{"schema_version":"dataset-v1","id":"petersen-witness-check","version":1,"title":"Check the witness","description":"Structural properties of the 112-vertex witness, recomputed from its edges.","license":"CC0-1.0 (computed values)","problems":["petersen-coloring"],"statements":[{"problem":"petersen-coloring","statement":"petersen-112-main-witness","role":"The stated size, girth and connectivity, recomputed."}],"figure":{"family":"exact-table","title":"Check the witness","caption":"Recomputed from the published adjacency list: the graph is a simple bridgeless cubic graph with the size, girth and connectivity the statement gives.","columns":["Property","Recomputed","Statement"],"boundary":"This checks the graph's structure only. That it has no Petersen coloring is the cited theorem and its formal proof; it is not recomputed here."},"provenance":{"method":"Degrees and simplicity counted; connectivity by graph search after deleting every single edge, every pair of edges and every pair of vertices; girth by breadth-first search from every vertex.","software":{"python":"3.12.15"},"precision":"Exact combinatorics.","generator":"openmath/scripts/build-datasets.py","generated_on":"2026-10-21"},"data":{"series":[],"marks":[],"rows":[{"key":"vertices","cells":["Vertices","112","matches"]},{"key":"edges","cells":["Edges","168","matches"]},{"key":"cubic","cells":["Every vertex has degree 3","yes","matches"]},{"key":"simple","cells":["Simple: no loops or parallel edges","yes","matches"]},{"key":"connected","cells":["Connected","yes","matches"]},{"key":"bridgeless","cells":["No bridge (removing any one edge)","yes","matches"]},{"key":"edge3","cells":["Edge-connectivity at least 3 (any two edges)","yes","matches"]},{"key":"vertex3","cells":["Vertex-connectivity at least 3 (any two vertices)","yes","matches"]},{"key":"girth","cells":["Girth (shortest cycle)","5","matches"]}]},"sha256":"a519f6a42f3f8a594c427af728423103bab8ea2c6a1707c6969db73859987bab"}