task_symbolic__chemical_equation__balanced_option_label

1) Identity

1. Domain: symbolic
2. Scene id: chemical_equation
3. Task id: task_symbolic__chemical_equation__balanced_option_label
4. Objective: select the coefficient option that balances the displayed chemical equation.

Program Contract

Program: chemical_equation.balanced_option_label(scene=chemical_equation, scope=blank_coefficient_slots_plus_option_cards, output=option_letter)

Candidate set: the four visible coefficient option cards labeled A..D. Operands: the visible atom chips grouped into molecule cards, side/operator layout, and option coefficient tuples. Operation: fill coefficient slots from left to right using each option and compare atom totals on both sides. Output binding: answer is the selected option label. Annotation witnesses: a scalar bbox around the selected option card. Query ids: single.

Reasoning Operations

Families: formula_evaluation

2) Scene + Task Contract

1. All coefficient slots in the equation are hidden as ? boxes.
2. Molecule cards show repeated atom chips only; formula strings are not drawn.
3. Each option card contains a left-to-right coefficient tuple for the equation terms.
4. Exactly one option balances all atom counts.
5. answer_gt.type: string
6. annotation_gt.type: bbox
7. Annotation schema: bbox
8. Candidate labels are A, B, C, and D.

3) Prompt Contract

1. Bundle: symbolic_chemical_equation_v1
2. scene_key: chemical_equation
3. task_key: balanced_option_label
4. Modes: answer_only, answer_and_annotation
5. Prompt text comes from the external prompt bundle.

4) Trace Contract

1. execution_trace.chemical_equation_metadata.reaction records formulas, balanced coefficients, and atom totals.
2. execution_trace.chemical_equation_metadata.options records each candidate tuple and whether it balances the equation.
3. render_map.option_bboxes_px contains option-card projections.
4. projected_annotation mirrors the selected option bbox.

5) Determinism + Tests

1. Deterministic generation and rendering from instance_seed.
2. Distractors are unique and rejected if they accidentally balance the equation.
3. Behavior tests: tests/test_symbolic_chemical_equation_tasks.py