task_symbolic__chemical_equation__missing_coefficient_value

1) Identity

1. Domain: symbolic
2. Scene id: chemical_equation
3. Task id: task_symbolic__chemical_equation__missing_coefficient_value
4. Objective: solve the one missing coefficient in a displayed chemical equation.

Program Contract

Program: chemical_equation.missing_coefficient_value(scene=chemical_equation, scope=one_blank_coefficient_plus_molecule_cards, output=integer)

Candidate set: the visible symbolic notation, tokens, rows, columns, cards, labels, components, and target markers inside the one_blank_coefficient_plus_molecule_cards objective scope.

Operands: the visible atom chips grouped into molecule cards, side/operator layout, and visible coefficients. Operation: count atoms per molecule card and apply coefficients so both sides match. Output binding: answer is the missing integer coefficient. Annotation witnesses: a bbox_set around the missing coefficient slot and each molecule card. Query ids: single.

Reasoning Operations

Families: formula_evaluation

2) Scene + Task Contract

1. Every coefficient, including 1, is explicitly drawn unless it is the one hidden ? slot.
2. Molecule cards show repeated atom chips only; formula strings are not drawn.
3. A coefficient multiplies the full adjacent molecule-card term.
4. Supported generated coefficients are integers from 1 through 5.
5. answer_gt.type: integer
6. annotation_gt.type: bbox_set
7. Annotation schema: bbox_set with multiple boxes: the blank coefficient slot box plus one molecule-card box for every term.
8. The scene contains a single hidden coefficient slot.

3) Prompt Contract

1. Bundle: symbolic_chemical_equation_v1
2. scene_key: chemical_equation
3. task_key: missing_coefficient_value
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.terms records term formulas, coefficients, hidden status, and atom counts.
3. render_map.item_bboxes_px contains coefficient-slot and molecule-card projections.
4. projected_annotation mirrors the public bbox_set annotation.

5) Determinism + Tests

1. Deterministic generation and rendering from instance_seed.
2. The hidden coefficient is sampled answer-first from the configured support unless pinned by params.
3. Behavior tests: tests/test_symbolic_chemical_equation_tasks.py