Progressive Cumulative Counting and Its Associated Integer Sequence

This document presents Version 3 (V3) of the Progressive Cumulative Counting procedure and its associated integer sequence.

Version 3 provides a refined mathematical definition, improved structural clarity, and an extended construction representation.

The sequence is generated using a two-stage deterministic counting process with a structural transition triggered after decimal base completion (digits 0–9). After this transition, the sequence evolves cumulatively using the previous result and the current counting position.

The sequence can be extended indefinitely and produces arbitrarily large integers.

This version supersedes Version 2.

Note: The core idea and underlying mechanism presented in this work were developed independently by the author. The mathematical formalization was refined with the support of assistive tools.