VR2(K4) = 20 — unrefereed candidate certificate-backed determination of two vertex-disjoint monochromatic K4s in K20

VR2(K4) is the least n such that every red-blue edge-colouring of the complete graph K_n contains two pairwise vertex-disjoint monochromatic copies of K4 (the two copies need not have the same colour). This record archives an unrefereed candidate certificate-backed determination that VR2(K4) = 20, comprising a hand-checkable 19-vertex lower-bound construction with a dependency-free direct verifier, and an upper bound that reuses — not independently reproduces — the exact two-core reduction and unsatisfiability certificate artifacts of the candidate z(20) = 6 result (z20-cochromatic tag candidate-2026-07-26, commit 3c7e520fdc0615f5c700761c2b1e5108dcc836e7).

Status: unrefereed candidate computer-assisted result. The lower-bound construction is hand-checkable and has a dependency-free direct verifier. The reused certificates were replayed locally by separately implemented checkers, including a formally verified CakeML checking core. The complete graph-theoretic result has not been independently reproduced, completely verified by a human mathematician, peer reviewed, or formalised end to end in a proof assistant. Deposit on Zenodo does not upgrade this status.

Provenance (repository-reported): credited authors GPT 5.6 Sol and Claude Opus 4.8 / 5, as recorded in the candidate paper. The human participant selected the problem and mediated between systems. Repository maintenance and publication: Ian Pitchford, CC0 affirmer only to the extent he holds the relevant rights.

Archive: the exact release archive of tag vr2-k4-v0.1-candidate (commit b303d7d61d1a4cdf6ff0f1c18eee40eded0583cc) of github.com/ipitchford/z20-cochromatic; SHA-256 recorded in the deposit receipt.