task_geometry__regular_polygon_decomposition__central_angle_value

Contract

1. Domain: geometry
2. Scene id: regular_polygon_decomposition
3. Task id: task_geometry__regular_polygon_decomposition__central_angle_value
4. Supported query_id values: single
5. Answer schema: integer
6. Annotation schema: point_map
7. Scalar annotation checked: true (not scalar-eligible; the task binds center and two angle-ray endpoint roles)

Program Contract

• solve_formula(regular_polygon_equal_wedge_decomposition, target=marked_central_angle, formula_schema=marked_wedge_count_times_360_degrees_divided_by_side_count); scene=regular_polygon_decomposition; scope=central_angle_value

Reasoning Operations

Families: counting, formula_evaluation

Query Semantics

• single asks for the measure of marked central angle AOB by counting the equal center wedges in the polygon and the one or two marked wedges between OA and OB.
• The number of polygon sides, selected wedge start, marked wedge count, style, font, layout jitter, and rotation are internal replay metadata; central-angle samples use one or two marked wedges.

Prompt Bundle

• Prompt text is loaded from src/trace_tasks/resources/prompts/geometry/regular_polygon_decomposition/geometry_regular_polygon_decomposition_v1.json.
• Prompt modes: answer_only and answer_and_annotation.

Annotation

Prompt-facing annotation uses pixel-space point map keys O, A, and B, marking the polygon center and the two visible rays that bound the requested center angle. Angle arcs and ? markers remain visible diagram content and private verifier metadata.

Determinism

Generation is deterministic for a fixed seed, params, config, and prompt bundle version.

Source

• Config: src/trace_tasks/resources/configs/domains/geometry/regular_polygon_decomposition.yaml
• Prompt bundle: src/trace_tasks/resources/prompts/geometry/regular_polygon_decomposition/geometry_regular_polygon_decomposition_v1.json
• Task module: src/trace_tasks/tasks/geometry/regular_polygon_decomposition/central_angle_value.py