The SALEN Axiom: Structural Archimedean Non–Coverage for Anchored Periodic Obstruction Systems
Abstract
We record the SALEN Axiom (Strong Archimedean Local Eventual Non–Coverage) as a foundational structural principle governing canonically anchored periodic obstruction systems on a discrete ordered axis. The axiom asserts that, under uniform bounded multiplicity, families of rigid periodic obstructions cannot cover arbitrarily long contiguous intervals beyond an explicit archimedean scale. The formulation is entirely abstract and independent of arithmetic, combinatorial, or dynamical interpretations. No proof is given here. The purpose of this note is to isolate SALEN as a reusable black--box principle, suitable for invocation in subsequent works once its hypotheses have been verified in a given framework.
Fields of Study & Subjects
Advanced Topology and Set Theory
Analytic Number Theory Research
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 13 January 2026
- Language
- EN
- Document type
- Preprint