Maximal Subharmonic Order among Inert Primes in the Fibonacci Division Fields

Among primes p == +/-2 (mod 5), the inert class of the golden unit, we studythe subharmonic order e(p) = 2(p+1)/pi(p). Within the division fieldsL_n = Q(sqrt(5), zeta_n, epsilon^(1/n)) we prove, by a Chebotarev argumentapplied at the central involution, that the maximal primes (e(p) = 1) havedensity C_e1 = (40/19) A in the inert class, A Artin's constant. This isunconditional at every fixed level; the completed product is establishedunder the Generalized Riemann Hypothesis (GRH), with the unconditionalconsequence limsup <= C_e1. The polarization law is unconditional:maximal inert primes split as (d,w) = (2, 4) for p == 1 (mod 4) and(1, 2) for p == 3 (mod 4). The inert mean of 1/e is the exact productprododd ell =/= 5 (ell^3 - ell - 1)/(ell^3 - 1) = 0.8402239546...;unconditionally it is an upper bound for the limsup of the finite means,with equality at GRH level. A reduction theorem isolates the liminfequality as the precise open problem, completing on the inert side thesplit-side program of Goettsch (1982) and Antoniadis (1984). MSC 2020: 11B39 (primary); 11R45, 11B50 (secondary). All computational claims are certified by the engine suite included in the deposit and independently reproduced during adversarial review by engines of separate authorship; the evidence manifest (evidence-manifest.txt) lists every file's SHA-256 hash. This work was carried out in partnership with AI research systems; the full division of contributions is disclosed in Section 8 of the paper.