LPP Admission Kernel: Formal Operational Semantics for Layer 0 AI-Triggered Action Admissibility

This preprint introduces the LPP Admission Kernel as a formal operational semantics for Layer 0 AI-triggered action admissibility. The paper builds on the first Lingua Pactum Protocol paper on constitutional admissibility and operationalizes that concept through a minimal Admission Kernel model. It defines Admission Requests, Authority Objects, Responsibility Chains, Revocation States, Risk Tiers, Admissibility Decisions, Execution Permits, and Collapse Reasons. The paper specifies a risk-tiered admissibility model, authority lifecycle, Layer 0 / Layer 1 interface, failure mode taxonomy, fail-closed semantics, and the formal decision function Admit₀(AR, G, Σ) → AD. Its central claim is that Layer 1 runtime systems should not independently determine whether an AI-triggered action is legitimate. Instead, Layer 1 systems should enforce constrained execution permits issued by Layer 0. No execution should proceed on the basis of silence, timeout, unavailable authority, incomplete responsibility chain, unverifiable permit, or malformed admissibility state.