LLM agents combine information from multiple principals while acting externally. We formalise privilege escalation (PE) as the system-level security objective: an action may proceed only if every principal that influenced it would allow it. Model-level defences remain probabilistic, so enforcement must sit outside model judgement. We present Conflux, a principal-context defence. Its kernel, ITES, derives authority from provenance and the organisation's existing access-control system and intersects the permissions of every influencing principal. We prove a conditional authority-confinement theorem: under complete mediation, no-laundering provenance, a known non-empty decision context, fresh permission checks, and action binding, the kernel admits no action that escalates privilege with respect to any recorded influencing principal. The theorem covers the represented value-influence fragment; control influence from tool, branch, recipient, or plan-step selection remains a refinement obligation. Conflux extends the kernel with independent policy ports, argument-aware authorisation, disclosure, consent, delegation, restriction, and exposure planning. We describe two system- level evaluators. SLED is a black-box evaluator: it exhaustively explores a declared finite model of a defence up to a bound. SLED-V is a white-box evaluator: it checks a serialisable intermediate representation against security and provenance properties. The evidence is bounded and partial. The appendix reports retained AgentDojo, SLED, and SLED-V results, including the limits of those runs. No result in this paper is an unbounded deployment guarantee.

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