Skip to content

task_geometry__paper_fold__folded_segment_length_value

Contract

  1. Domain: geometry
  2. Scene id: paper_fold
  3. Task id: task_geometry__paper_fold__folded_segment_length_value
  4. Query id: single
  5. Answer schema: integer
  6. Annotation schema: segment

Program Contract

  • solve_formula(visible_paper_fold_side_labels, unknown_role=folded_segment_length, formula_schema=pythagorean_leg_then_fold_correspondence, output=integer_length); scene=paper_fold; scope=folded_segment_length_value

Reasoning Operations

Families: transformation, formula_evaluation

Prompt Bundle

  • Prompt text is loaded from the scene prompt bundle configured for paper_fold.
  • Prompt modes: answer_only and answer_and_annotation.
  • The task prompt states that triangle AEF is folded along crease EF so A lands on P; this makes the side correspondence AE = PE and AF = PF visually grounded instead of implicit.

Annotation

Prompt-facing annotation is the requested folded segment only: [[x0,y0],[x1,y1]]. For example, if the prompt asks for FP, the segment endpoints are the visible points F and P.

Numeric labels, point labels, formulas, and construction metadata remain private verifier metadata unless they are themselves visual witnesses.

Sampling

The generator samples an integer target answer uniformly from a broad finite support built from integer right-triangle triples, then selects a compatible fold construction for that answer. One original leg and the crease length are visible; the target folded segment is equal to the missing original leg after folding.

Determinism

Generation is deterministic for a fixed seed, params, config, and prompt bundle version.

Source

  • Config: src/trace_tasks/resources/configs/domains/geometry/paper_fold.yaml
  • Task module: src/trace_tasks/tasks/geometry/paper_fold/folded_segment_length_value.py