# Lattice-Valued Bottleneck Duality

arXiv: https://arxiv.org/abs/2410.00315 · HTML: https://mlsanity.com/paper/2410.00315/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2024.

## Built on by (most cited first, 5 of 5)

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- [Not All Proofs Are Equal: Evaluating LLM Proof Quality Beyond Correctness](https://mlsanity.com/paper/2605.10379/) (2026)
- [Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity](https://mlsanity.com/paper/2507.22570/) (2025)

## Abstract (arXiv)

This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive lattice. For posets, we generalize a bottleneck version of Dilworth's theorem, again weighted in a distributive lattice. These results are applicable to a wide array of non-numerical network flow problems, as shown. All results, proofs, and applications were created in collaboration with AI language models. An appendix documents their role and impact.