NSEA: A Resilient ERP Framework Integrating Quantum-Safe Cryptography and Neuro-Symbolic Reasoning for Industrial Adaptability

Modern enterprise resource planning (ERP) systems confront dual challenges in mitigating quantum computing vulnerabilities and managing dynamic supply chain disruptions. This study proposes a neuro-symbolic ERP architecture (NSEA) incorporating post-quantum cryptographic protocols to enable real-time cybersecurity and adaptive operational optimization. The framework integrates CRYSTALS-Kyber lattice-based encryption with hierarchical graph neural-symbolic reasoning, achieving sub-5μs encryption latency across industrial IoT (IIoT) sensor edge nodes while maintaining 98.3% threat detection accuracy in simulated cyber-physical attacks. Validated through multi-tier consumer electronics supply chain deployments, the system demonstrates 19.8% operational cost reduction and 40.7% faster disruption recovery versus SAP S/4HANA baselines, with optimized outcomes particularly observed in Air Conditioning inventory synchronization (standard deviation reduced from 28.4% to 9.1%) and cross-plant production coordination. A digital resilience entropy metric (DRE=0.87±0.03) derived from Kolmogorov-Sinai entropy principles quantifies system stability under concurrent security breaches and logistics interruptions. Backward compatibility testing confirms 92.4% interoperability with legacy SAP MM/PP modules through dedicated API translation layers, providing a risk-averse upgrade pathway for Industry 4.0 implementations.