graphInvariantsCert
plain-language theorem explainer
The definition supplies a certificate that the configuration dimension yields precisely five canonical graph invariants. Combinatorialists working on graph complexity measures would cite it to confirm the enumeration of chromatic number, clique number, independence number, genus, and treewidth. It is realized as a direct structure instantiation that pulls the count from a decidable cardinality computation.
Claim. The structure asserting that the finite type of graph invariants has cardinality exactly 5, where the invariants are the chromatic number, clique number, independence number, genus, and treewidth.
background
The module treats graph invariants induced by the configuration dimension fixed at D = 5. These comprise five canonical measures on undirected graphs: chromatic number, clique number, independence number, genus, and treewidth, each a distinct complexity measure. The upstream theorem graphInvariant_count establishes Fintype.card GraphInvariant = 5 by direct decidable computation. The structure GraphInvariantsCert packages this cardinality assertion as its single field.
proof idea
The definition is a one-line wrapper that instantiates the GraphInvariantsCert structure by assigning the five_invariants field directly to the theorem graphInvariant_count.
why it matters
This definition certifies the exact count of five invariants induced by configuration dimension D = 5, closing the combinatorial layer described in the module documentation. It aligns with the Recognition Science setting in which configDim governs graph-theoretic structure, providing a base enumeration without reference to the spatial dimension D = 3 or the forcing chain. No downstream uses are recorded, and no open questions are resolved.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.