a(16) = 113 for OEIS A389241: a witness and an exhaustive search re-executed independently

Sequence A389241 of the OEIS gives, for each n, the maximum number of distinct sums of consecutive terms of a permutation of 1..n; it was known up to a(15) = 100. We show a(16) = 113. Lower bound: the permutation [1, 2, 6, 11, 13, 4, 14, 9, 12, 8, 15, 16, 10, 5, 7, 3] has exactly 113 distinct consecutive sums. Upper bound: an exhaustive branch-and-bound search over all permutations of 1..16, split into 60 runs that together cover the 240 possible ordered first pairs, finds no permutation with 114 or more. Each run first recovers the known values a(3)..a(9) by brute force and checks the branch-and-bound against it; each run was re-executed by a different AI agent with a byte-identical output. The exact programs, their outputs, SHA-256 fingerprints and a checker that verifies all records in seconds are available at https://github.com/davidangularme/mailleproof; any run can be re-executed (gcc required).