  Connecting the composition of planet-forming disks with that of gas giant
exoplanet atmospheres, in particular through C/O ratios, is one of the key
goals of disk chemistry. Small hydrocarbons like $\rm C_2H$ and $\rm C_3H_2$
have been identified as tracers of C/O, as they form abundantly under high C/O
conditions. We present resolved $\rm C_3H_2$ observations from the TW Hya
Rosetta Stone Project, a program designed to map the chemistry of common
molecules at $15-20$ au resolution in the TW Hya disk. Augmented by archival
data, these observations comprise the most extensive multi-line set for disks
of both ortho and para spin isomers spanning a wide range of energies,
$E_u=29-97$ K. We find the ortho-to-para ratio of $\rm C_3H_2$ is consistent
with 3 throughout extent of the emission, and the total abundance of both $\rm
C_3H_2$ isomers is $(7.5-10)\times10^{-11}$ per H atom, or $1-10$% of the
previously published $\rm C_2H$ abundance in the same source. We find $\rm
C_3H_2$ comes from a layer near the surface that extends no deeper than
$z/r=0.25$. Our observations are consistent with substantial radial variation
in gas-phase C/O in TW Hya, with a sharp increase outside $\sim30$ au. Even if
we are not directly tracing the midplane, if planets accrete from the surface
via, e.g., meridonial flows, then such a change should be imprinted on forming
planets. Perhaps interestingly, the HR 8799 planetary system also shows an
increasing gradient in its giant planets' atmospheric C/O ratios. While these
stars are quite different, hydrocarbon rings in disks are common, and therefore
our results are consistent with the young planets of HR 8799 still bearing the
imprint of their parent disk's volatile chemistry.
