Filgueiras–Moraes and other contexts

For $\beta =1/2$, their von Neumann boundary parameter ${\eta }_0$ maps through the small-radius coefficients to

in the energy units used in their equation (10) FM2007. That equation also includes the free longitudinal kinetic term. The ratio must select the real bound-state branch; in our boundary convention this is $\lambda <0$. The reported eight-point comparison is retained below.

The inverse-square analysis of DR2017 supplies broader operator context. The fermionic references SousaGerbert1989,BordagVoropaev1993,BdFS1999 concern different fields and boundary structures, not confirmations of the scalar tensor or current computed here.

The SAE source reports finding no direct scalar computation of all three observables for these zero-thickness ${\mathsf{E}}_0,{\mathsf{E}}_{\lambda },U(2)$ choices. That is retained as a limited search report, not a theorem of novelty or an exhaustive literature claim.