task_geometry__tangent_packing__circle_in_square_gap_area

Contract

1. Domain: geometry
2. Scene id: tangent_packing
3. Task id: task_geometry__tangent_packing__circle_in_square_gap_area
4. Supported query_id: single
5. Answer schema: number
6. Answer precision: one_decimal
7. Annotation schema: bbox

Program Contract

• curvilinear_gap_area(container=square, packed_shape=circle, given=square_side, target=shaded_area); scene=tangent_packing; scope=circle_in_square_gap_area

Reasoning Operations

Families: formula_evaluation

Prompt Bundle

• Prompt text is loaded from the v1 scene prompt bundle configured for tangent_packing.
• Prompt modes: answer_only and answer_and_annotation.

Annotation

Prompt-facing annotation is one scalar pixel bbox around the marked target geometric region or shape, excluding numeric labels and measurement text.

The answer placeholder label is not a separate annotation witness. Formula metadata remains 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/tangent_packing.yaml
• Task module: src/trace_tasks/tasks/geometry/tangent_packing/circle_in_square_gap_area.py