Order-Sensitive Sequential Interventions on Ideal Lattices
We study sequential interventions under prerequisite constraints. In this setting, admissible intervention sequences are paths in the ideal lattice of a finite prerequisite poset rather than unconstrained action strings. We give an exact local-to-global theory of order sensitivity on this state space. First, we prove that any two admissible paths with the same endpoints differ by a finite sequence of elementary diamond swaps. Second, for edge-additive path valuations, we show that path-independence is equivalent to vanishing diamond curvature, yielding an endpoint potential with a canonical Möbius parameterization on the ideal lattice. Third, we prove that a local diamond field is induced...
| Authors | Dmitry Pasechnyuk-Vilensky |
|---|---|
| Primary category | math.CO |
| Published | 29 April 2026 |
| Last updated at source | 29 April 2026 |
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