AGENTIC-NETS: Typed Transition Petri Nets for Executable Orchestration of Human-Centric AI Workflows

Modern LLM orchestration frameworks (e.g., agent graphs and prompt-chaining toolkits) provide rapid prototyping but lack formal workflow semantics and analysable safety properties. Conversely, classical workflow formalisms (workflow nets, YAWL, and Colored Petri Nets) provide rigorous semantics but do not expose AI-native primitives as first-class execution units. Concurrent work has shown Petri nets can coordinate LLM agents via agent-role typing in Colored Petri Nets C1. This paper introduces AGENTIC-NETS, a typed transition vocabulary over Petri net semantics that takes a complementary design axis: typing transitions by operation kind rather than typing agents by role. The framework defines six transition types, PASS, MAP, HTTP, LLM, AGENT, and COMMAND, that compose deterministic automation, bounded AI inference, bounded autonomous loops, and isolated actuation under a single formal token-flow substrate. Transition typing enables static partitioning of any workflow into a deterministic subnet and a bounded non-deterministic subnet, supporting compositional reasoning about safety and boundedness independent of which specific LLM/provider is deployed. We introduce a constrained, inspectable inscription schema as an operational contract; explicit deterministic/non-deterministic lane boundaries encoded by transition types; provenance-typed token metadata for audit; and an event-sourced runtime architecture with poll-based isolated executors. A case study and preliminary analytical evaluation show how AGENTIC-NETS expresses an extraction→validation→trust-elevation knowledge pipeline with bounded agent iterations, observable token provenance, and structurally identifiable guardrail insertion surfaces. AGENTIC-NETS provides a practical orchestration substrate that bridges formal workflow semantics and AI-native execution constraints.