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task_graph__binary_tree__lowest_common_ancestor_label

Program Contract

Program: label(lowest_common_ancestor(binary_tree, node_a, node_b)); scene=binary_tree; scope=lowest_common_ancestor_label

Candidate set: the visible graph, tree, network, route, matrix, table, node, edge, label, weight, path, and option elements inside the lowest_common_ancestor_label objective scope. Operands: visible scene state and prompt-bound operands named by lowest_common_ancestor, binary_tree, node_a, node_b, lowest_common_ancestor_label. Operation: evaluate label 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 string schema; generation binds a unique final answer. Annotation witnesses: annotation uses the point_map schema; the prompt/annotation contract defines the minimal visual witnesses. Query ids: single.

Reasoning Operations

Families: ranking, topology

Summary

  1. Domain: graph
  2. Scene id: binary_tree
  3. Scene: relation
  4. Task id: task_graph__binary_tree__lowest_common_ancestor_label
  5. Objective: return the lowest common ancestor label for two binary-tree nodes.

Query IDs

  1. single
  2. Query ids are internal replay metadata; public sampling is at the task-id level.
  3. The hidden generation axis relation_answer_scope targets non-root LCAs 75% of the time and root LCAs 25% of the time; it is recorded in trace metadata and is not a public query branch.

Answer And Annotation

  1. Answer type: string.
  2. Annotation schema: point_map.
  3. Annotation marks role-bound node-center pixel points for node_a, node_b, and lowest_common_ancestor.
  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.