A Computer-Assisted Lower Bound and an Explicit Scope-95 Witness for m(6,5)

An (n,k)-difference triangle set is a family of n rows of k+1 integers, each starting at 0, whose n*C(k+1,2) within-row differences are pairwise distinct; its scope is the largest difference, and m(n,k) is the minimum scope. The cell (6,5) is the first open case at k=5. This deposit contains the paper and its complete verification package, establishing 94 <= m(6,5) <= 95 with both ends resting on verifiable evidence. Lower bound: m(6,5) >= 94, by a computer-assisted exclusion of scope 93. A hand-checkable dual certificate settles m(6,5) >= 92 and provably exhausts the linear-programming relaxation; a finite evaluation of a Fourier obstruction of Ma and Yi gives >= 93; and a complete, independently audited exact-cover exhaustion over a finite universe of row-length sets, organised by an elementary partition bound, gives >= 94. Upper bound: m(6,5) <= 95, by an explicit witness — to the author's knowledge the first explicit scope-95 (6,5)-difference triangle set on record, which supplies a third-party-verifiable witness for the bound J. B. Shearer reported in 2008 without publishing one. The package (m65-dts-package.zip, 68 files) contains the nine-witness corpus with canonical hashes; the 114 hole-confinement certificates with an independent 50-digit verifier; the T=534, 535 and 536 elimination evidence with both solvers' sources; the 30-campaign global theorem artifact with its replay and an independent regeneration; the search and analysis programs; a documented literature check supporting the priority claim; and portable, fail-closed verification programs with positive and negative regression tests. Every verification command runs in a clean Python 3.8+ environment with nothing installed and no network access; a README maps each claim in the paper to the artifact and command that reproduce it. Integrity is checked with the included SHA256SUMS.txt. The paper also corrects and consolidates the k >= 5 lower-bound frontier, reports the verification methodology, and documents an explicit trust boundary: what is hand-checkable, what is audited computation, and what remains trusted.