What question did this study set out to answer?

This work aims to establish an analytic core-decomposition theory connecting discrete recurrence with number theory.

May 25, 2026Open Access

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

Key Points

This work aims to establish an analytic core-decomposition theory connecting discrete recurrence with number theory.
Developed the theory based on the discrete recurrence formula (An−2)An+1=n.
Utilized continuum limits and continued fractions to derive intrinsic constants.
Introduced a conjectural square-recurrence inequality related to sieve methods and number theory conjectures.
Derived constants: Kang constant κ, DeepSeek constant D=1/(e−2), golden constant G=5−1, and parity constant P=34P=43.
Proposed a conjectural square-recurrence inequality that could validate discussions of Goldbach, Legendre, 3n+1, and Fermat conjectures.
Bridged discrete dynamics, sieve methods, and automorphic LL-functions through a unified recurrence postulate.

Abstract

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

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

Key Points

Abstract

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