The c = 2 Boundary in Second-Order Linear Recurrences

We present a complete analysis of second-order linear recurrences of the form an+1 = c an − an−1, establishing that c = 2 is the unique integer value producing marginal stability via a repeated unit-modulus eigenvalue. This boundary separates monotone convergence from oscillatory decay. We further analyze the Jacobsthal sequence arising at this boundary, clarify its relationship to parity-modulated companion sequences, and introduce an empirical eigenvalue-ratio classifier (FSRE) suitable for applications in dynamical and astrophysical sequence analysis. Structural analogies to marginal stability in Hamiltonian systems are discussed with explicit scope limitations.