  Composite Higgs models must exhibit very different dynamics from quantum
chromodynamics (QCD) regardless whether they describe the Higgs boson as a
dilatonlike state or a pseudo-Nambu-Goldstone boson. Large separation of scales
and large anomalous dimensions are frequently desired by phenomenological
models. Mass-split systems are well-suited for composite Higgs models because
they are governed by a conformal fixed point in the ultraviolet but are
chirally broken in the infrared. In this work we use lattice field theory
calculations with domain wall fermions to investigate a system with four light
and six heavy flavors. We demonstrate how a nearby conformal fixed point
affects the properties of the four light flavors that exhibit chiral symmetry
breaking in the infrared. Specifically we describe hyperscaling of dimensionful
physical quantities and determine the corresponding anomalous mass dimension.
We obtain $y_m=1+\gamma^*= 1.47(5)$ suggesting that $N_f=10$ lies inside the
conformal window. Comparing the low energy spectrum to predictions of dilaton
chiral perturbation theory, we observe excellent agreement which supports the
expectation that the 4+6 mass-split system exhibits near-conformal dynamics
with a relatively light $0^{++}$ isosinglet scalar.
