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+ {
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+ "problem_setup": "The scene shows a tabletop Tower-of-Hanoi style setup recorded from an egocentric viewpoint. Three poles are placed left-to-right and remain fixed across the dataset. The poles are denoted as L, C, and R for left, center, and right from the viewer’s perspective. Up to six rings are used. Each ring has a unique color identifier and a unique size rank. The environment is controlled. The background is covered by a gray enclosure and hands wear sky-blue gloves to reduce appearance variation. The camera viewpoint is not mirrored or flipped. The pole order will not change. Each move relocates exactly one ring. Moving two or more rings at once is not allowed.",
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+ "state_notation": "We represent a configuration as L=..._C=..._R=.... For each pole, ring identifiers appear in bottom-to-top order. E denotes an empty pole.",
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+ },
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+ {
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+ "id": 7,
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+ }
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+ ]
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+ },
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+ "instructions": {
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+ "rule_setting": "Rule-based setting: A larger ring cannot be placed on a smaller ring.",
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+ "free_setting": "Free-rule setting: A larger ring may be placed on a smaller ring.",
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+ "pq_output_format": "Return PQ answers as JSON: {\"pq\": [[...],[...],[...],[...],[...],[...]]}. Each PQ is a sorted list of option numbers. Use [7] only if the pole is empty.",
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+ "oq_output_format": "Return next state only in the form L=<...>_C=<...>_R=<...> with no extra text."
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+ },
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+ "paths": {
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+ "states_dir": "./frames/states"
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+ },
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+ {
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+ "problem_id": "opt_rule_img__n1_CtoL__L=E_C=Y_R=E__TO__L=Y_C=E_R=E",
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+ "src": "C",
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+ "tgt": "L",
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+ "setting": "rule",
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+ "symbolic": false,
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+ "initial_state": "L=E_C=Y_R=E",
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+ "goal_state": "L=Y_C=E_R=E",
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+ "optimal_steps": 1,
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+ "max_steps": 100,
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+ "initial_image": "L=E_C=Y_R=E.jpg",
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+ "goal_image": "L=Y_C=E_R=E.jpg",
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+ "initial_state": "L=E_C=Y_R=E",
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+ "goal_state": "L=E_C=E_R=Y",
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+ "max_steps": 100,
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+ "initial_image": "L=E_C=Y_R=E.jpg",
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+ "problem_id": "opt_rule_img__n1_LtoC__L=Y_C=E_R=E__TO__L=E_C=Y_R=E",
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+ "pair_id": "n1_LtoC",
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+ "goal_state": "L=E_C=Y_R=E",
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+ "initial_image": "L=Y_C=E_R=E.jpg",
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+ "problem_id": "opt_rule_img__n1_LtoR__L=Y_C=E_R=E__TO__L=E_C=E_R=Y",
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+ "pair_id": "n1_LtoR",
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+ "initial_image": "L=Y_C=E_R=E.jpg",
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+ "goal_state": "L=E_C=Y_R=E",
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+ "max_steps": 100,
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+ "pair_id": "n1_RtoL",
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+ "n_rings": 1,
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+ "tgt": "L",
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+ "setting": "rule",
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+ "symbolic": false,
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+ "initial_state": "L=E_C=E_R=Y",
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+ "goal_state": "L=Y_C=E_R=E",
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+ "optimal_steps": 1,
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+ "max_steps": 100,
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+ "initial_image": "L=E_C=E_R=Y.jpg",
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+ "goal_image": "L=Y_C=E_R=E.jpg",
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+ "initial_state": "L=E_C=OY_R=E",
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+ "goal_state": "L=OY_C=E_R=E",
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+ "optimal_steps": 3,
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+ "max_steps": 100,
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+ "initial_image": "L=E_C=OY_R=E.jpg",
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+ "goal_image": "L=OY_C=E_R=E.jpg",
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+ "setting": "rule",
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+ "initial_state": "L=E_C=OY_R=E",
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+ "goal_state": "L=E_C=E_R=OY",
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+ "pair_id": "n5_LtoR",
3882
+ "n_rings": 5,
3883
+ "src": "L",
3884
+ "tgt": "R",
3885
+ "setting": "free",
3886
+ "symbolic": true,
3887
+ "initial_state": "L=YORSL_C=E_R=E",
3888
+ "goal_state": "L=E_C=E_R=YORSL",
3889
+ "optimal_steps": 31,
3890
+ "max_steps": 100,
3891
+ "initial_image": null,
3892
+ "goal_image": null
3893
+ },
3894
+ {
3895
+ "problem_id": "opt_free_sym__n5_RtoC__L=E_C=E_R=YORSL__TO__L=E_C=YORSL_R=E",
3896
+ "pair_id": "n5_RtoC",
3897
+ "n_rings": 5,
3898
+ "src": "R",
3899
+ "tgt": "C",
3900
+ "setting": "free",
3901
+ "symbolic": true,
3902
+ "initial_state": "L=E_C=E_R=YORSL",
3903
+ "goal_state": "L=E_C=YORSL_R=E",
3904
+ "optimal_steps": 31,
3905
+ "max_steps": 100,
3906
+ "initial_image": null,
3907
+ "goal_image": null
3908
+ },
3909
+ {
3910
+ "problem_id": "opt_free_sym__n5_RtoL__L=E_C=E_R=YORSL__TO__L=YORSL_C=E_R=E",
3911
+ "pair_id": "n5_RtoL",
3912
+ "n_rings": 5,
3913
+ "src": "R",
3914
+ "tgt": "L",
3915
+ "setting": "free",
3916
+ "symbolic": true,
3917
+ "initial_state": "L=E_C=E_R=YORSL",
3918
+ "goal_state": "L=YORSL_C=E_R=E",
3919
+ "optimal_steps": 31,
3920
+ "max_steps": 100,
3921
+ "initial_image": null,
3922
+ "goal_image": null
3923
+ },
3924
+ {
3925
+ "problem_id": "opt_free_sym__n6_CtoL__L=E_C=YORSLG_R=E__TO__L=YORSLG_C=E_R=E",
3926
+ "pair_id": "n6_CtoL",
3927
+ "n_rings": 6,
3928
+ "src": "C",
3929
+ "tgt": "L",
3930
+ "setting": "free",
3931
+ "symbolic": true,
3932
+ "initial_state": "L=E_C=YORSLG_R=E",
3933
+ "goal_state": "L=YORSLG_C=E_R=E",
3934
+ "optimal_steps": 63,
3935
+ "max_steps": 100,
3936
+ "initial_image": null,
3937
+ "goal_image": null
3938
+ },
3939
+ {
3940
+ "problem_id": "opt_free_sym__n6_CtoR__L=E_C=YORSLG_R=E__TO__L=E_C=E_R=YORSLG",
3941
+ "pair_id": "n6_CtoR",
3942
+ "n_rings": 6,
3943
+ "src": "C",
3944
+ "tgt": "R",
3945
+ "setting": "free",
3946
+ "symbolic": true,
3947
+ "initial_state": "L=E_C=YORSLG_R=E",
3948
+ "goal_state": "L=E_C=E_R=YORSLG",
3949
+ "optimal_steps": 63,
3950
+ "max_steps": 100,
3951
+ "initial_image": null,
3952
+ "goal_image": null
3953
+ },
3954
+ {
3955
+ "problem_id": "opt_free_sym__n6_LtoC__L=YORSLG_C=E_R=E__TO__L=E_C=YORSLG_R=E",
3956
+ "pair_id": "n6_LtoC",
3957
+ "n_rings": 6,
3958
+ "src": "L",
3959
+ "tgt": "C",
3960
+ "setting": "free",
3961
+ "symbolic": true,
3962
+ "initial_state": "L=YORSLG_C=E_R=E",
3963
+ "goal_state": "L=E_C=YORSLG_R=E",
3964
+ "optimal_steps": 63,
3965
+ "max_steps": 100,
3966
+ "initial_image": null,
3967
+ "goal_image": null
3968
+ },
3969
+ {
3970
+ "problem_id": "opt_free_sym__n6_LtoR__L=YORSLG_C=E_R=E__TO__L=E_C=E_R=YORSLG",
3971
+ "pair_id": "n6_LtoR",
3972
+ "n_rings": 6,
3973
+ "src": "L",
3974
+ "tgt": "R",
3975
+ "setting": "free",
3976
+ "symbolic": true,
3977
+ "initial_state": "L=YORSLG_C=E_R=E",
3978
+ "goal_state": "L=E_C=E_R=YORSLG",
3979
+ "optimal_steps": 63,
3980
+ "max_steps": 100,
3981
+ "initial_image": null,
3982
+ "goal_image": null
3983
+ },
3984
+ {
3985
+ "problem_id": "opt_free_sym__n6_RtoC__L=E_C=E_R=YORSLG__TO__L=E_C=YORSLG_R=E",
3986
+ "pair_id": "n6_RtoC",
3987
+ "n_rings": 6,
3988
+ "src": "R",
3989
+ "tgt": "C",
3990
+ "setting": "free",
3991
+ "symbolic": true,
3992
+ "initial_state": "L=E_C=E_R=YORSLG",
3993
+ "goal_state": "L=E_C=YORSLG_R=E",
3994
+ "optimal_steps": 63,
3995
+ "max_steps": 100,
3996
+ "initial_image": null,
3997
+ "goal_image": null
3998
+ },
3999
+ {
4000
+ "problem_id": "opt_free_sym__n6_RtoL__L=E_C=E_R=YORSLG__TO__L=YORSLG_C=E_R=E",
4001
+ "pair_id": "n6_RtoL",
4002
+ "n_rings": 6,
4003
+ "src": "R",
4004
+ "tgt": "L",
4005
+ "setting": "free",
4006
+ "symbolic": true,
4007
+ "initial_state": "L=E_C=E_R=YORSLG",
4008
+ "goal_state": "L=YORSLG_C=E_R=E",
4009
+ "optimal_steps": 63,
4010
+ "max_steps": 100,
4011
+ "initial_image": null,
4012
+ "goal_image": null
4013
+ }
4014
+ ],
4015
+ "prompt_templates": {
4016
+ "turn0_suffix": "Output format:\nReturn ONLY a single JSON object on one line with this schema:\n{\"pq\": [[...],[...],[...],[...],[...],[...]], \"reason\": \"<text>\"}\n- pq: list of 6 lists (PQ1..PQ6). Each inner list contains option IDs. Use [7] only if the pole is empty.\n- reason: 1-2 sentences about your plan approach (optional; keep short).\nDo not output any extra text.",
4017
+ "step_suffix": "Output format:\nReturn ONLY a single JSON object on one line with this schema:\n{\"state\": \"L=..._C=..._R=...\"}\nIf the current state already matches the goal state, return:\n{\"state\": \"DONE\"}\nDo not output any extra text."
4018
+ },
4019
+ "schemas": {
4020
+ "turn0": {
4021
+ "pq": "list[list[int]] length 6",
4022
+ "reason": "string"
4023
+ },
4024
+ "step": {
4025
+ "state": "string"
4026
+ }
4027
+ }
4028
+ }
problems/recursions.json ADDED
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