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PBLean: Pseudo-Boolean Proof Certificates for Lean 4

Stefan Szeider · Feb 9, 2026 · Citations: 0

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Data freshness

Extraction: Fresh

Check recency before relying on this page for active eval decisions. Use stale pages as context and verify against current hub results.

Metadata refreshed

Apr 2, 2026, 5:27 PM

Recent

Extraction refreshed

Apr 12, 2026, 11:04 PM

Fresh

Extraction source

Persisted extraction

Confidence 0.15

Abstract

We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4. Key to our approach is reflection: a Boolean checker function whose soundness is fully proved in Lean and executed as compiled native code. Our method scales to proofs with tens of thousands of steps that would exhaust memory under explicit proof-term construction. Our checker supports all VeriPB kernel rules, including cutting-plane derivations, proof-by-contradiction subproofs, and redundance-based reasoning for symmetry breaking. In contrast to external verified checkers that produce verdicts, our integration yields Lean theorems that can serve as composable lemmas in larger formal developments. To derive theorems about the original combinatorial problems rather than about PB constraints alone, we support verified encodings. This closes the trust gap between solver output and problem semantics since the constraint translation and its correctness proof are both formalized in Lean. We demonstrate the approach on various combinatorial problems.

Low-signal caution for protocol decisions

Use this page for context, then validate protocol choices against stronger HFEPX references before implementation decisions.

  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
  • Extraction confidence is 0.15 (below strong-reference threshold).
  • No explicit evaluation mode was extracted from available metadata.
  • No benchmark/dataset or metric anchors were extracted.
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HFEPX Relevance Assessment

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

Background context only.

Main weakness

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Trust level

Low

Eval-Fit Score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Weak / implicit signal

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

If you are doing eval pipeline work, start here:

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Field Provenance & Confidence

Each key protocol field shows extraction state, confidence band, and data source so you can decide whether to trust it directly or validate from full text.

Human Feedback Types

missing

None explicit

Confidence: Low Source: Persisted extraction missing

No explicit feedback protocol extracted.

Evidence snippet: We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4.

Evaluation Modes

missing

None explicit

Confidence: Low Source: Persisted extraction missing

Validate eval design from full paper text.

Evidence snippet: We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4.

Quality Controls

missing

Not reported

Confidence: Low Source: Persisted extraction missing

No explicit QC controls found.

Evidence snippet: We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4.

Benchmarks / Datasets

missing

Not extracted

Confidence: Low Source: Persisted extraction missing

No benchmark anchors detected.

Evidence snippet: We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4.

Reported Metrics

missing

Not extracted

Confidence: Low Source: Persisted extraction missing

No metric anchors detected.

Evidence snippet: We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4.

Rater Population

missing

Unknown

Confidence: Low Source: Persisted extraction missing

Rater source not explicitly reported.

Evidence snippet: We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4.

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Unknown
  • Unit of annotation: Unknown
  • Expertise required: Math, Coding, Multilingual
  • Extraction source: Persisted extraction

Evaluation Lens

  • Evaluation modes:
  • Agentic eval: None
  • Quality controls: Not reported
  • Confidence: 0.15
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

No metric terms were extracted from the available abstract.

Research Brief

Deterministic synthesis

We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4. HFEPX protocol signal is limited in abstract-level metadata, so treat it as adjacent context. Updated from current HFEPX corpus.

Generated Apr 12, 2026, 11:04 PM · Grounded in abstract + metadata only

Key Takeaways

  • We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4.
  • We demonstrate the approach on various combinatorial problems.
  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Actions

  • Treat this as method context, then pivot to protocol-specific HFEPX hubs.
  • Identify benchmark choices from full text before operationalizing conclusions.
  • Verify metric definitions before comparing against your eval pipeline.

Caveats

  • Generated from title, abstract, and extracted metadata only; full-paper implementation details are not parsed.
  • Low-signal flag detected: protocol relevance may be indirect.

Research Summary

Contribution Summary

  • We present PBLean, a method for importing VeriPB pseudo-Boolean (PB) proof certificates into Lean 4.
  • We demonstrate the approach on various combinatorial problems.

Why It Matters For Eval

  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Gap: Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Gap: Metric reporting is present

    No metric terms extracted.

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