A Multi-Axis Protocol for Aggregate Redistribution, Peak Strain, Intervention Mechanism, and Transient Exposure
Data Centers as a Primary Physical Test Case
Kevin L. Brown
August 2026
Engineering interventions in coupled physical systems are commonly evaluated by whether they relieve the specific operational constraint they target. In coupled networks, however, relieving one capacity limit frequently redistributes demand or capacity margins across secondary subsystems. Prior formulations summarized this dynamic using a scalar aggregate transfer ratio $\Gamma = A/D$ balancing total relieved versus induced utilization. Adversarial review demonstrated that scalar aggregates fail in critical edge cases: an L1 ratio can misclassify dispersed low-risk load as strongly amplifying while missing a small transfer that pushes a single saturated component past its operational limit.
This manuscript establishes an updated measurement protocol that explicitly separates aggregate cross-family redistribution from peak capacity proximity, intervention mechanism, and transient exposure. The resulting core Constraint Transfer State is locked to a fixed four-dimensional vector:
$S_{\text{CT}} = (\Gamma, P_\infty, E_\infty, M^*)$
The protocol incorporates five key structural repairs:
- Dual Registry and Aggregation Operators: To prevent channel cardinality from distorting aggregate statistics, $\Gamma$ is computed strictly across $K$ frozen, non-overlapping top-level constraint families governed by reproducible physical aggregation operators $Q_k$ and $B_k$. Instantaneous feasibility ($P_\infty$) and exceedance exposure ($E_\infty$) are monitored separately across all $n$ hard-limit channels.
- Exogenous Temporal Alignment: Dynamic transfer accounting uses a preregistered system-level temporal mapping $\tau$ based on exogenous workload markers. This eliminates phase jitter from registering simultaneously as gross relief and gross induction while preserving operationally meaningful timing shifts.
- Zero-Safe Mechanism Decomposition: Utilization changes are split into demand-mediated ($\Delta p_{q,k}$) and capacity-mediated ($\Delta p_{b,k}$) contributions via an exact symmetric finite additive decomposition. This avoids logarithmic zero-load singularities and compresses system-wide mechanism dominance into a scalar Mechanism Index $M^*$.
- Throughput Indexing: The state is indexed by system throughput, $S_{\text{CT}}(u;x)$, formally linking peak strain ($P_\infty \le 1$) to maximum feasible throughput $x^*(u)$ without using $\Gamma$ as an improper surrogate for feasibility.
- Sequential Ledger: Interventions are tracked sequentially, recording transition paths, active constraint switches, and state updates across successive engineering modifications.
AI data centers—combining grid interconnection, electrical distribution, cooling, water supply, thermal rejection, rack envelopes, backup energy, and network throughput—serve as the primary physical test case.
The framework does not claim novelty for cross-system trade-offs, active-constraint switching, burden shifting, or bottleneck migration, which are established in control, life-cycle assessment, and systems engineering. Its contribution is a narrow, prospective measurement architecture evaluated through five preregistered hypotheses (H1–H5). The framework is falsifiable: to demonstrate scientific utility, the prospective state $S_{\text{CT}}$ must outperform complexity-matched generic four-dimensional summaries and remain non-inferior to a full-information benchmark on held-out prediction or intervention-ranking tasks. The manuscript presents a formal, test-ready measurement protocol open to empirical validation.