CC degree formula conjecture for four-electron truncation varieties

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Let V{2}V_{\{2\}} be the coupled-cluster doubles truncation variety for d=4d=4, and set

m=6(n−42),s=(n−44).m=6\binom{n-4}{2},\qquad s=\binom{n-4}{4}.

CC degree formula conjecture. For d=4d=4 and n≤12n\leq 12, the CC degree of V{2}V_{\{2\}} is

CCdeg⁡4,n({2})=(m−s+2)2s−1.\operatorname{CCdeg}_{4,n}(\{2\})=(m-s+2)2^s-1.

Since VPV_P is a complete intersection for n≤12n\leq 12, the preceding generic graph-degree conjecture would imply this formula. The supplied source does not resolve whether the formula holds.

References

Primary source

Fabian M. Faulstich, Vincenzo Galgano, Elke Neuhaus and Irem Portakal, “On the Coupled Cluster Doubles Truncation Variety of Four Electrons”, arXiv:2602.16580 (2026).

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