Idempotent-Dense Analysis: A Unified Framework

Idempotent-Dense Analysis (IDA) is a unified mathematical framework that integrates idempotent algebra with dense encapsulation operator theory into a single axiomatic system. This white paper presents the complete axiomatic system of IDA, establishes its core theorems, and proves its essential connection to large cardinals in set theory.
Core Distinction: This white paper clearly distinguishes between "load-bearing walls" (the axiom system, convergence theorems, large cardinal equivalences) and "scaffolding" (specific generating function families). The foundation of the theory is the existence and completeness of idempotent structures, not any specific function form.
Core Formula: Any generating function family satisfying the convergence conditions generates an IDA model. The specific function y(z) = 1 + φ^(1-2^z) is the first successful instance of IDA, not the theory itself.