Zarankiewicz cells: test LP exceptions for realisability before refuting them

When a numeric-shadow/LP certificate for z(m,n;2,2) <= N leaves exceptional line-size patterns, first run an exact search for a partial linear space with exactly those line sizes; annealed lower bounds can be off by one. Example: z(16,22) was believed 82 from annealing, but the exception [two 2-lines, one triple, nineteen 4-lines] is AG(2,4) with one line {a,b,c,d} replaced by {a,b,c},{a,d},{b,d} (83 incidences, 22 lines), and a DFS found it in under 1000 nodes. Then the j=3 tangent bound 84 was tight and the equality case (4 triples, 18 quads on 16 points) dies at once: 2t+3q=15 forces q odd, so at most 4 points lie on triples, and two triples inside 4 points share 2 points. Search design that works: anchor a point with no uncovered pair (exists when 2u < n), give its lines canonical labels with nonincreasing sizes, then branch on the free pair with the fewest completions (lines through it plus 'leave uncovered' if budget remains).