Does a graph that needs six vertex colours force a short path of one colour whenever its edges are coloured with three colours? The path has three edges and four distinct vertices. This research dossier does not settle that question. It records useful partial progress and shows exactly where the remaining difficulty lies. Its strongest written result concerns graphs built from two collections of disjoint cliques, each with at most three vertices, together with a collection of stars. Even when the three coverings overlap, their union can be coloured with five vertex colours. The dossier also excludes critical counterexamples on fourteen vertices using structural arguments and checked finite classifications. Combining that result with an external catalogue gives a conditional lower bound of fifteen vertices. The catalogue completeness assumption remains explicit. At fifteen vertices, two specified classes are excluded, but graphs with forty-one, forty-two or forty-three edges remain unresolved. A second line of work studies how to repair an initial colouring. Small-defect cases work, while explicit examples show why several stronger shortcuts fail. The package includes the complete written arguments, colouring witnesses, portable replay code and records of stopped searches. Successful replay is not a proof of the full problem. This is an unrefereed Evidence Press candidate, dated the eighth of September, twenty twenty-six. The paper and evidence package are linked. This narration uses an OpenAI synthetic voice and provides no additional mathematical evidence.