RCHM × Hodge Research Round
R19 · Ancestry reduction and the novelty frontier
Ancestry Reduction for K3-Type Fano Families: Blow-Up Source Classification, Bridge Reuse, and Novelty Frontier Detection
'Ancestry reduction': for codimension-2 blow-ups H^4(Bl_Z Y) = H^4(Y) + H^2(Z)(−1), classifies the K3 block as parent-inherited / center-injected / mixed / none; Küchle c7 reuses a cubic-fourfold bridge, d3 reduces to a K3 center, and c5 is left as the novelty-frontier case.
R19 classifies the Küchle families as reused, reduced or novel; 'NOVEL' means only that no source reduction has been certified in the current graph.
The paper says 'Novelty Is Not Truth'. It depends on the 2021 classification by Bernardara–Fatighenti–Manivel–Tanturri (arXiv:2111.13030, which exists; 64 families confirmed).