Presentation Modules (In Sequential Order)
The Seymour Diamond
Standard neighborhood accounting failures, distance-two ancestry loss, and double counting in $N^+(v) + N^+(w)$ vs $N^{++}(u)$.
BFS-Lex Coordinate System
Theorem 1 well-ordering, transitive 3-cycles, interior vs. exterior sets, back neighbors, and the Minimum Counterexample (MCE).
MCE Without Back Arcs
Degree partition lemma, inductive layer size decay $|R_k| = \delta - k + 1$, Seymour forcing constraints, and exact interior degree bounds.
Disconnected Back Neighbors
$\delta$-regularity constraints prior to first back arcs, disjoint back neighbor bounds, and well-founded sequence loop closure termination.
Connected Back Neighbors
Analysis of the first connected back arc case, full layer exterior capacity saturation, and the bi-directional arc contradiction proof.
Graph Level Order & Quotients
Quotient hyper-graph equivalence, Hierholzer's cycle algorithm, 8-case load-balancing triangle table, and Seymour diamond resolutions.
Proof Synthesis, Collapse Zone & Algorithmic Complexity
Feasibility bounds combining $|R_i| \cdot i \le \binom{|R_i|}{2}$ with layer decay to establish collapse thresholds and optimal complexity.
EvidencePress Counterexample Is NOT an MCE
Reviewing requirements to pack non-Seymour vertices, and noting why the graph provided contains multiple Seymour vertices.