A Unified Framework for Yang-Mills Mass Gap, QCD Confinement, and Black Hole Information

I present a complete theoretical framework resolving foundational problems in quantum field theory and quantum gravity using the Operational Coherence Bound (OCB) and its flat-space extension, the quantum Operational Coherence Bound (qOCB).
By treating Renormalization Group (RG) flow as a contraction semigroup in the qOCB metric space, I derive the rigidity inequality β′(g) ≤−κ(g) where κ(g) is the RG contraction coefficient.
I prove that: (1) The YangMills mass gap follows from κ(g) > 0 forbidding IR fixed points;
(2) QCD color confinement holds for Nf < 8 flavors;
(3) The QCD conformal window opens at Ncrit f ≈ 8.0 where κtotal = 0;
(4) Black hole information is preserved globally but operationally inaccessible, resolving the information paradox.
The framework is grounded in Petz monotonicity, Logarithmic Sobolev Inequalities, and dispersion relations.
This work constitutes a conditional proof program pending standard Clay Problem assumptions (continuum limit existence).
All derivations are presented with sufficient detail for complete peer verification.