marcusala233-ai/modular-fibonacci-density: v1.0.0 Pre-print: Goldbach Partitions in Fibonacci Numbers

Initial Pre-print Release (v1.0.0) This release establishes the formal mathematical framework and public timestamp for the research article: "On the Modular Constrictions, Analytic Sieves, and Asymptotic Density of Goldbach Partitions in Fibonacci Numbers." Key Mathematical Contributions in this Release: Finite Field Projection: Establishes the Binet Formula isomorphism within $\mathbb{F}{11}$, proving the cyclic parity constant for even Fibonacci numbers ($F{3k}$). Topological Constrictions: Applies Dirichlet's Theorem on Arithmetic Progressions and Chen's Sieve to prove that prime constituent pairs ($p_1 + p_2 = F_{3k}$) are strictly confined to deterministic modular orbits, losing statistical independence. Asymptotic Density: Derives the precise density equation by fusing Binet's asymptotic limit with the extended Hardy-Littlewood conjecture, demonstrating exponential abundance modulated by primitive divisors. Included Assets: Compiled PDF: The complete, peer-review-ready research paper containing all formal proofs and lemmas. LaTeX Source: Full raw code for academic auditing. License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). Author: Marcus Ala Pedreira Roriz (IME - UFG).