Collision energy and asymptotic basis densities of rank-three matroids

We study the deficit delta=1-P of weighted basis density for rank-three matroids with bounded arc number. For positive stationary weights, the diffuse collision condition Q=o(delta) yields alpha(M) sqrt(delta)>=2-o(1), with a disjoint-line equality structure. A finite construction of actual arcs and a weighted de Caen inequality give an unrestricted absolute constant c_0>1/2 for the leading asymptotic deficit coefficient. The gain is existential; no numerical bound such as 0.51 or 6/11 is claimed. The candidate sharp unrestricted coefficient 1 remains open. A uniform stationary example shows why diffuse collisions are not automatic, and a necessary positive collision-core condition identifies a remaining obstruction. This is the first public preprint, not a peer-reviewed journal publication. The source and supplementary materials include exact algebraic checks and a reproducible plot and rational-value table for the uniform example. OpenAI Codex assisted mathematical exploration, proof development and inspection, literature searches, algebraic and programmatic checks, drafting and revision. The author takes full responsibility for the manuscript. No specific funding or competing interests are declared.