  Theory suggests that in high-energy elastic hadron+hadron scattering,
$t$-channel exchange of a family of colourless crossing-odd states -- the
odderon -- may generate differences between $p\bar p$ and $pp$ cross-sections
in the neighbourhood of the diffractive minimum. Using a mathematical approach
based on interpolation via continued fractions enhanced by statistical
sampling, we develop robust comparisons between $p\bar p$ elastic differential
cross-sections measured at $\surd s=1.96\,$TeV by the D0 Collaboration at the
Tevatron and function-form-unbiased extrapolations to this energy of kindred
$pp$ measurements at $\surd s /{\rm TeV} = 2.76, 7, 8, 13$ by the TOTEM
Collaboration at the LHC and a combination of these data with earlier
cross-section measurements at $\surd s/{\rm GeV} = 23.5, 30.7, 44.7, 52.8,
62.5$ made at the internal storage rings. Focusing on a domain that straddles
the diffractive minimum in the $p\bar p$ and $pp$ cross-sections, we find that
these two cross-sections differ at the $(2.2-2.6)\sigma$ level; hence, supply
evidence with this level of significance for the existence of the odderon. If
combined with evidence obtained through different experiment-theory
comparisons, whose significance is reported to lie in the range
$(3.4-4.6)\sigma$, one arrives at a $(4.0 - 5.2)\sigma$ signal for the odderon.
