  Recent photometric surveys of Trans-Neptunian Objects (TNOs) have revealed
that the cold classical TNOs have distinct z-band color characteristics, and
occupy their own distinct surface class. This suggested the presence of an
absorption band in the reflectance spectra of cold classicals at wavelengths
above 0.8 micron. Here we present reflectance spectra spanning 0.55-1.0 micron
for six TNOs occupying dynamically cold orbits at semimajor axes close to 44
au. Five of our spectra show a clear and broadly consistent reduction in
spectral gradient above 0.8 micron that diverges from their linear red optical
continuum and agrees with their reported photometric colour data. Despite
predictions, we find no evidence that the spectral flattening is caused by an
absorption band centered near 1.0 micron. We predict that the overall
consistent shape of these five spectra is related to the presence of similar
refractory organics on each of their surfaces, and/or their similar physical
surface properties such as porosity or grain size distribution. The observed
consistency of the reflectance spectra of these five targets aligns with
predictions that the cold classicals share a common history in terms of
formation and surface evolution. Our sixth target, which has been ambiguously
classified as either a hot or cold classical at various points in the past, has
a spectrum which remains nearly linear across the full range observed. This
suggests that this TNO is a hot classical interloper in the cold classical
dynamical range, and supports the idea that other such interlopers may be
identifiable by their linear reflectance spectra in the range 0.8-1.0 micron.
