Paper VI — Gap–Prime Structure

The Δ–Distinction Framework Series (Working Papers) This paper is part of the Δ–Distinction Framework Series, a set of interconnected working papers developing a formal framework in which distinction (Δ) is treated as a primitive structural operator underlying mathematical representation, number formation, and relational structure. Across the series, the central proposal is that classical mathematical symbols and numerical identities can be understood as compressed representations of underlying recursive distinctions rather than primitive units. The framework is developed progressively through ontological foundations, axiomatic formalization (Δ-Number Theory), gap analysis, resolution-gap modelling, and unified emergence considerations. These papers are released as timestamped working documents to preserve conceptual continuity, research transparency, and version traceability. They are not presented as final or definitive claims, but as a coherent exploratory research program situated at the intersection of foundations of mathematics, theoretical modelling, and complex systems. Later papers in the series extend and formalize concepts introduced in earlier parts; therefore, the documents are intended to be read as a unified sequence rather than isolated standalone works. All results and formulations should be interpreted within the context of ongoing theoretical development. Author: Eric NeedhamFramework context: ENSO / Δ-Distinction FormalismVersion: Working Paper Series (v1, Timestamped) Licenses Creative Commons Attribution Non Commercial No Derivatives 4.0 International