Exhibit 99.1

JOINT FILING AGREEMENT

AGREEMENT dated as of April 13, 2026, by and among Bleichroeder Sponsor 3 LLC, Andrew Gundlach and Michel Combes (together, the “Parties”).

Each Party hereto represents to the other Party that it is eligible to use Schedule 13G to report its beneficial ownership of Class A ordinary shares, $0.0001 par value, of Bleichroeder Acquisition Corp. III, as of July 8, 2026, relating to such beneficial ownership, being filed on behalf of each of them.

Each of the Parties agrees to be responsible for the timely filing of the Schedule 13G and any and all amendments thereto and for the completeness and accuracy of the information concerning itself contained in the Schedule 13G, and the other Party to the extent it knows or has reason to believe that any information about the other Party is inaccurate.