{
  "schema": "compositional_certificate_study_v1",
  "seed": 20260914,
  "cases_per_family": 128,
  "families": [
    "sum",
    "difference_of_sums",
    "mean",
    "range",
    "threshold",
    "equality",
    "clipped_sum",
    "product_of_differences"
  ],
  "domain": [
    0,
    9
  ],
  "cells": 4,
  "hidden_cells": [
    1,
    2
  ],
  "sampling": "independent_uniform_world_and_mask",
  "question": "deterministic_program_verbalization",
  "independence": "fresh worlds; no PlotQA groups, model outputs or hand adjudication",
  "oracle": "all finite completions; separate postfix executor",
  "baselines": [
    "schema_source_replay_render",
    "dependency_cut",
    "interval_propagation",
    "all_low_vs_all_high_witness"
  ],
  "scope": "descriptive synthetic finite-domain validation; not real-world prevalence"
}