Generalization Test on Cubic Fourfolds: Canonical Fano Bridges, Denominator-Aware Closure, and Conditional K3 Escalation

Applies the compiler to smooth cubic fourfolds: the Fano variety of lines (K3^[2] type, Abel–Jacobi isomorphism on primitive cohomology) lowers primitive (2,2) classes to divisors, giving rational closure with denominator 6 (integral closure left as a separate obligation); an associated K3 exists only for admissible special cubics (e.g. d = 14); the generic Kuga–Satake dimension is 2^20.

R16 reconstructs a known consequence (the rational Hodge conjecture for codimension-two classes on a smooth cubic fourfold); it is not a new proof. One sentence of the paper ('the bridge closes the rational Hodge conjecture for codimension-two classes on a smooth cubic fourfold') could be misread out of context; this is a classical known case, and the next sentence and §24 say it is not a new proof. The denominator-6 step was not independently checked.

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