Packing Dijoins in 5-Chordal Digraphs: A Weighted Min–Max Theorem and a Strongly Polynomial Algorithm

Status: This preprint presents a proposed proof. It has not been independently verified by a human expert. It was prepared with AI assistance, as described in the acknowledgements. Let D=(V,A) be a finite loopless digraph whose underlying simple undirected graph has no induced cycle of length at least six, and let w be a nonnegative integral capacity vector on its arcs. If τ is the minimum w-weight of a dicut, the manuscript proposes that the maximum size of a capacity-feasible dijoin packing is exactly τ, thereby resolving the 5-chordal conjecture of Cornuéjols, Liu, and Ravi. It also gives a compact strongly polynomial construction. With N=|V|+|A|, the algorithm returns O(N²) distinct dijoins with binary-encoded multiplicities in O(N⁶ + explicit output size) operations, independently of the capacity magnitudes. The argument reduces the input to a 4-chordal poset digraph, passes through a chordal-bipartite sink-regular instance, and synchronizes an anchored matroid-basis flow with the positive arcs. A quotient-residual decomposition and labelled lifting avoid both capacity-unit expansion and iteration τ times. The companion archive contains the complete LaTeX source, figures, bibliography, verification scripts, solver tests, machine-readable certificates, a reproducibility guide, and cryptographic checksums. Computational checks support reproducibility and falsification testing; they are not a substitute for independent mathematical proof verification.