id string | sample_id string | rule_template string | split string | task_type string | sample_path string | metadata_path string | mesh_path string | mesh_paths string | grid_paths string | candidate_paths string | grid_observation_mask string | target_position string | gt_index int8 | gt_label string | n_points int32 | k_h int8 | k_v int8 | focus string | rule_params string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Progression/sample_004426 | sample_004426 | Progression | train | matrix_3x3 | Progression/sample_004426 | Progression/sample_004426/meta.json | Progression/sample_004426 | ["Progression/sample_004426/grid_0_0.ply","Progression/sample_004426/grid_0_1.ply","Progression/sample_004426/grid_0_2.ply","Progression/sample_004426/grid_1_0.ply","Progression/sample_004426/grid_1_1.ply","Progression/sample_004426/grid_1_2.ply","Progression/sample_004426/grid_2_0.ply","Progression/sample_004426/grid_... | [["Progression/sample_004426/grid_0_0.ply","Progression/sample_004426/grid_0_1.ply","Progression/sample_004426/grid_0_2.ply"],["Progression/sample_004426/grid_1_0.ply","Progression/sample_004426/grid_1_1.ply","Progression/sample_004426/grid_1_2.ply"],["Progression/sample_004426/grid_2_0.ply","Progression/sample_004426/... | ["Progression/sample_004426/cand_0.ply","Progression/sample_004426/cand_1.ply","Progression/sample_004426/cand_2.ply","Progression/sample_004426/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=r). Per-T attribute change: all leaves change size_level by +1 per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal net size_level +1, vertical net size_level +2. | {"template":"Progression","axis":"r","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_002983 | sample_002983 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_002983 | Distribute-three/sample_002983/meta.json | Distribute-three/sample_002983 | ["Distribute-three/sample_002983/grid_0_0.ply","Distribute-three/sample_002983/grid_0_1.ply","Distribute-three/sample_002983/grid_0_2.ply","Distribute-three/sample_002983/grid_1_0.ply","Distribute-three/sample_002983/grid_1_1.ply","Distribute-three/sample_002983/grid_1_2.ply","Distribute-three/sample_002983/grid_2_0.pl... | [["Distribute-three/sample_002983/grid_0_0.ply","Distribute-three/sample_002983/grid_0_1.ply","Distribute-three/sample_002983/grid_0_2.ply"],["Distribute-three/sample_002983/grid_1_0.ply","Distribute-three/sample_002983/grid_1_1.ply","Distribute-three/sample_002983/grid_1_2.ply"],["Distribute-three/sample_002983/grid_2... | ["Distribute-three/sample_002983/cand_0.ply","Distribute-three/sample_002983/cand_1.ply","Distribute-three/sample_002983/cand_2.ply","Distribute-three/sample_002983/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_density). Per-T attribute change: density level follows Distribute-three order (0 -> 2 -> 4), forward. 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: horizo... | {"template":"Distribute-three","axis":"distribute_three_density","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Conservation/sample_002322 | sample_002322 | Conservation | train | matrix_3x3 | Conservation/sample_002322 | Conservation/sample_002322/meta.json | Conservation/sample_002322 | ["Conservation/sample_002322/grid_0_0.ply","Conservation/sample_002322/grid_0_1.ply","Conservation/sample_002322/grid_0_2.ply","Conservation/sample_002322/grid_1_0.ply","Conservation/sample_002322/grid_1_1.ply","Conservation/sample_002322/grid_1_2.ply","Conservation/sample_002322/grid_2_0.ply","Conservation/sample_0023... | [["Conservation/sample_002322/grid_0_0.ply","Conservation/sample_002322/grid_0_1.ply","Conservation/sample_002322/grid_0_2.ply"],["Conservation/sample_002322/grid_1_0.ply","Conservation/sample_002322/grid_1_1.ply","Conservation/sample_002322/grid_1_2.ply"],["Conservation/sample_002322/grid_2_0.ply","Conservation/sample... | ["Conservation/sample_002322/cand_0.ply","Conservation/sample_002322/cand_1.ply","Conservation/sample_002322/cand_2.ply","Conservation/sample_002322/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Conservation, axis=size_conservation). Per-T attribute change: size conservation triplet: leaf2:+1, leaf0:-1, leaf1:0. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 conserv... | {"template":"Conservation","axis":"size_conservation","leaf_idx":2,"leaf_indices":[2,0,1],"direction":0,"directions":[1,-1,0],"rot_axis":null,"source_indices":null} |
Count/sample_004514 | sample_004514 | Count | train | matrix_3x3 | Count/sample_004514 | Count/sample_004514/meta.json | Count/sample_004514 | ["Count/sample_004514/grid_0_0.ply","Count/sample_004514/grid_0_1.ply","Count/sample_004514/grid_0_2.ply","Count/sample_004514/grid_1_0.ply","Count/sample_004514/grid_1_1.ply","Count/sample_004514/grid_1_2.ply","Count/sample_004514/grid_2_0.ply","Count/sample_004514/grid_2_1.ply","Count/sample_004514/cand_0.ply","Count... | [["Count/sample_004514/grid_0_0.ply","Count/sample_004514/grid_0_1.ply","Count/sample_004514/grid_0_2.ply"],["Count/sample_004514/grid_1_0.ply","Count/sample_004514/grid_1_1.ply","Count/sample_004514/grid_1_2.ply"],["Count/sample_004514/grid_2_0.ply","Count/sample_004514/grid_2_1.ply",null]] | ["Count/sample_004514/cand_0.ply","Count/sample_004514/cand_1.ply","Count/sample_004514/cand_2.ply","Count/sample_004514/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. 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 count transitions; vertical applies T^1 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_000830 | sample_000830 | Symmetry | train | matrix_3x3 | Symmetry/sample_000830 | Symmetry/sample_000830/meta.json | Symmetry/sample_000830 | ["Symmetry/sample_000830/grid_0_0.ply","Symmetry/sample_000830/grid_0_1.ply","Symmetry/sample_000830/grid_0_2.ply","Symmetry/sample_000830/grid_1_0.ply","Symmetry/sample_000830/grid_1_1.ply","Symmetry/sample_000830/grid_1_2.ply","Symmetry/sample_000830/grid_2_0.ply","Symmetry/sample_000830/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_000830/grid_0_0.ply","Symmetry/sample_000830/grid_0_1.ply","Symmetry/sample_000830/grid_0_2.ply"],["Symmetry/sample_000830/grid_1_0.ply","Symmetry/sample_000830/grid_1_1.ply","Symmetry/sample_000830/grid_1_2.ply"],["Symmetry/sample_000830/grid_2_0.ply","Symmetry/sample_000830/grid_2_1.ply",null]] | ["Symmetry/sample_000830/cand_0.ply","Symmetry/sample_000830/cand_1.ply","Symmetry/sample_000830/cand_2.ply","Symmetry/sample_000830/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Conservation/sample_003661 | sample_003661 | Conservation | train | matrix_3x3 | Conservation/sample_003661 | Conservation/sample_003661/meta.json | Conservation/sample_003661 | ["Conservation/sample_003661/grid_0_0.ply","Conservation/sample_003661/grid_0_1.ply","Conservation/sample_003661/grid_0_2.ply","Conservation/sample_003661/grid_1_0.ply","Conservation/sample_003661/grid_1_1.ply","Conservation/sample_003661/grid_1_2.ply","Conservation/sample_003661/grid_2_0.ply","Conservation/sample_0036... | [["Conservation/sample_003661/grid_0_0.ply","Conservation/sample_003661/grid_0_1.ply","Conservation/sample_003661/grid_0_2.ply"],["Conservation/sample_003661/grid_1_0.ply","Conservation/sample_003661/grid_1_1.ply","Conservation/sample_003661/grid_1_2.ply"],["Conservation/sample_003661/grid_2_0.ply","Conservation/sample... | ["Conservation/sample_003661/cand_0.ply","Conservation/sample_003661/cand_1.ply","Conservation/sample_003661/cand_2.ply","Conservation/sample_003661/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Conservation, axis=size_conservation). Per-T attribute change: size conservation triplet: leaf2:+1, leaf1:-1, leaf0:0. 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 conserv... | {"template":"Conservation","axis":"size_conservation","leaf_idx":2,"leaf_indices":[2,1,0],"direction":1,"directions":[1,-1,0],"rot_axis":null,"source_indices":null} |
Progression/sample_003925 | sample_003925 | Progression | train | matrix_3x3 | Progression/sample_003925 | Progression/sample_003925/meta.json | Progression/sample_003925 | ["Progression/sample_003925/grid_0_0.ply","Progression/sample_003925/grid_0_1.ply","Progression/sample_003925/grid_0_2.ply","Progression/sample_003925/grid_1_0.ply","Progression/sample_003925/grid_1_1.ply","Progression/sample_003925/grid_1_2.ply","Progression/sample_003925/grid_2_0.ply","Progression/sample_003925/grid_... | [["Progression/sample_003925/grid_0_0.ply","Progression/sample_003925/grid_0_1.ply","Progression/sample_003925/grid_0_2.ply"],["Progression/sample_003925/grid_1_0.ply","Progression/sample_003925/grid_1_1.ply","Progression/sample_003925/grid_1_2.ply"],["Progression/sample_003925/grid_2_0.ply","Progression/sample_003925/... | ["Progression/sample_003925/cand_0.ply","Progression/sample_003925/cand_1.ply","Progression/sample_003925/cand_2.ply","Progression/sample_003925/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=R). Per-T attribute change: global_pose_deg.y rotates -60 degrees per T. 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 net rotation -120 degrees on y, vertical net ro... | {"template":"Progression","axis":"R","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":"y","source_indices":null} |
Symmetry/sample_001488 | sample_001488 | Symmetry | train | matrix_3x3 | Symmetry/sample_001488 | Symmetry/sample_001488/meta.json | Symmetry/sample_001488 | ["Symmetry/sample_001488/grid_0_0.ply","Symmetry/sample_001488/grid_0_1.ply","Symmetry/sample_001488/grid_0_2.ply","Symmetry/sample_001488/grid_1_0.ply","Symmetry/sample_001488/grid_1_1.ply","Symmetry/sample_001488/grid_1_2.ply","Symmetry/sample_001488/grid_2_0.ply","Symmetry/sample_001488/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_001488/grid_0_0.ply","Symmetry/sample_001488/grid_0_1.ply","Symmetry/sample_001488/grid_0_2.ply"],["Symmetry/sample_001488/grid_1_0.ply","Symmetry/sample_001488/grid_1_1.ply","Symmetry/sample_001488/grid_1_2.ply"],["Symmetry/sample_001488/grid_2_0.ply","Symmetry/sample_001488/grid_2_1.ply",null]] | ["Symmetry/sample_001488/cand_0.ply","Symmetry/sample_001488/cand_1.ply","Symmetry/sample_001488/cand_2.ply","Symmetry/sample_001488/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_002023 | sample_002023 | Count | train | matrix_3x3 | Count/sample_002023 | Count/sample_002023/meta.json | Count/sample_002023 | ["Count/sample_002023/grid_0_0.ply","Count/sample_002023/grid_0_1.ply","Count/sample_002023/grid_0_2.ply","Count/sample_002023/grid_1_0.ply","Count/sample_002023/grid_1_1.ply","Count/sample_002023/grid_1_2.ply","Count/sample_002023/grid_2_0.ply","Count/sample_002023/grid_2_1.ply","Count/sample_002023/cand_0.ply","Count... | [["Count/sample_002023/grid_0_0.ply","Count/sample_002023/grid_0_1.ply","Count/sample_002023/grid_0_2.ply"],["Count/sample_002023/grid_1_0.ply","Count/sample_002023/grid_1_1.ply","Count/sample_002023/grid_1_2.ply"],["Count/sample_002023/grid_2_0.ply","Count/sample_002023/grid_2_1.ply",null]] | ["Count/sample_002023/cand_0.ply","Count/sample_002023/cand_1.ply","Count/sample_002023/cand_2.ply","Count/sample_002023/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. 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 count transitions; vertical applies T^1 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_004993 | sample_004993 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_004993 | Distribute-three/sample_004993/meta.json | Distribute-three/sample_004993 | ["Distribute-three/sample_004993/grid_0_0.ply","Distribute-three/sample_004993/grid_0_1.ply","Distribute-three/sample_004993/grid_0_2.ply","Distribute-three/sample_004993/grid_1_0.ply","Distribute-three/sample_004993/grid_1_1.ply","Distribute-three/sample_004993/grid_1_2.ply","Distribute-three/sample_004993/grid_2_0.pl... | [["Distribute-three/sample_004993/grid_0_0.ply","Distribute-three/sample_004993/grid_0_1.ply","Distribute-three/sample_004993/grid_0_2.ply"],["Distribute-three/sample_004993/grid_1_0.ply","Distribute-three/sample_004993/grid_1_1.ply","Distribute-three/sample_004993/grid_1_2.ply"],["Distribute-three/sample_004993/grid_2... | ["Distribute-three/sample_004993/cand_0.ply","Distribute-three/sample_004993/cand_1.ply","Distribute-three/sample_004993/cand_2.ply","Distribute-three/sample_004993/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_shape). Per-T attribute change: all leaves share one primitive type and follow Distribute-three order (sphere -> box -> cylinder), reverse. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r... | {"template":"Distribute-three","axis":"distribute_three_shape","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Conservation/sample_004215 | sample_004215 | Conservation | train | matrix_3x3 | Conservation/sample_004215 | Conservation/sample_004215/meta.json | Conservation/sample_004215 | ["Conservation/sample_004215/grid_0_0.ply","Conservation/sample_004215/grid_0_1.ply","Conservation/sample_004215/grid_0_2.ply","Conservation/sample_004215/grid_1_0.ply","Conservation/sample_004215/grid_1_1.ply","Conservation/sample_004215/grid_1_2.ply","Conservation/sample_004215/grid_2_0.ply","Conservation/sample_0042... | [["Conservation/sample_004215/grid_0_0.ply","Conservation/sample_004215/grid_0_1.ply","Conservation/sample_004215/grid_0_2.ply"],["Conservation/sample_004215/grid_1_0.ply","Conservation/sample_004215/grid_1_1.ply","Conservation/sample_004215/grid_1_2.ply"],["Conservation/sample_004215/grid_2_0.ply","Conservation/sample... | ["Conservation/sample_004215/cand_0.ply","Conservation/sample_004215/cand_1.ply","Conservation/sample_004215/cand_2.ply","Conservation/sample_004215/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Conservation, axis=size_conservation). Per-T attribute change: size conservation triplet: leaf0:+1, leaf1:-1, leaf2:0. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 conserv... | {"template":"Conservation","axis":"size_conservation","leaf_idx":0,"leaf_indices":[0,1,2],"direction":1,"directions":[1,-1,0],"rot_axis":null,"source_indices":null} |
Symmetry/sample_001339 | sample_001339 | Symmetry | train | matrix_3x3 | Symmetry/sample_001339 | Symmetry/sample_001339/meta.json | Symmetry/sample_001339 | ["Symmetry/sample_001339/grid_0_0.ply","Symmetry/sample_001339/grid_0_1.ply","Symmetry/sample_001339/grid_0_2.ply","Symmetry/sample_001339/grid_1_0.ply","Symmetry/sample_001339/grid_1_1.ply","Symmetry/sample_001339/grid_1_2.ply","Symmetry/sample_001339/grid_2_0.ply","Symmetry/sample_001339/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_001339/grid_0_0.ply","Symmetry/sample_001339/grid_0_1.ply","Symmetry/sample_001339/grid_0_2.ply"],["Symmetry/sample_001339/grid_1_0.ply","Symmetry/sample_001339/grid_1_1.ply","Symmetry/sample_001339/grid_1_2.ply"],["Symmetry/sample_001339/grid_2_0.ply","Symmetry/sample_001339/grid_2_1.ply",null]] | ["Symmetry/sample_001339/cand_0.ply","Symmetry/sample_001339/cand_1.ply","Symmetry/sample_001339/cand_2.ply","Symmetry/sample_001339/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_004096 | sample_004096 | Symmetry | train | matrix_3x3 | Symmetry/sample_004096 | Symmetry/sample_004096/meta.json | Symmetry/sample_004096 | ["Symmetry/sample_004096/grid_0_0.ply","Symmetry/sample_004096/grid_0_1.ply","Symmetry/sample_004096/grid_0_2.ply","Symmetry/sample_004096/grid_1_0.ply","Symmetry/sample_004096/grid_1_1.ply","Symmetry/sample_004096/grid_1_2.ply","Symmetry/sample_004096/grid_2_0.ply","Symmetry/sample_004096/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_004096/grid_0_0.ply","Symmetry/sample_004096/grid_0_1.ply","Symmetry/sample_004096/grid_0_2.ply"],["Symmetry/sample_004096/grid_1_0.ply","Symmetry/sample_004096/grid_1_1.ply","Symmetry/sample_004096/grid_1_2.ply"],["Symmetry/sample_004096/grid_2_0.ply","Symmetry/sample_004096/grid_2_1.ply",null]] | ["Symmetry/sample_004096/cand_0.ply","Symmetry/sample_004096/cand_1.ply","Symmetry/sample_004096/cand_2.ply","Symmetry/sample_004096/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Conservation/sample_003274 | sample_003274 | Conservation | train | matrix_3x3 | Conservation/sample_003274 | Conservation/sample_003274/meta.json | Conservation/sample_003274 | ["Conservation/sample_003274/grid_0_0.ply","Conservation/sample_003274/grid_0_1.ply","Conservation/sample_003274/grid_0_2.ply","Conservation/sample_003274/grid_1_0.ply","Conservation/sample_003274/grid_1_1.ply","Conservation/sample_003274/grid_1_2.ply","Conservation/sample_003274/grid_2_0.ply","Conservation/sample_0032... | [["Conservation/sample_003274/grid_0_0.ply","Conservation/sample_003274/grid_0_1.ply","Conservation/sample_003274/grid_0_2.ply"],["Conservation/sample_003274/grid_1_0.ply","Conservation/sample_003274/grid_1_1.ply","Conservation/sample_003274/grid_1_2.ply"],["Conservation/sample_003274/grid_2_0.ply","Conservation/sample... | ["Conservation/sample_003274/cand_0.ply","Conservation/sample_003274/cand_1.ply","Conservation/sample_003274/cand_2.ply","Conservation/sample_003274/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Conservation, axis=size_conservation). Per-T attribute change: size conservation triplet: leaf0:+1, leaf1:-1, leaf2:0. 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 conserv... | {"template":"Conservation","axis":"size_conservation","leaf_idx":0,"leaf_indices":[0,1,2],"direction":1,"directions":[1,-1,0],"rot_axis":null,"source_indices":null} |
Permutation/sample_004432 | sample_004432 | Permutation | train | matrix_3x3 | Permutation/sample_004432 | Permutation/sample_004432/meta.json | Permutation/sample_004432 | ["Permutation/sample_004432/grid_0_0.ply","Permutation/sample_004432/grid_0_1.ply","Permutation/sample_004432/grid_0_2.ply","Permutation/sample_004432/grid_1_0.ply","Permutation/sample_004432/grid_1_1.ply","Permutation/sample_004432/grid_1_2.ply","Permutation/sample_004432/grid_2_0.ply","Permutation/sample_004432/grid_... | [["Permutation/sample_004432/grid_0_0.ply","Permutation/sample_004432/grid_0_1.ply","Permutation/sample_004432/grid_0_2.ply"],["Permutation/sample_004432/grid_1_0.ply","Permutation/sample_004432/grid_1_1.ply","Permutation/sample_004432/grid_1_2.ply"],["Permutation/sample_004432/grid_2_0.ply","Permutation/sample_004432/... | ["Permutation/sample_004432/cand_0.ply","Permutation/sample_004432/cand_1.ply","Permutation/sample_004432/cand_2.ply","Permutation/sample_004432/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step right shift per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 permut... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_000843 | sample_000843 | Count | train | matrix_3x3 | Count/sample_000843 | Count/sample_000843/meta.json | Count/sample_000843 | ["Count/sample_000843/grid_0_0.ply","Count/sample_000843/grid_0_1.ply","Count/sample_000843/grid_0_2.ply","Count/sample_000843/grid_1_0.ply","Count/sample_000843/grid_1_1.ply","Count/sample_000843/grid_1_2.ply","Count/sample_000843/grid_2_0.ply","Count/sample_000843/grid_2_1.ply","Count/sample_000843/cand_0.ply","Count... | [["Count/sample_000843/grid_0_0.ply","Count/sample_000843/grid_0_1.ply","Count/sample_000843/grid_0_2.ply"],["Count/sample_000843/grid_1_0.ply","Count/sample_000843/grid_1_1.ply","Count/sample_000843/grid_1_2.ply"],["Count/sample_000843/grid_2_0.ply","Count/sample_000843/grid_2_1.ply",null]] | ["Count/sample_000843/cand_0.ply","Count/sample_000843/cand_1.ply","Count/sample_000843/cand_2.ply","Count/sample_000843/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. 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 count transitions; vertical applies T^1 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_002856 | sample_002856 | Symmetry | train | matrix_3x3 | Symmetry/sample_002856 | Symmetry/sample_002856/meta.json | Symmetry/sample_002856 | ["Symmetry/sample_002856/grid_0_0.ply","Symmetry/sample_002856/grid_0_1.ply","Symmetry/sample_002856/grid_0_2.ply","Symmetry/sample_002856/grid_1_0.ply","Symmetry/sample_002856/grid_1_1.ply","Symmetry/sample_002856/grid_1_2.ply","Symmetry/sample_002856/grid_2_0.ply","Symmetry/sample_002856/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_002856/grid_0_0.ply","Symmetry/sample_002856/grid_0_1.ply","Symmetry/sample_002856/grid_0_2.ply"],["Symmetry/sample_002856/grid_1_0.ply","Symmetry/sample_002856/grid_1_1.ply","Symmetry/sample_002856/grid_1_2.ply"],["Symmetry/sample_002856/grid_2_0.ply","Symmetry/sample_002856/grid_2_1.ply",null]] | ["Symmetry/sample_002856/cand_0.ply","Symmetry/sample_002856/cand_1.ply","Symmetry/sample_002856/cand_2.ply","Symmetry/sample_002856/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_000380 | sample_000380 | Count | train | matrix_3x3 | Count/sample_000380 | Count/sample_000380/meta.json | Count/sample_000380 | ["Count/sample_000380/grid_0_0.ply","Count/sample_000380/grid_0_1.ply","Count/sample_000380/grid_0_2.ply","Count/sample_000380/grid_1_0.ply","Count/sample_000380/grid_1_1.ply","Count/sample_000380/grid_1_2.ply","Count/sample_000380/grid_2_0.ply","Count/sample_000380/grid_2_1.ply","Count/sample_000380/cand_0.ply","Count... | [["Count/sample_000380/grid_0_0.ply","Count/sample_000380/grid_0_1.ply","Count/sample_000380/grid_0_2.ply"],["Count/sample_000380/grid_1_0.ply","Count/sample_000380/grid_1_1.ply","Count/sample_000380/grid_1_2.ply"],["Count/sample_000380/grid_2_0.ply","Count/sample_000380/grid_2_1.ply",null]] | ["Count/sample_000380/cand_0.ply","Count/sample_000380/cand_1.ply","Count/sample_000380/cand_2.ply","Count/sample_000380/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. 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 count transitions; vertical applies T^1 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_001191 | sample_001191 | Count | train | matrix_3x3 | Count/sample_001191 | Count/sample_001191/meta.json | Count/sample_001191 | ["Count/sample_001191/grid_0_0.ply","Count/sample_001191/grid_0_1.ply","Count/sample_001191/grid_0_2.ply","Count/sample_001191/grid_1_0.ply","Count/sample_001191/grid_1_1.ply","Count/sample_001191/grid_1_2.ply","Count/sample_001191/grid_2_0.ply","Count/sample_001191/grid_2_1.ply","Count/sample_001191/cand_0.ply","Count... | [["Count/sample_001191/grid_0_0.ply","Count/sample_001191/grid_0_1.ply","Count/sample_001191/grid_0_2.ply"],["Count/sample_001191/grid_1_0.ply","Count/sample_001191/grid_1_1.ply","Count/sample_001191/grid_1_2.ply"],["Count/sample_001191/grid_2_0.ply","Count/sample_001191/grid_2_1.ply",null]] | ["Count/sample_001191/cand_0.ply","Count/sample_001191/cand_1.ply","Count/sample_001191/cand_2.ply","Count/sample_001191/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_001183 | sample_001183 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_001183 | Distribute-three/sample_001183/meta.json | Distribute-three/sample_001183 | ["Distribute-three/sample_001183/grid_0_0.ply","Distribute-three/sample_001183/grid_0_1.ply","Distribute-three/sample_001183/grid_0_2.ply","Distribute-three/sample_001183/grid_1_0.ply","Distribute-three/sample_001183/grid_1_1.ply","Distribute-three/sample_001183/grid_1_2.ply","Distribute-three/sample_001183/grid_2_0.pl... | [["Distribute-three/sample_001183/grid_0_0.ply","Distribute-three/sample_001183/grid_0_1.ply","Distribute-three/sample_001183/grid_0_2.ply"],["Distribute-three/sample_001183/grid_1_0.ply","Distribute-three/sample_001183/grid_1_1.ply","Distribute-three/sample_001183/grid_1_2.ply"],["Distribute-three/sample_001183/grid_2... | ["Distribute-three/sample_001183/cand_0.ply","Distribute-three/sample_001183/cand_1.ply","Distribute-three/sample_001183/cand_2.ply","Distribute-three/sample_001183/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_color). Per-T attribute change: entity color follows Distribute-three order (red -> green -> blue), forward. 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: ... | {"template":"Distribute-three","axis":"distribute_three_color","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Progression/sample_000372 | sample_000372 | Progression | train | matrix_3x3 | Progression/sample_000372 | Progression/sample_000372/meta.json | Progression/sample_000372 | ["Progression/sample_000372/grid_0_0.ply","Progression/sample_000372/grid_0_1.ply","Progression/sample_000372/grid_0_2.ply","Progression/sample_000372/grid_1_0.ply","Progression/sample_000372/grid_1_1.ply","Progression/sample_000372/grid_1_2.ply","Progression/sample_000372/grid_2_0.ply","Progression/sample_000372/grid_... | [["Progression/sample_000372/grid_0_0.ply","Progression/sample_000372/grid_0_1.ply","Progression/sample_000372/grid_0_2.ply"],["Progression/sample_000372/grid_1_0.ply","Progression/sample_000372/grid_1_1.ply","Progression/sample_000372/grid_1_2.ply"],["Progression/sample_000372/grid_2_0.ply","Progression/sample_000372/... | ["Progression/sample_000372/cand_0.ply","Progression/sample_000372/cand_1.ply","Progression/sample_000372/cand_2.ply","Progression/sample_000372/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=r). Per-T attribute change: all leaves change size_level by +1 per T. 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 net size_level +2, vertical net size_level +1. | {"template":"Progression","axis":"r","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_002703 | sample_002703 | Permutation | train | matrix_3x3 | Permutation/sample_002703 | Permutation/sample_002703/meta.json | Permutation/sample_002703 | ["Permutation/sample_002703/grid_0_0.ply","Permutation/sample_002703/grid_0_1.ply","Permutation/sample_002703/grid_0_2.ply","Permutation/sample_002703/grid_1_0.ply","Permutation/sample_002703/grid_1_1.ply","Permutation/sample_002703/grid_1_2.ply","Permutation/sample_002703/grid_2_0.ply","Permutation/sample_002703/grid_... | [["Permutation/sample_002703/grid_0_0.ply","Permutation/sample_002703/grid_0_1.ply","Permutation/sample_002703/grid_0_2.ply"],["Permutation/sample_002703/grid_1_0.ply","Permutation/sample_002703/grid_1_1.ply","Permutation/sample_002703/grid_1_2.ply"],["Permutation/sample_002703/grid_2_0.ply","Permutation/sample_002703/... | ["Permutation/sample_002703/cand_0.ply","Permutation/sample_002703/cand_1.ply","Permutation/sample_002703/cand_2.ply","Permutation/sample_002703/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step left shift per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 permuta... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_001584 | sample_001584 | Count | train | matrix_3x3 | Count/sample_001584 | Count/sample_001584/meta.json | Count/sample_001584 | ["Count/sample_001584/grid_0_0.ply","Count/sample_001584/grid_0_1.ply","Count/sample_001584/grid_0_2.ply","Count/sample_001584/grid_1_0.ply","Count/sample_001584/grid_1_1.ply","Count/sample_001584/grid_1_2.ply","Count/sample_001584/grid_2_0.ply","Count/sample_001584/grid_2_1.ply","Count/sample_001584/cand_0.ply","Count... | [["Count/sample_001584/grid_0_0.ply","Count/sample_001584/grid_0_1.ply","Count/sample_001584/grid_0_2.ply"],["Count/sample_001584/grid_1_0.ply","Count/sample_001584/grid_1_1.ply","Count/sample_001584/grid_1_2.ply"],["Count/sample_001584/grid_2_0.ply","Count/sample_001584/grid_2_1.ply",null]] | ["Count/sample_001584/cand_0.ply","Count/sample_001584/cand_1.ply","Count/sample_001584/cand_2.ply","Count/sample_001584/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_004922 | sample_004922 | Permutation | train | matrix_3x3 | Permutation/sample_004922 | Permutation/sample_004922/meta.json | Permutation/sample_004922 | ["Permutation/sample_004922/grid_0_0.ply","Permutation/sample_004922/grid_0_1.ply","Permutation/sample_004922/grid_0_2.ply","Permutation/sample_004922/grid_1_0.ply","Permutation/sample_004922/grid_1_1.ply","Permutation/sample_004922/grid_1_2.ply","Permutation/sample_004922/grid_2_0.ply","Permutation/sample_004922/grid_... | [["Permutation/sample_004922/grid_0_0.ply","Permutation/sample_004922/grid_0_1.ply","Permutation/sample_004922/grid_0_2.ply"],["Permutation/sample_004922/grid_1_0.ply","Permutation/sample_004922/grid_1_1.ply","Permutation/sample_004922/grid_1_2.ply"],["Permutation/sample_004922/grid_2_0.ply","Permutation/sample_004922/... | ["Permutation/sample_004922/cand_0.ply","Permutation/sample_004922/cand_1.ply","Permutation/sample_004922/cand_2.ply","Permutation/sample_004922/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step left shift per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 permuta... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_000752 | sample_000752 | Symmetry | train | matrix_3x3 | Symmetry/sample_000752 | Symmetry/sample_000752/meta.json | Symmetry/sample_000752 | ["Symmetry/sample_000752/grid_0_0.ply","Symmetry/sample_000752/grid_0_1.ply","Symmetry/sample_000752/grid_0_2.ply","Symmetry/sample_000752/grid_1_0.ply","Symmetry/sample_000752/grid_1_1.ply","Symmetry/sample_000752/grid_1_2.ply","Symmetry/sample_000752/grid_2_0.ply","Symmetry/sample_000752/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_000752/grid_0_0.ply","Symmetry/sample_000752/grid_0_1.ply","Symmetry/sample_000752/grid_0_2.ply"],["Symmetry/sample_000752/grid_1_0.ply","Symmetry/sample_000752/grid_1_1.ply","Symmetry/sample_000752/grid_1_2.ply"],["Symmetry/sample_000752/grid_2_0.ply","Symmetry/sample_000752/grid_2_1.ply",null]] | ["Symmetry/sample_000752/cand_0.ply","Symmetry/sample_000752/cand_1.ply","Symmetry/sample_000752/cand_2.ply","Symmetry/sample_000752/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_000031 | sample_000031 | Permutation | train | matrix_3x3 | Permutation/sample_000031 | Permutation/sample_000031/meta.json | Permutation/sample_000031 | ["Permutation/sample_000031/grid_0_0.ply","Permutation/sample_000031/grid_0_1.ply","Permutation/sample_000031/grid_0_2.ply","Permutation/sample_000031/grid_1_0.ply","Permutation/sample_000031/grid_1_1.ply","Permutation/sample_000031/grid_1_2.ply","Permutation/sample_000031/grid_2_0.ply","Permutation/sample_000031/grid_... | [["Permutation/sample_000031/grid_0_0.ply","Permutation/sample_000031/grid_0_1.ply","Permutation/sample_000031/grid_0_2.ply"],["Permutation/sample_000031/grid_1_0.ply","Permutation/sample_000031/grid_1_1.ply","Permutation/sample_000031/grid_1_2.ply"],["Permutation/sample_000031/grid_2_0.ply","Permutation/sample_000031/... | ["Permutation/sample_000031/cand_0.ply","Permutation/sample_000031/cand_1.ply","Permutation/sample_000031/cand_2.ply","Permutation/sample_000031/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step right shift per T. 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 permut... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_000189 | sample_000189 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_000189 | Distribute-three/sample_000189/meta.json | Distribute-three/sample_000189 | ["Distribute-three/sample_000189/grid_0_0.ply","Distribute-three/sample_000189/grid_0_1.ply","Distribute-three/sample_000189/grid_0_2.ply","Distribute-three/sample_000189/grid_1_0.ply","Distribute-three/sample_000189/grid_1_1.ply","Distribute-three/sample_000189/grid_1_2.ply","Distribute-three/sample_000189/grid_2_0.pl... | [["Distribute-three/sample_000189/grid_0_0.ply","Distribute-three/sample_000189/grid_0_1.ply","Distribute-three/sample_000189/grid_0_2.ply"],["Distribute-three/sample_000189/grid_1_0.ply","Distribute-three/sample_000189/grid_1_1.ply","Distribute-three/sample_000189/grid_1_2.ply"],["Distribute-three/sample_000189/grid_2... | ["Distribute-three/sample_000189/cand_0.ply","Distribute-three/sample_000189/cand_1.ply","Distribute-three/sample_000189/cand_2.ply","Distribute-three/sample_000189/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_density). Per-T attribute change: density level follows Distribute-three order (0 -> 2 -> 4), forward. 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: horizo... | {"template":"Distribute-three","axis":"distribute_three_density","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_004635 | sample_004635 | Count | train | matrix_3x3 | Count/sample_004635 | Count/sample_004635/meta.json | Count/sample_004635 | ["Count/sample_004635/grid_0_0.ply","Count/sample_004635/grid_0_1.ply","Count/sample_004635/grid_0_2.ply","Count/sample_004635/grid_1_0.ply","Count/sample_004635/grid_1_1.ply","Count/sample_004635/grid_1_2.ply","Count/sample_004635/grid_2_0.ply","Count/sample_004635/grid_2_1.ply","Count/sample_004635/cand_0.ply","Count... | [["Count/sample_004635/grid_0_0.ply","Count/sample_004635/grid_0_1.ply","Count/sample_004635/grid_0_2.ply"],["Count/sample_004635/grid_1_0.ply","Count/sample_004635/grid_1_1.ply","Count/sample_004635/grid_1_2.ply"],["Count/sample_004635/grid_2_0.ply","Count/sample_004635/grid_2_1.ply",null]] | ["Count/sample_004635/cand_0.ply","Count/sample_004635/cand_1.ply","Count/sample_004635/cand_2.ply","Count/sample_004635/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. 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 count transitions; vertical applies T^1 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_004674 | sample_004674 | Count | train | matrix_3x3 | Count/sample_004674 | Count/sample_004674/meta.json | Count/sample_004674 | ["Count/sample_004674/grid_0_0.ply","Count/sample_004674/grid_0_1.ply","Count/sample_004674/grid_0_2.ply","Count/sample_004674/grid_1_0.ply","Count/sample_004674/grid_1_1.ply","Count/sample_004674/grid_1_2.ply","Count/sample_004674/grid_2_0.ply","Count/sample_004674/grid_2_1.ply","Count/sample_004674/cand_0.ply","Count... | [["Count/sample_004674/grid_0_0.ply","Count/sample_004674/grid_0_1.ply","Count/sample_004674/grid_0_2.ply"],["Count/sample_004674/grid_1_0.ply","Count/sample_004674/grid_1_1.ply","Count/sample_004674/grid_1_2.ply"],["Count/sample_004674/grid_2_0.ply","Count/sample_004674/grid_2_1.ply",null]] | ["Count/sample_004674/cand_0.ply","Count/sample_004674/cand_1.ply","Count/sample_004674/cand_2.ply","Count/sample_004674/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_003291 | sample_003291 | Symmetry | train | matrix_3x3 | Symmetry/sample_003291 | Symmetry/sample_003291/meta.json | Symmetry/sample_003291 | ["Symmetry/sample_003291/grid_0_0.ply","Symmetry/sample_003291/grid_0_1.ply","Symmetry/sample_003291/grid_0_2.ply","Symmetry/sample_003291/grid_1_0.ply","Symmetry/sample_003291/grid_1_1.ply","Symmetry/sample_003291/grid_1_2.ply","Symmetry/sample_003291/grid_2_0.ply","Symmetry/sample_003291/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_003291/grid_0_0.ply","Symmetry/sample_003291/grid_0_1.ply","Symmetry/sample_003291/grid_0_2.ply"],["Symmetry/sample_003291/grid_1_0.ply","Symmetry/sample_003291/grid_1_1.ply","Symmetry/sample_003291/grid_1_2.ply"],["Symmetry/sample_003291/grid_2_0.ply","Symmetry/sample_003291/grid_2_1.ply",null]] | ["Symmetry/sample_003291/cand_0.ply","Symmetry/sample_003291/cand_1.ply","Symmetry/sample_003291/cand_2.ply","Symmetry/sample_003291/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_001653 | sample_001653 | Permutation | train | matrix_3x3 | Permutation/sample_001653 | Permutation/sample_001653/meta.json | Permutation/sample_001653 | ["Permutation/sample_001653/grid_0_0.ply","Permutation/sample_001653/grid_0_1.ply","Permutation/sample_001653/grid_0_2.ply","Permutation/sample_001653/grid_1_0.ply","Permutation/sample_001653/grid_1_1.ply","Permutation/sample_001653/grid_1_2.ply","Permutation/sample_001653/grid_2_0.ply","Permutation/sample_001653/grid_... | [["Permutation/sample_001653/grid_0_0.ply","Permutation/sample_001653/grid_0_1.ply","Permutation/sample_001653/grid_0_2.ply"],["Permutation/sample_001653/grid_1_0.ply","Permutation/sample_001653/grid_1_1.ply","Permutation/sample_001653/grid_1_2.ply"],["Permutation/sample_001653/grid_2_0.ply","Permutation/sample_001653/... | ["Permutation/sample_001653/cand_0.ply","Permutation/sample_001653/cand_1.ply","Permutation/sample_001653/cand_2.ply","Permutation/sample_001653/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step right shift per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 permut... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_001127 | sample_001127 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_001127 | Distribute-three/sample_001127/meta.json | Distribute-three/sample_001127 | ["Distribute-three/sample_001127/grid_0_0.ply","Distribute-three/sample_001127/grid_0_1.ply","Distribute-three/sample_001127/grid_0_2.ply","Distribute-three/sample_001127/grid_1_0.ply","Distribute-three/sample_001127/grid_1_1.ply","Distribute-three/sample_001127/grid_1_2.ply","Distribute-three/sample_001127/grid_2_0.pl... | [["Distribute-three/sample_001127/grid_0_0.ply","Distribute-three/sample_001127/grid_0_1.ply","Distribute-three/sample_001127/grid_0_2.ply"],["Distribute-three/sample_001127/grid_1_0.ply","Distribute-three/sample_001127/grid_1_1.ply","Distribute-three/sample_001127/grid_1_2.ply"],["Distribute-three/sample_001127/grid_2... | ["Distribute-three/sample_001127/cand_0.ply","Distribute-three/sample_001127/cand_1.ply","Distribute-three/sample_001127/cand_2.ply","Distribute-three/sample_001127/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_shape). Per-T attribute change: all leaves share one primitive type and follow Distribute-three order (sphere -> box -> cylinder), reverse. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r... | {"template":"Distribute-three","axis":"distribute_three_shape","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Progression/sample_001763 | sample_001763 | Progression | train | matrix_3x3 | Progression/sample_001763 | Progression/sample_001763/meta.json | Progression/sample_001763 | ["Progression/sample_001763/grid_0_0.ply","Progression/sample_001763/grid_0_1.ply","Progression/sample_001763/grid_0_2.ply","Progression/sample_001763/grid_1_0.ply","Progression/sample_001763/grid_1_1.ply","Progression/sample_001763/grid_1_2.ply","Progression/sample_001763/grid_2_0.ply","Progression/sample_001763/grid_... | [["Progression/sample_001763/grid_0_0.ply","Progression/sample_001763/grid_0_1.ply","Progression/sample_001763/grid_0_2.ply"],["Progression/sample_001763/grid_1_0.ply","Progression/sample_001763/grid_1_1.ply","Progression/sample_001763/grid_1_2.ply"],["Progression/sample_001763/grid_2_0.ply","Progression/sample_001763/... | ["Progression/sample_001763/cand_0.ply","Progression/sample_001763/cand_1.ply","Progression/sample_001763/cand_2.ply","Progression/sample_001763/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=R). Per-T attribute change: global_pose_deg.z rotates +60 degrees per T. 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 net rotation +120 degrees on z, vertical net ro... | {"template":"Progression","axis":"R","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":"z","source_indices":null} |
Distribute-three/sample_002594 | sample_002594 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_002594 | Distribute-three/sample_002594/meta.json | Distribute-three/sample_002594 | ["Distribute-three/sample_002594/grid_0_0.ply","Distribute-three/sample_002594/grid_0_1.ply","Distribute-three/sample_002594/grid_0_2.ply","Distribute-three/sample_002594/grid_1_0.ply","Distribute-three/sample_002594/grid_1_1.ply","Distribute-three/sample_002594/grid_1_2.ply","Distribute-three/sample_002594/grid_2_0.pl... | [["Distribute-three/sample_002594/grid_0_0.ply","Distribute-three/sample_002594/grid_0_1.ply","Distribute-three/sample_002594/grid_0_2.ply"],["Distribute-three/sample_002594/grid_1_0.ply","Distribute-three/sample_002594/grid_1_1.ply","Distribute-three/sample_002594/grid_1_2.ply"],["Distribute-three/sample_002594/grid_2... | ["Distribute-three/sample_002594/cand_0.ply","Distribute-three/sample_002594/cand_1.ply","Distribute-three/sample_002594/cand_2.ply","Distribute-three/sample_002594/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 2 | 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^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective str... | {"template":"Distribute-three","axis":"distribute_three_size","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Progression/sample_002988 | sample_002988 | Progression | train | matrix_3x3 | Progression/sample_002988 | Progression/sample_002988/meta.json | Progression/sample_002988 | ["Progression/sample_002988/grid_0_0.ply","Progression/sample_002988/grid_0_1.ply","Progression/sample_002988/grid_0_2.ply","Progression/sample_002988/grid_1_0.ply","Progression/sample_002988/grid_1_1.ply","Progression/sample_002988/grid_1_2.ply","Progression/sample_002988/grid_2_0.ply","Progression/sample_002988/grid_... | [["Progression/sample_002988/grid_0_0.ply","Progression/sample_002988/grid_0_1.ply","Progression/sample_002988/grid_0_2.ply"],["Progression/sample_002988/grid_1_0.ply","Progression/sample_002988/grid_1_1.ply","Progression/sample_002988/grid_1_2.ply"],["Progression/sample_002988/grid_2_0.ply","Progression/sample_002988/... | ["Progression/sample_002988/cand_0.ply","Progression/sample_002988/cand_1.ply","Progression/sample_002988/cand_2.ply","Progression/sample_002988/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=R). Per-T attribute change: global_pose_deg.y rotates -60 degrees per T. 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 net rotation -120 degrees on y, vertical net ro... | {"template":"Progression","axis":"R","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":"y","source_indices":null} |
Progression/sample_002299 | sample_002299 | Progression | train | matrix_3x3 | Progression/sample_002299 | Progression/sample_002299/meta.json | Progression/sample_002299 | ["Progression/sample_002299/grid_0_0.ply","Progression/sample_002299/grid_0_1.ply","Progression/sample_002299/grid_0_2.ply","Progression/sample_002299/grid_1_0.ply","Progression/sample_002299/grid_1_1.ply","Progression/sample_002299/grid_1_2.ply","Progression/sample_002299/grid_2_0.ply","Progression/sample_002299/grid_... | [["Progression/sample_002299/grid_0_0.ply","Progression/sample_002299/grid_0_1.ply","Progression/sample_002299/grid_0_2.ply"],["Progression/sample_002299/grid_1_0.ply","Progression/sample_002299/grid_1_1.ply","Progression/sample_002299/grid_1_2.ply"],["Progression/sample_002299/grid_2_0.ply","Progression/sample_002299/... | ["Progression/sample_002299/cand_0.ply","Progression/sample_002299/cand_1.ply","Progression/sample_002299/cand_2.ply","Progression/sample_002299/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=r). Per-T attribute change: all leaves change size_level by -1 per T. 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 net size_level -2, vertical net size_level -1. | {"template":"Progression","axis":"r","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_001969 | sample_001969 | Symmetry | train | matrix_3x3 | Symmetry/sample_001969 | Symmetry/sample_001969/meta.json | Symmetry/sample_001969 | ["Symmetry/sample_001969/grid_0_0.ply","Symmetry/sample_001969/grid_0_1.ply","Symmetry/sample_001969/grid_0_2.ply","Symmetry/sample_001969/grid_1_0.ply","Symmetry/sample_001969/grid_1_1.ply","Symmetry/sample_001969/grid_1_2.ply","Symmetry/sample_001969/grid_2_0.ply","Symmetry/sample_001969/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_001969/grid_0_0.ply","Symmetry/sample_001969/grid_0_1.ply","Symmetry/sample_001969/grid_0_2.ply"],["Symmetry/sample_001969/grid_1_0.ply","Symmetry/sample_001969/grid_1_1.ply","Symmetry/sample_001969/grid_1_2.ply"],["Symmetry/sample_001969/grid_2_0.ply","Symmetry/sample_001969/grid_2_1.ply",null]] | ["Symmetry/sample_001969/cand_0.ply","Symmetry/sample_001969/cand_1.ply","Symmetry/sample_001969/cand_2.ply","Symmetry/sample_001969/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Progression/sample_003762 | sample_003762 | Progression | train | matrix_3x3 | Progression/sample_003762 | Progression/sample_003762/meta.json | Progression/sample_003762 | ["Progression/sample_003762/grid_0_0.ply","Progression/sample_003762/grid_0_1.ply","Progression/sample_003762/grid_0_2.ply","Progression/sample_003762/grid_1_0.ply","Progression/sample_003762/grid_1_1.ply","Progression/sample_003762/grid_1_2.ply","Progression/sample_003762/grid_2_0.ply","Progression/sample_003762/grid_... | [["Progression/sample_003762/grid_0_0.ply","Progression/sample_003762/grid_0_1.ply","Progression/sample_003762/grid_0_2.ply"],["Progression/sample_003762/grid_1_0.ply","Progression/sample_003762/grid_1_1.ply","Progression/sample_003762/grid_1_2.ply"],["Progression/sample_003762/grid_2_0.ply","Progression/sample_003762/... | ["Progression/sample_003762/cand_0.ply","Progression/sample_003762/cand_1.ply","Progression/sample_003762/cand_2.ply","Progression/sample_003762/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=r). Per-T attribute change: all leaves change size_level by -1 per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal net size_level -1, vertical net size_level -2. | {"template":"Progression","axis":"r","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_004754 | sample_004754 | Symmetry | train | matrix_3x3 | Symmetry/sample_004754 | Symmetry/sample_004754/meta.json | Symmetry/sample_004754 | ["Symmetry/sample_004754/grid_0_0.ply","Symmetry/sample_004754/grid_0_1.ply","Symmetry/sample_004754/grid_0_2.ply","Symmetry/sample_004754/grid_1_0.ply","Symmetry/sample_004754/grid_1_1.ply","Symmetry/sample_004754/grid_1_2.ply","Symmetry/sample_004754/grid_2_0.ply","Symmetry/sample_004754/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_004754/grid_0_0.ply","Symmetry/sample_004754/grid_0_1.ply","Symmetry/sample_004754/grid_0_2.ply"],["Symmetry/sample_004754/grid_1_0.ply","Symmetry/sample_004754/grid_1_1.ply","Symmetry/sample_004754/grid_1_2.ply"],["Symmetry/sample_004754/grid_2_0.ply","Symmetry/sample_004754/grid_2_1.ply",null]] | ["Symmetry/sample_004754/cand_0.ply","Symmetry/sample_004754/cand_1.ply","Symmetry/sample_004754/cand_2.ply","Symmetry/sample_004754/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_000515 | sample_000515 | Count | train | matrix_3x3 | Count/sample_000515 | Count/sample_000515/meta.json | Count/sample_000515 | ["Count/sample_000515/grid_0_0.ply","Count/sample_000515/grid_0_1.ply","Count/sample_000515/grid_0_2.ply","Count/sample_000515/grid_1_0.ply","Count/sample_000515/grid_1_1.ply","Count/sample_000515/grid_1_2.ply","Count/sample_000515/grid_2_0.ply","Count/sample_000515/grid_2_1.ply","Count/sample_000515/cand_0.ply","Count... | [["Count/sample_000515/grid_0_0.ply","Count/sample_000515/grid_0_1.ply","Count/sample_000515/grid_0_2.ply"],["Count/sample_000515/grid_1_0.ply","Count/sample_000515/grid_1_1.ply","Count/sample_000515/grid_1_2.ply"],["Count/sample_000515/grid_2_0.ply","Count/sample_000515/grid_2_1.ply",null]] | ["Count/sample_000515/cand_0.ply","Count/sample_000515/cand_1.ply","Count/sample_000515/cand_2.ply","Count/sample_000515/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_004010 | sample_004010 | Count | train | matrix_3x3 | Count/sample_004010 | Count/sample_004010/meta.json | Count/sample_004010 | ["Count/sample_004010/grid_0_0.ply","Count/sample_004010/grid_0_1.ply","Count/sample_004010/grid_0_2.ply","Count/sample_004010/grid_1_0.ply","Count/sample_004010/grid_1_1.ply","Count/sample_004010/grid_1_2.ply","Count/sample_004010/grid_2_0.ply","Count/sample_004010/grid_2_1.ply","Count/sample_004010/cand_0.ply","Count... | [["Count/sample_004010/grid_0_0.ply","Count/sample_004010/grid_0_1.ply","Count/sample_004010/grid_0_2.ply"],["Count/sample_004010/grid_1_0.ply","Count/sample_004010/grid_1_1.ply","Count/sample_004010/grid_1_2.ply"],["Count/sample_004010/grid_2_0.ply","Count/sample_004010/grid_2_1.ply",null]] | ["Count/sample_004010/cand_0.ply","Count/sample_004010/cand_1.ply","Count/sample_004010/cand_2.ply","Count/sample_004010/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. 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 count transitions; vertical applies T^1 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_001359 | sample_001359 | Count | train | matrix_3x3 | Count/sample_001359 | Count/sample_001359/meta.json | Count/sample_001359 | ["Count/sample_001359/grid_0_0.ply","Count/sample_001359/grid_0_1.ply","Count/sample_001359/grid_0_2.ply","Count/sample_001359/grid_1_0.ply","Count/sample_001359/grid_1_1.ply","Count/sample_001359/grid_1_2.ply","Count/sample_001359/grid_2_0.ply","Count/sample_001359/grid_2_1.ply","Count/sample_001359/cand_0.ply","Count... | [["Count/sample_001359/grid_0_0.ply","Count/sample_001359/grid_0_1.ply","Count/sample_001359/grid_0_2.ply"],["Count/sample_001359/grid_1_0.ply","Count/sample_001359/grid_1_1.ply","Count/sample_001359/grid_1_2.ply"],["Count/sample_001359/grid_2_0.ply","Count/sample_001359/grid_2_1.ply",null]] | ["Count/sample_001359/cand_0.ply","Count/sample_001359/cand_1.ply","Count/sample_001359/cand_2.ply","Count/sample_001359/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_003351 | sample_003351 | Permutation | train | matrix_3x3 | Permutation/sample_003351 | Permutation/sample_003351/meta.json | Permutation/sample_003351 | ["Permutation/sample_003351/grid_0_0.ply","Permutation/sample_003351/grid_0_1.ply","Permutation/sample_003351/grid_0_2.ply","Permutation/sample_003351/grid_1_0.ply","Permutation/sample_003351/grid_1_1.ply","Permutation/sample_003351/grid_1_2.ply","Permutation/sample_003351/grid_2_0.ply","Permutation/sample_003351/grid_... | [["Permutation/sample_003351/grid_0_0.ply","Permutation/sample_003351/grid_0_1.ply","Permutation/sample_003351/grid_0_2.ply"],["Permutation/sample_003351/grid_1_0.ply","Permutation/sample_003351/grid_1_1.ply","Permutation/sample_003351/grid_1_2.ply"],["Permutation/sample_003351/grid_2_0.ply","Permutation/sample_003351/... | ["Permutation/sample_003351/cand_0.ply","Permutation/sample_003351/cand_1.ply","Permutation/sample_003351/cand_2.ply","Permutation/sample_003351/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step left shift per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 permuta... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Progression/sample_002906 | sample_002906 | Progression | train | matrix_3x3 | Progression/sample_002906 | Progression/sample_002906/meta.json | Progression/sample_002906 | ["Progression/sample_002906/grid_0_0.ply","Progression/sample_002906/grid_0_1.ply","Progression/sample_002906/grid_0_2.ply","Progression/sample_002906/grid_1_0.ply","Progression/sample_002906/grid_1_1.ply","Progression/sample_002906/grid_1_2.ply","Progression/sample_002906/grid_2_0.ply","Progression/sample_002906/grid_... | [["Progression/sample_002906/grid_0_0.ply","Progression/sample_002906/grid_0_1.ply","Progression/sample_002906/grid_0_2.ply"],["Progression/sample_002906/grid_1_0.ply","Progression/sample_002906/grid_1_1.ply","Progression/sample_002906/grid_1_2.ply"],["Progression/sample_002906/grid_2_0.ply","Progression/sample_002906/... | ["Progression/sample_002906/cand_0.ply","Progression/sample_002906/cand_1.ply","Progression/sample_002906/cand_2.ply","Progression/sample_002906/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=r). Per-T attribute change: all leaves change size_level by -1 per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal net size_level -1, vertical net size_level -2. | {"template":"Progression","axis":"r","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_002308 | sample_002308 | Symmetry | train | matrix_3x3 | Symmetry/sample_002308 | Symmetry/sample_002308/meta.json | Symmetry/sample_002308 | ["Symmetry/sample_002308/grid_0_0.ply","Symmetry/sample_002308/grid_0_1.ply","Symmetry/sample_002308/grid_0_2.ply","Symmetry/sample_002308/grid_1_0.ply","Symmetry/sample_002308/grid_1_1.ply","Symmetry/sample_002308/grid_1_2.ply","Symmetry/sample_002308/grid_2_0.ply","Symmetry/sample_002308/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_002308/grid_0_0.ply","Symmetry/sample_002308/grid_0_1.ply","Symmetry/sample_002308/grid_0_2.ply"],["Symmetry/sample_002308/grid_1_0.ply","Symmetry/sample_002308/grid_1_1.ply","Symmetry/sample_002308/grid_1_2.ply"],["Symmetry/sample_002308/grid_2_0.ply","Symmetry/sample_002308/grid_2_1.ply",null]] | ["Symmetry/sample_002308/cand_0.ply","Symmetry/sample_002308/cand_1.ply","Symmetry/sample_002308/cand_2.ply","Symmetry/sample_002308/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_002536 | sample_002536 | Symmetry | train | matrix_3x3 | Symmetry/sample_002536 | Symmetry/sample_002536/meta.json | Symmetry/sample_002536 | ["Symmetry/sample_002536/grid_0_0.ply","Symmetry/sample_002536/grid_0_1.ply","Symmetry/sample_002536/grid_0_2.ply","Symmetry/sample_002536/grid_1_0.ply","Symmetry/sample_002536/grid_1_1.ply","Symmetry/sample_002536/grid_1_2.ply","Symmetry/sample_002536/grid_2_0.ply","Symmetry/sample_002536/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_002536/grid_0_0.ply","Symmetry/sample_002536/grid_0_1.ply","Symmetry/sample_002536/grid_0_2.ply"],["Symmetry/sample_002536/grid_1_0.ply","Symmetry/sample_002536/grid_1_1.ply","Symmetry/sample_002536/grid_1_2.ply"],["Symmetry/sample_002536/grid_2_0.ply","Symmetry/sample_002536/grid_2_1.ply",null]] | ["Symmetry/sample_002536/cand_0.ply","Symmetry/sample_002536/cand_1.ply","Symmetry/sample_002536/cand_2.ply","Symmetry/sample_002536/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_002326 | sample_002326 | Symmetry | train | matrix_3x3 | Symmetry/sample_002326 | Symmetry/sample_002326/meta.json | Symmetry/sample_002326 | ["Symmetry/sample_002326/grid_0_0.ply","Symmetry/sample_002326/grid_0_1.ply","Symmetry/sample_002326/grid_0_2.ply","Symmetry/sample_002326/grid_1_0.ply","Symmetry/sample_002326/grid_1_1.ply","Symmetry/sample_002326/grid_1_2.ply","Symmetry/sample_002326/grid_2_0.ply","Symmetry/sample_002326/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_002326/grid_0_0.ply","Symmetry/sample_002326/grid_0_1.ply","Symmetry/sample_002326/grid_0_2.ply"],["Symmetry/sample_002326/grid_1_0.ply","Symmetry/sample_002326/grid_1_1.ply","Symmetry/sample_002326/grid_1_2.ply"],["Symmetry/sample_002326/grid_2_0.ply","Symmetry/sample_002326/grid_2_1.ply",null]] | ["Symmetry/sample_002326/cand_0.ply","Symmetry/sample_002326/cand_1.ply","Symmetry/sample_002326/cand_2.ply","Symmetry/sample_002326/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_001753 | sample_001753 | Symmetry | train | matrix_3x3 | Symmetry/sample_001753 | Symmetry/sample_001753/meta.json | Symmetry/sample_001753 | ["Symmetry/sample_001753/grid_0_0.ply","Symmetry/sample_001753/grid_0_1.ply","Symmetry/sample_001753/grid_0_2.ply","Symmetry/sample_001753/grid_1_0.ply","Symmetry/sample_001753/grid_1_1.ply","Symmetry/sample_001753/grid_1_2.ply","Symmetry/sample_001753/grid_2_0.ply","Symmetry/sample_001753/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_001753/grid_0_0.ply","Symmetry/sample_001753/grid_0_1.ply","Symmetry/sample_001753/grid_0_2.ply"],["Symmetry/sample_001753/grid_1_0.ply","Symmetry/sample_001753/grid_1_1.ply","Symmetry/sample_001753/grid_1_2.ply"],["Symmetry/sample_001753/grid_2_0.ply","Symmetry/sample_001753/grid_2_1.ply",null]] | ["Symmetry/sample_001753/cand_0.ply","Symmetry/sample_001753/cand_1.ply","Symmetry/sample_001753/cand_2.ply","Symmetry/sample_001753/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_002955 | sample_002955 | Permutation | train | matrix_3x3 | Permutation/sample_002955 | Permutation/sample_002955/meta.json | Permutation/sample_002955 | ["Permutation/sample_002955/grid_0_0.ply","Permutation/sample_002955/grid_0_1.ply","Permutation/sample_002955/grid_0_2.ply","Permutation/sample_002955/grid_1_0.ply","Permutation/sample_002955/grid_1_1.ply","Permutation/sample_002955/grid_1_2.ply","Permutation/sample_002955/grid_2_0.ply","Permutation/sample_002955/grid_... | [["Permutation/sample_002955/grid_0_0.ply","Permutation/sample_002955/grid_0_1.ply","Permutation/sample_002955/grid_0_2.ply"],["Permutation/sample_002955/grid_1_0.ply","Permutation/sample_002955/grid_1_1.ply","Permutation/sample_002955/grid_1_2.ply"],["Permutation/sample_002955/grid_2_0.ply","Permutation/sample_002955/... | ["Permutation/sample_002955/cand_0.ply","Permutation/sample_002955/cand_1.ply","Permutation/sample_002955/cand_2.ply","Permutation/sample_002955/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step right shift per T. 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 permut... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Progression/sample_003575 | sample_003575 | Progression | train | matrix_3x3 | Progression/sample_003575 | Progression/sample_003575/meta.json | Progression/sample_003575 | ["Progression/sample_003575/grid_0_0.ply","Progression/sample_003575/grid_0_1.ply","Progression/sample_003575/grid_0_2.ply","Progression/sample_003575/grid_1_0.ply","Progression/sample_003575/grid_1_1.ply","Progression/sample_003575/grid_1_2.ply","Progression/sample_003575/grid_2_0.ply","Progression/sample_003575/grid_... | [["Progression/sample_003575/grid_0_0.ply","Progression/sample_003575/grid_0_1.ply","Progression/sample_003575/grid_0_2.ply"],["Progression/sample_003575/grid_1_0.ply","Progression/sample_003575/grid_1_1.ply","Progression/sample_003575/grid_1_2.ply"],["Progression/sample_003575/grid_2_0.ply","Progression/sample_003575/... | ["Progression/sample_003575/cand_0.ply","Progression/sample_003575/cand_1.ply","Progression/sample_003575/cand_2.ply","Progression/sample_003575/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=r). Per-T attribute change: all leaves change size_level by -1 per T. 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 net size_level -2, vertical net size_level -1. | {"template":"Progression","axis":"r","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Conservation/sample_004025 | sample_004025 | Conservation | train | matrix_3x3 | Conservation/sample_004025 | Conservation/sample_004025/meta.json | Conservation/sample_004025 | ["Conservation/sample_004025/grid_0_0.ply","Conservation/sample_004025/grid_0_1.ply","Conservation/sample_004025/grid_0_2.ply","Conservation/sample_004025/grid_1_0.ply","Conservation/sample_004025/grid_1_1.ply","Conservation/sample_004025/grid_1_2.ply","Conservation/sample_004025/grid_2_0.ply","Conservation/sample_0040... | [["Conservation/sample_004025/grid_0_0.ply","Conservation/sample_004025/grid_0_1.ply","Conservation/sample_004025/grid_0_2.ply"],["Conservation/sample_004025/grid_1_0.ply","Conservation/sample_004025/grid_1_1.ply","Conservation/sample_004025/grid_1_2.ply"],["Conservation/sample_004025/grid_2_0.ply","Conservation/sample... | ["Conservation/sample_004025/cand_0.ply","Conservation/sample_004025/cand_1.ply","Conservation/sample_004025/cand_2.ply","Conservation/sample_004025/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Conservation, axis=size_conservation). Per-T attribute change: size conservation triplet: leaf0:+1, leaf2:-1, leaf1:0. 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 conserv... | {"template":"Conservation","axis":"size_conservation","leaf_idx":0,"leaf_indices":[0,2,1],"direction":2,"directions":[1,-1,0],"rot_axis":null,"source_indices":null} |
Count/sample_004199 | sample_004199 | Count | train | matrix_3x3 | Count/sample_004199 | Count/sample_004199/meta.json | Count/sample_004199 | ["Count/sample_004199/grid_0_0.ply","Count/sample_004199/grid_0_1.ply","Count/sample_004199/grid_0_2.ply","Count/sample_004199/grid_1_0.ply","Count/sample_004199/grid_1_1.ply","Count/sample_004199/grid_1_2.ply","Count/sample_004199/grid_2_0.ply","Count/sample_004199/grid_2_1.ply","Count/sample_004199/cand_0.ply","Count... | [["Count/sample_004199/grid_0_0.ply","Count/sample_004199/grid_0_1.ply","Count/sample_004199/grid_0_2.ply"],["Count/sample_004199/grid_1_0.ply","Count/sample_004199/grid_1_1.ply","Count/sample_004199/grid_1_2.ply"],["Count/sample_004199/grid_2_0.ply","Count/sample_004199/grid_2_1.ply",null]] | ["Count/sample_004199/cand_0.ply","Count/sample_004199/cand_1.ply","Count/sample_004199/cand_2.ply","Count/sample_004199/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. 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 count transitions; vertical applies T^1 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Progression/sample_003911 | sample_003911 | Progression | train | matrix_3x3 | Progression/sample_003911 | Progression/sample_003911/meta.json | Progression/sample_003911 | ["Progression/sample_003911/grid_0_0.ply","Progression/sample_003911/grid_0_1.ply","Progression/sample_003911/grid_0_2.ply","Progression/sample_003911/grid_1_0.ply","Progression/sample_003911/grid_1_1.ply","Progression/sample_003911/grid_1_2.ply","Progression/sample_003911/grid_2_0.ply","Progression/sample_003911/grid_... | [["Progression/sample_003911/grid_0_0.ply","Progression/sample_003911/grid_0_1.ply","Progression/sample_003911/grid_0_2.ply"],["Progression/sample_003911/grid_1_0.ply","Progression/sample_003911/grid_1_1.ply","Progression/sample_003911/grid_1_2.ply"],["Progression/sample_003911/grid_2_0.ply","Progression/sample_003911/... | ["Progression/sample_003911/cand_0.ply","Progression/sample_003911/cand_1.ply","Progression/sample_003911/cand_2.ply","Progression/sample_003911/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=r). Per-T attribute change: all leaves change size_level by -1 per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal net size_level -1, vertical net size_level -2. | {"template":"Progression","axis":"r","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_003413 | sample_003413 | Permutation | train | matrix_3x3 | Permutation/sample_003413 | Permutation/sample_003413/meta.json | Permutation/sample_003413 | ["Permutation/sample_003413/grid_0_0.ply","Permutation/sample_003413/grid_0_1.ply","Permutation/sample_003413/grid_0_2.ply","Permutation/sample_003413/grid_1_0.ply","Permutation/sample_003413/grid_1_1.ply","Permutation/sample_003413/grid_1_2.ply","Permutation/sample_003413/grid_2_0.ply","Permutation/sample_003413/grid_... | [["Permutation/sample_003413/grid_0_0.ply","Permutation/sample_003413/grid_0_1.ply","Permutation/sample_003413/grid_0_2.ply"],["Permutation/sample_003413/grid_1_0.ply","Permutation/sample_003413/grid_1_1.ply","Permutation/sample_003413/grid_1_2.ply"],["Permutation/sample_003413/grid_2_0.ply","Permutation/sample_003413/... | ["Permutation/sample_003413/cand_0.ply","Permutation/sample_003413/cand_1.ply","Permutation/sample_003413/cand_2.ply","Permutation/sample_003413/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step left shift per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 permuta... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Conservation/sample_002095 | sample_002095 | Conservation | train | matrix_3x3 | Conservation/sample_002095 | Conservation/sample_002095/meta.json | Conservation/sample_002095 | ["Conservation/sample_002095/grid_0_0.ply","Conservation/sample_002095/grid_0_1.ply","Conservation/sample_002095/grid_0_2.ply","Conservation/sample_002095/grid_1_0.ply","Conservation/sample_002095/grid_1_1.ply","Conservation/sample_002095/grid_1_2.ply","Conservation/sample_002095/grid_2_0.ply","Conservation/sample_0020... | [["Conservation/sample_002095/grid_0_0.ply","Conservation/sample_002095/grid_0_1.ply","Conservation/sample_002095/grid_0_2.ply"],["Conservation/sample_002095/grid_1_0.ply","Conservation/sample_002095/grid_1_1.ply","Conservation/sample_002095/grid_1_2.ply"],["Conservation/sample_002095/grid_2_0.ply","Conservation/sample... | ["Conservation/sample_002095/cand_0.ply","Conservation/sample_002095/cand_1.ply","Conservation/sample_002095/cand_2.ply","Conservation/sample_002095/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Conservation, axis=size_conservation). Per-T attribute change: size conservation triplet: leaf2:+1, leaf1:-1, leaf0:0. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 conserv... | {"template":"Conservation","axis":"size_conservation","leaf_idx":2,"leaf_indices":[2,1,0],"direction":1,"directions":[1,-1,0],"rot_axis":null,"source_indices":null} |
Progression/sample_004619 | sample_004619 | Progression | train | matrix_3x3 | Progression/sample_004619 | Progression/sample_004619/meta.json | Progression/sample_004619 | ["Progression/sample_004619/grid_0_0.ply","Progression/sample_004619/grid_0_1.ply","Progression/sample_004619/grid_0_2.ply","Progression/sample_004619/grid_1_0.ply","Progression/sample_004619/grid_1_1.ply","Progression/sample_004619/grid_1_2.ply","Progression/sample_004619/grid_2_0.ply","Progression/sample_004619/grid_... | [["Progression/sample_004619/grid_0_0.ply","Progression/sample_004619/grid_0_1.ply","Progression/sample_004619/grid_0_2.ply"],["Progression/sample_004619/grid_1_0.ply","Progression/sample_004619/grid_1_1.ply","Progression/sample_004619/grid_1_2.ply"],["Progression/sample_004619/grid_2_0.ply","Progression/sample_004619/... | ["Progression/sample_004619/cand_0.ply","Progression/sample_004619/cand_1.ply","Progression/sample_004619/cand_2.ply","Progression/sample_004619/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=R). Per-T attribute change: global_pose_deg.x rotates -60 degrees per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal net rotation -60 degrees on x, vertical net rot... | {"template":"Progression","axis":"R","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":"x","source_indices":null} |
Distribute-three/sample_004012 | sample_004012 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_004012 | Distribute-three/sample_004012/meta.json | Distribute-three/sample_004012 | ["Distribute-three/sample_004012/grid_0_0.ply","Distribute-three/sample_004012/grid_0_1.ply","Distribute-three/sample_004012/grid_0_2.ply","Distribute-three/sample_004012/grid_1_0.ply","Distribute-three/sample_004012/grid_1_1.ply","Distribute-three/sample_004012/grid_1_2.ply","Distribute-three/sample_004012/grid_2_0.pl... | [["Distribute-three/sample_004012/grid_0_0.ply","Distribute-three/sample_004012/grid_0_1.ply","Distribute-three/sample_004012/grid_0_2.ply"],["Distribute-three/sample_004012/grid_1_0.ply","Distribute-three/sample_004012/grid_1_1.ply","Distribute-three/sample_004012/grid_1_2.ply"],["Distribute-three/sample_004012/grid_2... | ["Distribute-three/sample_004012/cand_0.ply","Distribute-three/sample_004012/cand_1.ply","Distribute-three/sample_004012/cand_2.ply","Distribute-three/sample_004012/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_density). Per-T attribute change: density level follows Distribute-three order (0 -> 2 -> 4), forward. 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: horizo... | {"template":"Distribute-three","axis":"distribute_three_density","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_000848 | sample_000848 | Count | train | matrix_3x3 | Count/sample_000848 | Count/sample_000848/meta.json | Count/sample_000848 | ["Count/sample_000848/grid_0_0.ply","Count/sample_000848/grid_0_1.ply","Count/sample_000848/grid_0_2.ply","Count/sample_000848/grid_1_0.ply","Count/sample_000848/grid_1_1.ply","Count/sample_000848/grid_1_2.ply","Count/sample_000848/grid_2_0.ply","Count/sample_000848/grid_2_1.ply","Count/sample_000848/cand_0.ply","Count... | [["Count/sample_000848/grid_0_0.ply","Count/sample_000848/grid_0_1.ply","Count/sample_000848/grid_0_2.ply"],["Count/sample_000848/grid_1_0.ply","Count/sample_000848/grid_1_1.ply","Count/sample_000848/grid_1_2.ply"],["Count/sample_000848/grid_2_0.ply","Count/sample_000848/grid_2_1.ply",null]] | ["Count/sample_000848/cand_0.ply","Count/sample_000848/cand_1.ply","Count/sample_000848/cand_2.ply","Count/sample_000848/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_004615 | sample_004615 | Permutation | train | matrix_3x3 | Permutation/sample_004615 | Permutation/sample_004615/meta.json | Permutation/sample_004615 | ["Permutation/sample_004615/grid_0_0.ply","Permutation/sample_004615/grid_0_1.ply","Permutation/sample_004615/grid_0_2.ply","Permutation/sample_004615/grid_1_0.ply","Permutation/sample_004615/grid_1_1.ply","Permutation/sample_004615/grid_1_2.ply","Permutation/sample_004615/grid_2_0.ply","Permutation/sample_004615/grid_... | [["Permutation/sample_004615/grid_0_0.ply","Permutation/sample_004615/grid_0_1.ply","Permutation/sample_004615/grid_0_2.ply"],["Permutation/sample_004615/grid_1_0.ply","Permutation/sample_004615/grid_1_1.ply","Permutation/sample_004615/grid_1_2.ply"],["Permutation/sample_004615/grid_2_0.ply","Permutation/sample_004615/... | ["Permutation/sample_004615/cand_0.ply","Permutation/sample_004615/cand_1.ply","Permutation/sample_004615/cand_2.ply","Permutation/sample_004615/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step right shift per T. 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 permut... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_002103 | sample_002103 | Permutation | train | matrix_3x3 | Permutation/sample_002103 | Permutation/sample_002103/meta.json | Permutation/sample_002103 | ["Permutation/sample_002103/grid_0_0.ply","Permutation/sample_002103/grid_0_1.ply","Permutation/sample_002103/grid_0_2.ply","Permutation/sample_002103/grid_1_0.ply","Permutation/sample_002103/grid_1_1.ply","Permutation/sample_002103/grid_1_2.ply","Permutation/sample_002103/grid_2_0.ply","Permutation/sample_002103/grid_... | [["Permutation/sample_002103/grid_0_0.ply","Permutation/sample_002103/grid_0_1.ply","Permutation/sample_002103/grid_0_2.ply"],["Permutation/sample_002103/grid_1_0.ply","Permutation/sample_002103/grid_1_1.ply","Permutation/sample_002103/grid_1_2.ply"],["Permutation/sample_002103/grid_2_0.ply","Permutation/sample_002103/... | ["Permutation/sample_002103/cand_0.ply","Permutation/sample_002103/cand_1.ply","Permutation/sample_002103/cand_2.ply","Permutation/sample_002103/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step left shift per T. 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 permuta... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_001054 | sample_001054 | Count | train | matrix_3x3 | Count/sample_001054 | Count/sample_001054/meta.json | Count/sample_001054 | ["Count/sample_001054/grid_0_0.ply","Count/sample_001054/grid_0_1.ply","Count/sample_001054/grid_0_2.ply","Count/sample_001054/grid_1_0.ply","Count/sample_001054/grid_1_1.ply","Count/sample_001054/grid_1_2.ply","Count/sample_001054/grid_2_0.ply","Count/sample_001054/grid_2_1.ply","Count/sample_001054/cand_0.ply","Count... | [["Count/sample_001054/grid_0_0.ply","Count/sample_001054/grid_0_1.ply","Count/sample_001054/grid_0_2.ply"],["Count/sample_001054/grid_1_0.ply","Count/sample_001054/grid_1_1.ply","Count/sample_001054/grid_1_2.ply"],["Count/sample_001054/grid_2_0.ply","Count/sample_001054/grid_2_1.ply",null]] | ["Count/sample_001054/cand_0.ply","Count/sample_001054/cand_1.ply","Count/sample_001054/cand_2.ply","Count/sample_001054/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Progression/sample_003266 | sample_003266 | Progression | train | matrix_3x3 | Progression/sample_003266 | Progression/sample_003266/meta.json | Progression/sample_003266 | ["Progression/sample_003266/grid_0_0.ply","Progression/sample_003266/grid_0_1.ply","Progression/sample_003266/grid_0_2.ply","Progression/sample_003266/grid_1_0.ply","Progression/sample_003266/grid_1_1.ply","Progression/sample_003266/grid_1_2.ply","Progression/sample_003266/grid_2_0.ply","Progression/sample_003266/grid_... | [["Progression/sample_003266/grid_0_0.ply","Progression/sample_003266/grid_0_1.ply","Progression/sample_003266/grid_0_2.ply"],["Progression/sample_003266/grid_1_0.ply","Progression/sample_003266/grid_1_1.ply","Progression/sample_003266/grid_1_2.ply"],["Progression/sample_003266/grid_2_0.ply","Progression/sample_003266/... | ["Progression/sample_003266/cand_0.ply","Progression/sample_003266/cand_1.ply","Progression/sample_003266/cand_2.ply","Progression/sample_003266/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=R). Per-T attribute change: global_pose_deg.y rotates -60 degrees per T. 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 net rotation -120 degrees on y, vertical net ro... | {"template":"Progression","axis":"R","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":"y","source_indices":null} |
Symmetry/sample_003481 | sample_003481 | Symmetry | train | matrix_3x3 | Symmetry/sample_003481 | Symmetry/sample_003481/meta.json | Symmetry/sample_003481 | ["Symmetry/sample_003481/grid_0_0.ply","Symmetry/sample_003481/grid_0_1.ply","Symmetry/sample_003481/grid_0_2.ply","Symmetry/sample_003481/grid_1_0.ply","Symmetry/sample_003481/grid_1_1.ply","Symmetry/sample_003481/grid_1_2.ply","Symmetry/sample_003481/grid_2_0.ply","Symmetry/sample_003481/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_003481/grid_0_0.ply","Symmetry/sample_003481/grid_0_1.ply","Symmetry/sample_003481/grid_0_2.ply"],["Symmetry/sample_003481/grid_1_0.ply","Symmetry/sample_003481/grid_1_1.ply","Symmetry/sample_003481/grid_1_2.ply"],["Symmetry/sample_003481/grid_2_0.ply","Symmetry/sample_003481/grid_2_1.ply",null]] | ["Symmetry/sample_003481/cand_0.ply","Symmetry/sample_003481/cand_1.ply","Symmetry/sample_003481/cand_2.ply","Symmetry/sample_003481/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_003347 | sample_003347 | Symmetry | train | matrix_3x3 | Symmetry/sample_003347 | Symmetry/sample_003347/meta.json | Symmetry/sample_003347 | ["Symmetry/sample_003347/grid_0_0.ply","Symmetry/sample_003347/grid_0_1.ply","Symmetry/sample_003347/grid_0_2.ply","Symmetry/sample_003347/grid_1_0.ply","Symmetry/sample_003347/grid_1_1.ply","Symmetry/sample_003347/grid_1_2.ply","Symmetry/sample_003347/grid_2_0.ply","Symmetry/sample_003347/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_003347/grid_0_0.ply","Symmetry/sample_003347/grid_0_1.ply","Symmetry/sample_003347/grid_0_2.ply"],["Symmetry/sample_003347/grid_1_0.ply","Symmetry/sample_003347/grid_1_1.ply","Symmetry/sample_003347/grid_1_2.ply"],["Symmetry/sample_003347/grid_2_0.ply","Symmetry/sample_003347/grid_2_1.ply",null]] | ["Symmetry/sample_003347/cand_0.ply","Symmetry/sample_003347/cand_1.ply","Symmetry/sample_003347/cand_2.ply","Symmetry/sample_003347/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_000757 | sample_000757 | Symmetry | train | matrix_3x3 | Symmetry/sample_000757 | Symmetry/sample_000757/meta.json | Symmetry/sample_000757 | ["Symmetry/sample_000757/grid_0_0.ply","Symmetry/sample_000757/grid_0_1.ply","Symmetry/sample_000757/grid_0_2.ply","Symmetry/sample_000757/grid_1_0.ply","Symmetry/sample_000757/grid_1_1.ply","Symmetry/sample_000757/grid_1_2.ply","Symmetry/sample_000757/grid_2_0.ply","Symmetry/sample_000757/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_000757/grid_0_0.ply","Symmetry/sample_000757/grid_0_1.ply","Symmetry/sample_000757/grid_0_2.ply"],["Symmetry/sample_000757/grid_1_0.ply","Symmetry/sample_000757/grid_1_1.ply","Symmetry/sample_000757/grid_1_2.ply"],["Symmetry/sample_000757/grid_2_0.ply","Symmetry/sample_000757/grid_2_1.ply",null]] | ["Symmetry/sample_000757/cand_0.ply","Symmetry/sample_000757/cand_1.ply","Symmetry/sample_000757/cand_2.ply","Symmetry/sample_000757/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_001611 | sample_001611 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_001611 | Distribute-three/sample_001611/meta.json | Distribute-three/sample_001611 | ["Distribute-three/sample_001611/grid_0_0.ply","Distribute-three/sample_001611/grid_0_1.ply","Distribute-three/sample_001611/grid_0_2.ply","Distribute-three/sample_001611/grid_1_0.ply","Distribute-three/sample_001611/grid_1_1.ply","Distribute-three/sample_001611/grid_1_2.ply","Distribute-three/sample_001611/grid_2_0.pl... | [["Distribute-three/sample_001611/grid_0_0.ply","Distribute-three/sample_001611/grid_0_1.ply","Distribute-three/sample_001611/grid_0_2.ply"],["Distribute-three/sample_001611/grid_1_0.ply","Distribute-three/sample_001611/grid_1_1.ply","Distribute-three/sample_001611/grid_1_2.ply"],["Distribute-three/sample_001611/grid_2... | ["Distribute-three/sample_001611/cand_0.ply","Distribute-three/sample_001611/cand_1.ply","Distribute-three/sample_001611/cand_2.ply","Distribute-three/sample_001611/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 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), forward. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective str... | {"template":"Distribute-three","axis":"distribute_three_size","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_002310 | sample_002310 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_002310 | Distribute-three/sample_002310/meta.json | Distribute-three/sample_002310 | ["Distribute-three/sample_002310/grid_0_0.ply","Distribute-three/sample_002310/grid_0_1.ply","Distribute-three/sample_002310/grid_0_2.ply","Distribute-three/sample_002310/grid_1_0.ply","Distribute-three/sample_002310/grid_1_1.ply","Distribute-three/sample_002310/grid_1_2.ply","Distribute-three/sample_002310/grid_2_0.pl... | [["Distribute-three/sample_002310/grid_0_0.ply","Distribute-three/sample_002310/grid_0_1.ply","Distribute-three/sample_002310/grid_0_2.ply"],["Distribute-three/sample_002310/grid_1_0.ply","Distribute-three/sample_002310/grid_1_1.ply","Distribute-three/sample_002310/grid_1_2.ply"],["Distribute-three/sample_002310/grid_2... | ["Distribute-three/sample_002310/cand_0.ply","Distribute-three/sample_002310/cand_1.ply","Distribute-three/sample_002310/cand_2.ply","Distribute-three/sample_002310/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 2 | 1 | 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 str... | {"template":"Distribute-three","axis":"distribute_three_size","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_003329 | sample_003329 | Permutation | train | matrix_3x3 | Permutation/sample_003329 | Permutation/sample_003329/meta.json | Permutation/sample_003329 | ["Permutation/sample_003329/grid_0_0.ply","Permutation/sample_003329/grid_0_1.ply","Permutation/sample_003329/grid_0_2.ply","Permutation/sample_003329/grid_1_0.ply","Permutation/sample_003329/grid_1_1.ply","Permutation/sample_003329/grid_1_2.ply","Permutation/sample_003329/grid_2_0.ply","Permutation/sample_003329/grid_... | [["Permutation/sample_003329/grid_0_0.ply","Permutation/sample_003329/grid_0_1.ply","Permutation/sample_003329/grid_0_2.ply"],["Permutation/sample_003329/grid_1_0.ply","Permutation/sample_003329/grid_1_1.ply","Permutation/sample_003329/grid_1_2.ply"],["Permutation/sample_003329/grid_2_0.ply","Permutation/sample_003329/... | ["Permutation/sample_003329/cand_0.ply","Permutation/sample_003329/cand_1.ply","Permutation/sample_003329/cand_2.ply","Permutation/sample_003329/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step right shift per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 permut... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_004367 | sample_004367 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_004367 | Distribute-three/sample_004367/meta.json | Distribute-three/sample_004367 | ["Distribute-three/sample_004367/grid_0_0.ply","Distribute-three/sample_004367/grid_0_1.ply","Distribute-three/sample_004367/grid_0_2.ply","Distribute-three/sample_004367/grid_1_0.ply","Distribute-three/sample_004367/grid_1_1.ply","Distribute-three/sample_004367/grid_1_2.ply","Distribute-three/sample_004367/grid_2_0.pl... | [["Distribute-three/sample_004367/grid_0_0.ply","Distribute-three/sample_004367/grid_0_1.ply","Distribute-three/sample_004367/grid_0_2.ply"],["Distribute-three/sample_004367/grid_1_0.ply","Distribute-three/sample_004367/grid_1_1.ply","Distribute-three/sample_004367/grid_1_2.ply"],["Distribute-three/sample_004367/grid_2... | ["Distribute-three/sample_004367/cand_0.ply","Distribute-three/sample_004367/cand_1.ply","Distribute-three/sample_004367/cand_2.ply","Distribute-three/sample_004367/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_color). Per-T attribute change: entity color follows Distribute-three order (red -> green -> blue), reverse. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: ... | {"template":"Distribute-three","axis":"distribute_three_color","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_001195 | sample_001195 | Permutation | train | matrix_3x3 | Permutation/sample_001195 | Permutation/sample_001195/meta.json | Permutation/sample_001195 | ["Permutation/sample_001195/grid_0_0.ply","Permutation/sample_001195/grid_0_1.ply","Permutation/sample_001195/grid_0_2.ply","Permutation/sample_001195/grid_1_0.ply","Permutation/sample_001195/grid_1_1.ply","Permutation/sample_001195/grid_1_2.ply","Permutation/sample_001195/grid_2_0.ply","Permutation/sample_001195/grid_... | [["Permutation/sample_001195/grid_0_0.ply","Permutation/sample_001195/grid_0_1.ply","Permutation/sample_001195/grid_0_2.ply"],["Permutation/sample_001195/grid_1_0.ply","Permutation/sample_001195/grid_1_1.ply","Permutation/sample_001195/grid_1_2.ply"],["Permutation/sample_001195/grid_2_0.ply","Permutation/sample_001195/... | ["Permutation/sample_001195/cand_0.ply","Permutation/sample_001195/cand_1.ply","Permutation/sample_001195/cand_2.ply","Permutation/sample_001195/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step right shift per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 permut... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_001888 | sample_001888 | Permutation | train | matrix_3x3 | Permutation/sample_001888 | Permutation/sample_001888/meta.json | Permutation/sample_001888 | ["Permutation/sample_001888/grid_0_0.ply","Permutation/sample_001888/grid_0_1.ply","Permutation/sample_001888/grid_0_2.ply","Permutation/sample_001888/grid_1_0.ply","Permutation/sample_001888/grid_1_1.ply","Permutation/sample_001888/grid_1_2.ply","Permutation/sample_001888/grid_2_0.ply","Permutation/sample_001888/grid_... | [["Permutation/sample_001888/grid_0_0.ply","Permutation/sample_001888/grid_0_1.ply","Permutation/sample_001888/grid_0_2.ply"],["Permutation/sample_001888/grid_1_0.ply","Permutation/sample_001888/grid_1_1.ply","Permutation/sample_001888/grid_1_2.ply"],["Permutation/sample_001888/grid_2_0.ply","Permutation/sample_001888/... | ["Permutation/sample_001888/cand_0.ply","Permutation/sample_001888/cand_1.ply","Permutation/sample_001888/cand_2.ply","Permutation/sample_001888/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step left shift per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 permuta... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_000442 | sample_000442 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_000442 | Distribute-three/sample_000442/meta.json | Distribute-three/sample_000442 | ["Distribute-three/sample_000442/grid_0_0.ply","Distribute-three/sample_000442/grid_0_1.ply","Distribute-three/sample_000442/grid_0_2.ply","Distribute-three/sample_000442/grid_1_0.ply","Distribute-three/sample_000442/grid_1_1.ply","Distribute-three/sample_000442/grid_1_2.ply","Distribute-three/sample_000442/grid_2_0.pl... | [["Distribute-three/sample_000442/grid_0_0.ply","Distribute-three/sample_000442/grid_0_1.ply","Distribute-three/sample_000442/grid_0_2.ply"],["Distribute-three/sample_000442/grid_1_0.ply","Distribute-three/sample_000442/grid_1_1.ply","Distribute-three/sample_000442/grid_1_2.ply"],["Distribute-three/sample_000442/grid_2... | ["Distribute-three/sample_000442/cand_0.ply","Distribute-three/sample_000442/cand_1.ply","Distribute-three/sample_000442/cand_2.ply","Distribute-three/sample_000442/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 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), forward. Horizontal relation E[r,c+1]=T^2(E[r,c]); vertical relation E[r+1,c]=T^1(E[r,c]). Effective str... | {"template":"Distribute-three","axis":"distribute_three_size","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_004468 | sample_004468 | Symmetry | train | matrix_3x3 | Symmetry/sample_004468 | Symmetry/sample_004468/meta.json | Symmetry/sample_004468 | ["Symmetry/sample_004468/grid_0_0.ply","Symmetry/sample_004468/grid_0_1.ply","Symmetry/sample_004468/grid_0_2.ply","Symmetry/sample_004468/grid_1_0.ply","Symmetry/sample_004468/grid_1_1.ply","Symmetry/sample_004468/grid_1_2.ply","Symmetry/sample_004468/grid_2_0.ply","Symmetry/sample_004468/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_004468/grid_0_0.ply","Symmetry/sample_004468/grid_0_1.ply","Symmetry/sample_004468/grid_0_2.ply"],["Symmetry/sample_004468/grid_1_0.ply","Symmetry/sample_004468/grid_1_1.ply","Symmetry/sample_004468/grid_1_2.ply"],["Symmetry/sample_004468/grid_2_0.ply","Symmetry/sample_004468/grid_2_1.ply",null]] | ["Symmetry/sample_004468/cand_0.ply","Symmetry/sample_004468/cand_1.ply","Symmetry/sample_004468/cand_2.ply","Symmetry/sample_004468/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_003029 | sample_003029 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_003029 | Distribute-three/sample_003029/meta.json | Distribute-three/sample_003029 | ["Distribute-three/sample_003029/grid_0_0.ply","Distribute-three/sample_003029/grid_0_1.ply","Distribute-three/sample_003029/grid_0_2.ply","Distribute-three/sample_003029/grid_1_0.ply","Distribute-three/sample_003029/grid_1_1.ply","Distribute-three/sample_003029/grid_1_2.ply","Distribute-three/sample_003029/grid_2_0.pl... | [["Distribute-three/sample_003029/grid_0_0.ply","Distribute-three/sample_003029/grid_0_1.ply","Distribute-three/sample_003029/grid_0_2.ply"],["Distribute-three/sample_003029/grid_1_0.ply","Distribute-three/sample_003029/grid_1_1.ply","Distribute-three/sample_003029/grid_1_2.ply"],["Distribute-three/sample_003029/grid_2... | ["Distribute-three/sample_003029/cand_0.ply","Distribute-three/sample_003029/cand_1.ply","Distribute-three/sample_003029/cand_2.ply","Distribute-three/sample_003029/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_shape). Per-T attribute change: all leaves share one primitive type and follow Distribute-three order (sphere -> box -> cylinder), forward. Horizontal relation E[r,c+1]=T^2(E[r,c]); vertical relation E[r+1,c]=T^1(E[r... | {"template":"Distribute-three","axis":"distribute_three_shape","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_001020 | sample_001020 | Permutation | train | matrix_3x3 | Permutation/sample_001020 | Permutation/sample_001020/meta.json | Permutation/sample_001020 | ["Permutation/sample_001020/grid_0_0.ply","Permutation/sample_001020/grid_0_1.ply","Permutation/sample_001020/grid_0_2.ply","Permutation/sample_001020/grid_1_0.ply","Permutation/sample_001020/grid_1_1.ply","Permutation/sample_001020/grid_1_2.ply","Permutation/sample_001020/grid_2_0.ply","Permutation/sample_001020/grid_... | [["Permutation/sample_001020/grid_0_0.ply","Permutation/sample_001020/grid_0_1.ply","Permutation/sample_001020/grid_0_2.ply"],["Permutation/sample_001020/grid_1_0.ply","Permutation/sample_001020/grid_1_1.ply","Permutation/sample_001020/grid_1_2.ply"],["Permutation/sample_001020/grid_2_0.ply","Permutation/sample_001020/... | ["Permutation/sample_001020/cand_0.ply","Permutation/sample_001020/cand_1.ply","Permutation/sample_001020/cand_2.ply","Permutation/sample_001020/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step left shift per T. 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 permuta... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Conservation/sample_002629 | sample_002629 | Conservation | train | matrix_3x3 | Conservation/sample_002629 | Conservation/sample_002629/meta.json | Conservation/sample_002629 | ["Conservation/sample_002629/grid_0_0.ply","Conservation/sample_002629/grid_0_1.ply","Conservation/sample_002629/grid_0_2.ply","Conservation/sample_002629/grid_1_0.ply","Conservation/sample_002629/grid_1_1.ply","Conservation/sample_002629/grid_1_2.ply","Conservation/sample_002629/grid_2_0.ply","Conservation/sample_0026... | [["Conservation/sample_002629/grid_0_0.ply","Conservation/sample_002629/grid_0_1.ply","Conservation/sample_002629/grid_0_2.ply"],["Conservation/sample_002629/grid_1_0.ply","Conservation/sample_002629/grid_1_1.ply","Conservation/sample_002629/grid_1_2.ply"],["Conservation/sample_002629/grid_2_0.ply","Conservation/sample... | ["Conservation/sample_002629/cand_0.ply","Conservation/sample_002629/cand_1.ply","Conservation/sample_002629/cand_2.ply","Conservation/sample_002629/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Conservation, axis=size_conservation). Per-T attribute change: size conservation triplet: leaf0:+1, leaf2:-1, leaf1:0. 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 conserv... | {"template":"Conservation","axis":"size_conservation","leaf_idx":0,"leaf_indices":[0,2,1],"direction":2,"directions":[1,-1,0],"rot_axis":null,"source_indices":null} |
Progression/sample_001191 | sample_001191 | Progression | train | matrix_3x3 | Progression/sample_001191 | Progression/sample_001191/meta.json | Progression/sample_001191 | ["Progression/sample_001191/grid_0_0.ply","Progression/sample_001191/grid_0_1.ply","Progression/sample_001191/grid_0_2.ply","Progression/sample_001191/grid_1_0.ply","Progression/sample_001191/grid_1_1.ply","Progression/sample_001191/grid_1_2.ply","Progression/sample_001191/grid_2_0.ply","Progression/sample_001191/grid_... | [["Progression/sample_001191/grid_0_0.ply","Progression/sample_001191/grid_0_1.ply","Progression/sample_001191/grid_0_2.ply"],["Progression/sample_001191/grid_1_0.ply","Progression/sample_001191/grid_1_1.ply","Progression/sample_001191/grid_1_2.ply"],["Progression/sample_001191/grid_2_0.ply","Progression/sample_001191/... | ["Progression/sample_001191/cand_0.ply","Progression/sample_001191/cand_1.ply","Progression/sample_001191/cand_2.ply","Progression/sample_001191/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=r). Per-T attribute change: all leaves change size_level by +1 per T. 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 net size_level +2, vertical net size_level +1. | {"template":"Progression","axis":"r","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_000166 | sample_000166 | Permutation | train | matrix_3x3 | Permutation/sample_000166 | Permutation/sample_000166/meta.json | Permutation/sample_000166 | ["Permutation/sample_000166/grid_0_0.ply","Permutation/sample_000166/grid_0_1.ply","Permutation/sample_000166/grid_0_2.ply","Permutation/sample_000166/grid_1_0.ply","Permutation/sample_000166/grid_1_1.ply","Permutation/sample_000166/grid_1_2.ply","Permutation/sample_000166/grid_2_0.ply","Permutation/sample_000166/grid_... | [["Permutation/sample_000166/grid_0_0.ply","Permutation/sample_000166/grid_0_1.ply","Permutation/sample_000166/grid_0_2.ply"],["Permutation/sample_000166/grid_1_0.ply","Permutation/sample_000166/grid_1_1.ply","Permutation/sample_000166/grid_1_2.ply"],["Permutation/sample_000166/grid_2_0.ply","Permutation/sample_000166/... | ["Permutation/sample_000166/cand_0.ply","Permutation/sample_000166/cand_1.ply","Permutation/sample_000166/cand_2.ply","Permutation/sample_000166/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step right shift per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 permut... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Conservation/sample_004628 | sample_004628 | Conservation | train | matrix_3x3 | Conservation/sample_004628 | Conservation/sample_004628/meta.json | Conservation/sample_004628 | ["Conservation/sample_004628/grid_0_0.ply","Conservation/sample_004628/grid_0_1.ply","Conservation/sample_004628/grid_0_2.ply","Conservation/sample_004628/grid_1_0.ply","Conservation/sample_004628/grid_1_1.ply","Conservation/sample_004628/grid_1_2.ply","Conservation/sample_004628/grid_2_0.ply","Conservation/sample_0046... | [["Conservation/sample_004628/grid_0_0.ply","Conservation/sample_004628/grid_0_1.ply","Conservation/sample_004628/grid_0_2.ply"],["Conservation/sample_004628/grid_1_0.ply","Conservation/sample_004628/grid_1_1.ply","Conservation/sample_004628/grid_1_2.ply"],["Conservation/sample_004628/grid_2_0.ply","Conservation/sample... | ["Conservation/sample_004628/cand_0.ply","Conservation/sample_004628/cand_1.ply","Conservation/sample_004628/cand_2.ply","Conservation/sample_004628/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Conservation, axis=size_conservation). Per-T attribute change: size conservation triplet: leaf2:+1, leaf0:-1, leaf1:0. 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 conserv... | {"template":"Conservation","axis":"size_conservation","leaf_idx":2,"leaf_indices":[2,0,1],"direction":0,"directions":[1,-1,0],"rot_axis":null,"source_indices":null} |
Conservation/sample_004917 | sample_004917 | Conservation | train | matrix_3x3 | Conservation/sample_004917 | Conservation/sample_004917/meta.json | Conservation/sample_004917 | ["Conservation/sample_004917/grid_0_0.ply","Conservation/sample_004917/grid_0_1.ply","Conservation/sample_004917/grid_0_2.ply","Conservation/sample_004917/grid_1_0.ply","Conservation/sample_004917/grid_1_1.ply","Conservation/sample_004917/grid_1_2.ply","Conservation/sample_004917/grid_2_0.ply","Conservation/sample_0049... | [["Conservation/sample_004917/grid_0_0.ply","Conservation/sample_004917/grid_0_1.ply","Conservation/sample_004917/grid_0_2.ply"],["Conservation/sample_004917/grid_1_0.ply","Conservation/sample_004917/grid_1_1.ply","Conservation/sample_004917/grid_1_2.ply"],["Conservation/sample_004917/grid_2_0.ply","Conservation/sample... | ["Conservation/sample_004917/cand_0.ply","Conservation/sample_004917/cand_1.ply","Conservation/sample_004917/cand_2.ply","Conservation/sample_004917/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Conservation, axis=size_conservation). Per-T attribute change: size conservation triplet: leaf1:+1, leaf0:-1, leaf2:0. 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 conserv... | {"template":"Conservation","axis":"size_conservation","leaf_idx":1,"leaf_indices":[1,0,2],"direction":0,"directions":[1,-1,0],"rot_axis":null,"source_indices":null} |
Count/sample_001206 | sample_001206 | Count | train | matrix_3x3 | Count/sample_001206 | Count/sample_001206/meta.json | Count/sample_001206 | ["Count/sample_001206/grid_0_0.ply","Count/sample_001206/grid_0_1.ply","Count/sample_001206/grid_0_2.ply","Count/sample_001206/grid_1_0.ply","Count/sample_001206/grid_1_1.ply","Count/sample_001206/grid_1_2.ply","Count/sample_001206/grid_2_0.ply","Count/sample_001206/grid_2_1.ply","Count/sample_001206/cand_0.ply","Count... | [["Count/sample_001206/grid_0_0.ply","Count/sample_001206/grid_0_1.ply","Count/sample_001206/grid_0_2.ply"],["Count/sample_001206/grid_1_0.ply","Count/sample_001206/grid_1_1.ply","Count/sample_001206/grid_1_2.ply"],["Count/sample_001206/grid_2_0.ply","Count/sample_001206/grid_2_1.ply",null]] | ["Count/sample_001206/cand_0.ply","Count/sample_001206/cand_1.ply","Count/sample_001206/cand_2.ply","Count/sample_001206/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_003203 | sample_003203 | Count | train | matrix_3x3 | Count/sample_003203 | Count/sample_003203/meta.json | Count/sample_003203 | ["Count/sample_003203/grid_0_0.ply","Count/sample_003203/grid_0_1.ply","Count/sample_003203/grid_0_2.ply","Count/sample_003203/grid_1_0.ply","Count/sample_003203/grid_1_1.ply","Count/sample_003203/grid_1_2.ply","Count/sample_003203/grid_2_0.ply","Count/sample_003203/grid_2_1.ply","Count/sample_003203/cand_0.ply","Count... | [["Count/sample_003203/grid_0_0.ply","Count/sample_003203/grid_0_1.ply","Count/sample_003203/grid_0_2.ply"],["Count/sample_003203/grid_1_0.ply","Count/sample_003203/grid_1_1.ply","Count/sample_003203/grid_1_2.ply"],["Count/sample_003203/grid_2_0.ply","Count/sample_003203/grid_2_1.ply",null]] | ["Count/sample_003203/cand_0.ply","Count/sample_003203/cand_1.ply","Count/sample_003203/cand_2.ply","Count/sample_003203/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_004621 | sample_004621 | Count | train | matrix_3x3 | Count/sample_004621 | Count/sample_004621/meta.json | Count/sample_004621 | ["Count/sample_004621/grid_0_0.ply","Count/sample_004621/grid_0_1.ply","Count/sample_004621/grid_0_2.ply","Count/sample_004621/grid_1_0.ply","Count/sample_004621/grid_1_1.ply","Count/sample_004621/grid_1_2.ply","Count/sample_004621/grid_2_0.ply","Count/sample_004621/grid_2_1.ply","Count/sample_004621/cand_0.ply","Count... | [["Count/sample_004621/grid_0_0.ply","Count/sample_004621/grid_0_1.ply","Count/sample_004621/grid_0_2.ply"],["Count/sample_004621/grid_1_0.ply","Count/sample_004621/grid_1_1.ply","Count/sample_004621/grid_1_2.ply"],["Count/sample_004621/grid_2_0.ply","Count/sample_004621/grid_2_1.ply",null]] | ["Count/sample_004621/cand_0.ply","Count/sample_004621/cand_1.ply","Count/sample_004621/cand_2.ply","Count/sample_004621/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_002750 | sample_002750 | Symmetry | train | matrix_3x3 | Symmetry/sample_002750 | Symmetry/sample_002750/meta.json | Symmetry/sample_002750 | ["Symmetry/sample_002750/grid_0_0.ply","Symmetry/sample_002750/grid_0_1.ply","Symmetry/sample_002750/grid_0_2.ply","Symmetry/sample_002750/grid_1_0.ply","Symmetry/sample_002750/grid_1_1.ply","Symmetry/sample_002750/grid_1_2.ply","Symmetry/sample_002750/grid_2_0.ply","Symmetry/sample_002750/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_002750/grid_0_0.ply","Symmetry/sample_002750/grid_0_1.ply","Symmetry/sample_002750/grid_0_2.ply"],["Symmetry/sample_002750/grid_1_0.ply","Symmetry/sample_002750/grid_1_1.ply","Symmetry/sample_002750/grid_1_2.ply"],["Symmetry/sample_002750/grid_2_0.ply","Symmetry/sample_002750/grid_2_1.ply",null]] | ["Symmetry/sample_002750/cand_0.ply","Symmetry/sample_002750/cand_1.ply","Symmetry/sample_002750/cand_2.ply","Symmetry/sample_002750/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_004209 | sample_004209 | Count | train | matrix_3x3 | Count/sample_004209 | Count/sample_004209/meta.json | Count/sample_004209 | ["Count/sample_004209/grid_0_0.ply","Count/sample_004209/grid_0_1.ply","Count/sample_004209/grid_0_2.ply","Count/sample_004209/grid_1_0.ply","Count/sample_004209/grid_1_1.ply","Count/sample_004209/grid_1_2.ply","Count/sample_004209/grid_2_0.ply","Count/sample_004209/grid_2_1.ply","Count/sample_004209/cand_0.ply","Count... | [["Count/sample_004209/grid_0_0.ply","Count/sample_004209/grid_0_1.ply","Count/sample_004209/grid_0_2.ply"],["Count/sample_004209/grid_1_0.ply","Count/sample_004209/grid_1_1.ply","Count/sample_004209/grid_1_2.ply"],["Count/sample_004209/grid_2_0.ply","Count/sample_004209/grid_2_1.ply",null]] | ["Count/sample_004209/cand_0.ply","Count/sample_004209/cand_1.ply","Count/sample_004209/cand_2.ply","Count/sample_004209/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->3->2->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Progression/sample_001698 | sample_001698 | Progression | train | matrix_3x3 | Progression/sample_001698 | Progression/sample_001698/meta.json | Progression/sample_001698 | ["Progression/sample_001698/grid_0_0.ply","Progression/sample_001698/grid_0_1.ply","Progression/sample_001698/grid_0_2.ply","Progression/sample_001698/grid_1_0.ply","Progression/sample_001698/grid_1_1.ply","Progression/sample_001698/grid_1_2.ply","Progression/sample_001698/grid_2_0.ply","Progression/sample_001698/grid_... | [["Progression/sample_001698/grid_0_0.ply","Progression/sample_001698/grid_0_1.ply","Progression/sample_001698/grid_0_2.ply"],["Progression/sample_001698/grid_1_0.ply","Progression/sample_001698/grid_1_1.ply","Progression/sample_001698/grid_1_2.ply"],["Progression/sample_001698/grid_2_0.ply","Progression/sample_001698/... | ["Progression/sample_001698/cand_0.ply","Progression/sample_001698/cand_1.ply","Progression/sample_001698/cand_2.ply","Progression/sample_001698/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=r). Per-T attribute change: all leaves change size_level by -1 per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal net size_level -1, vertical net size_level -2. | {"template":"Progression","axis":"r","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_000225 | sample_000225 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_000225 | Distribute-three/sample_000225/meta.json | Distribute-three/sample_000225 | ["Distribute-three/sample_000225/grid_0_0.ply","Distribute-three/sample_000225/grid_0_1.ply","Distribute-three/sample_000225/grid_0_2.ply","Distribute-three/sample_000225/grid_1_0.ply","Distribute-three/sample_000225/grid_1_1.ply","Distribute-three/sample_000225/grid_1_2.ply","Distribute-three/sample_000225/grid_2_0.pl... | [["Distribute-three/sample_000225/grid_0_0.ply","Distribute-three/sample_000225/grid_0_1.ply","Distribute-three/sample_000225/grid_0_2.ply"],["Distribute-three/sample_000225/grid_1_0.ply","Distribute-three/sample_000225/grid_1_1.ply","Distribute-three/sample_000225/grid_1_2.ply"],["Distribute-three/sample_000225/grid_2... | ["Distribute-three/sample_000225/cand_0.ply","Distribute-three/sample_000225/cand_1.ply","Distribute-three/sample_000225/cand_2.ply","Distribute-three/sample_000225/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_shape). Per-T attribute change: all leaves share one primitive type and follow Distribute-three order (sphere -> box -> cylinder), forward. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r... | {"template":"Distribute-three","axis":"distribute_three_shape","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_000158 | sample_000158 | Symmetry | train | matrix_3x3 | Symmetry/sample_000158 | Symmetry/sample_000158/meta.json | Symmetry/sample_000158 | ["Symmetry/sample_000158/grid_0_0.ply","Symmetry/sample_000158/grid_0_1.ply","Symmetry/sample_000158/grid_0_2.ply","Symmetry/sample_000158/grid_1_0.ply","Symmetry/sample_000158/grid_1_1.ply","Symmetry/sample_000158/grid_1_2.ply","Symmetry/sample_000158/grid_2_0.ply","Symmetry/sample_000158/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_000158/grid_0_0.ply","Symmetry/sample_000158/grid_0_1.ply","Symmetry/sample_000158/grid_0_2.ply"],["Symmetry/sample_000158/grid_1_0.ply","Symmetry/sample_000158/grid_1_1.ply","Symmetry/sample_000158/grid_1_2.ply"],["Symmetry/sample_000158/grid_2_0.ply","Symmetry/sample_000158/grid_2_1.ply",null]] | ["Symmetry/sample_000158/cand_0.ply","Symmetry/sample_000158/cand_1.ply","Symmetry/sample_000158/cand_2.ply","Symmetry/sample_000158/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Progression/sample_000652 | sample_000652 | Progression | train | matrix_3x3 | Progression/sample_000652 | Progression/sample_000652/meta.json | Progression/sample_000652 | ["Progression/sample_000652/grid_0_0.ply","Progression/sample_000652/grid_0_1.ply","Progression/sample_000652/grid_0_2.ply","Progression/sample_000652/grid_1_0.ply","Progression/sample_000652/grid_1_1.ply","Progression/sample_000652/grid_1_2.ply","Progression/sample_000652/grid_2_0.ply","Progression/sample_000652/grid_... | [["Progression/sample_000652/grid_0_0.ply","Progression/sample_000652/grid_0_1.ply","Progression/sample_000652/grid_0_2.ply"],["Progression/sample_000652/grid_1_0.ply","Progression/sample_000652/grid_1_1.ply","Progression/sample_000652/grid_1_2.ply"],["Progression/sample_000652/grid_2_0.ply","Progression/sample_000652/... | ["Progression/sample_000652/cand_0.ply","Progression/sample_000652/cand_1.ply","Progression/sample_000652/cand_2.ply","Progression/sample_000652/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 0 | A | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=r). Per-T attribute change: all leaves change size_level by +1 per T. 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 net size_level +2, vertical net size_level +1. | {"template":"Progression","axis":"r","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Progression/sample_000017 | sample_000017 | Progression | train | matrix_3x3 | Progression/sample_000017 | Progression/sample_000017/meta.json | Progression/sample_000017 | ["Progression/sample_000017/grid_0_0.ply","Progression/sample_000017/grid_0_1.ply","Progression/sample_000017/grid_0_2.ply","Progression/sample_000017/grid_1_0.ply","Progression/sample_000017/grid_1_1.ply","Progression/sample_000017/grid_1_2.ply","Progression/sample_000017/grid_2_0.ply","Progression/sample_000017/grid_... | [["Progression/sample_000017/grid_0_0.ply","Progression/sample_000017/grid_0_1.ply","Progression/sample_000017/grid_0_2.ply"],["Progression/sample_000017/grid_1_0.ply","Progression/sample_000017/grid_1_1.ply","Progression/sample_000017/grid_1_2.ply"],["Progression/sample_000017/grid_2_0.ply","Progression/sample_000017/... | ["Progression/sample_000017/cand_0.ply","Progression/sample_000017/cand_1.ply","Progression/sample_000017/cand_2.ply","Progression/sample_000017/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Progression, axis=R). Per-T attribute change: global_pose_deg.z rotates -60 degrees per T. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal net rotation -60 degrees on z, vertical net rot... | {"template":"Progression","axis":"R","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":"z","source_indices":null} |
Count/sample_000570 | sample_000570 | Count | train | matrix_3x3 | Count/sample_000570 | Count/sample_000570/meta.json | Count/sample_000570 | ["Count/sample_000570/grid_0_0.ply","Count/sample_000570/grid_0_1.ply","Count/sample_000570/grid_0_2.ply","Count/sample_000570/grid_1_0.ply","Count/sample_000570/grid_1_1.ply","Count/sample_000570/grid_1_2.ply","Count/sample_000570/grid_2_0.ply","Count/sample_000570/grid_2_1.ply","Count/sample_000570/cand_0.ply","Count... | [["Count/sample_000570/grid_0_0.ply","Count/sample_000570/grid_0_1.ply","Count/sample_000570/grid_0_2.ply"],["Count/sample_000570/grid_1_0.ply","Count/sample_000570/grid_1_1.ply","Count/sample_000570/grid_1_2.ply"],["Count/sample_000570/grid_2_0.ply","Count/sample_000570/grid_2_1.ply",null]] | ["Count/sample_000570/cand_0.ply","Count/sample_000570/cand_1.ply","Count/sample_000570/cand_2.ply","Count/sample_000570/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->3->2->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Symmetry/sample_001818 | sample_001818 | Symmetry | train | matrix_3x3 | Symmetry/sample_001818 | Symmetry/sample_001818/meta.json | Symmetry/sample_001818 | ["Symmetry/sample_001818/grid_0_0.ply","Symmetry/sample_001818/grid_0_1.ply","Symmetry/sample_001818/grid_0_2.ply","Symmetry/sample_001818/grid_1_0.ply","Symmetry/sample_001818/grid_1_1.ply","Symmetry/sample_001818/grid_1_2.ply","Symmetry/sample_001818/grid_2_0.ply","Symmetry/sample_001818/grid_2_1.ply","Symmetry/sampl... | [["Symmetry/sample_001818/grid_0_0.ply","Symmetry/sample_001818/grid_0_1.ply","Symmetry/sample_001818/grid_0_2.ply"],["Symmetry/sample_001818/grid_1_0.ply","Symmetry/sample_001818/grid_1_1.ply","Symmetry/sample_001818/grid_1_2.ply"],["Symmetry/sample_001818/grid_2_0.ply","Symmetry/sample_001818/grid_2_1.ply",null]] | ["Symmetry/sample_001818/cand_0.ply","Symmetry/sample_001818/cand_1.ply","Symmetry/sample_001818/cand_2.ply","Symmetry/sample_001818/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 1 | 3x3 matrix completion using dual symmetry rules: horizontal uses T_h and vertical uses inverse-like T_v. Horizontal axis=r, vertical axis=r. Horizontal relation E[r,c+1]=T_h^1(E[r,c]); vertical relation E[r+1,c]=T_v^1(E[r,c]). | {"template":"Symmetry","axis":"r","leaf_idx":0,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_001589 | sample_001589 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_001589 | Distribute-three/sample_001589/meta.json | Distribute-three/sample_001589 | ["Distribute-three/sample_001589/grid_0_0.ply","Distribute-three/sample_001589/grid_0_1.ply","Distribute-three/sample_001589/grid_0_2.ply","Distribute-three/sample_001589/grid_1_0.ply","Distribute-three/sample_001589/grid_1_1.ply","Distribute-three/sample_001589/grid_1_2.ply","Distribute-three/sample_001589/grid_2_0.pl... | [["Distribute-three/sample_001589/grid_0_0.ply","Distribute-three/sample_001589/grid_0_1.ply","Distribute-three/sample_001589/grid_0_2.ply"],["Distribute-three/sample_001589/grid_1_0.ply","Distribute-three/sample_001589/grid_1_1.ply","Distribute-three/sample_001589/grid_1_2.ply"],["Distribute-three/sample_001589/grid_2... | ["Distribute-three/sample_001589/cand_0.ply","Distribute-three/sample_001589/cand_1.ply","Distribute-three/sample_001589/cand_2.ply","Distribute-three/sample_001589/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 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), forward. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective str... | {"template":"Distribute-three","axis":"distribute_three_size","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_001834 | sample_001834 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_001834 | Distribute-three/sample_001834/meta.json | Distribute-three/sample_001834 | ["Distribute-three/sample_001834/grid_0_0.ply","Distribute-three/sample_001834/grid_0_1.ply","Distribute-three/sample_001834/grid_0_2.ply","Distribute-three/sample_001834/grid_1_0.ply","Distribute-three/sample_001834/grid_1_1.ply","Distribute-three/sample_001834/grid_1_2.ply","Distribute-three/sample_001834/grid_2_0.pl... | [["Distribute-three/sample_001834/grid_0_0.ply","Distribute-three/sample_001834/grid_0_1.ply","Distribute-three/sample_001834/grid_0_2.ply"],["Distribute-three/sample_001834/grid_1_0.ply","Distribute-three/sample_001834/grid_1_1.ply","Distribute-three/sample_001834/grid_1_2.ply"],["Distribute-three/sample_001834/grid_2... | ["Distribute-three/sample_001834/cand_0.ply","Distribute-three/sample_001834/cand_1.ply","Distribute-three/sample_001834/cand_2.ply","Distribute-three/sample_001834/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_shape). Per-T attribute change: all leaves share one primitive type and follow Distribute-three order (sphere -> box -> cylinder), forward. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r... | {"template":"Distribute-three","axis":"distribute_three_shape","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_002770 | sample_002770 | Count | train | matrix_3x3 | Count/sample_002770 | Count/sample_002770/meta.json | Count/sample_002770 | ["Count/sample_002770/grid_0_0.ply","Count/sample_002770/grid_0_1.ply","Count/sample_002770/grid_0_2.ply","Count/sample_002770/grid_1_0.ply","Count/sample_002770/grid_1_1.ply","Count/sample_002770/grid_1_2.ply","Count/sample_002770/grid_2_0.ply","Count/sample_002770/grid_2_1.ply","Count/sample_002770/cand_0.ply","Count... | [["Count/sample_002770/grid_0_0.ply","Count/sample_002770/grid_0_1.ply","Count/sample_002770/grid_0_2.ply"],["Count/sample_002770/grid_1_0.ply","Count/sample_002770/grid_1_1.ply","Count/sample_002770/grid_1_2.ply"],["Count/sample_002770/grid_2_0.ply","Count/sample_002770/grid_2_1.ply",null]] | ["Count/sample_002770/cand_0.ply","Count/sample_002770/cand_1.ply","Count/sample_002770/cand_2.ply","Count/sample_002770/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->3->2->1. 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 count transitions; vertical applies T^1 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_004513 | sample_004513 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_004513 | Distribute-three/sample_004513/meta.json | Distribute-three/sample_004513 | ["Distribute-three/sample_004513/grid_0_0.ply","Distribute-three/sample_004513/grid_0_1.ply","Distribute-three/sample_004513/grid_0_2.ply","Distribute-three/sample_004513/grid_1_0.ply","Distribute-three/sample_004513/grid_1_1.ply","Distribute-three/sample_004513/grid_1_2.ply","Distribute-three/sample_004513/grid_2_0.pl... | [["Distribute-three/sample_004513/grid_0_0.ply","Distribute-three/sample_004513/grid_0_1.ply","Distribute-three/sample_004513/grid_0_2.ply"],["Distribute-three/sample_004513/grid_1_0.ply","Distribute-three/sample_004513/grid_1_1.ply","Distribute-three/sample_004513/grid_1_2.ply"],["Distribute-three/sample_004513/grid_2... | ["Distribute-three/sample_004513/cand_0.ply","Distribute-three/sample_004513/cand_1.ply","Distribute-three/sample_004513/cand_2.ply","Distribute-three/sample_004513/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 1 | 2 | 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^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective str... | {"template":"Distribute-three","axis":"distribute_three_size","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Count/sample_002011 | sample_002011 | Count | train | matrix_3x3 | Count/sample_002011 | Count/sample_002011/meta.json | Count/sample_002011 | ["Count/sample_002011/grid_0_0.ply","Count/sample_002011/grid_0_1.ply","Count/sample_002011/grid_0_2.ply","Count/sample_002011/grid_1_0.ply","Count/sample_002011/grid_1_1.ply","Count/sample_002011/grid_1_2.ply","Count/sample_002011/grid_2_0.ply","Count/sample_002011/grid_2_1.ply","Count/sample_002011/cand_0.ply","Count... | [["Count/sample_002011/grid_0_0.ply","Count/sample_002011/grid_0_1.ply","Count/sample_002011/grid_0_2.ply"],["Count/sample_002011/grid_1_0.ply","Count/sample_002011/grid_1_1.ply","Count/sample_002011/grid_1_2.ply"],["Count/sample_002011/grid_2_0.ply","Count/sample_002011/grid_2_1.ply",null]] | ["Count/sample_002011/cand_0.ply","Count/sample_002011/cand_1.ply","Count/sample_002011/cand_2.ply","Count/sample_002011/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 2 | C | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Count, axis=count). Per-T attribute change: leaf_count follows cycle 1->2->3->1. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizontal applies T^1 count transitions; vertical applies T^2 count... | {"template":"Count","axis":"count","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Permutation/sample_002255 | sample_002255 | Permutation | train | matrix_3x3 | Permutation/sample_002255 | Permutation/sample_002255/meta.json | Permutation/sample_002255 | ["Permutation/sample_002255/grid_0_0.ply","Permutation/sample_002255/grid_0_1.ply","Permutation/sample_002255/grid_0_2.ply","Permutation/sample_002255/grid_1_0.ply","Permutation/sample_002255/grid_1_1.ply","Permutation/sample_002255/grid_1_2.ply","Permutation/sample_002255/grid_2_0.ply","Permutation/sample_002255/grid_... | [["Permutation/sample_002255/grid_0_0.ply","Permutation/sample_002255/grid_0_1.ply","Permutation/sample_002255/grid_0_2.ply"],["Permutation/sample_002255/grid_1_0.ply","Permutation/sample_002255/grid_1_1.ply","Permutation/sample_002255/grid_1_2.ply"],["Permutation/sample_002255/grid_2_0.ply","Permutation/sample_002255/... | ["Permutation/sample_002255/cand_0.ply","Permutation/sample_002255/cand_1.ply","Permutation/sample_002255/cand_2.ply","Permutation/sample_002255/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 2 | 1 | 3x3 matrix completion using one fixed rule instance T (template=Permutation, axis=slot_permutation). Per-T attribute change: slot assignment is permuted by one-step left shift per T. 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 permuta... | {"template":"Permutation","axis":"slot_permutation","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_002895 | sample_002895 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_002895 | Distribute-three/sample_002895/meta.json | Distribute-three/sample_002895 | ["Distribute-three/sample_002895/grid_0_0.ply","Distribute-three/sample_002895/grid_0_1.ply","Distribute-three/sample_002895/grid_0_2.ply","Distribute-three/sample_002895/grid_1_0.ply","Distribute-three/sample_002895/grid_1_1.ply","Distribute-three/sample_002895/grid_1_2.ply","Distribute-three/sample_002895/grid_2_0.pl... | [["Distribute-three/sample_002895/grid_0_0.ply","Distribute-three/sample_002895/grid_0_1.ply","Distribute-three/sample_002895/grid_0_2.ply"],["Distribute-three/sample_002895/grid_1_0.ply","Distribute-three/sample_002895/grid_1_1.ply","Distribute-three/sample_002895/grid_1_2.ply"],["Distribute-three/sample_002895/grid_2... | ["Distribute-three/sample_002895/cand_0.ply","Distribute-three/sample_002895/cand_1.ply","Distribute-three/sample_002895/cand_2.ply","Distribute-three/sample_002895/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 3 | D | 4,096 | 2 | 1 | 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), forward. Horizontal relation E[r,c+1]=T^2(E[r,c]); vertical relation E[r+1,c]=T^1(E[r,c]). Effective str... | {"template":"Distribute-three","axis":"distribute_three_size","leaf_idx":null,"leaf_indices":null,"direction":1,"directions":null,"rot_axis":null,"source_indices":null} |
Distribute-three/sample_000788 | sample_000788 | Distribute-three | train | matrix_3x3 | Distribute-three/sample_000788 | Distribute-three/sample_000788/meta.json | Distribute-three/sample_000788 | ["Distribute-three/sample_000788/grid_0_0.ply","Distribute-three/sample_000788/grid_0_1.ply","Distribute-three/sample_000788/grid_0_2.ply","Distribute-three/sample_000788/grid_1_0.ply","Distribute-three/sample_000788/grid_1_1.ply","Distribute-three/sample_000788/grid_1_2.ply","Distribute-three/sample_000788/grid_2_0.pl... | [["Distribute-three/sample_000788/grid_0_0.ply","Distribute-three/sample_000788/grid_0_1.ply","Distribute-three/sample_000788/grid_0_2.ply"],["Distribute-three/sample_000788/grid_1_0.ply","Distribute-three/sample_000788/grid_1_1.ply","Distribute-three/sample_000788/grid_1_2.ply"],["Distribute-three/sample_000788/grid_2... | ["Distribute-three/sample_000788/cand_0.ply","Distribute-three/sample_000788/cand_1.ply","Distribute-three/sample_000788/cand_2.ply","Distribute-three/sample_000788/cand_3.ply"] | [[true,true,true],[true,true,true],[true,true,false]] | [2,2] | 1 | B | 4,096 | 1 | 2 | 3x3 matrix completion using one fixed rule instance T (template=Distribute-three, axis=distribute_three_density). Per-T attribute change: density level follows Distribute-three order (0 -> 2 -> 4), reverse. Horizontal relation E[r,c+1]=T^1(E[r,c]); vertical relation E[r+1,c]=T^2(E[r,c]). Effective stride detail: horizo... | {"template":"Distribute-three","axis":"distribute_three_density","leaf_idx":null,"leaf_indices":null,"direction":-1,"directions":null,"rot_axis":null,"source_indices":null} |
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