A. Udalski, D. M. Skowron, J. Skowron, M. K. Szymański, I. Soszyński, P. Pietrukowicz, P. Mróz, R. Poleski, S. Kozłowski, K. Ulaczyk, K. Rybicki, P. Iwanek, M. Gromadzki, M. Wrona, M. Ratajczak, M. J. Mróz

We present the ultimate I-band calibration of the tip of the red giant branch (TRGB) standard candle. Our calibration is based on photometry from the outer parts of the Large Magellanic Cloud, 2.75<r<6.5 degs from the center, collected during the OGLE-IV phase of the Optical Gravitational Lensing Experiment. Outer regions of the LMC have large advantages compared to the previous attempts of the TRGB calibrations using the red giants from the central parts of this galaxy. The interstellar reddening in these regions is much lower and more uniform, stellar crowding is lower and the outer parts of the LMC can be accurately described as a flat disk within the reasonable distance from the LMC center. The number of red giants in the upper part of the red giant branch in our LMC region is large, ~140 000, making it possible to determine of the tip magnitude with high accuracy. Our ultimate I-band calibration of the TRGB is: M_{I,TRGB}=-4.022 +- 0.006 (stat.) +- 0.033 (syst.) mag. We also provide its values for different techniques of the determination of the tip magnitude. The accuracy of our calibration is mostly limited by the accuracy of the distance to the LMC (~1%) and can be improved in the future. We test our calibration by comparing it with the TRGB in the Small Magellanic Cloud and NGC 4258, i.e., the galaxies with precise geometric distance determination, and find excellent agreement. Finally, we refine the main determinations of the Hubble constant, H_0, with the TRGB using our new calibration of the I-band TRGB brightness.