I parsed the 25 codewords out of the paper's own witness block and re-verified everything independently rather than trusting the construction narrative. Result: all 25 lines have weight exactly 4, all entries lie in 0..18, all 25 blocks are distinct, and across all C(25,2)=300 pairs the maximum intersection is 1 (zero violations), so d=2(w-1)=6 holds exactly as claimed. The degree sequence is twelve points with r=5, six points with r=6, and one point (18) with r=4, summing to 100=4*25, and the 'leave' (uncovered pairs) is exactly 171-150=21 edges, which factors cleanly into five triangles plus a 6-edge matching. I also rebuilt the group from the two stated generators: it has order exactly 6, is non-abelian (element orders 1,2,2,2,3,3, the S3 signature), and its point orbits are {0-5},{6-11},{12,13,14},{15,16,17},{18} with sizes 6,6,3,3,1, exactly as the paper states. The 25 blocks decompose into orbits of size 6,6,3,3,3,3,1 under this group, so the invariance claim is genuine, not decorative. Every self-certifying claim in the paper checks out.
Where the paper falls short is everywhere around that certified core. First, the Schonheim bound of 28 is correctly computed (t=2, floor(18/3)=6, floor(19*6/4)=28), but it is not tight: a short degree-parity argument on the leave graph (if b=28 then the leave has exactly 3 edges, and the resulting leave-degree distribution is impossible in a simple graph -- either one vertex needs degree 6 with no partner, or two vertices need degree 3 each but can carry only 1 edge between them) rules out b=28, so the true upper bound is at most 27. The paper's own phrasing ('the gap is 3 and is not closed by this construction') implies live headroom up to 28 that in fact never existed, and deriving this refinement was well within reach of the same analysis the paper already performs elsewhere.
Second, and more importantly for novelty: packing 4-subsets of a 19-set so that any two meet in at most one point is precisely the classical K4-packing problem for K19, and A(19,6,4)=25 is a decades-old published exact value (the exceptional v=19 case in Brouwer's 1979 determination of K4-packing numbers, where the true maximum sits 3 below the Schonheim bound -- matching this paper's gap of exactly 3). My own literature search corroborates this. So the paper does not merely fail to claim optimality; it has, by its own numbers, silently reproduced a 47-year-old sporadic result using a standard prescribed-automorphism-group search (orbit generation, compatibility graph, maximum-weight clique -- the Kramer-Mesner method, 1976) and then explicitly declines to check whether 25 'improves on published values,' handing that duty to reviewers rather than doing it themselves.
Third, the survey section (163 groups tried, 161 produced a code, exhaustive maxima reported for 155 groups) supplies no group list, no code, no runtimes, and no completeness argument for any exhaustiveness claim -- the rubric is explicit that such claims must be scored on the completeness argument, and none is offered. The subsequent conjectures ('small, nonsemiregular groups... can be favorable,' 'many fixed points are often harmful') carry no quantifier or threshold and are not falsifiable as stated.
On the positive side, the paper is a model of self-certifying clarity: explicit generators, an explicit iff validity criterion, and a plain witness block that a reader can check with nothing but a pairwise scan -- which is exactly what I did. That transparency is real value, just not novel or significant value on its own.