{
  "schema": "finite_solver_comparison_v2",
  "seed": 20260915,
  "original_cases": 1024,
  "holdout_cases": 432,
  "holdout_generator": "recursive random syntax tree; original family generator is not called",
  "maximum_depths": [
    2,
    4,
    6
  ],
  "maximum_nodes": 31,
  "domains": [
    [
      0,
      9
    ],
    [
      -3,
      6
    ],
    [
      0,
      4
    ]
  ],
  "hidden_counts": [
    1,
    2,
    3
  ],
  "cases_per_depth_domain_hidden_cell": 16,
  "leaf_stop_probability": 0.25,
  "leaf_cell_probability": 0.75,
  "leaf_cell_sampling": "uniform over indices 0,1,2,3",
  "leaf_constants_inclusive": [
    -3,
    12
  ],
  "leaf_constants_sampling": "uniform integers",
  "division_denominators_uniform": [
    -3,
    -2,
    -1,
    1,
    2,
    3
  ],
  "source_values_sampling": "four independent uniform integers in the declared domain",
  "hidden_sampling": "uniform subset without replacement, stored in sorted order",
  "child_node_budget": "floor((parent_budget-1)/2) for each child; depth cap 6 realizes at most depth 4",
  "operators_uniform": [
    "add",
    "sub",
    "mul",
    "div",
    "min",
    "max",
    "gt",
    "eq"
  ],
  "smt_timeout_ms": 1000,
  "smt_random_seed": 0,
  "unknown_policy": "retain as unresolved, never relabel constant",
  "oracle": "complete enumeration with separate postfix executor",
  "scope": "author-generated finite stress test; no natural-image or prevalence claim",
  "original_protocol": {
    "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"
  }
}