AbstractWe construct the fundamental obstruction object of Chromatic Obstruction Sheaf Theorywithin the relational descent environment developed in COST I. Starting from a smallfinitely complete relational site (C, J) and its hypercomplete ∞-topos X = ShvhypS (C, J),we define an intrinsic finite-stage obstruction functor by measuring pointed relative de-fects associated to hypercover realizations. These defects are represented by finite relativecofiber objects, and their colimit produces a canonical pointed objectOfund ∈ X∗,the fundamental unstable obstruction carrier. We prove that Ofund represents the rela-tional obstruction functor and is therefore determined by the descent structure up tocontractible equivalence.We then pass to the stable spectral imageFfund := Σ∞Ofund ∈ Sp(X ),without identifying this stable image with the original unstable carrier. For connectiveFfund, the Postnikov tower yields stable coefficient sheaves Afund,n := πn(Ffund), primarystable obstruction classesostfund,n(s) ∈ Hn+1(U ; Afund,n),and associated obstruction sheaves obtained by sheafifying the corresponding local coho-mology presheaves. These classes satisfy the usual vanishing and torsor criteria for liftingthrough successive Postnikov stages.Finally, we organize the stable obstruction package by chromatic localization, heightfiltration, fracture reconstruction, base change, and admissible Morita invariance. Chro-matic localization is applied at the stable level, producing height-filtered coefficient andobstruction sheaves, while fracture data give Mayer–Vietoris compatibility conditionsfor reconstructing obstruction classes from height pieces. Under explicit compatibilityhypotheses, the fundamental obstruction carrier, its stable image, coefficient sheaves, ob-struction classes, chromatic localizations, and fracture data are invariant under admissiblechanges of relational presentation. Thus COST II supplies the canonical obstruction-theoretic core of the theory: an unstable universal carrier together with its stable chro-matic obstruction package, forming the foundation for subsequent directive, moduli, andcotangent constructions.