An Exact Transcendental Identity Connecting e and π via the Qi Constant (Ver.2)

This research presents a fundamental shift in understanding universal constants by demonstrating that Euler's constant (2.71828...) does not exist as an independent entity, but rather emerges from the interaction between Pi and another transcendental constant (Qi). While traditional studies view as the limit of continuous growth [1], we prove within the framework of Energy Continuum Theory (ECT) that is essentially an emergent property—a "mathematical ghost" generated from the compression interaction between the smooth material universe () and a matter core oscillating at a specific angular frequency . By decoding with the participation of the transformation constant and differential Spin layers, we establish a deterministic simulation model achieving ~44 decimal digits of precision with the base 6-layer Spin model, and propose an expansion roadmap for higher precision. The study also introduces the ECT axiomatic system, in which space is defined as a dimensionless geometric property of energy.