task_games__counterfactual_board__board_dimension_count

Program Contract

Program: count(board_grid.visible_units, unit=row|column, style=chess_checkers|sudoku); scene=counterfactual_board; scope=board_dimension_count

Candidate set: the visible game board, pieces, tokens, cards, tiles, marked state, legal-move cues, result panels, and labeled options inside the board_dimension_count objective scope. Operands: visible scene state and prompt-bound operands named by board_grid, visible_units, unit, row, column, style, chess_checkers, sudoku, counterfactual_board, board_dimension_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; image-pixel row or column bboxes for all counted visible board units; bbox-set cardinality equals answer. Query ids: row_count, column_count.

Reasoning Operations

Families: counting

2) Scene + task contract

1. Entities/relations: A visible board grid rendered in a chess/checkers or Sudoku-like style.
2. Supported query_id values: row_count, column_count
3. answer_gt.type: integer
4. Annotation schema: bbox_set
5. Alternate annotation forms: none
6. Annotation witness policy: image-pixel row or column bboxes for all counted visible board units; bbox-set cardinality equals answer.
7. Overlap/touch policy: counted row/column boxes cover the full visible board span for that unit.

3) Prompt contract

1. prompt_bundle_id: games_counterfactual_board_v1
2. scene_key: counterfactual_board
3. task_key: board_grid_count_query
4. Prompt query keys: row_count, column_count
5. Required slots: output-mode slots from the prompt bundle only.
6. JSON example validity rule: bbox-set cardinality equals the integer answer.
7. Output modes: answer_only, answer_and_annotation

4) Determinism + constraints

1. Seed namespaces used: task-local query/style/dimension namespaces plus shared counterfactual-board layout/style/noise namespaces.
2. Unique-answer policy: the sampled visible row or column count directly determines the answer.
3. Reject/resample conditions: invalid explicit style, dimensions, or query values raise and retry/propagate.
4. No-auto-relaxation guarantee: semantic constraints are not relaxed.