A negative answer to Nevo's homology-sphere decomposition question

A finite pure two-dimensional abstract simplicial complex is constructed which is doubly Cohen-Macaulay over every characteristic-zero field but contains no two-dimensional homology-sphere subcomplex over any field. This gives a full negative answer to Nevo's sphere replacement question, OWR17/2005 Problem8 (printed961) and Discrete and Computational Geometry39(2008) Problem3.7 (printed417). Homology sphere includes all face-link conditions, not merely global sphere homology. No subdivision or enlargement is used. The construction is a finite congruence quotient of the affine PGL3 building over F11((y)). A faithful polynomial representation and reduction modulo t^9 give sufficient displacement and unchanged projective-plane links. A direct deleted-link spectral estimate and a complete weighted cocycle proof verify every vertex deletion. An Euler characteristic count excludes all permitted sphere pieces. The earlier building and representation of Lubotzky-Samuels-Vishne, degree/congruence mechanism of Lubotzky-Meshulam, Garland-type criterion of Ballmann-Swiatkowski, and curvature obstruction of Januszkiewicz-Swiatkowski receive explicit credit. Root and three extensive priority approaches found no earlier recorded full answer in inspected accessible material;176 query inputs contain167 exact distinct strings and are not a count of unique works. This is not a firstness, causal-independence or continued-global-openness certificate. Material unread full-body leads include Chari1997 and Baclawski1982; other original bodies, books, theses, versions and subscription indexes remain uninspected. Exact versions and selective reading scopes are preserved. The source archive contains the complete paper source, labelled historical PR inputs, three fresh full mathematical reviews, three priority approaches, root analysis, and portable offline verification. Standard-library checks reproduce the exact finite projective incidence data, every single-vertex deletion, and a rational torus boundary control. Complete positive outputs are compared in normal and optimized Python and six actual wrong-construction failures are reproduced. An optional NumPy program separately checks the explicit neighbor matrices. No program enumerates the finite quotient or replaces the universal proof. Third-party source bodies and extracts are excluded. AI tools were extensively used in developing, writing, literature research, computation and adversarial verification. Exposure and reading limits are documented. This preprint is unrefereed. Internal AI reviews are not external human peer review, journal refereeing or formal proof verification.