Theorem · version 1
Earlier version 1. View current version 2 →
If C is a cycle double cover of a finite graph G, then the sum of the lengths of the cycles in C, with multiplicity, equals 2|E(G)|.
A counting consequence of a cover, not a proof that every bridgeless graph admits one.
Proved
Counting the total length of any double cover, independently of universal existence.
A proof of the cycle double cover conjecture · Main theorem and flow-to-cover construction →
Observed Oct 13, 2026
In this problem · publication v1 · Selected context
Supporting result · Proved
Relationship not independently reviewed. This concerns its use in this problem.
A new argument is reported to construct a cycle double cover for every finite loopless bridgeless multigraph.
paraphrase · OpenMath supplies original paraphrases and links; no proof text is republished.
OpenAI · Preprint · Publication date Jul 10, 2026
Public manuscript or exposition; publication does not imply independent OpenMath review.
Source revision: 2026-07-10. Observed Oct 13, 2026.
OpenAI reports a GPT-5.6 Sol Ultra multi-agent discovery workflow. This provenance is first-party and is not independent mathematical review.
Source updated Jul 10, 2026.
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proved
Counting the total length of any double cover, independently of universal existence.
Observed Oct 13, 2026 · Source passage →