Multi-Construction Entropy-Proof Benchmark (MCE-220)

MCE-220 is a frozen benchmark of 220 synthetic Shannon-type entropy-inequality proof problems. It spans 10 through 20 random variables with 20 questions at every value of n.

The benchmark is balanced across five construction families. At every n, it contains four questions from each family:

• weighted modular / hypergraphical constructions;
• finite-field linearly representable constructions over GF(61);
• directed-acyclic-graph constructions;
• deterministic finite-field functional constructions; and
• finite abelian 2-group quotient constructions.

It is also divided evenly into 110 condition-required questions and 110 Shannon-only questions. The benchmark is intended for evaluating automated entropy-inequality provers, proof-search systems, and exact symbolic verification pipelines.

Dataset structure

The Hub dataset exposes one test split from data/questions.jsonl. Each of its 220 records has:

• id: stable benchmark identifier;
• n: number of random variables;
• ineq: target entropy expression, interpreted as ineq >= 0;
• conditions: supplied equality conditions, represented as paired one-sided inequalities; and
• sha256: digest of the canonical semantic question representation.

The files under audit/ are reproducibility evidence and are intentionally excluded from the dataset split:

• provenance.jsonl: construction witness, planted certificate, tokenization, seeds, and structural metadata for every question;
• generation-report.jsonl: per-cell generation and rejection accounting;
• run-manifest.json: frozen configuration, dependency hashes, tokenizer identity, output hashes, and completion summary;
• validation-report.json: exact certificate and artifact-integrity audit; and
• diversity-audit.json: balance, uniqueness, and structural-diversity audit.

The generation configuration is preserved as generation/e2n_v2.toml.

Generation and tokenization

MCE-220 was generated from a preregistered grid of 11 values of n, five construction families, and four proof recipes. Each selected problem retains a planted exact certificate and a construction witness. Token counts use the fast tokenizer for Qwen/Qwen3-0.6B at commit c1899de289a04d12100db370d81485cdf75e47ca, without special tokens.

The five construction families provide complementary entropic witnesses: modular component coverage, finite-field matrix ranks, rational Bayesian networks, deterministic polynomial transformations, and quotient profiles of finite abelian groups.

Validation and integrity

The frozen package contains 220 unique question records and 220 matching provenance records. All selected certificates pass exact sparse rational verification. The validation report records zero errors, and the diversity audit passes all declared balance and uniqueness checks.

Primary artifact SHA-256 values:

• questions.jsonl: 1ff45298389fa9a0cc6000b833302d610c489334c88d40a07b28b45ea76c762a
• provenance.jsonl: cbd708a699899127a254d7367df6f129fcc6eec73b50f05db86f01b5a732e189
• generation-report.jsonl: 50304ef59e263296d675bf63f79ceb04857deaba339bf7b491dca5d0752ca12c

Intended use and limitations

MCE-220 is an evaluation benchmark, not a training corpus or a representative sample of every entropy inequality. Its questions are synthetic and constructed to have planted Shannon-type certificates. The controlled sparse construction does not establish performance on arbitrary dense inequalities or non-Shannon inequalities. Planted certificate length is not necessarily the minimum proof length, because a question may admit other valid proofs.

The benchmark supplies equality conditions because the evaluated AITIP workflow supports equality premises. Results should retain question-level accounting, exact proof verification, and resource or timeout settings.

Citation

The associated manuscript is forthcoming/unpublished:

@unpublished{wong2026automated,
  title  = {Automated Proving of Shannon-Type Entropy Inequalities via Fine-Tuned Language Models and Guided Tree Search},
  author = {Wong, Shing Yin and Liu, Shaocheng and Song, Linqi and Gohari, Amin and Li, Cheuk Ting},
  year   = {2026},
  note   = {Manuscript in preparation}
}

No reuse license has been assigned to this private release.