task_puzzles__balance_scale__missing_object_weight_value

Program Contract

Program: solve_value(direct_and_compound_balance_equations, target=query_object_weight, unknowns=A|B|C, panels=3); scene=balance_scale; scope=missing_object_weight_value

Candidate set: the visible balance-scale panels, object symbols, object counts, side relations, and query markers inside the missing_object_weight_value objective scope. Operands: visible scene state and prompt-bound operands named by direct_and_compound_balance_equations, query_object_weight, unknowns, A, B, C, panels, balance_scale, missing_object_weight_value. Operation: evaluate solve_value 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 bbox schema; the scalar bbox marks the question-mark value box in the query row. Query ids: single.

Reasoning Operations

Families: formula_evaluation

2) Scene + task contract

1. Entities/relations: Three balanced pan-scale panels with three labeled unknown object tokens, numbered weights, at least one direct single-object value panel, at least one compound/context panel, and a query row showing one object equal to a question-mark value.
2. Supported query_id values: single
3. answer_gt.type: integer
4. Annotation schema: bbox
5. Alternate annotation forms: none
6. Annotation witness policy: the scalar bbox marks the question-mark value box in the query row.
7. Overlap/touch policy: annotation must be the rendered question-mark value box, not the surrounding query row, object token, panel, or scale bbox.

3) Prompt contract

1. prompt_bundle_id: puzzles_balance_scale_v1
2. scene_key: balance_scale
3. task_key: balance_scale_query
4. Optional query-id prompt mapping: missing_object_weight_value is stored as prompt_query_key; the public query_id is single.
5. Required slots:
6. answer output: answer_hint, json_example_answer_only
7. answer+annotation mode: annotation_hint, answer_hint, json_example
8. JSON example validity rule: the example must use one bbox and an integer answer valid for the task schema.
9. Variant counts: 5 scene templates, 5 query templates, and 5 output templates per output mode.
10. Output modes: answer_only, answer_and_annotation

4) Determinism + constraints

1. Seed namespaces used: task-local label/object/equation namespaces plus shared balance scene/style/font/unit-size namespaces.
2. Unique-answer policy: the three equations must imply exactly one target object value over the configured support.
3. Reject/resample conditions: any panel count other than three, missing direct target-value panel, unbalanced generated panels, target ambiguity, missing annotation bbox, or unsupported answer values raise and retry within max_attempts.
4. No-auto-relaxation guarantee: semantic constraints are not relaxed; generation retries rather than accepting ambiguous equations.

5) Tests

1. Determinism test: tests/test_puzzles_balance_scale_tasks.py::test_balance_scale_task_is_deterministic
2. Answer/annotation consistency test: tests/test_puzzles_balance_scale_tasks.py::test_balance_scale_task_emits_public_contract
3. Prompt metadata/placeholder test: covered by source-layout checks and prompt-system tests.
4. Constraint-specific tests: tests/test_puzzles_balance_scale_tasks.py::test_balance_scale_equations_are_balanced_and_unique