This is an announcement for the paper "An Inverse Ackermannian Lower Bound on the Local Unconditionality Constant of the James Space" by Henry Towsner. Abstract: The proof that the James space is not locally unconditional appears to be non-constructive, since it makes use of an ultraproduct construction. Using proof mining, we extract a constructive proof and obtain a lower bound on the growth of the local unconditionality constants. Archive classification: math.LO math.FA Mathematics Subject Classification: 46B15 Submitted from: htowsner@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1503.04745 or http://arXiv.org/abs/1503.04745