This study demonstrates 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 arbitrary entanglement of any subset of qubits via hyperedges, represent more general resource states for quantum information processing. The research confirms genuine multipartite entanglement in hypergraph states using entanglement witnesses and Mermin inequalities, without any closure of distance or detection loopholes. A basic measurement-based protocol and efficient resource state verification using color-encoded stabilizers are implemented with local Pauli measurements to benchmark the building blocks for hypergraph-state quantum computation. The study shows that hypergraph states can be prepared using a sequence of multiqubit entangling gates, and that the quantum chip enables the on-chip generation and manipulation of these states. The chip uses a qudit-qubit mapping to encode four-qubit states into two-quartet states of photons, allowing arbitrary entangling operations. The quantum chip is capable of implementing multi-qubit controlled unitary gates, such as the CCCZ gate, with high fidelity. The study also demonstrates the efficient verification of hypergraph states using color-encoded stabilizers, which allows for the certification of state fidelity with a lower bound of 0.91. The research highlights the potential of hypergraph states as a general resource for quantum information processing, with applications in blind quantum computing and the simulation of complex quantum systems. The results demonstrate the feasibility of hypergraph-state quantum computing and provide a foundation for further advancements in quantum information processing. The study also discusses the scalability of hypergraph-state quantum devices, including the use of high-efficiency photon sources, multi-photon multi-dimensional entanglement devices, and large-scale silicon-photonic quantum circuits. The findings contribute to the understanding of complex entanglement structures in hypergraph states and the development of applications in Pauli-universal blind quantum computations.This study demonstrates 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 arbitrary entanglement of any subset of qubits via hyperedges, represent more general resource states for quantum information processing. The research confirms genuine multipartite entanglement in hypergraph states using entanglement witnesses and Mermin inequalities, without any closure of distance or detection loopholes. A basic measurement-based protocol and efficient resource state verification using color-encoded stabilizers are implemented with local Pauli measurements to benchmark the building blocks for hypergraph-state quantum computation. The study shows that hypergraph states can be prepared using a sequence of multiqubit entangling gates, and that the quantum chip enables the on-chip generation and manipulation of these states. The chip uses a qudit-qubit mapping to encode four-qubit states into two-quartet states of photons, allowing arbitrary entangling operations. The quantum chip is capable of implementing multi-qubit controlled unitary gates, such as the CCCZ gate, with high fidelity. The study also demonstrates the efficient verification of hypergraph states using color-encoded stabilizers, which allows for the certification of state fidelity with a lower bound of 0.91. The research highlights the potential of hypergraph states as a general resource for quantum information processing, with applications in blind quantum computing and the simulation of complex quantum systems. The results demonstrate the feasibility of hypergraph-state quantum computing and provide a foundation for further advancements in quantum information processing. The study also discusses the scalability of hypergraph-state quantum devices, including the use of high-efficiency photon sources, multi-photon multi-dimensional entanglement devices, and large-scale silicon-photonic quantum circuits. The findings contribute to the understanding of complex entanglement structures in hypergraph states and the development of applications in Pauli-universal blind quantum computations.