task_puzzles__cell_board__largest_component_size

Program Contract

Program: max_component_size(cell_board, cells=color_equals_query_color, adjacency=orthogonal_4_neighbor); scene=cell_board; scope=largest_component_size

Candidate set: the visible grid cells, cell colors/states, labels, walls, start/goal markers, and mirror or connectivity cues inside the largest_component_size objective scope. Operands: visible scene state and prompt-bound operands named by cell_board, cells, color_equals_query_color, adjacency, orthogonal_4_neighbor, largest_component_size. Operation: evaluate max_component_size over the candidate set using the visible states, constraints, transforms, comparisons, counts, paths, or option-selection rules 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 cell bboxes for all cells in the unique largest component; bbox-set cardinality equals the answer. Query ids: single.

Reasoning Operations

Families: counting, ranking, topology

2) Scene + task contract

1. Entities/relations: A rectangular colored cell board with a single largest target-color component containing one or more cells.
2. Supported query_id values: single
3. answer_gt.type: integer
4. Annotation schema: bbox_set
5. Alternate annotation forms: none
6. Annotation witness policy: image-pixel cell bboxes for all cells in the unique largest component; bbox-set cardinality equals the answer.
7. Overlap/touch policy: diagonal contact does not merge components.

3) Prompt contract

1. prompt_bundle_id: puzzles_cell_board_v1
2. scene_key: cell_board
3. task_key: cell_board_topology_query
4. Prompt query key: largest_component_size
5. Required slots: query_color, plus output-mode slots from the prompt bundle.
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 largest-component/color namespaces plus shared cell-board layout/style/font/noise namespaces.
2. Unique-answer policy: construction verifies a single target-color component has the configured largest size.
3. Reject/resample conditions: non-unique largest component or size mismatch raises and retries.
4. No-auto-relaxation guarantee: semantic constraints are not relaxed.