  New thermal phase of QCD, featuring scale invariance in the infrared (IR),
was proposed to exist both in the pure-glue (N$_f$=0) and the ``real-world"
(N$_f$=2+1) settings. Among key aspects of the proposal is that the system in
this {\it IR phase} separates into two independent components: the
scale-invariant IR part and the non-invariant bulk. Such scenario requires
non-analyticities in the theory and, in case of pure-glue QCD, they were found
to arise via Anderson-like mobility edges in Dirac spectra ($\lambda_\fir \!=\!
0$, $\pm \lambda_\text{A} \!\neq\! 0$) manifested in dimension function
$d_\fir(\lambda)$. Here we present first evidence that this mechanism is also
at work in ``real-world QCD" (N$_f$=2+1 theory at physical quark masses and
$a\!=\!0.105\,$fm), supporting the existence of the proposed IR regime. Indeed,
at $T\!=\!234\,$MeV, we find the dimensional jump between zero modes and lowest
near-zero modes very close to unity ($d_\fir\!=\!3$ to $d_\fir \!\simeq \!2$),
exactly like in pure-glue QCD in IR phase. However, no jump is found at
$T\!=\!187\,$ MeV which is in the intermediate region between chiral crossover
at $T_c \approx 155\,$MeV and the onset $T_\fir$ of IR phase, originally
estimated at $200 < T_\fir < 250\,$MeV.
