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Hipparcos calibration of the tip of the Red Giant Branch

We have detected the tip of the Red Giant Branch (TRGB) in the solar neighborhood using near infrared photometry from the 2MASS and DIRBE catalogs, and revised Hipparcos parallaxes. We confirm that the revised Hipparcos parallaxes are superior to the original ones, and that this improvement is necessary to detect the TRGB. We find a tip absolute magnitude of M_K=-6.85+/-0.03, in agreement with that expected from previous tip measurements of the Large Magellanic Cloud, Small Magellanic Cloud, and Bulge. This represents the first geometric calibration of the TRGB and extends previous calibrations, based on metal-poor globular clusters, to solar metallicities. We attempted to use the TRGB to confirm the presence of the Lutz-Kelker bias, with inconclusive results. Attempts to detect the tip in the I-band also produced inconsistent results, due to a lack of precise, homogeneous photometry for these bright stars.