task_games__ultimate_tictactoe__macro_threat_board_count

Contract

1. Domain: games
2. Scene: ultimate_tictactoe
3. Scene id: ultimate_tictactoe
4. Public task id: task_games__ultimate_tictactoe__macro_threat_board_count
5. Supported query_id values: x_immediate_win_board_count, o_immediate_win_board_count
6. Answer schema: integer_count
7. Annotation schema: bbox_set

Program Contract

Program: count(filter(local_boards, status=open and immediate_win_exists(player))); scene=ultimate_tictactoe; scope=macro_threat_board_count

Candidate set: the visible game board, pieces, tokens, cards, tiles, marked state, legal-move cues, result panels, and labeled options inside the macro_threat_board_count objective scope. Operands: visible scene state and prompt-bound operands named by filter, local_boards, status, open, immediate_win_exists, player, ultimate_tictactoe, macro_threat_board_count plus the active query_id branch. Operation: evaluate count over the candidate set using the visible game state, rules, legal moves, comparisons, counts, simulations, or option-selection constraints encoded in the program expression; generation enforces a unique final answer. Output binding: answer uses the integer schema; generation binds a unique final answer. Annotation witnesses: annotation uses the bbox_set schema; the prompt/annotation contract defines the minimal visual witnesses. Query ids: x_immediate_win_board_count, o_immediate_win_board_count.

Reasoning Operations

Families: filtering, counting, logical_composition

Generation Notes

1. Query ids choose whether X or O immediate-win boards are counted.
2. Annotation contains the small-board bboxes for every counted board.
3. Empty annotation is valid when the answer is 0.
4. scalar_annotation_checked=true