arXiv:2604.01732v1 Announce Type: new Abstract: Cutting rectangular items from stock sheets to satisfy demands while minimizing waste is a central manufacturing task. The Two-Dimensional Single Stock Size Cutting Stock Problem (2D-CSSP) generalizes bin packing by requiring multiple copies of each item type, which causes a strong combinatorial blow-up. We present a SAT-based framework where item types are expanded by demand, each copy has a sheet-assignment variable and non-overlap constraints are activated only for copies assigned to the same sheet. We also introduce an infeasible-orientation elimination rule that fixes rotation variables when only one orientation can fit the sheet. For minimizing the number of sheets, we compare three approaches: non-incremental SAT with binary search, incremental SAT with clause reuse across iterations and weighted partial MaxSAT. On the Cui--Zhao benchmark suite, our best SAT configurations certify two to three times more instances as provably optimal and achieve lower optimality gaps than OR-Tools, CPLEX and Gurobi. The relative ranking among SAT approaches depends on rotation: incremental SAT is strongest without rotation, while non-incremental SAT is more effective when rotation increases formula size.

arXiv:2604.01483v1 Announce Type: cross Abstract: The rapid evolution of autonomous, agentic artificial intelligence within financial services has introduced an existential architectural crisis: large language models (LLMs) are probabilistic, non-deterministic systems operating in domains that demand absolute, mathematically verifiable compliance guarantees. Existing guardrail solutions -- including NVIDIA NeMo Guardrails and Guardrails AI -- rely on probabilistic classifiers and syntactic validators that are fundamentally inadequate for enforcing complex multi-variable regulatory constraints mandated by the SEC, FINRA, and OCC. This paper presents the Lean-Agent Protocol, a formal-verification-based AI guardrail platform that leverages the Aristotle neural-symbolic model developed by Harmonic AI to auto-formalize institutional policies into Lean 4 code. Every proposed agentic action is treated as a mathematical conjecture: execution is permitted if and only if the Lean 4 kernel proves that the action satisfies pre-compiled regulatory axioms. This architecture provides cryptographic-level compliance certainty at microsecond latency, directly satisfying SEC Rule 15c3-5, OCC Bulletin 2011-12, FINRA Rule 3110, and CFPB explainability mandates. A three-phase implementation roadmap from shadow verification through enterprise-scale deployment is provided.

arXiv:2602.08692v2 Announce Type: replace-cross 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.