Universal scalar monotone beyond strong subadditivity

Establish a universal scalar radial monotone for holographic renormalization-group flows derived from entropy inequalities beyond strong subadditivity, overcoming the sign-indefinite shape response in the odd-cyclic construction and the Markov-equality restriction in the five-party shell construction.

Background

The paper derives two beyond-SSA constraints: a conditional radial growth bound from a five-party inequality, which requires a Markov equality, and an odd-cyclic angular inequality, whose Lorentz-covariant form includes a radial derivative but also a shape response with no definite sign.

Neither construction produces a universal scalar analogue of the three-dimensional F-function. The authors therefore identify the existence of such a monotone as an unresolved problem rather than a result of the paper.