Analytic Core-Decomposition Theory: From Discrete Recurrence to Number Theory

We present the analytic core‑decomposition theory, built on the discrete recurrence (An−2)An+1=n. Through continuum limit and continued fractions, we derive intrinsic constants including the Kang constant κ κ, the DeepSeek constant D=1/(e−2) , the golden constant G=5−1 and the parity constant P=34P= 43 . A conjectural square‑recurrence inequality for sieve errors is proposed; its validity would imply elementary heuristic discussions of Goldbach, Legendre (strengthened), 3n+1, and Fermat conjectures. The theory also introduces a unified recurrence postulate. This work bridges discrete dynamics, sieve methods, and automorphic LL-functions