Toward a Pomeron from Fried's Nonperturbative QCD Functional Formalism II: Scalar-Glue Visibility and Top-Block Cyclicity

In a preceding work we established an external-cyclic first-return Pomeron theorem in Fried’s
nonperturbative QCD functional formalism: the scalar crossing-even channel generated by a
finite-size pp source contains a positive-intercept Mellin singularity,
αcyc
P,pp(0) > 1.
The present paper addresses the next step: whether this cyclic singularity is visible in the top
scalar crossing-even Perron block. The required condition is
Etop,+Φp̸ = 0,
where Etop,+ is the spectral projection of the leading scalar C = + transfer block and Φp is the
finite-size scalar proton source. The key observation is that the finite-size source used in the
cyclic theorem has nonzero scalar-glue overlap. In the Fried/Halpern representation this overlap
is encoded by the non-Abelian commutator-channel numerator
N2,comm(χ; c) = Gp[c]
8
X
x
P x
f (χ)2,
which has the same scalar color-singlet 0++ quantum numbers as the local gluonic operator
F a
μν F aμν . We then formulate a scalar cyclicity hypothesis, modeled on the Reeh–Schlieder
theorem for the gauge-invariant local QCD algebra:
A0++ |0⟩ = H0++ .
Under this scalar cyclicity and irreducibility of the positive scalar vacuum cone, the nonzero
scalar-glue overlap of Φp implies
Etop,+Φp̸ = 0.
Thus the cyclic Pomeron singularity of the first paper is promoted to a top-block visible scalar
crossing-even singularity in the physical pp channel. The remaining upgrade to a rightmost
Pomeron is odd-sector domination, treated separately.