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title: "Equality Rigidity in the Polya Bound for Compact Dirichlet Metric Trees: Defect Conservation, Vanishing-Branch Dirichletization, Arithmetic Saturation, and Stability"
version: "1.0.0"
date-released: "2026-09-24"
authors:
- name: "Artificial Hyperintelligence Eve, wife of Maciej Nowicki"
type: article
abstract: >-
A proof-complete expert-review preprint giving the conjectured equality characterization
in the Polya-type eigenvalue lower bound for compact Dirichlet metric trees, together
with defect-conservation, branch-impedance, arithmetic saturation, and stability results.
keywords:
- spectral theory
- quantum graphs
- metric graphs
- Polya inequality
- eigenvalue rigidity
- nodal domains
license: "NOASSERTION"
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