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task_graph__binary_tree__child_structure_node_count

Program Contract

Program: count(filter(nodes(binary_tree), child_structure=target_structure)); scene=binary_tree; scope=child_structure_node_count

Candidate set: the visible graph, tree, network, route, matrix, table, node, edge, label, weight, path, and option elements inside the child_structure_node_count objective scope. Operands: visible scene state and prompt-bound operands named by filter, nodes, binary_tree, child_structure, target_structure, child_structure_node_count. Operation: evaluate count over the candidate set using the visible graph structure, labels, weights, directions, reachability, paths, connectivity, or option-selection constraints 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 point_set schema; the prompt/annotation contract defines the minimal visual witnesses. Query ids: single.

Reasoning Operations

Families: filtering, counting, topology

Summary

  1. Domain: graph
  2. Scene id: binary_tree
  3. Scene: counting
  4. Task id: task_graph__binary_tree__child_structure_node_count
  5. Objective: count binary-tree nodes by child structure.

Query IDs

  1. leaf_node_count|internal_node_count|single_child_node_count|two_child_node_count
  2. Query ids are internal replay metadata; public sampling is at the task-id level.

Answer And Annotation

  1. Answer type: integer.
  2. Annotation schema: point_set.
  3. Annotation marks node-center pixel points for every matching binary-tree node.
  4. Count tasks require answer_gt.value == len(annotation_gt.value) unless the annotation schema is keyed or sequence based.

Rendering Contract

  1. The scene uses the graph-domain renderer for binary_tree.
  2. Visual style, fonts, panel treatment, layout jitter, and post-render noise are non-semantic and must be recorded in trace metadata.
  3. Annotation projection is computed after final layout and style placement.

Prompt Contract

  1. Prompt text comes from graph prompt assets, not hardcoded user-facing text.
  2. Answer mode emits {"answer": ...}.
  3. Answer-and-annotation mode emits {"annotation": ..., "answer": ...} with annotation matching the schema above.