The Genesis of Idempotent-Dense Analysis: A Historical Account

This manuscript presents the complete historical genesis of Idempotent-Dense Analysis (IDA), tracing its origins from the discovery of the Infinite Tower and the Three-Space Theory, through the probing of large cardinal theory and the formulation of the dual expansion formula between measurable cardinals and zero, to the construction of Idempotent Analysis 1.0 and its later extension into Dense Analysis.