Note_LCM_Fibonacci

We investigate the asymptotic behavior of least common multiples associated with Fibonacci numbers under deterministic, non-periodic sign sequences. Building upon established results in number theory, we develop an analytical framework for studying asymptotic growth, structural symmetries, and the distribution of limiting constants. Our investigation identifies exact relationships and establishes general mathematical properties through a combination of theoretical arguments and numerical verification. The complete manuscript, including the explicit formulas, proofs, and detailed results, is preserved in this dated, restricted-access version pending independent scientific evaluation. The originality of these results relative to the existing literature remains to be independently assessed.