# A property-registry contract for retrieve-or-refuse thermal-mechanical lattice search

arXiv: https://arxiv.org/abs/2609.14741 · HTML: https://mlsanity.com/paper/2609.14741/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 72 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Builds on (most cited first, 12 of 12)

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- [A numerical method for computing the overall response of nonlinear composites with complex microstructure](https://mlsanity.com/paper/2012.08962/) (2020)
- [OptiChat: Bridging Optimization Models and Practitioners with Large Language Models](https://mlsanity.com/paper/2501.08406/) (2025)
- [A Large Language Model and Denoising Diffusion Framework for Targeted Design of Microstructures with Commands in Natural Language](https://mlsanity.com/paper/2409.14473/) (2024)
- [Algebraic Language Models for Inverse Design of Metamaterials via Diffusion Transformers](https://mlsanity.com/paper/2507.15753/) (2025)
- [MetaGen: A DSL, Database, and Benchmark for VLM-Assisted Metamaterial Generation](https://mlsanity.com/paper/2508.17568/) (2025)
- [Toward a Robust and Generalizable Metamaterial Foundation Model](https://mlsanity.com/paper/2507.02436/) (2025)
- [Multi-Objective Infeasibility Diagnosis for Routing Problems Using Large Language Models](https://mlsanity.com/paper/2508.03406/) (2025)
- [Why Not? Solver-Grounded Certificates for Explainable Mission Planning](https://mlsanity.com/paper/2603.00469/) (2026)
- [AutoMS: Multi-Agent Evolutionary Search for Cross-Physics Inverse Microstructure Design](https://mlsanity.com/paper/2603.27195/) (2026)
- [METASYMBO: Multi-Agent Language-Guided Metamaterial Discovery via Symbolic Latent Evolution](https://mlsanity.com/paper/2604.27300/) (2026)

## Abstract (arXiv)

Early thermal-mechanical lattice requirements are knowledge-intensive and often jointly unsatisfiable: an engineer asks for a cell that is light, stiff, laterally conducting and cheap, and no cell in the library satisfies it. A design system should say so, and say which requirement to loosen and by how much, rather than return the nearest row. A generative model can return a candidate even when the library holds none. This work applies established conflict diagnosis to a catalogue of homogenised properties. Search over 1,397 homogenised unit cells and 19 base materials (26,543 combinations) returns a catalogue row that a second solver can rebuild, or, for an empty feasible set of at most eight constraints, inclusion-minimal unsatisfiable subsets (MUS) and the slack of a repair, not a neighbour. One registry declaration generates the prompt and the evaluator, so undeclared parsed keys cannot reach search. On a frozen suite of 64 typed queries, retrieve-or-refuse matches min-repair on every feasible query (48/48) and refuses every empty one (16/16) with MUS and slack. Constraint-ignoring nearest-neighbour and penalty search violate stated cost or density limits. On 216 empty queries, repairs printed at three significant figures and rounded outward stay feasible in every case (216/216). When density and cost must be kept, a list of minimum-cardinality repairs keeps them on 209 of 211 queries; a protection-first repair keeps them on all 211, the same as full diagnosis. A 308-request parse benchmark is a template-text check, not unconstrained engineer prose.