Cost–Support Frontiers of Internally Stable Continuations on Trees and Cacti: Realizability, Obstructions, and Representation Size
Year: 2026
Type: preprint
Abstract: This research preprint investigates the realizability and representation size of cost–support frontiers arising from internally stable continuations in binary polymatrix games on rooted trees and cacti. The results establish a rooted-tree correspondence with zero–one knapsack value functions, an explicit frontier that no binary polymatrix cactus can realize, and a family requiring a quadratic number of interior players. The analysis also identifies structural constraints imposed by cactus interfaces and demonstrates information loss under scalar tropical evaluation. The results concern fixed-reference, at-most-budget continuations with the root’s Nash inequality deferred. They do not establish dynamic-update complexity bounds or a complete characterization of cactus frontiers. A separate reproducibility archive provides the LaTeX manuscript source, executable verification programs, expected outputs, and reproducibility instructions. Version 1.0 — Research preprint. External peer review and exhaustive historical-priority assessment have not been completed.
Author: Kelly Rhys
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225599468