Abstract
<jats:p>Standard numerical invariants can agree even when the integral geometry assembling singular strata differs. We make this hidden structure computable for double-octic Calabi–Yau threefolds. Motivated by Hodge atoms, we associate to an admissible eight-plane arrangement A a local Hodge atom inventory \(HA_{\mathrm{loc}}(A)\), recording singular-stratum multiplicities, and a source assembly complex \(HA_R^{(2)}(A)=[R\langle\mathcal L(A)\rangle\xrightarrow{d_A}R\langle\mathcal P(A)\rangle]\), recording how double lines meet selected multiple points. The notation HA marks their HodgeCY role; neither object is yet a mixed-Hodge-theoretic Hodge atom spectrum. Exact computations show that 239,240,241 share one local inventory but determine two rational and three integral assembly types. In particular, 239 and 240 are isomorphic over QQ but not over ZZ, proving that rational assembly does not determine its integral refinement. More strikingly, 84 and 84a have identical local inventories and Hodge data \((h^{1,2},h^{1,1},e)=(0,40,80)\), yet distinct integral and automorphism-resolved assembly types. Thus source assembly detects coefficient- and symmetry-sensitive structure invisible to local counts and Hodge numbers. For explicit quartic perturbations of 84 and 84a, we also certify zero-dimensional saturated Jacobian schemes of degree 112.</jats:p>