CC degree formula conjecture for four-electron truncation varieties

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

m=6(n42),s=(n44).m=6\binom{n-4}{2},\qquad s=\binom{n-4}{4}.

CC degree formula conjecture. For d=4d=4 and n12n\leq 12, the CC degree of V{2}V_{\{2\}} is

CCdeg4,n({2})=(ms+2)2s1.\operatorname{CCdeg}_{4,n}(\{2\})=(m-s+2)2^s-1.

Since VPV_P is a complete intersection for n12n\leq 12, the preceding generic graph-degree conjecture would imply this formula. The supplied source does not resolve whether the formula holds.

Sources & referencesView supporting material

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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