Four-Particle Monochromatic Quantum Graphs
For four particles and local dimension , can a complete edge-coloured, complex-weighted graph have unit perfect-matching amplitude for every monochromatic inherited colouring and zero for every nonmonochromatic one? Ruled out for the whole family, including the real-, integer- and trinary-weight variants.
- Result
- Disproved(see note)
- Status
- Partial result
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Quantum optics & graph amplitudes
- Posed by
- —
- Year posed
- 2017
- Years open
- 9y
- Solved
- 2026-05-21
- Model
- AlphaProof Nexus
- Vendor
- Google DeepMind
- Collaborators
- —
- Verification
- Lean-verified
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
the N = 4, D ≥ 4 family is fully ruled out; the general two-parameter problem remains open
What the AI did
Solved autonomously by AlphaProof Nexus, with the proofs formally verified in Lean.
Verification
Lean-checked; formal proofs published with DeepMind's AlphaProof Nexus report (arXiv:2605.22763).