Fried's Gluon Bundle and the Weak-Coupling Boundary of Eikonal QCD

We study the weak-coupling boundary of Fried’s QCD functional formalism in the high-
energy eikonal sector. The formalism was developed for nonperturbative QCD, but consistency
requires that its source-functional representation reproduce ordinary perturbative behavior when
g → 0. We show that, when the weak-coupling limit is taken at the unreduced Schwinger-
functional level, the Fried functional reduces to the free gauge-field generating functional. The
apparent singularity of the reduced kernel (gf · χ)−1, which appears in the effective-locality
representation, is therefore an order-of-limits artifact. Defining the Fried gluon bundle as the
connected Wilson-line exponent, we show that its leading weak-coupling coefficient reproduces
ordinary one-gluon exchange between colored quarks in the eikonal limit. For color-singlet
hadrons, this O(g2) contribution vanishes, so the leading strong elastic exchange begins at
O(g4). We then use a symmetric Gaussian proton model to compute a two-gluon color form
factor and show that the finite-size color-neutral coupling naturally produces the δ4
q (E) factor
appearing in Fried-style proton-proton formulas. Finally, we present a finite Gaussian profile
reconstruction of the retained one-bundle and two-bundle elastic structures. The result is a weak-
coupling consistency bridge, not a complete first-principles derivation of the full nonperturbative
proton-proton amplitude.