Exact Action Depth in a Two-Probe Partition Planner: An n + 1 Diameter Law on Partition Lattices

We prove the exact worst-case action depth of a two-probe planner on the partition lattice: [ D_2(n)=n+1 \qquad (n\ge5). ] The result is achieved by matching structural upper and lower bounds, with explicit extremal families, mechanical certificates, and a source-level Lean 4 formalization.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-05
DOI
https://doi.org/10.5281/zenodo.22394897
Primary Topic
DNA and Biological Computing
Type
preprint
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preprint

Exact Action Depth in a Two-Probe Partition Planner: An n + 1 Diameter Law on Partition Lattices

benjamin lenoir
Zenodo (CERN European Organization for Nuclear Research)
DNA and Biological Computing
preprint

Exact Action Depth in a Two-Probe Partition Planner: An n + 1 Diameter Law on Partition Lattices

benjamin lenoir
preprint en

Abstract

We prove the exact worst-case action depth of a two-probe planner on the partition lattice: [ D_2(n)=n+1 \qquad (n\ge5). ] The result is achieved by matching structural upper and lower bounds, with explicit extremal families, mechanical certificates, and a source-level Lean 4 formalization.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
DNA and Biological Computing
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