left": { "type": "leaf", "id": 0, "prim": "cylinder", "size": "S", "local_pose_deg": [ 120, 300, 0 ], "slot": -1, "delta_level": "Mid" }, "right": { "type": "leaf", "id": 1, "prim": "box", "size": "S", "local_pose_deg": [ 180, 0, 0 ], "slot": 0, "delta_level": "Mid" } }, "right": { "type": "leaf", "id": 2, "prim": "cylinder", "size": "S", "local_pose_deg": [ 180, 0, 120 ], "slot": 1, "delta_level": "Mid" } }, "obs": { "global_pose_deg": [ 300, 240, 60 ], "global_translation": [ 0.0, 0.0, 0.0 ], "sampling_mode": "surface", "n_points": 8192, "part_sampling_weights": null, "density_preset_idx": 2, "color_preset_idx": 0 }, "expr": "Union(Union(Cylinder,Box),Cylinder)" }, { "csg": { "type": "op", "op": "union", "left": { "type": "op", "op": "union", "left": { "type": "leaf", "id": 0, "prim": "cylinder", "size": "M", "local_pose_deg": [ 120, 300, 0 ], "slot": -1, "delta_level": "Mid" }, "right": { "type": "leaf", "id": 1, "prim": "box", "size": "M", "local_pose_deg": [ 180, 0, 0 ], "slot": 0, "delta_level": "Mid" } }, "right": { "type": "leaf", "id": 2, "prim": "cylinder", "size": "M", "local_pose_deg": [ 180, 0, 120 ], "slot": 1, "delta_level": "Mid" } }, "obs": { "global_pose_deg": [ 300, 240, 60 ], "global_translation": [ 0.0, 0.0, 0.0 ], "sampling_mode": "surface", "n_points": 8192, "part_sampling_weights": null, "density_preset_idx": 2, "color_preset_idx": 2 }, "expr": "Union(Union(Cylinder,Box),Cylinder)" }, { "csg": { "type": "leaf", "id": 0, "prim": "cylinder", "size": "M", "local_pose_deg": [ 120, 300, 0 ], "slot": 0, "delta_level": "Mid" }, "obs": { "global_pose_deg": [ 300, 240, 60 ], "global_translation": [ 0.0, 0.0, 0.0 ], "sampling_mode": "surface", "n_points": 11264, "part_sampling_weights": null, "density_preset_idx": 0, "color_preset_idx": 2 }, "expr": "Cylinder" }, { "csg": { "type": "op", "op": "union", "left": { "type": "op", "op": "union", "left": { "type": "leaf", "id": 0, "prim": "cylinder", "size": "L", "local_pose_deg": [ 120, 300, 0 ], "slot": -1, "delta_level": "Mid" }, "right": { "type": "leaf", "id": 1, "prim": "box", "size": "L", "local_pose_deg": [ 180, 0, 0 ], "slot": 0, "delta_level": "Mid" } }, "right": { "type": "leaf", "id": 2, "prim": "cylinder", "size": "L", "local_pose_deg": [ 180, 0, 120 ], "slot": 1, "delta_level": "Mid" } }, "obs": { "global_pose_deg": [ 300, 240, 60 ], "global_translation": [ 0.0, 0.0, 0.0 ], "sampling_mode": "surface", "n_points": 8192, "part_sampling_weights": null, "density_preset_idx": 2, "color_preset_idx": 2 }, "expr": "Union(Union(Cylinder,Box),Cylinder)" } ] }, "notes": { "candidate_notes": [ "符合替代关系 T',但不符合真实关系 T", "真实关系 T 的唯一正确补全", "数量干扰项:仅改变几何体数量,不满足真实/替代关系", "尺寸干扰项:仅改变尺寸档位" ], "alt_relations": [ { "rule_template": "Distribute-three", "rule_params": { "template": "Distribute-three", "axis": "distribute_three_color", "leaf_idx": null, "leaf_indices": null, "direction": -1, "directions": null, "rot_axis": null, "source_indices": null } } ] } }