task_puzzles__cell_board__symmetry_violation_count

Program Contract

Program: count_mirror_mismatches(cell_board, axis=vertical|horizontal, counted_side=left|top); scene=cell_board; scope=symmetry_violation_count

Candidate set: the visible grid cells, cell colors/states, labels, walls, start/goal markers, and mirror or connectivity cues inside the symmetry_violation_count objective scope. Operands: visible scene state and prompt-bound operands named by cell_board, axis, vertical, horizontal, counted_side, left, top, symmetry_violation_count. Operation: evaluate count_mirror_mismatches 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 segment_set schema; one image-pixel segment from each counted-side violating cell center to its mirror-cell center. Query ids: single.

Reasoning Operations

Families: counting, transformation, matching

2) Scene + task contract

1. Entities/relations: A rectangular colored cell board with a sampled vertical or horizontal mirror check.
2. Supported query_id values: single
3. answer_gt.type: integer
4. Annotation schema: segment_set
5. Alternate annotation forms: none
6. Annotation witness policy: one image-pixel segment from each counted-side violating cell center to its mirror-cell center.
7. Overlap/touch policy: only the side named in the prompt determines answer cardinality; mirror cells appear only as segment endpoints.

3) Prompt contract

1. prompt_bundle_id: puzzles_cell_board_v1
2. scene_key: cell_board
3. task_key: cell_board_symmetry_query
4. Prompt query key: symmetry_violation_count; mirror axis and counted side are trace metadata and prompt slots, not public query ids.
5. Required slots: mirror_axis, counted_side, plus output-mode slots from the prompt bundle.
6. JSON example validity rule: segment-set cardinality equals the integer answer.
7. Output modes: answer_only, answer_and_annotation

4) Determinism + constraints

1. Seed namespaces used: task-local symmetry namespaces plus shared cell-board layout/style/font/noise namespaces.
2. Unique-answer policy: construction fixes and verifies the counted-side mismatch total on a 3x3 to 5x5 board.
3. Reject/resample conditions: insufficient mirror pairs or mismatch-count drift raises and retries.
4. No-auto-relaxation guarantee: semantic constraints are not relaxed.