A Stabilizer Obstruction for Anonymous and Object-Neutral Classification Aggregation

Abstract

We disprove a conjectured prime-divisor characterization for anonymous and object-neutral classification aggregation. A general stabilizer obstruction and explicit profile gadgets show that, for every m ≥ 5, ρ = m − 2, and n ≥ 2, no deterministic resolute anonymous and object-neutral classification aggregation function exists. In particular, the previously unresolved instance (n, m, ρ) = (7, 5, 3) is impossible even though the only prime divisor of 7 exceeds 5. The deposit includes the research note, an explicit seven-individual certificate, independent Rust and Python verifiers, verification logs, and checksums.