The Omega Tower: Role Non-Impersonation and Authority Preservation in Agentic AI

his preprint presents a conditional architecture theorem for role separation in agentic AI authority systems. It argues that an authority stack must preserve distinct roles for obstruction detection, finite terminalization, certified transport, comparison, finite-shadow authority, and residual closure. Proposals enter the stack, but proposals do not themselves constitute authority. The paper states the Role Non-Impersonation Program: under declared Omega Tower role contracts, removing or impersonating a role leaves an undischarged obligation and admits a characteristic authority failure unless equivalent machinery is reintroduced. The associated Omega Anti-Cheat Lemma is presented as a conditional architecture result: proposal systems cannot terminalize their own outputs, representation changes cannot transport authority without loss accounting, comparison cannot create authority by aggregation, continuum objects cannot outrank finite query-relative witnesses, residuals cannot be renamed as closure, and tower roles cannot impersonate one another without preserving the relevant machinery. The paper includes a six-role collapse table, a worked finite residual example over F₂³, a query-relative finite-shadow authority definition, a residual honesty taxonomy, and an engineering evaluation program for measuring false terminalization, replay stability, transport coverage, residual reduction, and local-green/global-red failures. Lean support in omega_engine/lean4/Paper029 mechanizes finite kernels for the role/failure constructor table, collapse classification, refusal propagation, terminal disjointness, residual classification, query-relative scope, and primitive-difference role-erasure boundaries. These Lean kernels do not replace the home-layer theorems or close the remaining semantic obligation PL-029-1. The full semantic proof of pairwise role-failure disjointness and per-case discharge against home-layer contracts remains open. This is a v0.1 preprint and cross-tower synthesis paper. It is not an empirical AI-safety validation, not a full proof of the entire GTLA/Omega Tower, and not a claim that the six named layers are the only possible implementation packaging. The claim is narrower: the six authority obligations cannot be erased; they may be compressed only if the resulting architecture still discharges the same obligations and preserves the corresponding failure terminals.