task_physics__switch_circuit__lit_bulb_count

Summary

• Domain: physics
• Scene id: switch_circuit
• Implementation source: src/trace_tasks/tasks/physics/switch_circuit/lit_bulb_count.py

Task Contract

Counts how many labeled bulbs will be on in a mixed branch battery circuit with visibly open and closed switches.

Program Contract

Program: count(filter(bulbs, lies_on_complete_path(bulb_edge, battery_positive, battery_negative, closed_switches))); scene=switch_circuit; scope=lit_bulb_count

Candidate set: the visible switch states, bulb symbols, wire topology, and bulb labels inside the lit_bulb_count objective scope. Operands: bulbs (visual_candidate_set, allowed five_labeled_bulbs_b1_through_b5, source program_schema_concrete); closed_switches (semantic_role, allowed visible_open_closed_switches_s1_through_s5, source program_schema_concrete); mixed_branch_topology (semantic_role, allowed parallel_branches_with_local_sub_branch, source program_schema_concrete); battery_positive_negative (semantic_role, allowed visible_ideal_battery_terminals, source program_schema_concrete). Operation: evaluate count over the candidate set using the visible quantities, relations, branch semantics, and formulas encoded in the program expression; generation enforces a unique final answer. Output binding: answer uses the integer schema; The answer value is the count of bulbs whose bulb edge lies on at least one complete path from battery positive to battery negative through closed switches. Supported answers are 0..5. Annotation witnesses: bbox_set witnesses from the finalized render. Annotation is the unordered set of bboxes around bulb symbols that will be on. If the answer is 0, annotation is an empty array. Query ids: single.

Reasoning Operations

Families: filtering, counting, topology

Query Branches

Query id	Program schema
single	count(filter(bulbs, lies_on_complete_path(bulb_edge, battery_positive, battery_negative, closed_switches))); scene=switch_circuit; scope=lit_bulb_count; query_branch=lit_bulb_count

Program Metadata

• Program signatures: physics.switch_circuit_lit_bulb_count
• Base program contract: count(filter(bulbs, lies_on_complete_path(bulb_edge, battery_positive, battery_negative, closed_switches))); scene=switch_circuit; scope=lit_bulb_count
• Parameter axes: target_answer, switch_states, accent_color_name
• Arguments:
• bulbs: visual_candidate_set; allowed five_labeled_bulbs_b1_through_b5; source program_schema_concrete
• closed_switches: semantic_role; allowed visible_open_closed_switches_s1_through_s5; source program_schema_concrete
• mixed_branch_topology: semantic_role; allowed parallel_branches_with_local_sub_branch; source program_schema_concrete
• battery_positive_negative: semantic_role; allowed visible_ideal_battery_terminals; source program_schema_concrete
• Argument metadata status: curated
• Supported query ids: single

Answer Contract

• Answer schema: integer
• Generator answer_gt.type: integer
• The answer value is the count of bulbs whose bulb edge lies on at least one complete path from battery positive to battery negative through closed switches. Supported answers are 0..5.

Annotation Contract

• Annotation schema: bbox_set
• Generator annotation_gt.type: bbox_set
• Annotation is the unordered set of bboxes around bulb symbols that will be on.
• If the answer is 0, annotation is an empty array.
• Annotation must not mark switch bboxes, wires, battery chrome, labels alone, decorative grid lines, or derived current paths.
• Annotation and answer must be projected from the same generated execution trace, not inferred from pixels or prompt text.

Prompt And Trace Requirements

• Prompt text must come from the physics_switch_circuit_v1 prompt bundle, with scene and task/query layers selected deterministically and recorded in metadata.
• Render randomness, sampled fonts/styles, switch states, graph edges, lit bulb ids, and verifier payloads must be explicit in the instance trace.
• Bulbs must not visually glow or otherwise encode the answer; the count comes from switch connectivity.