This paper reports the experimental preparation, certification, and processing of complete categories of four-qubit hypergraph states on a fully reprogrammable silicon-photonic quantum chip. Hypergraph states, which generalize graph states by allowing any subset of qubits to be arbitrarily entangled via hyperedges, represent more general resource states that enable arbitrary quantum computation with Pauli universality. The authors demonstrate genuine multipartite entanglement in hypergraph states by characterizing entanglement witnesses and observing violations of Mermin inequalities without closing distance or detection loopholes. They implement a basic measurement-based protocol and an efficient resource state verification using color-encoding stabilizers, showcasing the building blocks for hypergraph-state quantum computation. The work prototypes hypergraph entanglement as a general resource for quantum information processing, highlighting its potential for blind quantum computing and other advanced applications.This paper reports the experimental preparation, certification, and processing of complete categories of four-qubit hypergraph states on a fully reprogrammable silicon-photonic quantum chip. Hypergraph states, which generalize graph states by allowing any subset of qubits to be arbitrarily entangled via hyperedges, represent more general resource states that enable arbitrary quantum computation with Pauli universality. The authors demonstrate genuine multipartite entanglement in hypergraph states by characterizing entanglement witnesses and observing violations of Mermin inequalities without closing distance or detection loopholes. They implement a basic measurement-based protocol and an efficient resource state verification using color-encoding stabilizers, showcasing the building blocks for hypergraph-state quantum computation. The work prototypes hypergraph entanglement as a general resource for quantum information processing, highlighting its potential for blind quantum computing and other advanced applications.