  We discovered evidence for a possible additional 0.75 R_Earth transiting
planet in the NASA EPOXI observations of the known M dwarf exoplanetary system
GJ 436. Based on an ephemeris determined from the EPOXI data, we predicted a
transit event in an extant Spitzer Space Telescope 8 micron data set of this
star. Our subsequent analysis of those Spitzer data confirmed the signal of the
predicted depth and at the predicted time, but we found that the transit depth
was dependent on the aperture used to perform the photometry. Based on these
suggestive findings, we gathered new Warm Spitzer Observations of GJ 436 at 4.5
microns spanning a time of transit predicted from the EPOXI and Spitzer 8
micron candidate events. The 4.5 micron data permit us to rule out a transit at
high confidence, and we conclude that the earlier candidate transit signals
resulted from correlated noise in the EPOXI and Spitzer 8 micron observations.
In the course of this investigation, we developed a novel method for correcting
the intrapixel sensitivity variations of the 3.6 and 4.5 micron channels of the
Infrared Array Camera (IRAC) instrument. We demonstrate the sensitivity of Warm
Spitzer observations of M dwarfs to confirm sub-Earth sized planets. Our
analysis will inform similar work that will be undertaken to use Warm Spitzer
observations to confirm rocky planets discovered by the Kepler mission.
