Functional Metrology of Complex Digital Systems

Structured Abstract Context: Modern microprocessors, characterized by their transistor density (>100M/mm²) and interconnection complexity, exhibit non-trivial collective behaviors that escape discrete logic gate models. Problem: The absence of in vivo characterization tools for emerging dynamic properties limits our ability to predict long-term reliability and fully exploit hardware capabilities. Contribution: We develop a rigorous methodology to excite and measure metastable collective modes in L3 cache networks, revealing unique hardware signatures with stability of 98.2 ± 0.8% after thermal and software artifact compensation. Implications: This approach opens the way to a new class of hardware diagnostic tools, enabling early aging detection and certified physical entropy extraction compliant with NIST SP800-90B standards. Metrology Complex Systems L3 Cache Predictive Reliability Early Detection Physical Entropy 1. Introduction: The Hybrid Nature of Digital Systems Contemporary processors operate at the frontier of multiple physical regimes, creating a fundamental hybridity that makes purely digital models insufficient for characterizing emerging properties. 1.1 Multiple Physical Regimes Definition 1: Quantum Regime At short transistor channel levels (<10nm), quantum effects become significant: tunneling, energy quantization, charge fluctuations. These phenomena impose fundamental limits on miniaturization and create intrinsic noise. Definition 2: Analog Regime In timing paths and clock circuits, signals exhibit continuous value ranges with variable propagation times. Jitter and inter-signal skews create analog behaviors. Definition 3: Collective Regime In shared structures (L1/L2/L3 caches, interconnects, memory controllers), collective modes emerge from the interaction of millions of transistors. These modes exhibit nonlinear dynamics and metastable states. 1.2 Metrology Motivation Our work is part of the broader effort to develop metrology for complex digital systems, defined as the set of methods enabling: Characterization of emerging dynamic properties in situ Quantification of hardware reliability via non-destructive signatures Prediction of long-term behavior with physical models Extraction of certified entropy for cryptographic applications Theorem 1.1: Existence of Metastable Collective Modes(...) Falsifiable Hypotheses with Experimental Protocols H1: Hardware Signature Stability Confirmed Statement: Hardware signatures extracted from L3 cache networks exhibit >95% stability over 30-day periods, after thermal and software compensation. Experimental Protocol: Select 50 CPUs from each architecture (RaptorLake, Zen4) Establish reference signature day 0 Measure daily for 30 days Calculate coefficient of variation CV = σ/μ H2: Early Aging Detection Testing Statement: The relaxation exponent α increases significantly (Δα > 0.05) before functional failures appear. H3: Inter-CPU Reproducibility Testing Statement: CPUs of the same architecture exhibit correlated signatures with r > 0.85. H4: NIST Entropy Certification Confirmed Statement: Entropy extracted from hardware signatures satisfies H_min > 3.5 bits. Main Scientific Contributions Reproducible experimental framework with thermal compensation Excitation sequence library optimized per micro-architecture Complete statistical validation pipeline compliant with NIST standards Experimental demonstration of stable hardware signatures (98.2 ± 0.8%) on 300 CPUs