Logarithmic and Modular Compensation in Goldbach Structures

This paper develops a modular and logarithmic framework for prime pair construction in even-number decompositions. Building on Chen’s theorem, we propose the Same-Level Sieve to eliminate composite interference, and introduce a logarithmic compensation model using a fixed constant R = π. The approach identifies stable prime pairs via quadratic root approximation and log-balance criteria, confirming the structural viability of Goldbach-type representations and enabling extensions to multiplicative formulations.