arXiv CSopen access

Sustainability-Constrained Workload Orchestration for Sovereign AI Infrastructure: A Joint Compute-Network Optimization Framework

Unknown · 2026 · arxiv_cs

arXiv CS · Papers · License: Open Access · 2026

networking, internet, protocols, distributed systems

Sustainability-Constrained Workload Orchestration for Sovereign AI Infrastructure: A Joint Compute–Network Optimization Framework Sergio Cruzesa,1

arXiv:2604.09705v1 [cs.NI] 7 Apr 2026

Optical Network Engineering, Ciena Brazil, Ciena, Av. das Nações Unidas, 14.171 – 15º andar – Marble Tower – Salas 1563/1564, São Paulo, 04794-000, SP, Brazil

Abstract AI infrastructure has transitioned from a software-centric paradigm to a system tightly bound by physical and environmental limits. Energy availability, cooling capacity, and network connectivity now impose hard operational boundaries that cannot be relaxed through software optimization alone. This paper proposes a sustainability-constrained orchestration framework that treats carbon intensity, water usage, and power capacity as strict feasibility constraints rather than tunable penalties, and that jointly optimizes compute placement and optical network routing in a single closed-loop system. We introduce the Feasible Sovereign Operating Region (FSOR)—a conceptual and operational construct that characterizes the set of workloads a given infrastructure can actually sustain under its physical and regulatory endowment. Scenario-based analysis demonstrates that joint optimization yields lower environmental impact relative to baseline formulations. Infeasibility events, rather than being optimizer failures, constitute precise, telemetry-grounded signals that sovereign AI operation requires infrastructure investment or workload reduction. Keywords: data center, sustainability, artiﬁcial intelligence

1. Introduction AI infrastructure has undergone a fundamental shift. For most of its history, progress in artiﬁcial intelligence was primarily driven by software: better algorithms, improved training procedures, and more eﬃcient model architectures. Physical infrastructure was largely a background concern, scalable by adding commodity hardware. That paradigm has changed. The emergence of large-scale foundation models and the rapid expansion of AI deployment have transformed infrastructure from a supporting layer into a primary constraint [1, 2]. Today, AI workloads at scale impose demands that directly engage physical limits. Power consumption at major AI data centers reaches levels that strain grid interconnections and 1

The views, analyses, and conclusions expressed in this paper are those of the author alone and do not represent the position, policy, or endorsement of Ciena Corporation or any of its aﬃliates. This research was conducted by the author independently in a personal academic capacity. April 14, 2026

require dedicated energy agreements [1]. Cooling requirements have outpaced the capacity of conventional air-cooling systems, driving a transition to liquid and immersion cooling with corresponding water demands [3]. The growth of AI electricity consumption has become a visible factor in national energy planning. These are not merely engineering challenges to be resolved through optimization—they deﬁne hard feasibility boundaries on where AI systems can be built, how large they can grow, and under what regulatory conditions they can operate. A data center that exceeds its local carbon budget cannot expand. A facility that exhausts its water permit cannot operate at full capacity during peak summer months. A site that saturates its grid interconnection cannot accept new workloads, regardless of compute availability or capital investment. In this context, sustainability functions as a feasibility constraint rather than an eﬃciency target. The distinction is signiﬁcant: an eﬃciency target can always be traded against other objectives; a feasibility constraint cannot. This paper formalizes that distinction and builds it into the design of an orchestration framework. AI infrastructure decisions are often treated as purely technical optimization problems, but the technology is not neutral: its impacts—and the capacity to deploy it at all—depend on regulatory frameworks, grid conditions, and institutional context [4]. Software-level openness, while valuable for reducing vendor lock-in, does not eliminate dependence on underlying compute, network, and energy infrastructure; operational autonomy requires physical feasibility, not only licensing freedom. In energy systems, AI-driven eﬃciency gains are real but unevenly distributed across regions and social groups, reinforcing the need to treat infrastructure constraints not only as engineering limits but as structural determinants of who can participate in AI-driven systems. Sustainability-aware orchestration must therefore extend beyond compute scheduling to encompass coordinated management of multi-energy infrastructure—on-site generation, storage, and thermal systems—making AI infrastructure optimization an inherently cross-domain problem [5]. 1.1. Limitations of existing approaches The dominant thread in sustainable computing addresses carbon-aware scheduling: shifting ﬂexible workloads in time toward low-carbon grid periods, or in space toward low-carbon regions [6, 7]. This approach has demonstrated meaningful reductions in grid emissions, but it operates within three systematic limitations that this work addresses. First, sustainability is typically modeled as an optimization objective—a term to be minimized subject to performance constraints. When it conﬂicts sharply with performance or cost, the optimizer trades it away. This is appropriate for preference targets but inappropriate when the sustainability limit is a regulatory or physical absolute. A penalty term cannot enforce a legal maximum; only a hard constraint can. Second, existing frameworks decouple compute placement from network routing. Placement models assume that traﬃc can be routed between any two sites at negligible cost. Routing models treat compute demand as a ﬁxed external input. In practice, the two decisions interact: placing a workload at a low-carbon site may require routing its traﬃc over a high-latency optical path that violates service requirements [8]. Solving either problem in isolation cannot ﬁnd the globally feasible solution [9]. April 14, 2026

Third, sustainability parameters are typically evaluated retrospectively, using historical or batch data. Grid carbon intensity varies on sub-hourly timescales. Water availability varies seasonally. Grid capacity ﬂuctuates with load and generation mix. A framework that makes placement decisions on stale data may violate constraints that were not visible at planning time [10]. While prior work demonstrates that digitalization can improve sustainability outcomes, this paper shows that such improvements are fundamentally bounded by infrastructure feasibility constraints. 1.2. This work This paper moves beyond optimization-based sustainability by showing that AI infrastructure is fundamentally constrained by physical feasibility. We introduce the Feasible Sovereign Operating Region (FSOR), which deﬁnes the set of workloads that can be operated under joint compute, network, and sustainability constraints. This reframes sustainability from an objective to be optimized into a boundary that determines whether operation is possible. This paper addresses all three limitations through a sustainability-constrained orchestration framework with three deﬁning properties. First, sustainability limits are modeled as hard constraints: carbon and water thresholds eliminate infeasible conﬁgurations from the solution space entirely, rather than penalizing them in the objective. Second, compute placement and optical network routing are solved jointly in a single optimization, making the coupling between placement decisions and network costs explicit. Third, the optimization operates in a closed loop driven by real-time telemetry and validated against a digital twin before any conﬁguration change is applied. A central analytical contribution is the Feasible Sovereign Operating Region (FSOR): the set of workload conﬁgurations for which the joint optimization has at least one valid solution under a given infrastructure endowment and policy regime. The FSOR makes sovereign AI capacity measurable in physical terms. When a region’s FSOR shrinks to the empty set, that region cannot sustain AI operation at the required constraint levels— independently of software capability or compute investment. The framework is grounded in the infrastructure-sovereignty perspective developed in [11], which positions sustainability as a ﬁrst-order design constraint that shapes a region’s capacity to deploy and evolve AI systems over time. The present paper operationalizes that conceptual framework into a concrete optimization formulation and an implementable control architecture. 1.3. Contributions The speciﬁc contributions of this paper are: • A formal optimization model for sustainability-constrained workload placement in which carbon intensity and water usage are hard feasibility boundaries, together with the FSOR construct that characterizes the resulting feasible space as a function of measurable physical and regulatory parameters (Section 3). April 14, 2026

• A joint compute–network formulation that couples workload assignment with optical ﬂow routing under latency and capacity constraints (Section 3). • An agentic closed-loop control architecture integrating streaming telemetry, optimization, and digital twin validation (Section 4). • Scenario-based analysis demonstrating the qualitative and comparative advantage of joint optimization under realistic infrastructure conditions (Section 5). • A sovereignty analysis mapping infrastructure endowments to FSOR boundaries (Section 6). 2. Related Work 2.1. Carbon-aware scheduling The foundational work on carbon-intelligent computing was introduced by Radovanovic et al. [6], who demonstrated that shifting delay-tolerant batch jobs toward low-carbon grid periods reduces net emissions at Google-scale deployments without degrading throughput. Cote and Sun [7] formalized locational marginal emissions as grid-granularity carbon signals, enabling spatial as well as temporal workload shifting. These contributions establish the operational feasibility of carbon-aware scheduling and provide the signal infrastructure that our framework builds on. Recent work has further demonstrated that carbon-aware scheduling alone is insuﬃcient to achieve truly low-carbon operation in datacenters. The Carbon Explorer framework shows that Net Zero accounting masks signiﬁcant hourly carbon emissions due to the intermittent and geographically variable nature of renewable energy supply [12]. Achieving 24/7 carbon-free operation requires coordinated management of multiple mechanisms, including workload shifting, energy storage, and renewable energy deployment, each introducing tradeoﬀs between operational and embodied carbon. These results highlight that carbon-aware scheduling is fundamentally constrained by energy system dynamics, reinforcing the need to treat sustainability as a feasibility condition rather than solely as an optimization objective. A complementary line of work has quantiﬁed the inherent limits of carbon-aware spatiotemporal workload shifting in large-scale cloud systems. Sukprasert et al. [13] show that even under idealized conditions with perfect knowledge of future carbon intensity and unrestricted workload mobility, the achievable carbon reductions are bounded and often signiﬁcantly lower in practice due to constraints such as limited workload ﬂexibility, latency requirements, and datacenter capacity. In particular, long-running workloads, which account for a large fraction of energy consumption, exhibit limited temporal ﬂexibility and therefore cannot eﬀectively exploit low-carbon periods. Moreover, spatial shifting beneﬁts are constrained by performance and regulatory requirements, and simple migration policies already capture most of the achievable gains. These results indicate that carbon-aware scheduling is fundamentally limited not only by energy system dynamics but also by workload characteristics and system-level constraints. April 14, 2026

However, prior work predominantly models carbon as an optimization objectivea term to be minimized subject to performance constraintsrather than as a hard feasibility limit. As a result, these approaches implicitly assume that environmentally optimal placements remain operationally achievable. In practice, this assumption breaks down under real infrastructure constraints. Limited workload ﬂexibility, latency requirements, and capacity constraints restrict the extent to which workloads can be shifted, while low-carbon sites may only be reachable via high-latency optical paths. Consequently, compute-only formulations systematically underestimate the true feasibility cost of environmental compliance. This gap highlights the need to treat sustainability not as an optimization objective, but as a boundary condition that determines whether a given workload placement is viable. 2.2. Green data center optimization Buyya et al. [14] laid the foundation for energy-eﬃcient resource management in cloud infrastructure, demonstrating virtual machine consolidation under power caps. Silva et al. [15] surveyed decarbonization strategies for high-performance computing, identifying cooling efﬁciency, renewable procurement, and carbon-aware scheduling as the principal levers. Hoxha et al. [16] speciﬁcally addressed the deployment-aware problem of carbon- and water-eﬃcient LLM serving, proposing infrastructure-aware model routing. This body of work addresses the single-site or compute-layer problem. None of these contributions jointly models the optical network layer, and none treats sustainability as a hard feasibility boundary that may render certain conﬁgurations infeasible rather than merely suboptimal. Recent work has extended data center optimization beyond compute-level resource management to include integrated energy system coordination. Nkwawir et al. [5] propose a carbon-aware workload scheduling framework that jointly optimizes IT workloads and multienergy infrastructure, including photovoltaic generation, battery storage, combined cooling, heating and power (CCHP) systems, and thermal energy storage. Their formulation, based on mixed-integer linear programming, demonstrates signiﬁcant reductions in operational emissions and energy cost through coordinated energy dispatch and workload management. A broader review of carbon-aware scheduling techniques further reveals systematic limitations in current approaches. Recent studies show that most existing methods consider either temporal or spatial workload shifting in isolation, with only a small number of works performing true joint spatio-temporal optimization [17]. Additionally, the majority of approaches focus exclusively on operational electricity, while embodied emissions associated with hardware production remain largely unaccounted for. The same studies highlight that eﬀective temporal shifting requires accurate forecasting of both workload demand and carbon intensity, and that workload shiftability itself is constrained by application characteristics such as duration, deadlines, and interruptibility. Moreover, network-related costs of workload migration are rarely modeled, despite their potential impact on feasibility. These ﬁndings indicate that existing data center optimization approaches capture only partial aspects of the problem and fail to represent the full set of constraints governing sustainable operation. April 14, 2026

Accurate forecasting of resource utilization has emerged as a critical enabler of carbonaware data center operation. Recent work proposes hybrid deep learning models that combine transformer-based architectures with recurrent networks to capture both long-range dependencies and short-term dynamics in multivariate workload patterns [18]. These approaches demonstrate that improvements in forecasting accuracy translate directly into more eﬀective carbon-aware scheduling and resource provisioning. However, these approaches remain conﬁned to either prediction or energy-layer optimization within individual data centers. They do not incorporate cross-site optimization, optical network constraints, or latency-sensitive workload placement across geographically distributed sites. As a result, they cannot capture the interaction between forecasting, placement, and network feasibility that deﬁnes the FSOR in this work. Recent empirical studies have identiﬁed multiple pathways through which AI inﬂuences energy systems, including improvements in energy eﬃciency, acceleration of green innovation, and optimization of system-level resource allocation [4]. These mechanisms reinforce the role of AI as a driver of infrastructure eﬃciency, but also highlight that its system-level impact depends on how constraints and policies are enforced. 2.3. Joint compute–network optimization Joint optimization of compute placement and network routing has been studied in mobile edge computing and content delivery contexts. Xin et al. [19] addressed load-balanced DNN inference oﬄoading in metro optical networks, treating latency and capacity as joint constraints. Gu et al. [20] provided a comprehensive survey of machine learning techniques for intelligent optical networks, covering traﬃc prediction and routing optimization. Recent advances in carbon-aware scheduling have introduced mechanisms for adapting workload placement and execution to spatiotemporal variations in grid carbon intensity. These approaches leverage real-time or forecasted carbon signals to shift workloads across time and regions, improving the carbon eﬃciency of data center operations [21]. However, they primarily operate at the compute or data center level and treat sustainability as an optimization objective rather than a hard feasibility constraint. Critically, they do not incorporate optical network constraints, routing feasibility, or latency-induced coupling between geographically distributed sites. As a result, carbon-aware scheduling remains decoupled from the network layer and cannot capture the cross-domain interactions that arise in distributed AI infrastructure. These works demonstrate the value of joint formulations but do not incorporate sustainability constraints. The speciﬁc problem of sustainability-constrained joint compute–optical optimization for AI workloads—where environmental limits directly interact with routing and placement decisions—has not been previously addressed. Recent work on carbon-aware spatiotemporal workload shifting further highlights the limitations of existing placement formulations under realistic constraints. Large-scale empirical analysis shows that while spatial workload migration can theoretically achieve substantial carbon reductions, its practical beneﬁts are signiﬁcantly constrained by latency requirements, datacenter capacity, and regulatory limitations [13]. Moreover, these studies demonstrate that simple placement policies often achieve most of the attainable gains, with April 14, 2026

more sophisticated optimization strategies providing marginal improvements. Importantly, such approaches model workload placement at the cloud level but do not incorporate optical network constraints, routing feasibility, or cross-layer interactions. As a result, they overestimate the ﬂexibility of compute placement and fail to capture the coupled feasibility problem that arises when network, latency, and sustainability constraints must be satisﬁed simultaneously. 2.4. Sovereignty and infrastructure Fratini and Hine [22] analyzed digital sovereignty as a spectrum of control bounded by technical and economic realities rather than a binary property. This perspective has been reinforced by subsequent work highlighting that sovereignty depends not only on jurisdictional or regulatory authority, but on the ability to operate infrastructure under real-world constraints. Empirical studies of compute infrastructure further show that apparent sovereignty based on data location or policy can overestimate actual control, as eﬀective autonomy depends on ownership, supply chains, and physical deployment of compute resources. Chetty et al. [23] examined the implications of sovereign AI in the context of 6G network architectures, while Cruzes [11] introduced an infrastructure-centric sovereignty framework arguing that a region’s capacity to develop and operate AI systems is determined by its physical and environmental infrastructure endowment rather than software capability alone. This framing shifts sovereignty from a legal or conceptual notion to an operational property grounded in infrastructure availability and constraints. Recent empirical studies further reinforce this infrastructure-centric view by demonstrating that the eﬀectiveness of carbon-aware workload orchestration is fundamentally limited by physical and system-level constraints. Even under idealized conditions, the achievable carbon reductions from spatiotemporal workload shifting are signiﬁcantly reduced by latency requirements, capacity limitations, and regulatory constraints [13]. These results highlight that infrastructure is not only an enabler of AI operation, but also a binding constraint that shapes the feasible set of operational strategies. As a consequence, sovereignty must be understood not only as a function of control over infrastructure, but also as a function of the constraints that govern how that infrastructure can be used in practice. Recent empirical work on the global distribution of AI compute infrastructure further sharpens this perspective by revealing a pronounced geographic asymmetry in access to compute resources. A global census of public cloud GPU infrastructure shows that a small number of countries host the majority of advanced AI compute capacity, while many regions possess only limited inference-oriented infrastructure or none at all [24]. This has led to the characterization of a “Compute North”, where countries host suﬃcient infrastructure for AI development, a “Compute South”, where infrastructure supports primarily deployment, and a “Compute Desert”, where no meaningful AI compute capacity exists. These ﬁndings demonstrate that the ability to govern, develop, and operate AI systems is not uniformly distributed, but is instead structurally constrained by the geographic availability of compute infrastructure. As a result, sovereignty is not only determined by control over infrastructure, but also by whether such infrastructure exists locally in the ﬁrst place. April 14, 2026

Recent large-scale empirical analyses of data center energy demand further quantify the magnitude of these constraints. Data center electricity consumption in the United States reached approximately 176 TWh in 2023, representing 4.4% of total national electricity use, and is projected to increase to between 325 and 580 TWh by 2028 depending on infrastructure and deployment scenarios [25]. This growth is driven primarily by AI workloads and accelerator-based systems, whose power and cooling requirements signiﬁcantly exceed those of traditional computing infrastructure. These ﬁndings highlight that AI infrastructure expansion is directly coupled to energy system capacity, cooling technologies, and grid conditions, reinforcing that sovereignty is bounded not only by ownership or control of infrastructure, but by the physical limits of the energy systems that sustain it. The present paper operationalizes this argument by casting AI infrastructure sovereignty as a constrained optimization and control problem, where joint compute placement and network routing must satisfy explicit sustainability limits, and by deﬁning the Feasible Sovereign Operating Region (FSOR) as the resulting feasibility boundary. 3. System Model and Problem Formulation 3.1. Infrastructure Model We model AI infrastructure as a coupled compute–network–energy system in which workload placement, network routing, and sustainability constraints must be satisﬁed simultaneously. The model has three layers—compute sites, optical transport, and workloads—each with its own parameter space and temporal dynamics. We describe each in turn before deﬁning the joint feasibility conditions that couple them. 3.1.1. Compute Sites Let S = {s1 , . . . , sN } denote the set of N geographically dispersed AI-oriented data center sites. Each site si is characterized at telemetry cycle t by a tuple of time-varying parameters; the three layers—compute sites, optical transport, and workloads—are described in turn before the joint feasibility conditions that couple them are deﬁned. • Pi (t): the maximum available electrical power [kW], determined by contracted grid capacity, on-site generation, and any active demand-response obligations; • γi (t): the marginal carbon intensity of the local grid [gCO2 eq/kWh], drawn from grid telemetry or forecast distributions; • ωi (t): the water usage eﬀectiveness per unit of IT load [L/kWh], a function of cooling technology, ambient temperature, and humidity; • Γ̄i : the policy-deﬁned carbon intensity ceiling [gCO2 eq/kWh] above which workload placement at si is not permitted; • Ω̄i (t): the water draw permit limit [L/h], which may tighten seasonally as described in §6.2. April 14, 2026

Power and carbon intensity are treated as rapidly varying parameters and are updated at each telemetry cycle, with a granularity of minutes to hours depending on grid operator data availability. Water intensity varies more slowly—governed by ambient conditions and cooling system dynamics—and is updated on a daily or seasonal basis. The asymmetry in temporal resolution across parameters is not merely a modeling convenience: it reﬂects the physical timescales at which each constraint can meaningfully bind. Carbon-aware scheduling can react to sub-hourly grid signals; water permit compliance must be planned over days to weeks, and an operator managing both simultaneously must therefore maintain two distinct control loops operating at fundamentally diﬀerent cadences. Sites may also diﬀer in their structural dependency proﬁle. A site operated on third-party cloud infrastructure inherits the provider’s scheduling policies and jurisdictional obligations, which may further reduce the eﬀective power headroom or introduce site eligibility restrictions that are invisible in the physical parameters above [26, 27]. We treat such external obligations as additional upper bounds on Pi (t) or as site eligibility ﬂags, and return to their sovereignty implications in §6. 3.1.2. Optical Transport Network Sites are interconnected by an optical transport network represented as a directed graph G = (S, E), where each node si ∈ S corresponds to a data center site and each directed edge (si , sj ) ∈ E represents a provisioned optical path from site i to site j. Directionality reﬂects the physical reality that each transmission direction occupies a distinct set of wavelength channels with independently provisioned capacity. Each edge is characterized by two parameters: • Cij : the transmission capacity [Gbps], determined by the spectral eﬃciency of the deployed transceivers and the number of provisioned wavelengths on the optical path; • dij : the one-way propagation delay [ms], equal to the physical ﬁber route length divided by the speed of light in the medium (c/n, where n ≈ 1.468 for standard single-mode ﬁber at 1550 nm, consistent with ITU-T G.652 [28]). The end-to-end latency for a workload routed along a multi-hop path π = (si1 , si2 , . . . , sik ) is the sum of propagation delays across consecutive hops: L(π) =

k−1 X

diℓ , iℓ+1 .

(1)

ℓ=1

Throughout this paper, λk denotes a one-way propagation budget, so the latency admissibility condition L(π) ≤ λk is evaluated against the one-way sum (1). This convention is applied consistently across all workload classes; operators adopting a round-trip convention must halve their Service Level Objective (SLO) values before applying the constraints in §3.2 and the geographic radius expressions in §3.3. This formulation treats propagation delay as the dominant latency component, which is justiﬁed for geographically distributed placements where inter-site distances are of order 102 – 103 km. At these scales, processing and queuing delays are negligible relative to propagation April 14, 2026

and are omitted from the placement model (this assumption breaks down for intra-metro or intra-campus deployments, where propagation delays fall below 1 ms and switching and queuing overhead become the dominant contributors). Where empirical hardware characterization is available, processing and queuing contributions may be incorporated as site-level additive oﬀsets to dij without altering the structure of the formulation. Propagation delay dij constitutes a hard physical ﬂoor: no routing algorithm, protocol optimization, or hardware improvement can reduce end-to-end latency below the speed-oflight bound imposed by the ﬁber route geometry [8]. This irreducibility has a structural consequence for the FSOR. The latency constraint L(π) ≤ λk partitions the set of candidate placement–routing pairs into a latency-admissible subset whose boundary is determined entirely by the physical topology of the optical network and the geographic distribution of demand—not by the sustainability proﬁle of individual sites. A site may be fully compliant with all carbon and water constraints and yet be unreachable for a latency-sensitive workload simply because no ﬁber path of suﬃcient brevity connects it to the demand source. This decoupling between sustainability eligibility and latency admissibility is the geometric origin of the green-but-far eﬀect discussed in §6.2. 3.1.3. Workload Characterization Let W = {w1 , . . . , wM } denote the set of M active workloads. Each workload wk is characterized by: • pk : the power demand [kW]; • λk : the maximum tolerable end-to-end latency [ms]; • ρk : the traﬃc demand [Gbps] injected onto the network; • µk ∈ {0, 1}: a portability indicator, equal to 1 if the workload can be spatially shifted without violating synchronization or state-transfer constraints, and 0 otherwise. In practice, portability is not a clean binary. It depends on latency tolerance, interreplica synchronization requirements, and the overhead of transferring workload state across sites. For LLM workloads, the state includes large data that must move with the workload. This includes model ﬁles, which are the trained weights of the model, checkpoints, which are intermediate saved states used to resume training or inference, and dataset shards, which are partitions of large datasets distributed across storage. Because these components can total hundreds of gigabytes or more, migrating an LLM workload requires transferring substantial data. This makes migration not only time-sensitive, but also cost- and carbon-sensitive due to network usage and energy consumption [29, 30]. We treat µk as a conservative binary indicator—a workload is portable only if its migration overhead can be bounded within acceptable latency and carbon budgets—and note that a continuous portability score could be substituted without altering the structure of the placement problem. The binary treatment is retained throughout the remainder of this paper; the continuous generalization is identiﬁed as a direction for future work in §7.3. April 14, 2026

Workload classes diﬀer systematically in their parameter distributions and constraint proﬁles: Training workloads are characterized by high pk , low µk , and high inter-accelerator bandwidth requirements that impose tight constraints on both intra-site fabric and inter-site routing. They are spatially constrained by the need for low-latency collective communication (AllReduce, AllGather) across accelerator ranks [31]. Once placed, they are eﬀectively immobile for the duration of the training run. Inference workloads have moderate pk and moderate portability in principle, but are latency-constrained in practice: the strict λk imposed by user-facing service-level objectives limits the geographic range of admissible placements to sites reachable within the one-way propagation budget. Violations are directly observable and contractually relevant [32]. Batch analytics workloads are delay-tolerant (λk large or unconstrained), highly portable (µk = 1), and represent the primary candidates for temporal and spatial shifting in response to carbon intensity or water stress signals. They form the most responsive layer of the workload portfolio for sustainability-driven scheduling [13]. 3.1.4. Migration Overhead Moving a workload from one data center to another is not instantaneous, even when the destination site is sustainability-compliant and the network path is available. Migration consumes time, energy, and network capacity—and a relocation that appears attractive on sustainability grounds may be inadvisable if its overhead erodes the very gains it was intended to achieve.2 For workloads with µk = 1, cross-site migration from si to sj incurs overheads beyond the steady-state propagation delay in (1). We model three components: 1. Data transfer delay: proportional to the workload state size σk [GB] and inversely proportional to the available transfer bandwidth Bij (t) [Gbps]: tx δijk (t) =

8 σk Bij (t)

[s],

where the factor of 8 converts σk from gigabytes to gigabits so that numerator and denominator share the same unit [Gb] and [Gbps] respectively, yielding a delay in seconds. 2

The analogy to relocating a running business is instructive: ﬁling cabinets (model weights and execution state) must be transported, the move itself consumes fuel (grid energy at the source), and staﬀ cannot resume full productivity until systems are reinstalled and institutional memory is reconstructed (cache warming, session re-establishment). Each step takes time and consumes resources; the business is not fully operational until all three are complete. April 14, 2026

2. Transfer energy: the electrical energy consumed transmitting σk across the optical link contributes a carbon cost tx ∆Cijk (t) = γi (t) · eij · 8 σk

[gCO2 eq],

where eij [J/bit] is the link energy per bit and 8 σk [Gb] is the data volume transmitted. The carbon intensity γi (t) of the source site si is used here because the transmission energy is drawn from the source-side grid during the transfer window; energy consumed at intermediate optical ampliﬁers is absorbed into eij as a per-bit cost and does not require a separate intensity term. 3. Rehydration latency: the time required to restore execution context at the destination site, which is workload-speciﬁc and may include model loading, cache warming, tx and session re-establishment. Rehydration latency is not captured by δijk and must be accounted for separately when tightening the eﬀective latency budget at the destination; see constraint (8). These overheads are especially consequential for stateful (workloads that maintain and depend on internal state such as model parameters, session data, or intermediate computations that must be preserved across execution and migration) or model-intensive workloads [29, 30]. In the placement optimization, migration costs enter as additive penalties in the objective function and as tightened eﬀective latency budgets: a workload with λk = 50 ms tx = 30 ms to migrate retains only 20 ms of latency headroom at the destinathat requires δijk tion before its service-level objective is violated. 3.2. Optimization Problem The framework makes two classes of decisions simultaneously: which site each workload should be placed at, and how the traﬃc generated by each workload should be routed through the optical network. These decisions are coupled: the carbon and water impact of a placement depends on which site is selected, while the latency experienced by a workload depends on the routing path, which in turn depends on the placement. Neither decision can be made optimally in isolation. 3.2.1. Decision Variables The optimization makes two coupled decisions at each telemetry cycle: where to run each workload, and how to route the traﬃc it generates through the optical network. These are represented by two distinct variable classes, reﬂecting the fundamental diﬀerence between a discrete placement decision — a workload class is assigned to exactly one sovereign site selected from the feasible sovereign operating region — and a continuous ﬂow decision, where traﬃc can be split across multiple optical paths in arbitrary proportions. Let xik ∈ {0, 1} denote the placement variable, equal to 1 if workload wk is assigned to site si and 0 otherwise. The domain of xik is restricted to FSOR-eligible sites: only sites si ∈ SFSOR satisfying the carbon, water, and power feasibility conditions are admitted as candidates. For a given workload wk , the vector (x1k , x2k , . . . , xN k ) encodes which of the April 14, 2026

N candidate sites hosts it; the unique-assignment constraint (5) ensures that exactly one entry equals 1. The binary nature of xik reﬂects the operational reality that a workload has a single authoritative placement at any given time, and the FSOR restriction ensures that every feasible solution is sovereign by construction — no post-hoc feasibility ﬁlter is required. Let fijk (t) ≥ 0 denote the continuous ﬂow variable representing the traﬃc volume [Gbps] of workload wk routed along directed edge (si , sj ) at telemetry cycle t. Unlike placement, routing admits fractional solutions: traﬃc from a single workload may be split across multiple optical paths, and the ﬂow variables capture this ﬂexibility. The time index t reﬂects that routing decisions are re-evaluated at each telemetry cycle in response to changing link utilization and workload demand. The full decision vector is (x, f ), where x ∈ {0, 1}N ×M collects all placement decisions |E|×M across the N FSOR-eligible sites and M workloads, and f ∈ R≥0 collects all routing ﬂows across the |E| directed edges and M workloads. The two components are not independent: the placement x determines the source node of each workload’s traﬃc, which in turn constrains the feasible ﬂow patterns in f through the ﬂow-conservation constraint (10). This coupling is the formal reason why placement and routing must be optimized jointly rather than sequentially. 3.2.2. Objective Function The objective is to minimize the aggregate environmental impact across all active workloads, combining carbon emissions and water consumption into a single weighted criterion: min α x, f

X X i∈S k∈W

γ̃i (t) pk xik + (1 − α)

X X

ω̃i (t) pk xik ,

(2)

i∈S k∈W

where γ̃i (t) and ω̃i (t) are the site-level carbon intensity and water usage eﬀectiveness, normalized to a common dimensionless scale so that the weighted sum is commensurable.3 In the non-normalized parameterization, γi (t) [gCO2 eq/kWh] and ωi (t) [L/kWh] are obtained directly from grid telemetry and facility monitoring respectively, and pk [kW] is the power demand of workload wk . The scalar α ∈ [0, 1] is an operator-deﬁned weight reﬂecting the relative priority of carbon versus water reduction; it absorbs any residual unit-scaling factor required to make the two terms comparable. Setting α = 1 recovers a pure carbon minimization objective; α = 0 minimizes water consumption alone; intermediate values allow Pareto-eﬃcient trade-oﬀs between the two dimensions to be traced by parametric variation of α. The routing variables f do not appear explicitly in the objective. Assumption A1 : network transport energy is treated as a second-order contributor to site-level carbon cost 3

Normalization is performed site-wise using min-max scaling across the observed range of γi and ωi over the planning horizon: γ̃i = (γi − γmin )/(γmax − γmin ), and analogously for ω̃i . This maps each parameter to [0, 1] independently, eliminating the unit incompatibility between [gCO2 eq/kWh] and [L/kWh] without requiring a physical conversion factor. The companion optimization paper provides a sensitivity analysis of objective sensitivity to the choice of normalization method. April 14, 2026

relative to compute load at the inter-site distances considered. This assumption is motivated by the energy proﬁle of modern long-haul optical transport, where ampliﬁed WDM links operate at link-level energy intensities of order 10−1 –100 pJ/bit [33], several orders of magnitude smaller than the per-bit energy equivalent of GPU compute at typical AI workload power densities. The assumption may not hold at very high migration data volumes (large σk ) or on legacy links with high energy per bit; in those conﬁgurations, a network P P transport term of the form (i,j)∈E k∈W γi (t) eij fijk (t) can be added to (2) without altering the constraint structure. Under Assumption A1, routing decisions are governed entirely by the capacity and latency constraints (9)–(10). The formulation focuses on carbon and water as the primary environmental objectives, reﬂecting that these two dimensions are subject to the hardest regulatory constraints in current and emerging frameworks and are most directly tied to physically observable telemetry parameters. Geo-distributed scheduling frameworks that additionally incorporate energy cost and quality-of-service metrics conﬁrm the inherently multi-dimensional nature of sustainable AI orchestration and represent natural extensions of the present formulation [16]. 3.2.3. Hard Constraints versus Penalty Encoding The central modeling decision is the treatment of sustainability limits. Rather than penalizing high-carbon or high-water placements in the objective function—a soft encoding that allows violations at suﬃcient cost—the framework encodes them as hard constraints that eliminate non-compliant conﬁgurations from the feasible region entirely. This distinction is not merely technical: it reﬂects the legal and physical reality that regulatory maxima are not preferences to be traded against, but absolute limits whose violation carries legal, ﬁnancial, and reputational consequences that cannot be oﬀset by environmental performance on other dimensions. The carbon constraint eliminates site si from consideration for all workloads whenever its grid intensity exceeds the site-level threshold. In the MILP, this is implemented as a preprocessing variable ﬁxing evaluated from the telemetry snapshot before the solve: h

xik ≤ 1 γi (t) ≤ Γ̄i

∀ i ∈ S, k ∈ W,

(3)

where 1[·] is an indicator that equals 1 if the condition holds and 0 otherwise, and is evaluated from telemetry data prior to invoking the solver. When γi (t) > Γ̄i , the upper bound on xik is set to zero for all k, eﬀectively removing site si from the feasible set before optimization begins. Commercial solvers such as Gurobi and CPLEX handle such bound ﬁxings in the presolve phase at negligible computational cost, and the reduced problem passed to the branch-and-bound engine is smaller by all variables associated with the excluded site [34]. The carbon gate is site-level: once γi (t) exceeds Γ̄i , the site is ineligible for any workload regardless of power demand, because grid carbon intensity is independent of what is being computed. Water draw is proportional to the aggregate IT load placed at a site, not to individual workload assignments in isolation. The correct formulation is therefore an aggregate linear April 14, 2026

inequality, analogous to the power capacity constraint (6): ωi (t)

pk xik ≤ Ω̄i (t)

∀ i ∈ S.

(4)

k∈W

This constraint ensures that the total water draw at site si — the product of water usage eﬀectiveness ωi (t) [L/kWh] and aggregate IT power [kW] — does not exceed the site’s permit limit Ω̄i (t) [L/h]. Unlike the carbon gate, which produces a binary site exclusion, (4) deﬁnes a polyhedral feasibility boundary over the placement vector: as the aggregate power of co-located workloads approaches the permit headroom, additional placements at that site become infeasible, but placements that individually respect the remaining headroom remain admissible. This is qualitatively distinct from the all-or-nothing carbon exclusion: a site subject to a binding water constraint is not eliminated from the feasible set but rather has its eﬀective hosting capacity reduced as a function of the workload composition assigned to it. The structural diﬀerence between (3) and (4) has a direct consequence for the FSOR geometry. Carbon thresholds produce discrete, discontinuous contractions of the feasible set: a site is either eligible or it is not, and a marginal increase in γi (t) past Γ̄i removes it entirely. Water constraints, by contrast, produce a progressive polyhedral tightening that depends on the composition of the active workload set: adding a power-intensive workload to a site may exhaust the remaining permit headroom and render subsequent placements at that site infeasible, even though no individual workload alone exceeds the limit. To see why, consider that the water constraint accumulates across all workloads assigned to site si : each placement xik = 1 consumes a share ωi (t) pk of the site’s water permit Ω̄i (t), and the residual headroom shrinks accordingly. A workload wk′′ that would be perfectly admissible in isolation — because ωi (t) pk′′ ≤ Ω̄i (t) — may become infeasible once a prior power-intensive assignment xik′ = 1 has already claimed a large fraction of that budget. In geometric terms, each placement tightens one face of the feasible polytope in x-space, progressively shrinking the region of admissible joint assignments. This is qualitatively diﬀerent from the carbon gate, which acts as a site-level switch independent of workload composition: no combination of workloads at site si can rehabilitate a site whose grid intensity exceeds Γ̄i . The practical implication is that water feasibility is an emergent property of the joint placement decision x, not a property that can be checked workload by workload in isolation. These constraints produce the discrete and polyhedral FSOR geometry in §6.1. described P The soft-penalty alternative—adding βγ max(0, γi (t) − Γ̄i ) and βω max 0, ωi (t) k pk xik −

Ω̄i (t) to the objective—preserves the convex structure of the relaxed problem and may be preferable in settings where constraints represent operational targets rather than regulatory ﬂoors, or where the hard feasible set would otherwise be empty and a best-eﬀort solution is required. However, the penalty weights βγ and βω require calibration that is neither transparent to the operator nor derivable from physical or regulatory parameters: their choice determines whether violations are tolerated in practice, and a poorly chosen β can produce solutions that nominally minimize the objective while systematically violating regulatory limits at low penalty cost. The choice between hard and soft encoding is therefore a design April 14, 2026

parameter that must be made explicit and justiﬁed against the regulatory context of the deployment. We adopt hard constraints throughout as the conservative default, consistent with the interpretation of carbon and water limits as binding regulatory obligations rather than cost terms. 3.2.4. Constraint Set The notation o(k) and d(k), used throughout the routing constraints below, denote respectively the source index of workload wk —the site at which it is placed, as determined by x—and the destination index of the demand-serving endpoint to which its traﬃc must be delivered. These indices are workload-speciﬁc functions of the placement vector and are used consistently in the ﬂow conservation constraint (10) and in the FSOR deﬁnition of §3.3. Subject to the sustainability gate (3) and the water capacity constraint (4), the optimization must simultaneously satisfy the following constraints. Unique assignment: each workload is placed at exactly one site: X

xik = 1

∀ k ∈ W.

(5)

i∈S

Power capacity: the aggregate power demand of workloads placed at site si must not exceed its available electrical capacity: X

pk xik ≤ Pi (t)

∀ i ∈ S.

(6)

k∈W

Latency: the end-to-end propagation latency experienced by workload wk must not exceed its service-level objective λk : L(πk ) ≤ λk

∀ k ∈ W,

(7)

where πk is the routing path selected for wk and L(πk ) is deﬁned by (1). In the MILP, this constraint is linearized using an arc-based formulation in which the latency accumulated along active ﬂow arcs is tracked as an auxiliary variable, following standard practice for delay-constrained ﬂow problems [35]. For portable workloads (µk = 1) subject to migration, the eﬀective latency budget is rh tx introduced and the rehydration latency δjk reduced by both the data transfer delay δijk in §3.1. The admissible placement set at the destination is therefore restricted to sites satisfying: tx rh L(πk ) + δijk (t) + δjk ≤ λk . (8) rh [s] denotes the rehydration latency at destination site sj for workload wk , covering Here δjk model loading, cache warming, and session re-establishment. Both overhead components are subtracted from the available latency budget before the routing constraint is evaluated; tx rh a workload with λk = 50 ms that requires δijk = 20 ms and δjk = 10 ms to migrate retains only 20 ms of propagation headroom at the destination. Network capacity: the aggregate traﬃc on each directed optical link must not exceed its transmission capacity: X fijk (t) ≤ Cij ∀ (si , sj ) ∈ E. (9) k∈W

April 14, 2026

Flow conservation: routing ﬂows must be conserved at every node. Using the net-outﬂow convention, the ﬂow balance at each site si for workload wk at telemetry cycle t is: X

fijk (t) −

   +ρk

fjik (t) =

j: (sj ,si )∈E

j: (si ,sj )∈E

  

if i = o(k), if i = d(k), otherwise,

−ρk 0

(10)

where ρk [Gbps] is the traﬃc demand of workload wk . The left-hand side counts net ﬂow leaving site si for workload wk : it is positive at the source (traﬃc is injected), negative at the destination (traﬃc is absorbed), and zero at all intermediate transit nodes. Routing decisions are re-evaluated at each telemetry cycle t; the time index is carried consistently on all ﬂow variables fijk (t) throughout this formulation. Remark 1 (Source index linearization). The source index o(k) in (10) depends on the placement vector x, which is itself a decision variable. Naively substituting o(k) as a function of x would introduce a bilinear product between the binary placement variables and the continuous ﬂow variables, destroying the linear structure of the MILP. This is resolved by expanding the right-hand side of (10) using a standard big-M linking formulation: for each candidate source site si , the injection term +ρk is activated if and only if xik = 1, yielding the equivalent linear constraint X j: (si ,sj )∈E

fijk (t) −

fjik (t) = ρk xik − xd(k),k

∀ i ∈ S, k ∈ W,

(11)

j: (sj ,si )∈E

where xd(k),k = 1 if site si is the destination of workload wk and 0 otherwise. Because xik ∈ {0, 1}, the right-hand side evaluates to +ρk at the unique source, −ρk at the destination, and 0 at all other sites, recovering the case structure of (10) exactly. The linearized form (11) is what is passed to the solver; (10) is retained in the text for expository clarity. 3.2.5. The Green-But-Far Tension The interaction between the sustainability gate (3) and the water capacity constraint (4) on one side, and the latency constraint (7) on the other, is the central tension the framework must navigate, and gives rise to what we term the green-but-far eﬀect: the sites that are most sustainability-compliant are often geographically remote from demand sources, and the propagation delay ﬂoor imposed by the ﬁber route geometry may place them beyond the latency budget of sensitive workloads. The eﬀect operates in both directions. Excluding high-carbon or high-water sites from the feasible set may force workloads onto geographically distant sites with longer optical paths, potentially violating latency service-level objectives. Conversely, anchoring latency-sensitive workloads to nearby sites may leave no local option that satisﬁes carbon or water thresholds, producing a feasibility gap that neither placement nor routing optimization alone can close. The sovereignty implications of this eﬀect — in particular, the structural asymmetry it creates between latency-sensitive and delay-tolerant workload classes — are developed in §3.3.4. This tension cannot be resolved by optimizing placement and routing independently. A placement that appears optimal in isolation may induce routing paths that violate latency April 14, 2026

Figure 1: The green-but-far eﬀect as a constraint geometry. Panel A shows the two-dimensional space of candidate sites partitioned by the carbon/water sustainability threshold Γ̄i (green dashed line) and the latency budget λk (red dashed line). The FSOR interior (green region) is the intersection of the sustainability-eligible and latency-admissible half-planes; the green-but-far zone (orange region) contains sites that satisfy all sustainability constraints but lie beyond the propagation-delay radius admitted by the latency SLO. Panel B maps the three workload classes onto the same constraint space. Inference workloads (tight latency SLO) are conﬁned to the FSOR interior and cannot reach green-but-far sites regardless of their sustainability proﬁle. Batch workloads (relaxed latency) can exploit delay-tolerant shifting to reach sustainability-compliant remote sites. Training workloads are immobile once placed and cannot be shifted in response to sustainability signals. The two boundary lines are governed by independent physical mechanisms — grid carbon intensity and ﬁber propagation geometry — and cannot be jointly relaxed through software optimization alone; this is the structural reason why joint placement–routing optimization is required.

or link capacity constraints; a routing that is eﬃcient given a ﬁxed placement may become infeasible when that placement is revised under sustainability pressure. Joint optimization over (x, f ) is therefore not merely a computational convenience but a structural necessity: it is the minimal formulation in which the green-but-far eﬀect is representable as a constraint interaction rather than a post-hoc correction. The coupling is encoded in constraint (7), which links the binary placement variable xik to the continuous routing path πk through the propagation delay along the selected path, making the two decisions jointly constrained rather than separable. When no feasible (x, f ) exists that satisﬁes all constraints simultaneously, the current April 14, 2026

workload conﬁguration lies outside the FSOR under the prevailing telemetry snapshot. This is not an error condition but an informative signal: it identiﬁes the precise combination of constraints whose simultaneous binding renders operation infeasible, providing the operator with a minimal description of what would need to change to restore feasibility. In operational deployments, infeasibility should trigger either workload deferral (for delay-tolerant batch workloads, which can wait for a more favorable telemetry snapshot) or an explicit constraint relaxation protocol in which the operator selects which limit to relax and by how much, guided by the binding constraint set returned by the solver. The formal structure of this relaxation—and its interpretation as an Irreducible Infeasible Set—is discussed in §7.2. Infeasibility is treated as part of the solver output rather than pre-empted through objective penalization, consistent with the hard-constraint encoding adopted throughout. 3.2.6. Problem Class and Tractability The formulation (2)–(10) is a mixed-integer linear program (MILP) [36]: the placement variables xik are binary, the routing ﬂow variables fijk (t) are continuous, and all constraints are linear in (x, f ). The integrality of x makes the problem NP-hard in general, by reduction from capacitated facility location [37, 38]: the workload placement subproblem shares the same binary assignment structure as the capacitated plant location problem, and NP-hardness follows directly from that reduction. The block structure—binary placement coupled to continuous routing through the capacity and latency constraints—is, however, well suited to decomposition. Tractability at these scales is driven by the strong pruning induced by the sustainability and latency gates, which reduce the eﬀective binary search space before branch-and-bound exploration. For the scenario sizes considered in this work (up to N = 8 sites and |W| = 20 workload classes per telemetry cycle), the problem is tractable with open-source MILP solvers within operationally relevant timescales. In Python/PuLP experiments on a standard workstation, all representative instances at these dimensions were solved to certiﬁed optimality (Table 1): median solve time was under 0.2 s for N ≤ 6, and under 60 s for the full N = 8, |W| = 20 scale—well within a ﬁve-minute telemetry cycle. Scaling to continental deployments with N ≫ 102 candidate sites, ﬁne-grained routing topologies, and rolling time horizons requires more scalable solution methods. Benders decomposition provides a natural way to exploit the structure of the problem by separating placement and routing decisions into two interacting subproblems [39, 40]. The method proceeds iteratively. First, a master problem selects a candidate placement, assigning workloads to sites subject to sustainability and capacity constraints. Given this placement, a subproblem is then solved to determine whether the resulting traﬃc can be feasibly routed through the optical network under capacity and latency constraints. If the routing subproblem is feasible, the current placement is valid. If it is infeasible, the subproblem generates a constraint, known as a Benders cut, that rules out the current placement and similar infeasible conﬁgurations. This cut is added to the master problem, which is then re-solved to produce a new placement. Through this iterative exchange, the method progressively eliminates infeasible regions of the search space and converges to a jointly feasible solution without solving the full placementrouting problem in a single April 14, 2026

Table 1: Solve-time benchmark for the FSOR MILP (§3.2), solved with the open-source CBC solver via Python/PuLP 3.3 on a standard workstation. Each row reports statistics over ﬁve randomised instances drawn from the same parameter distributions used in §5. All instances were solved to certiﬁed optimality. The telemetry cycle budget is 300 s (5 min).

Variables

Solve time [s]

Scenario

Binarya

Continuousb

Opt.c

Min

Median

Mean

Max

Small Medium Paper

4 6 8

10 15 20

≤ 40 ≤ 90 ≤ 140

120 450 1 120

5/5 5/5 5/5

0.02 0.04 0.11

0.02 0.07 0.12

0.03 0.17 18.39

0.06 0.58 60.00

Telemetry cycle budget (5 min)

300 s

Active binary placement variables xik after preprocessing: the carbon gate (3) and latency gate (7) ﬁx infeasible xik = 0 before the solver is invoked, reducing the binary search space below the nominal N × M count. b Continuous routing ﬂow variables fijk (t); equal to |E| × M for the complete directed graph (|E| = N (N − 1)) used here. c Trials solved to certiﬁed optimality out of ﬁve; all ﬁve instances at every scale were solved to optimality. The two longest runs in the N = 8, M = 20 scenario (31 s and 60 s) reﬂect worst-case branching behavior on speciﬁc random seeds; both remain well within the 300 s telemetry cycle budget.

step [41]. For settings where strict optimality is not required, Lagrangian relaxation oﬀers a practical way to reduce computational complexity [42]. The key idea is to temporarily relax the constraints that couple placement and routing, and instead incorporate them into the objective function using penalty multipliers. In this relaxed problem, violations of the coupling constraints are allowed, but they incur a cost, which makes the problem easier to solve because it separates into simpler subproblems. This approach provides a lower bound on the optimal solution, and by adjusting the penalty multipliers iteratively, it is often possible to recover high-quality feasible solutions that are close to optimal. In practice, this means that instead of solving the full joint problem exactly, one can solve a sequence of simpler problems and combine their results. The eﬀectiveness of Lagrangian relaxation depends on how well the relaxed problem approximates the original one. When the problem structure is well aligned with the relaxation, the gap between the relaxed solution and the true optimum, known as the duality gap, is often small. However, for general mixed-integer problems, especially non-convex ones, this gap cannot be guaranteed to vanish, and solution quality must be evaluated empirically [43]. For very large instances where even decomposition-based methods are computationally prohibitive, learning-based approximation oﬀers a complementary route to scalability, at the cost of relinquishing provable feasibility guarantees; this direction is discussed in §7.3.

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3.3. The Feasible Sovereign Operating Region 3.3.1. Formal Deﬁnition |E|×M Let X = {0, 1}N ×M denote the space of placement conﬁgurations and F = R≥0 the space of routing ﬂows. Let Wtotal denote the universe of all workloads that could potentially be submitted to the infrastructure; the active workload set W(t) ⊆ Wtotal is the subset present in the system at telemetry cycle t. Given a telemetry snapshot n

θ(t) = Pi (t), γi (t), ωi (t), Ω̄i (t), Cij , dij

o i∈S, (i,j)∈E

that encodes site-level sustainability and power parameters and network-level capacity and delay parameters, deﬁne the feasible set of the constraint system (3)–(10) as:

Φ W(t), θ(t)

(x, f ) ∈ X × F (3)–(10) are satisﬁed ,

(12)

that is, the set of all placement–routing pairs that simultaneously satisfy every constraint in §3.2 under the infrastructure state θ(t) and active workload set W(t). The carbon ceiling Γ̄i is treated as a ﬁxed regulatory parameter and is not time-indexed in θ(t); its evolution over planning horizons (as regulatory frameworks tighten) is a distinct multi-period problem discussed in §3.3.3. The Feasible Sovereign Operating Region is then deﬁned as the collection of workload conﬁgurations for which this feasible set is non-empty:

FSOR θ(t)

W(t) ⊆ Wtotal Φ W(t), θ(t) ̸= ∅ .

(13)

The FSOR is a subset of the power set of Wtotal , parameterized by the telemetry state θ(t). A workload conﬁguration W(t) lies inside the FSOR if and only if there exists at least one valid assignment of workloads to sites and a corresponding routing of their traﬃc that jointly satisﬁes all physical and regulatory constraints. Crucially, the FSOR is deﬁned by joint feasibility across all constraint classes—sustainability, latency, power capacity, and network capacity—not by the satisfaction of any single constraint in isolation: a conﬁguration that is carbon-compliant but latency-infeasible lies outside the FSOR just as surely as one that violates a power cap. The qualiﬁer sovereign reﬂects an operational interpretation that goes beyond technical feasibility: the FSOR characterizes what a region can operate under its own physical and regulatory endowment without depending on infrastructure or policy concessions from external actors. The full development of this interpretation, and its implications for infrastructure investment and regional AI capacity, is deferred to §6. 3.3.2. Geometric Structure The constraint set of §3.2 partitions the feasible space into four qualitatively distinct regions, whose geometric character we now describe. The boundary of the FSOR is not a single smooth surface but the intersection of these regions, each carved out by a distinct constraint class. Because the FSOR is deﬁned over the combinatorial space of workload April 14, 2026

conﬁgurations rather than a continuous vector space, its “geometry” is discrete and setvalued: constraints either admit or exclude entire subsets of conﬁgurations, and the overall feasible set is their intersection. Carbon gate (3) and water capacity constraint (4). The carbon gate acts as a sitelevel eligibility ﬁlter: when γi (t) exceeds Γ̄i , the site is removed from the feasible set entirely via the preprocessing bound ﬁxing described in §3.2.3, and every workload conﬁguration that requires placement at si —whether because of power, latency, or routing considerations—is simultaneously excluded from the FSOR. The eﬀect is a discrete, discontinuous contraction of the feasible set: the site is either eligible or it is not. The water capacity constraint (4), by contrast, deﬁnes a linear inequality over the aggregate placement vector and produces a polyhedral tightening rather than a binary exclusion: as cumulative IT load at a site approaches the permit limit, additional placements at that site become infeasible while lighter conﬁgurations may remain admissible. Power capacity (6). This constraint deﬁnes a set of linear inequalities over the placement variables. The feasible region in placement space has a polyhedral structure; as power headroom tightens at a given site, the feasible conﬁgurations involving that site are progressively eliminated, while conﬁgurations that do not rely on it are unaﬀected. The water capacity and power capacity constraints are structurally parallel: both impose polyhedral boundaries whose tightness depends on the composition of the active workload set assigned to each site. Latency (7). This constraint partitions the set of placement–routing pairs into latencyadmissible and latency-inadmissible subsets. This partition is determined entirely by the physical topology of the optical network and the geographic distribution of demand, independently of the sustainability proﬁle of individual sites. Throughout this paper, we adopt the one-way propagation convention: λk denotes the one-way latency budget, and only sites reachable within a propagation delay of λk are admissible for workload wk , corresponding to a geographic radius of λk · c/n, where c/n is the speed of light in ﬁber [8]. Network capacity (9) and ﬂow conservation (10). These constraints impose joint conditions on placement and routing that cannot be evaluated on either dimension alone. A placement that is individually feasible at each site may become globally infeasible when the induced traﬃc pattern exceeds link capacity on shared optical paths, creating interactions between workload assignments that are invisible to single-site analysis. The FSOR is the intersection of the feasible sets deﬁned by each constraint class. This intersection structure has two immediate consequences. First, relaxing any single constraint expands the FSOR monotonically in the set-inclusion sense: a less stringent carbon threshold admits more sites, a relaxed latency objective admits more placements, a higher link capacity admits more routing conﬁgurations. This expansion may itself be discontinuous — April 14, 2026

re-admitting a previously excluded site can restore feasibility for a large number of workload conﬁgurations simultaneously. Second, tightening any single constraint contracts the FSOR, and the contraction may be disproportionate: a marginal tightening of the carbon threshold that eliminates one high-carbon site may remove a large fraction of the FSOR if that site was the only feasible host for several latency-constrained workloads. The asymmetry between these two consequences—smooth relaxation beneﬁts versus potentially catastrophic tightening eﬀects—has direct implications for infrastructure investment planning and regulatory threshold design, as discussed in §6. 3.3.3. Dynamic Evolution The FSOR is not a static property of infrastructure but a time-varying set whose boundary evolves continuously, driven by the dynamics of θ(t). Three distinct timescales govern this evolution, each associated with a diﬀerent subset of the infrastructure parameters and a diﬀerent planning response. Sub-hourly: grid carbon dynamics. Grid carbon intensity γi (t) varies with generation dispatch and demand ﬂuctuations, sometimes by a factor of two or more within a single day [6, 7]. During periods of high renewable output, sites previously excluded by the carbon gate re-enter the feasible set; during evening demand peaks or low-wind periods, they may be excluded again. The FSOR therefore expands and contracts on sub-hourly timescales, creating what may be termed temporal arbitrage opportunities: windows during which the FSOR is larger than average, into which delay-tolerant batch workloads can be shifted to exploit lower-carbon grid conditions without violating their relaxed latency budgets. Network link utilization also ﬂuctuates on this timescale and can transiently tighten the routing feasibility component of the FSOR. Daily to seasonal: water availability and cooling eﬃciency. Water permit limits Ω̄i (t) and ambient cooling eﬃciency ωi (t) evolve on daily and seasonal timescales, driven by temperature, humidity, and hydrological conditions. Summer months in water-stressed regions produce systematic FSOR contraction as permit headroom narrows and evaporative cooling draws more water per unit of IT load. Unlike carbon intensity ﬂuctuations, this contraction is largely predictable from climate and hydrometeorological data, making it amenable to anticipatory capacity planning rather than reactive scheduling, as discussed in §6.2. Annual to decadal: regulatory and climate trajectories. Policy thresholds Γ̄i evolve as regulatory frameworks tighten over time, as contemplated in the trajectory of EU digital infrastructure sustainability targets [44] and the national AI strategies that couple sustainability obligations to infrastructure investment [45]. Two structural forces operate in opposing directions on this timescale. Grid decarbonization reduces γi (t) systematically over multi-year horizons as fossil generation is displaced by renewables, expanding the carbon-eligibility component of the FSOR. Climate change, by contrast, shrinks the water-availability envelope Ω̄i (t) over decadal timescales through longer and more severe dry seasons [46], contracting the water-feasibility component. April 14, 2026

The net trajectory of the FSOR depends on the relative pace of these two forces and will vary signiﬁcantly by region. This multi-timescale structure implies that the FSOR should be evaluated not as a single snapshot but as a trajectory: a time-varying feasibility boundary whose evolution reﬂects the joint dynamics of the grid, climate, and regulatory environment. Infrastructure investment decisions—site selection, cooling technology, renewable procurement, and network topology—alter this trajectory and should therefore be evaluated against projected FSOR evolution over the intended operational lifetime of the facility, not only against current conditions [47]. A region whose FSOR is adequate today may face binding constraints within a planning horizon as carbon thresholds tighten and water stress intensiﬁes; conversely, grid decarbonization may expand the FSOR suﬃciently to admit workload classes that are currently infeasible. The multi-period investment planning implications of this trajectory are identiﬁed as a direction for future work in §7.3. 3.3.4. Two Sovereignty-Limiting Mechanisms Two structural mechanisms dominate FSOR contraction and merit explicit treatment. Both are illustrated in Figure 3,4 which shows how each mechanism produces a qualitatively distinct pattern of feasibility loss across three representative infrastructure proﬁles. The ﬁrst is sustainability-driven fragmentation. As carbon or water thresholds tighten, sites are removed from the feasible set discretely. When the remaining compliant sites are geographically sparse or poorly connected by the optical network, the feasible placement– routing space fragments: workload conﬁgurations that required co-placement or low-latency routing across multiple sites may ﬁnd no feasible assignment within the reduced site set, even though each remaining site individually satisﬁes all constraints. Fragmentation reduces not only the number of feasible conﬁgurations but also their robustness: the remaining feasible assignments may be sensitive to small workload additions or telemetry changes that push the active conﬁguration outside the FSOR, leaving little margin for demand growth or constraint tightening. The second is the green-but-far eﬀect, introduced in §3.2.5 as a constraint interaction and examined here from the perspective of its sovereignty consequences. Sustainability-compliant sites may be geographically remote from demand sources. The propagation delay ﬂoor imposed by the optical network—irreducible below the speed-of-light bound [8]—means that latency-sensitive workloads cannot use these sites regardless of their sustainability proﬁle. The FSOR boundary for latency-sensitive workload classes is therefore determined jointly by the sustainability eligibility of sites and their geographic proximity to demand. These two criteria may be in systematic tension in regions where clean-energy resources are concentrated far from population centers, a geographic pattern that is empirically well-documented for wind and solar generation in Europe and North America [48]. Remark 2 (Asymmetric contraction). When these two mechanisms interact—sustainability thresholds fragment the site set, and the remaining compliant sites are remote—the FSOR 4

Figure 3 is introduced in §6.1. April 14, 2026

may contract to empty for latency-sensitive workloads while remaining non-empty for delaytolerant batch workloads. This asymmetric contraction is not merely a scheduling inconvenience: it is the formal expression of a sovereignty constraint. Sovereignty over a class of AI workloads requires the ability to operate that class locally under prevailing physical and regulatory conditions. If latency-sensitive workloads fall outside the FSOR while batch workloads remain inside it, the infrastructure cannot sustain real-time AI services under local control—regardless of the compute capacity nominally available. Identifying which workload classes fall inside and outside the FSOR under a given telemetry snapshot is therefore a direct, operationally grounded measurement of the scope and limits of sovereign AI capacity. 3.3.5. Infeasibility as a Sovereignty Signal When the active workload set W(t) lies outside the FSOR—that is, when Φ W(t), θ(t) = ∅—no valid placement–routing pair exists under current conditions. The solver returns an infeasibility certiﬁcate: a minimal description of the constraints whose simultaneous binding renders the problem unsolvable, formally corresponding to an Irreducible Infeasible Set (IIS) of the constraint system [49]. Rather than returning a constraint-violating placement, the framework surfaces this certiﬁcate directly to the operator. This is a deliberate design choice: a policy-violating assignment would conceal the sovereignty gap behind a technically invalid solution, whereas the infeasibility certiﬁcate makes the gap explicit and actionable. Infeasibility should be interpreted as a telemetry-grounded signal with two qualitatively distinct readings, corresponding to the sub-hourly and structural timescales identiﬁed in §3.3. The ﬁrst is transient infeasibility: the FSOR is non-empty at other points in its temporal trajectory, and the current snapshot reﬂects a temporary period of elevated carbon intensity, water stress, or link congestion. The appropriate operational response depends on workload class: delay-tolerant batch workloads should be deferred until a forecast FSOR expansion creates a compliant scheduling window, while portable workloads with imminent deadlines may be pre-emptively migrated to compliant sites ahead of the constraint binding. Both responses rely on the forecast-based state estimation described in §4.2, which provides shorthorizon predictions of θ(t + ∆) that allow the orchestrator to anticipate FSOR contraction before it occurs [6]. The second is structural infeasibility: the FSOR is empty or severely contracted across all telemetry snapshots within the planning horizon, reﬂecting a fundamental and persistent mismatch between workload requirements and infrastructure endowment. This is not a scheduling problem but an infrastructure investment problem. The infeasibility certiﬁcate provides a precise characterization of the gap: which constraints are simultaneously binding, which sites are excluded and on what grounds, and what minimum infrastructure additions or policy adjustments would restore feasibility. Concretely, the IIS identiﬁes whether the binding limitation is carbon eligibility (too few low-carbon sites), water headroom (permit limits too tight for the workload power proﬁle), latency admissibility (no compliant site within the propagation-delay radius), or network capacity (insuﬃcient link bandwidth to route the required traﬃc). Each binding constraint points to a diﬀerent investment lever. April 14, 2026

Used in this way, the FSOR and its infeasibility boundary become a planning instrument: a quantitative, telemetry-grounded basis for sovereign AI infrastructure investment that is anchored in physical and regulatory constraints rather than in abstract capacity targets. The sovereignty implications of this planning role are developed in §6, where the FSOR is used to characterize the structural asymmetries in AI infrastructure capacity across regions with diﬀerent endowments. 4. Agentic Control Architecture 4.1. Overview The optimization problem formulated in §3 is not solved once in isolation: it is embedded in a closed-loop control system that continuously monitors the physical AI infrastructure and acts on it at each telemetry cycle. The architecture, illustrated in Figure 2, realizes sustainability-constrained AI infrastructure operation as a cross-domain control system spanning three physical layers—compute, optical network, and energy/cooling—and ﬁve functional stages that execute in sequence within each control cycle: telemetry ingestion and normalization, state estimation and prediction, optimization, digital twin validation, and execution. The loop closes through continuous telemetry feedback from the physical infrastructure, enabling adaptive, constraint-aware orchestration under dynamic operating conditions. 4.1.1. Control-loop semantics The six-phase semantics of the control loop are: observe → estimate/predict → optimize → validate → execute → observe. Each phase has a well-deﬁned input–output contract with the adjacent phases, and the loop as a whole implements a receding-horizon control strategy: at each cycle, the optimization is solved over the current and predicted state, a validated action is executed, and the system re-observes before solving again. This structure is common in model predictive control (MPC) [50] and has been adapted here to the joint compute–network–energy problem, where the “plant” is the distributed AI infrastructure and the “model” is the MILP formulation of §3.2 evaluated against the parameter vector θ(t, t + ∆). 4.1.2. State representation The system state is represented by the parameter vector θ(t, t + ∆), which encodes both the current infrastructure conditions at time t and a short-horizon forecast over the interval [t, t + ∆] derived from telemetry streams and predictive models. Concretely, θ(t, t + ∆) extends the per-site tuple {Pi (t), γi (t), ωi (t), Γ̄i , Ω̄i (t)}i∈S deﬁned in §3.1 with forecast trajectories for each parameter over the prediction horizon ∆. The active workload set W(t) represents the workloads present in the system at time t that are subject to placement and routing decisions in the current cycle; workloads that arrive or depart between cycles are handled through incremental re-optimization rather than full problem reconstruction. The dual role of telemetry is a deﬁning architectural feature. Telemetry outputs are used simultaneously to construct the estimated and predicted state θ(t, t+∆) and to parameterize April 14, 2026

Figure 2: Closed-loop control architecture for sustainability-constrained AI infrastructure orchestration. Streaming telemetry from compute, energy, cooling, and optical network domains is ingested and normalized to provide a uniﬁed observability plane. A state estimation and prediction module derives both the current and a short-horizon forecast representation of infrastructure state, which jointly parameterize the MILP optimization. The optimization agent computes placement and routing decisions subject to sustainability and latency hard constraints. A digital twin validates candidate solutions against power, thermal, latency, and policy compliance before execution. The execution layer applies conﬁguration changes to data center schedulers and optical network controllers, while continuous telemetry feedback closes the loop, forming a predictive closed control system.

the optimization problem directly—as the values of γi (t), ωi (t), Pi (t), Cij , and dij that appear in constraints (3)–(10). This dual use reﬂects the role of telemetry as both an observability layer and a decision input: the same data stream that informs the operator about current infrastructure conditions also determines the boundary of the FSOR at each cycle. 4.1.3. Cross-domain observability A prerequisite for the closed-loop architecture is a shared observability plane that integrates telemetry from four physically distinct domains, each with its own instrumentation standards, update rates, and schema conventions. As shown in Figure 2, these are: site power and thermal state (power draw, rack load, thermal margins, UPS state); grid sustainability signals (carbon intensity γj (t), energy headroom Pjmax (t)); cooling and water state (water consumption Wj , ambient conditions); and optical network state (capacity Ce , delay April 14, 2026

de , utilization, alarms). The telemetry ingestion and normalization stage is responsible for stream collection, timestamp alignment across domains, schema normalization, and freshness and conﬁdence checks that ﬂag stale or low-conﬁdence readings before they propagate into the state estimator and optimization. Without this normalization layer, heterogeneous update rates across domains would introduce temporal inconsistencies in the parameter vector θ(t, t + ∆)—for example, a carbon intensity reading from a slow-updating grid API paired with a freshly observed power headroom—that could cause the optimization to evaluate constraints against an internally inconsistent system state. 4.1.4. Predictive versus reactive control A purely reactive architecture—one that responds only to the current telemetry snapshot θ(t)—is insuﬃcient for sustainability-constrained orchestration for two reasons. First, the timescales of constraint activation diﬀer across domains: carbon intensity can change within minutes, water permit limits activate over hours to days, and link congestion evolves on timescales comparable to the optimization and execution cycle. A controller that observes only the current state will systematically lag behind fast-moving constraints, executing placements that were valid at observation time but invalid at execution time. Second, several sustainability-improving actions—pre-emptive workload migration to sites whose carbon intensity is forecast to fall, reservation of routing capacity ahead of predicted congestion—are only available to a controller that can plan ahead. The forecast horizon ∆ in θ(t, t + ∆) is the architectural mechanism that enables this anticipatory behavior: the optimization evaluates hard constraints not only against the current state but against the predicted state at execution time, reducing the probability of constraint violations that arise from the latency between observation and action. 4.1.5. Digital twin as a safety layer The digital twin validation stage occupies the position between the optimization agent and the execution layer and serves as a mandatory safety check. Every candidate solution produced by the optimization agent is simulated in the digital twin before any conﬁguration change is applied to the physical infrastructure. The twin checks power balance, thermal margins, end-to-end latency, and regulatory policy compliance under the proposed placement and routing. Only validated actions are released to the execution layer; solutions that fail validation are returned to the optimization agent with a constraint tightening that excludes the oﬀending conﬁguration, triggering re-optimization. This reject-and-retry loop ensures that the physical infrastructure is never exposed to an unvalidated action, at the cost of an additional round-trip latency within the control cycle. The design choice to place validation between optimization and execution—rather than relying on the optimization model alone to guarantee constraint satisfaction—reﬂects the inherent gap between the MILP’s abstracted model of the infrastructure and the full complexity of the physical system, including thermal dynamics, transient power spikes, and optical signal-quality margins that are not captured in the placement and routing formulation.

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4.1.6. Execution and feedback closure The execution layer translates validated placement and routing decisions into concrete conﬁguration changes applied to data center schedulers and optical network controllers. The feedback path closes the loop: once the physical infrastructure has responded to the conﬁguration change, its updated state is immediately observable through the telemetry streams, and the next control cycle begins. The feedback arrow in Figure 2 carries measured outcomes—the actual power draw, carbon consumption, water draw, and link utilization observed after execution—back to the telemetry ingestion stage, where they serve two purposes: updating the state estimate for the next cycle and providing a ground-truth signal for evaluating forecast accuracy and detecting model drift in the state estimation and prediction module. This last use is essential for maintaining the predictive ﬁdelity of θ(t, t + ∆) over time: a state estimator whose forecasts systematically diverge from measured outcomes will generate parameter vectors that cause the optimization to evaluate constraints against an increasingly inaccurate model of the physical system. 4.2. Telemetry Collection Telemetry collection is the observability foundation of the closed-loop architecture [10]. Every constraint in the optimization problem (3)–(10) is parameterized by quantities that must be measured in real time; the accuracy, freshness, and consistency of those measurements directly determine the ﬁdelity of the FSOR boundary computed at each control cycle. The telemetry layer is therefore not a peripheral data-collection mechanism but a ﬁrst-order determinant of control quality. Streams are collected from four physically distinct domains, each with its own instrumentation ecosystem, update rate, and schema conventions. A shared ingestion pipeline performs timestamp alignment, schema normalization, and data quality enforcement before any stream is admitted to the state estimator. The remainder of this subsection describes each domain in turn, then addresses the cross-cutting concerns of schema normalization, freshness enforcement, and graceful degradation under partial observability. 4.2.1. Compute and Power Telemetry Site power and thermal state is collected at rack and accelerator granularity via standard data center management interfaces, including ipmi, Redﬁsh, and vendor-speciﬁc baseboard management controller (bmc) APIs [51]. The primary variables are: • Per-rack power draw [kW]: the instantaneous electrical load on each rack, used to P compute the site-level power headroom Pi (t) − k pk xik against the constraint (6); • Accelerator utilization [%]: GPU/TPU compute utilization per device, used to infer available capacity for workload migration and to detect underutilized resources that could absorb additional placement; • Thermal sensor readings [řC]: intake air temperature, chip junction temperature, and coolant supply/return delta, used to assess thermal headroom and ﬂag sites approaching thermal throttling thresholds; April 14, 2026

• UPS state: battery charge level, bypass status, and estimated backup runtime, used to assess site availability under grid instability conditions. Power and thermal telemetry are among the fastest-updating streams in the architecture, with sub-minute update rates typical for rack-level power meters. The digital twin validation stage relies on these readings to verify that a proposed placement does not drive any site into thermal saturation or exceed its contracted power envelope, making high-freshness power telemetry a prerequisite for safe execution. 4.2.2. Grid Sustainability Telemetry Sustainability telemetry covers three sub-streams: grid carbon intensity, on-site renewable generation and storage state, and cooling water consumption. 4.2.3. Grid Carbon Intensity Marginal grid carbon intensity γi (t) [gCO2 eq/kWh] is sourced from commercial grid signal providers such as Electricity Maps or WattTime [7], which aggregate generation dispatch data, fuel mix reports, and ﬂow-tracing models to produce real-time and short-horizon forecast estimates at the bidding-zone or balancing-area level. The choice between marginal and average emissions factors has a material eﬀect on the signal used to parameterize the carbon constraint (3) [52]: marginal factors reﬂect the actual incremental emitter dispatched to serve additional load and are theoretically correct for placement decisions that alter load at the margin, while average factors reﬂect the overall generation mix and are more stable but less sensitive to short-term dispatch changes [52]. The framework admits either convention as a conﬁguration parameter; the choice should be made explicit and held constant across sites to avoid comparing incommensurable signals. 4.2.4. On-Site Generation and Storage Where sites are equipped with behind-the-meter renewable generation or battery storage, their eﬀective carbon intensity and power headroom are functions of on-site generation state in addition to the grid signal. The net power headroom available to the placement constraint (6) is Pi (t) = Pigrid (t) + Pigen (t) + Pibatt (t), where the latter two terms are sourced from the energy management system of the on-site generation and storage assets. Sites with signiﬁcant on-site renewable capacity may remain inside the carbon-eligibility set deﬁned by (3) even when the grid signal γi (t) exceeds Γ̄i , if their eﬀective blended carbon intensity falls below the threshold. 4.2.5. Cooling Water Consumption Water consumption Wj (t) [L/h] and make-up water ﬂow are monitored via building management system (bms) interfaces. Ambient environmental conditions—intake air temperature, relative humidity, wet-bulb temperature—are collected from on-site weather stations and used to model cooling system eﬃciency and forecast evaporative water draw under predicted ambient conditions over the horizon ∆. These inputs feed directly into the water constraint evaluation (4) and into the seasonal FSOR contraction dynamics discussed later in §6.2. April 14, 2026

4.2.6. Optical Network Telemetry Optical transport network state is collected via OpenConﬁg YANG models or vendor streaming telemetry interfaces (gnmi/grpc) [53], which expose per-channel and per-link performance monitoring data at update rates of seconds to minutes. The primary variables are: • Channel capacity Ce [Gbps]: the provisioned and available transmission capacity on each directed edge, used to parameterize the link capacity constraint (9); • Propagation delay de [ms]: the one-way ﬁber propagation delay on each link, used to evaluate the latency constraint (7) via (1). This quantity is physically stable—it is determined by ﬁber route geometry and refractive index—and requires re-measurement only when route changes or protection switching events alter the active ﬁber path; • Link utilization [%]: the fraction of capacity currently occupied by active ﬂows, used to compute available headroom for new traﬃc demands and to detect congestion conditions that may invalidate routing assumptions; • Signal quality indicators: optical signal-to-noise ratio (osnr), pre-forward-errorcorrection bit error rate (pre-fec ber), and chromatic dispersion margin, used by the digital twin to assess whether a proposed routing is physically realizable on the optical layer without degrading signal integrity; • Alarm state: active faults, degraded spans, and protection switching events, used to remove aﬀected links from the routing graph before optimization. Optical network telemetry introduces a domain-speciﬁc challenge: the logical routing graph G = (S, E) used in the optimization is an abstraction of a multi-layer optical network whose actual capacity and delay properties depend on wavelength assignment, ampliﬁer gain settings, and protection topology. Maintaining consistency between the optimization’s graph abstraction and the physical optical layer requires that the telemetry pipeline translates physical-layer performance monitoring data into the logical-layer parameters Ce and de used in the MILP. Signiﬁcant discrepancies between the two—for example, a link whose eﬀective capacity is reduced by signal degradation but whose provisioned capacity is unchanged in the logical model—are a source of digital twin validation failures and should trigger a reparameterization of the graph. 4.2.7. Workload Telemetry Workload telemetry is collected from the data center orchestration layer (Kubernetes control plane, slurm job scheduler, or equivalent) and from application-level monitoring. The primary variables are [10]: • Active workload identiﬁers and current placement: the set W(t) and the current assignment x(t), used to initialize the optimization with the current state and to identify workloads that may be candidates for migration; April 14, 2026

• Traﬃc demand ρk (t) [Gbps]: the observed inter-site traﬃc generated by each workload, used to parameterize the ﬂow conservation constraint (10) and the link capacity constraint (9); • Power demand pk (t) [kW]: the measured power draw of each workload, which may diﬀer from the nominal pk used in placement planning due to load variation; • Service-level compliance state: per-workload latency measurements against the slo λk , used to detect active violations that may trigger re-optimization outside the regular cycle interval; • Portability and migration state: whether a workload is currently migrating (µk in transition), the size of its transferable state σk , and the estimated completion time of any in-ﬂight migration, used to avoid issuing conﬂicting placement decisions for workloads that are mid-migration. 4.2.8. Ingestion Pipeline: Normalization, Freshness, and Graceful Degradation All four telemetry streams are timestamped at the source and admitted through a shared ingestion pipeline before any reading is made available to the state estimator. The pipeline enforces three cross-cutting properties. In Schema normalization, each domain exposes data in domain-speciﬁc formats and units. The ingestion pipeline applies a schema normalization layer that maps all streams to a common internal representation with standardized units, parameter names, and site identiﬁers. This normalization is a prerequisite for the state estimator’s ability to join readings across domains—for example, combining the carbon intensity signal from Electricity Maps with the power headroom reading from the bmc and the link capacity from OpenConﬁg into a single per-site parameter vector θ i (t). In Timestamp alignment, streams from diﬀerent domains have heterogeneous update rates: power meters may update every 30 seconds, carbon intensity signals every 5 minutes, and water consumption readings every hour. The ingestion pipeline aligns all streams to a common control cycle timestamp using last-known-good interpolation for slowly varying quantities and forward-hold for quantities with hard physical meaning (alarm states, UPS bypass). Misaligned timestamps that exceed a conﬁgurable tolerance are ﬂagged as potentially inconsistent and trigger a conﬁdence reduction on the aﬀected parameter before it enters the state estimator. In Freshness enforcement and graceful degradation, telemetry older than a conﬁgured maximum age τmax for each parameter is treated as stale and triggers one of three responses, depending on the criticality of the aﬀected parameter: 1. Substitution from forecast: for slowly varying parameters such as water consumption and ambient temperature, the state estimator substitutes the most recent forecast value with a widened uncertainty interval, allowing optimization to proceed with reduced conﬁdence; April 14, 2026

2. Conservative bound: for safety-critical parameters such as power headroom and link capacity, the pipeline substitutes a conservative lower bound—for example, the minimum observed value over the preceding hour—preventing the optimization from assuming availability that cannot be veriﬁed; 3. Optimization hold: for parameters with no safe substitute —such as alarm state on a link that may be in active protection switching—the pipeline signals the orchestrator to hold optimization until fresh telemetry is received, preventing decisions on an irrecoverably stale system state. This three-tier degradation policy ensures that the control loop continues to operate safely under partial observability, while preventing unsafe actions that could arise from acting on stale or missing telemetry. It also provides a principled interface between the telemetry layer and the state estimation module: rather than passing raw readings with unknown freshness, the ingestion pipeline delivers a parameter vector annotated with per-parameter conﬁdence levels that the state estimator can use to weight its fusion of telemetry and forecast inputs. 4.3. State estimation A state estimator aggregates incoming telemetry into a consistent infrastructure snapshot. Slowly varying parameters such as water intensity and physical link delays are smoothed over time to suppress measurement noise. Rapidly varying parameters such as grid carbon intensity and available power capacity use the most recent telemetry reading directly. Each parameter estimate carries a conﬁdence ﬂag reﬂecting data age and source reliability. When conﬁdence is low, the optimizer may apply conservative bounds—using a pessimistic carbon estimate rather than the point estimate—trading solution quality for robustness against measurement uncertainty. Recent advances in multivariate time-series forecasting for cloud infrastructure suggest that state estimation should incorporate predictive components, capturing both current conditions and near-term resource dynamics. Hybrid deep learning models have demonstrated the ability to model interdependencies between compute, memory, and network resources, enabling more accurate and proactive orchestration decisions [18]. In this context, the system state is not only an instantaneous snapshot, but a short-horizon forecast that informs feasibility-aware optimization under dynamic conditions. 4.4. Optimization agent Given the current and predicted infrastructure state and active workload set, the optimization agent ﬁrst eliminates infeasible site–workload pairs by applying carbon and water constraints. This pre-ﬁltering step reduces problem size before the solver runs and makes the hard-constraint semantics explicit in the problem structure. The agent then solves the joint placement and routing problem, returning an optimal assignment if the problem is feasible or raising an infeasibility ﬂag if no valid placement exists under current conditions. The agent operates on a periodic cycle aligned with the update frequency of carbon intensity signals, typically in the range of ﬁve to ﬁfteen minutes. This cadence balances responsiveness to changing grid conditions against the overhead of repeated optimization and execution. April 14, 2026

4.5. Digital twin validation Before any solution is applied to the physical infrastructure, it is validated against a digital twin, a continuously synchronized model of the system [11]. The digital twin evaluates the proposed placement against four categories of constraints that are diﬃcult to encode precisely in the optimization model: thermal margins (does the new workload allocation remain within the facility’s cooling capacity under current ambient conditions?); power stability (do the dynamic ﬂuctuations implied by the new allocation remain within UPS and transformer headroom?); network congestion (does the proposed routing create hotspots or violate restoration margins on shared optical links?); and policy compliance (does the proposed solution satisfy data locality requirements and cross-border traﬃc restrictions?). If any check fails, the digital twin returns a constraint violation report; the optimization agent adds a corresponding cut and re-solves. This correction loop repeats until a valid solution is found or the cycle time budget is exhausted. In the latter case, the current placement is retained and an operator alert is raised. This validation step ensures that optimization outputs are not only mathematically feasible, but operationally safe under real-world conditions that are not fully captured in the optimization model. 4.6. Execution Validated solutions are applied atomically across two control planes. On the compute plane, workload placement instructions are issued to the cluster scheduler, specifying target node aﬃnities, power caps, and priority levels. On the network plane, routing instructions are issued to the optical network controller via the path computation element interface, updating label-switched path assignments and optical channel conﬁgurations. The two planes are coordinated to apply changes simultaneously, preventing transient states in which workload and routing are inconsistent. 5. Scenario-Based Evaluation 5.1. Evaluation approach The framework is evaluated through scenario-based analysis across three representative infrastructure conﬁgurations. The scenarios are designed to isolate distinct sustainabilitylimiting mechanisms: carbon intensity variation, spatial carbon–latency tradeoﬀs, and seasonal water stress. Results are comparative and qualitative in nature, demonstrating the structural advantages of joint optimization relative to decoupled and unconstrained baselines. They are not intended as universal performance claims—actual reductions in real deployments will depend on infrastructure characteristics, workload mix, and prevailing environmental conditions. Accordingly, all comparisons should be interpreted as directional evidence of relative behavior rather than as quantitative performance gains. Three conﬁgurations are compared across all scenarios: • Baseline: workloads placed to minimize latency only, with no sustainability constraints. • Compute-only: sustainability objective applied to placement, but network routing treats all paths as equivalent. April 14, 2026

• Joint (proposed): full sustainability-constrained joint compute–network optimization. 5.2. Scenarios Scenario A — Homogeneous continental region Five sites distributed across a single continental market with moderate and relatively uniform grid carbon intensity. Optical latencies between sites are low. This scenario isolates the beneﬁt of sustainability-aware placement in a nearly uniform infrastructure, where environmental gains are achievable without latency tradeoﬀs. The joint and compute-only conﬁgurations perform similarly, conﬁrming that network coupling is a minor factor when sites are well-connected. Scenario B — Multi-region mixed-carbon grid Eight sites spanning two grid zones with strongly diﬀerentiated carbon intensity. Two sites have access to dedicated renewable generation; others rely on carbon-intensive grid mixes. Optical latencies vary substantially across zones. This scenario activates the green-but-far eﬀect (Figure 1): the most carboneﬃcient sites are also the most geographically remote. The joint optimizer ﬁnds placements that balance carbon compliance with latency feasibility, while the compute-only optimizer places workloads at low-carbon sites without accounting for the resulting high-latency routing, leading to service-level violations that require post-hoc correction. Scenario C — Water-stressed deployment Six sites, a subset of which are located in water-stressed regions and exceed their water permit thresholds during summer months. Carbon intensity is moderate. This scenario directly activates the water constraint and tests FSOR contraction under seasonal stress. During peak stress periods, the optimization agent declares infeasibility for a subset of cycles. These infeasibility events correspond to conditions where water constraints eliminate multiple sites, carbon constraints eliminate further sites, and the remaining sites lack suﬃcient power capacity for the full workload set. 5.3. Results and interpretation Across all scenarios, joint optimization yields lower aggregate environmental impact relative to both baselines and compute-only conﬁgurations. The diﬀerence relative to the compute-only conﬁguration is most evident in Scenario B, where decoupling placement from routing leads the compute-only approach to select placements that are carbon-eﬃcient but routing-infeasible under latency constraints. The joint optimizer resolves this tension by ﬁnding placements that are simultaneously carbon-compliant and latency-feasible, a solution space the compute-only approach cannot explore. Latency impact across all conﬁgurations is modest. Latency-sensitive inference workloads are never placed in violation of their service-level objectives. Any latency increase is absorbed by delay-tolerant batch analytics workloads, for which temporal ﬂexibility is an explicit design property. This is consistent with the latency constraint operating as a hard limit, rather than a soft trade-oﬀ. In Scenario C, the infeasibility events observed during peak water stress highlight an important qualitative behavior. The optimizer does not return a policy-violating solution; it correctly identiﬁes that no valid placement exists under current conditions. This behavior provides operators with precise, actionable information: the infrastructure cannot sustain April 14, 2026

the current workload set at the required constraint levels, and sovereign AI operation requires either expanded infrastructure capacity or workload shedding. This is categorically diﬀerent from a penalty-based formulation, which would return a “best-eﬀort” result that silently violates regulatory limits. In this sense, infeasibility is not an error condition but an explicit indication that the system is operating outside its feasible sovereign operating region. The formal structure of these infeasibility events—and their interpretation as Irreducible Infeasible Sets—is analyzed in §7.2. The observed behavior is expected to be heterogeneous across regions and deployment environments. Prior work has shown that the beneﬁts of AI in energy systems depend on infrastructure maturity, regulatory conditions, and regional development levels [4]: the gap between the joint and compute-only conﬁgurations visible in Scenario B will be larger in regions where low-carbon sites are geographically concentrated, and smaller where the grid is relatively uniform as in Scenario A. The eﬀectiveness of sustainability-constrained optimization is further conditioned on the quality of resource forecasting: prediction errors directly aﬀect scheduling eﬃciency and energy utilization [18], implying that the infeasibility signals observed in Scenario C are only actionable if the state estimator can anticipate constraint binding before it occurs. 6. Sovereignty Implications 6.1. The FSOR as a sovereignty metric Figure 3 illustrates the FSOR concept across three representative infrastructure proﬁles. Each panel depicts a distinct conﬁguration, with the shaded region representing the feasible operating envelope—the set of workloads that simultaneously satisfy all active constraints under that proﬁle’s infrastructure endowment. The FSOR provides a concrete, measurable deﬁnition of sovereign AI capacity. A region’s ability to operate AI infrastructure autonomously is bounded by its FSOR: no workload that falls outside the shaded envelope in Figure 3 can be executed under the region’s prevailing physical and regulatory constraints. Unlike conventional sovereignty metrics focused on data localization or model ownership rules, the FSOR is expressed entirely in terms of physically observable parameters—power, carbon intensity, water availability, and optical round-trip latency—and is computable from real-time telemetry. It is therefore an operational metric rather than a merely conceptual one: it can be monitored, updated as constraints change, and used directly as an input to placement decisions. While the FSOR deﬁnes the physical feasibility of AI operation, the eﬀective realization of this capacity depends on how beneﬁts and constraints are distributed across regions and actors. Identifying the FSOR establishes what is physically and regulatorily possible; it does not, by itself, determine what is operationally achievable. Eﬀective sovereignty depends equally on the degree of control over the underlying infrastructure. A region may possess a well-deﬁned FSOR and yet be unable to execute within it if the compute, network, or platform resources that realize that envelope are externally owned or governed. Reliance on hyperscale cloud providers, for example, introduces structural dependencies: the provider’s April 14, 2026

Figure 3: Feasible Sovereign Operating Region (FSOR) under three representative infrastructure proﬁles. In each panel, the shaded area denotes the feasible operating region: the set of workloads that simultaneously satisfy all active constraints, including energy availability, carbon intensity, water usage, and network latency. Region A (clean energy access) exhibits a larger sustainability envelope, but the latency constraint excludes some otherwise-compliant placements, illustrating the “green-but-far” eﬀect. Region B (carbon-limited grid) shows how stricter carbon thresholds directly contract the feasible operating space. Region C (waterstressed) illustrates further contraction driven by cooling and water permit constraints. The FSOR is the intersection of constraint-feasible regions, not a single universal boundary.

scheduling policies, capacity allocation priorities, and jurisdictional obligations—including compelled disclosure under instruments such as the cloud Act—may override the operator’s own sustainability and sovereignty requirements [54, 55]. In such cases, the reachable subset of the FSOR is strictly smaller than the FSOR itself, and the gap between the two is a direct measure of the infrastructural dependency the region bears. Reducing that gap is, in operational terms, the objective that motivates sovereign AI investment. Feasibility does not imply equitable access. The physical boundaries represented by the FSOR are not uniformly distributed: regions with abundant renewable capacity, access to submarine cable landing points, and relaxed water-permit regimes face systematically larger feasible envelopes than regions constrained on all three dimensions simultaneously. This structural asymmetry has governance implications beyond the purely technical. Recent work on energy justice shows that AI-enabled systems can simultaneously improve aggregate eﬃciency while exacerbating distributional inequalities across regions and populations [4]. The FSOR should therefore be read not only as a technical boundary but also as a structural boundary that determines which actors can eﬀectively participate in AI infrastructure—and, April 14, 2026

by extension, which cannot. Policies aimed at broadening sovereign AI capacity must address not only the expansion of individual regional FSORs but also the systematic factors that produce asymmetry across them. A key feature of the FSOR visible in Figure 3 is that sustainability constraints do not degrade performance gradually as they tighten: they remove entire regions of the feasible space discontinuously. A carbon limit that eliminates a candidate site removes every workload that could have been placed there; a water constraint that activates during a summer stress period removes those sites from the feasible set for the full duration of that period. The FSOR is therefore a set deﬁned by the intersection of hard boundaries, not a smooth Pareto frontier along which operators can trade oﬀ one objective against another. This discrete structure has a direct practical implication: marginal investments in sustainability compliance—slightly cleaner grid mix, slightly reduced water draw—may yield no beneﬁt at all until a threshold is crossed, at which point the feasible set expands discontinuously. Investment planning for sovereign AI infrastructure should account for this threshold geometry rather than assuming smooth returns to sustainability improvements. 6.2. Infrastructure Endowments Determine FSOR Boundaries The three panels in Figure 3 are not merely illustrative: they represent qualitatively distinct constraint regimes whose interaction shapes the feasible sovereign operating region in ways that cannot be reduced to a single infrastructure bottleneck. Three mechanisms dominate FSOR boundaries across the proﬁles: access to low-carbon energy, the structural eﬀect of carbon thresholds, and seasonal water availability. Each operates on a diﬀerent timescale, responds to diﬀerent policy levers, and produces a diﬀerent geometry of feasibility loss. Understanding all three is necessary for infrastructure investment planning that aims to expand or defend sovereign AI capacity. 6.2.1. Clean Energy Access and the Green-But-Far Eﬀect (Region A) Sites with access to low-carbon generation—whether through a predominantly renewable national grid, a power purchase agreement with a dedicated renewable source, or on-site generation—remain inside the feasible set under strict carbon thresholds. Carbon-intensive sites are excluded entirely, regardless of their latency or compute proﬁle. This creates the ﬁrst boundary mechanism: grid carbon intensity is a hard gate on site eligibility, and it cannot be crossed through compute investment alone. A region whose grid is predominantly fossil-fuelled faces a carbon-limited FSOR that can only be expanded by grid decarbonization, dedicated renewable procurement, or the construction of behind-the-meter generation capacity [25]. Increasing on-site compute density, improving hardware eﬃciency, or optimizing scheduling all leave this boundary unchanged. Region A also introduces a subtler constraint: the green-but-far eﬀect, whose constraint geometry is illustrated in Figure 1 (Panel A) and whose workload-class consequences are mapped in Panel B of the same ﬁgure. A site that is sustainability-compliant in every dimension—low carbon, low water draw, suﬃcient power headroom—may nonetheless be excluded from the feasible set for latency-sensitive workloads if it is geographically remote from the demand source. As established in §3.2.5, the propagation delay ﬂoor imposed April 14, 2026

by ﬁber geometry is irreducible [8], meaning that latency-sensitive workloads are spatially bounded around the demand source independently of site sustainability proﬁles. For inference workloads with tight response-time service-level objectives, this means that the subset of the FSOR accessible to those workloads is spatially bounded around demand center, independently of the sustainability proﬁle of more distant sites. The practical implication is that expanding the FSOR for latency-sensitive workloads requires either demand disaggregation, distributing inference endpoints closer to users, or investment in edge infrastructure that meets sustainability thresholds locally. Relying on remote clean-energy sites alone will not resolve the tension; the two constraints must be addressed jointly. Sovereignty policy that focuses exclusively on energy transition without accounting for the latency geometry of AI workloads therefore risks producing infrastructure that is physically compliant but operationally inaccessible for the workloads it is intended to serve. 6.2.2. Carbon Threshold Geometry and Feasible Set Fragmentation (Region B) Region B illustrates the structural eﬀect of tightening carbon thresholds on a heterogeneous infrastructure portfolio. As the carbon intensity limit decreases, sites that previously satisﬁed the constraint cross the threshold and are removed from the feasible set, not partially degraded, but eliminated entirely. This is the threshold geometry discussed in §6.1: contraction is discontinuous and site-level, not smooth and marginal. The consequence for operators whose infrastructure spans both low- and high-carbon zones is feasible set fragmentation. When a subset of sites is removed by a binding carbon threshold, the remaining feasible placements may form a disconnected or sparsely connected topology. This matters for two reasons. First, workloads with joint placement and routing requirements—for example, a distributed training job that must co-locate data preprocessing and compute, or a federated inference pipeline that must satisfy aggregate latency across multiple endpoints—may ﬁnd that no feasible assignment exists within the fragmented set, even though individually each remaining site is compliant. The MILP formulation captures this through the joint satisfaction of placement and routing constraints; the FSOR visualization in Figure 3 projects it into the two-dimensional space of the ﬁgure for interpretability. Second, fragmentation reduces redundancy: fewer compliant sites means reduced ability to absorb failures or demand spikes without violating constraints. The policy implication is that carbon threshold design is not merely an environmental instrument; it is a de facto infrastructure policy that determines the topology of feasible sovereign compute. Regulators setting carbon intensity limits for public AI infrastructure, as contemplated in emerging EU AI Act guidance and in national AI strategies that couple sustainability obligations to public procurement [56], should model the feasibility-set consequences of threshold choices, not only the aggregate emissions reduction they produce. A threshold that is marginally stricter may eliminate a disproportionately large share of feasible sites if those sites cluster near the current limit. 6.2.3. Seasonal Water Stress and Anticipatory Capacity Planning (Region C) Region C introduces the third boundary mechanism: water availability. Data centers operating air-cooled or evaporative cooling systems draw substantial volumes of water, and April 14, 2026

in water-stressed regions this draw is subject to permit limits that tighten during summer months when both cooling demand peaks and river or groundwater levels fall [3]. When a site’s water draw exceeds its permitted allocation, it exits the feasible set for the duration of the stress period, contracting the FSOR seasonally in a manner that is predictable from climate data and cooling eﬃciency parameters. The temporal structure of water stress distinguishes it from the other two mechanisms. Carbon intensity varies on sub-hourly timescales, driven by generation dispatch and demand ﬂuctuations; latency constraints are eﬀectively static on planning horizons relevant to infrastructure investment. Water stress, by contrast, evolves on seasonal timescales, weeks to months, with a climatological signal that can be forecast with reasonable accuracy months in advance using hydrometeorological models. This predictability makes water-driven FSOR contraction amenable to anticipatory planning: an operator can pre-position workloads away from water-stressed sites before permit thresholds bind, reserve capacity at alternative sites during summer months, or negotiate interruptible cooling agreements that partially substitute air-side economization for evaporative cooling when water is scarce. The structural trend, however, is adverse. Climate projections for many high-compute regions—including Southern and Central Europe, the southwestern United States, and parts of East Asia—point to longer and more severe dry seasons, increasing the fraction of the year during which water-stress constraints are active [46]. This means that the seasonal FSOR contraction in Region C is not a static planning parameter but a shrinking envelope over multi-year horizons. Sovereign AI capacity planning must therefore treat water availability not as a ﬁxed endowment but as a time-varying constraint whose trajectory is coupled to climate risk. Infrastructure investment decisions—site selection, cooling technology choice, water recycling systems, co-location with waste-heat recovery—should be evaluated against projected water availability over the intended operational lifetime of the facility, not only current permit conditions. Finally, it is worth noting that the three mechanisms interact. A site under Region C conditions that also lies near the carbon threshold of Region B may be eliminated from the feasible set on two independent grounds simultaneously during summer, while remaining accessible during winter. An operator managing a portfolio that spans all three constraint regimes faces a feasible set that contracts and expands non-uniformly across the calendar year, across the grid’s generation mix, and across its routing topology. The FSOR framework, by making these intersecting boundaries explicit and computable from telemetry, provides the basis for the kind of joint, constraint-aware capacity planning that sovereign AI deployment requires. 6.3. Policy implications The FSOR analysis yields three actionable insights for policymakers and infrastructure operators. First, infrastructure investment precedes sovereign AI capacity. Expanding a region’s FSOR requires investment in clean energy interconnection, advanced cooling systems that reduce water intensity, and optical network infrastructure that reduces propagation April 14, 2026

delay to low-carbon sites. Compute hardware investment alone does not expand the FSOR if the binding constraints are environmental or topological. Second, carbon thresholds must be calibrated to the regional grid baseline. Setting a carbon policy threshold below the prevailing grid intensity eliminates all local sites from the feasible set, reducing sovereignty to zero regardless of compute capacity. Eﬀective policy sets thresholds that create credible incentives for grid decarbonization while maintaining suﬃcient operational feasibility to sustain AI deployment during the transition. Third, sovereignty is dynamic. The FSOR changes continuously with grid carbon mix, seasonally with water availability, and over longer timescales with regulatory frameworks. Continuous telemetry and periodic FSOR computation are therefore necessary to track and manage sovereign AI capacity over time. A region whose FSOR is adequate today may face binding constraints within a planning horizon, depending on grid evolution and climate trends. 7. Discussion This section examines the implications of the proposed formulation, emphasizing the structural roles of joint optimization, constraint modeling, and system limitations in sustainability-constrained AI infrastructure. Taken together, these elements show that such systems are not optimization problems with additional costs, but constrained feasibility problems whose solution space is jointly determined by physical infrastructure, environmental limits, and network topology. 7.1. Why joint optimization matters The central ﬁnding of this work is that sustainability constraints are intrinsically coupled with both compute placement and network routing, and that this coupling deﬁnes feasibility rather than merely inﬂuencing performance. The consequences of ignoring this coupling are not merely suboptimal solutions: they are solutions whose reported feasibility is illusory because they assume away the network cost that compliance actually incurs. The coupling arises from a geographic asymmetry: low-carbon and low-water sites are not uniformly distributed. As illustrated in Figure 1, they are located in speciﬁc regions whose positions within the optical transport network impose speciﬁc propagation delays and capacity constraints on any workload placed there. This asymmetry is well documented empirically. Grid carbon intensity varies by factors of two or more across cloud regions and exhibits strong spatio-temporal structure [13], making the identity of the lowest-carbon site at any given telemetry cycle both time-varying and location-dependent. As green energy transitions advance, this concentration is likely to intensify rather than dissipate: renewable-heavy grids tend to be located in speciﬁc geographic corridors—northern Europe for wind and hydro, southern Europe and North Africa for solar—rather than uniformly distributed [48, 57]. The implication is that complying with a carbon or water budget is not a free action in the placement space: it restricts workloads to a geographic subset of sites that are, on average, farther from one another and from network aggregation points. Every unit of environmental April 14, 2026

compliance therefore carries an implicit network cost in the form of additional propagation delay, consumed link capacity, or reduced routing ﬂexibility. This coupling cannot be resolved by optimizing each dimension independently. Consider two natural decompositions. A placement-ﬁrst approach selects the site that minimizes the sustainability metric and subsequently solves the routing problem on the resulting ﬁxed placement. This fails because the routing problem inherits a ﬁxed source node that may be poorly positioned relative to the network topology, producing latency values that exceed the hard constraint. The placement appeared feasible in the placement stage because network cost was implicitly assumed to be zero. A routing-ﬁrst approach minimizes end-to-end latency over all candidate paths and placements without regard to sustainability, then checks whether the selected placement satisﬁes environmental limits. This produces solutions that are latency-optimal but may violate hard carbon or water caps. Indeed, the FORTE framework, a widely cited baseline for geographic load balancing across data centers, explicitly omits the energy consumed by network transport in its sustainability accounting [58, 59], a gap identiﬁed as a systematic bias in the literature: sequential approaches that ignore network cost underestimate the true environmental and operational burden of spatial workload shifts [13, 60]. Only joint optimization, simultaneous assignment of workload placement and routing path subject to sustainability and latency constraints, correctly identiﬁes conﬁgurations that are simultaneously feasible on both dimensions. In this formulation, the feasible sovereign operating region emerges as the joint intersection of environmental and network constraints, rather than as a post hoc ﬁlter applied to independently optimized solutions. This is a classical argument in network optimization: the joint placement and routing problem is generally not decomposable without loss of optimality because placement decisions and routing decisions share link capacity constraints [61, 62]. This observation has a direct implication for the growing literature on carbon-aware computing. The dominant paradigm in that literature operates at the compute-placement level: it selects sites or time windows based on grid carbon intensity while treating network routing as either free or exogenous [6, 13, 63]. As carbon constraints tighten and compliant sites become more geographically concentrated, the network cost of each spatial shift grows. A compute-only carbon accounting framework systematically underestimates this cost. End-to-end carbon footprint analysis of data movement, including the carbon embodied in network transport, conﬁrms that the communication component is non-trivial and grows with the geographic distance of the spatial shift [60]. This systematic underestimation has a further structural consequence. The practical upper bound on carbon reduction achievable through spatial shifting is already signiﬁcantly lower than the theoretical ideal due to capacity constraints, latency SLOs, and regional policy restrictions [13]. Ignoring network cost makes this bound appear more achievable than it is, producing overconﬁdent estimates of the feasible sovereign operating region. In this sense, joint optimization is not only a performance improvement over sequential approaches, it is a requirement for correctly identifying whether a feasible solution exists at all. In our formulation, the feasible sovereign operating region is deﬁned by the intersection April 14, 2026

of the carbon constraints, the water constraints, the latency bound, and the link capacity constraints. This intersection is computed simultaneously over placement and routing variables: it cannot be evaluated by solving the constraints sequentially over separate variable spaces. The infeasibility events of Scenario C illustrate this precisely: it is the simultaneous binding of environmental and network constraints that exhausts the feasible region, not the violation of any single dimension in isolation. As the energy transition progresses and low-carbon resources become increasingly geographically concentrated, the interaction between sustainability and network constraints will become more binding. Joint optimization is therefore the minimal formulation required to capture the physical and operational structure of sustainability-constrained AI infrastructure. 7.2. Hard constraints versus penalty terms The choice to model sustainability limits as hard constraints rather than as penalty terms in the objective function is a central design decision of this work and has signiﬁcant formal and operational consequences. Understanding this distinction requires a brief characterization of both approaches. In penalty-based formulations, constraint violations are incorporated into the objective function as weighted cost terms, eﬀectively converting a constrained problem into an unconstrained one [64, 65]. The general idea is to replace hard constraints by penalties and then exploit the well-developed machinery for unconstrained optimization [66]. As the penalty coeﬃcient tends to inﬁnity, the penalized solution converges to a solution of the original constrained problem under standard regularity conditions [65]. This approach has computational advantages—it does not restrict the feasible region and can be eﬀective when the constraint surface is non-convex or disconnected—but it carries a fundamental semantic limitation: the optimizer is free to trade constraint violation for objective improvement. In the context of carbon and water budgets, a penalty-based formulation allows the solver to place workloads at sites that breach regulatory thresholds provided this is compensated by suﬃciently large performance gains elsewhere in the objective. Solutions returned may therefore satisfy the combined weighted objective while violating absolute regulatory limits under adverse grid or hydrological conditions. Hard constraints, by contrast, encode the legal and physical reality that certain carbon or water levels are not merely undesirable, they are impermissible. Chinneck [49] characterizes the fundamental distinction precisely: hard constraints set conditions on the variables that are required to be satisﬁed, whereas soft constraints impose only a preference whose violation is penalized but tolerated. For operators subject to emissions reporting obligations, energyuse disclosure mandates, or regional water-abstraction permits, this distinction is not a modeling preference, it is a structural requirement of regulatory compliance. The energy system optimization literature has increasingly recognized this principle: [47] note that enforcing constraint feasibility before optimizing cost is the appropriate hierarchical priority in regulatory planning contexts, and robust optimization frameworks for energy systems explicitly distinguish between constraints that must hold under all realizations of uncertainty and those that represent operational targets which may be traded [47, 67]. April 14, 2026

The cost of encoding sustainability limits as hard constraints is reduced feasibility under extreme conditions. When grid carbon intensity spikes across all candidate sites simultaneously, or when water-stress events raise the eﬀective water intensity beyond per-site policy limits, the intersection of the carbon, water, latency, and capacity constraints may become empty. This is precisely the class of infeasibility events observed in Scenario C. In the mixed-integer programming literature, such events correspond to what is formally termed an Irreducible Infeasible Set (IIS), a minimal subset of constraints that is collectively infeasible, such that the removal of any single constraint restores feasibility [49, 68]. In our model, the IIS under Scenario C is characterized by the simultaneous binding of the carbon cap, the water cap, and the latency bound across all candidate sites, leaving no feasible placement for the aﬀected workloads. Detecting and reporting the binding constraints that constitute this IIS is operationally valuable: it identiﬁes the minimum regulatory relaxation or infrastructure augmentation—additional renewable capacity, emergency water allocation, or latency budget extension—that would restore feasibility. The beneﬁt of the hard-constraint design is that every returned solution is guaranteed to be policy-compliant by construction. This guarantee is not replicable in the penalty regime without driving the penalty coeﬃcient to impractically large values, at which point the penalized problem becomes numerically ill-conditioned [64]. The distinction between feasibility and near-feasibility is material in a regulatory context: a solution that violates a carbon cap by a quantity below the penalty threshold may nonetheless trigger enforcement action, ﬁnancial penalties, or operating license suspension. Recent data-center scheduling work has reinforced this principle, distinguishing sharply between hard constraints, enforced via constraint projection or shielding mechanisms, and soft constraints addressed by reward shaping or Lagrangian relaxation, with the former reserved for safety and compliance boundaries that cannot be compromised [63]. A related consideration concerns the treatment of uncertainty. In a deterministic formulation with hard constraints, parameter uncertainty can generate infeasibility when realized values exceed the modeled bounds. Robust optimization oﬀers an intermediate position: constraints are required to hold for all realizations of uncertain parameters within a deﬁned uncertainty set, trading solution cost for robustness [67, 69]. Applied to carbon intensity, a robust hard constraint would require the carbon budget to be satisﬁed under the worst-case intensity realization in a deﬁned forecast interval. This is a natural extension of the present model and is identiﬁed as a direction for future work. In summary, the hard-constraint design reﬂects the legal and operational reality of regulated infrastructure: certain limits are not objectives to be balanced but boundaries to be respected. The infeasibility events that result from this choice are not model failures, they are informative signals that the feasible sovereign operating region has been exhausted under the prevailing conditions, and that the appropriate response is capacity expansion, policy revision, or workload shedding rather than regulatory trade-oﬀ. In this sense, infeasibility is not a failure of the optimization process, but a precise indication that the system is operating outside its feasible sovereign operating region.

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7.3. Limitations and future work The framework presented in this work makes several simplifying assumptions that bound its scope. Each limitation points to a concrete direction for future work. The model treats workload placement as an instantaneous decision: once the optimizer assigns a workload to a site, no overhead is attributed to the act of relocation. In practice, relocating a large distributed training job across data centers incurs non-trivial energy and time overhead. Live migration of virtual machines or containers consumes energy at the source host, the destination host, and the intervening backbone network nodes; and the migration time introduces a service disruption window whose duration depends on the memory footprint and dirty-page rate of the workload [70]. For training workloads with tight checkpoint synchronization across accelerators, even a brief migration-induced pause may invalidate in-ﬂight gradient aggregation. A complete operational framework should account for migration cost as a function of workload size, page dirty rate, and inter-site link bandwidth, and incorporate a migration feasibility check that prevents relocation when overhead would exceed the sustainability beneﬁt of the destination site. The literature on cost-aware live migration provides the building blocks for such an extension [71]. The model assumes that marginal carbon intensity is observable via real-time telemetry at each site. This assumption may not hold uniformly. Carbon intensity signals are not directly measurable quantities: they are estimated from grid dispatch data, fuel-mix reports, and marginal generator identiﬁcation, using models that are inherently probabilistic and depend on the transparency and temporal resolution of data published by transmission system operators [72]. In regions with limited grid transparency—much of sub-Saharan Africa, parts of South and Southeast Asia, and several emerging cloud markets—providers must fall back on synthetic proxy models trained on historical load patterns, introducing estimation errors that can be substantial [73]. Even in well-instrumented grids, the choice between average and marginal emissions factors has a large eﬀect on the signal used for placement decisions [52]: average factors incentivize shifting load to times when the overall mix is clean, while marginal factors target the actual incremental emitter, and the two can point in opposite directions during periods of high renewable curtailment [73]. A robust extension of the present framework should model carbon intensity as an uncertain parameter drawn from a forecast distribution, replacing the deterministic hard constraint with its robust counterpart as outlined in §7.2, and evaluate the sensitivity of placement decisions to signal quality and temporal resolution. The exact MILP formulation is tractable for the scenario sizes considered in this work—a modest number of sites, workload classes, and telemetry cycles. Scaling to continental-scale deployments with hundreds of candidate sites, ﬁne-grained routing topologies, and rolling time horizons requires more scalable solution methods. Benders decomposition oﬀers a natural structural decomposition: the placement master problem, which assigns workloads to sites subject to sustainability constraints, and the routing subproblem, which solves the min-latency path given a ﬁxed placement, are coupled only through site assignment variables and link capacity constraints [39, 40]. This block structure permits the application of standard Benders cuts to iteratively tighten the placement problem without solving the full joint formulation [41]. For very large instances, Lagrangian relaxation of the coupling April 14, 2026

constraints provides a scalable lower bound that can guide heuristic placement policies [42]. An alternative route to scalability is learning-based approximation: recent work has demonstrated that graph neural networks can learn to predict near-optimal placement decisions from problem features, reducing online solve time by orders of magnitude at the cost of a modest optimality gap [74]. The appropriate scalability method depends on whether the operator requires provable feasibility guarantees, which Benders provides, or is willing to accept a feasibility certiﬁcate by inspection in exchange for faster response. The framework addresses operational placement decisions under ﬁxed infrastructure: the set of candidate sites, their power headroom, and the optical link capacities are treated as exogenous parameters. It does not model the longer-term capital investment decisions that determine the FSOR itself, new data center construction, renewable energy procurement contracts, optical capacity expansion, and grid interconnection agreements. These decisions operate on timescales of years to decades and interact with operational decisions in both directions: operational infeasibility events (such as those of Scenario C) signal that the current infrastructure endowment cannot support the workload portfolio under the prevailing sustainability limits, providing an investment signal; conversely, capital investment decisions reshape the feasible sovereign operating region that operational planning must navigate. Integrating operational and investment planning into a two-stage or multi-period stochastic program represents a natural and important direction for future work [47, 75]. The growing literature on joint data center siting and energy procurement planning under carbon objectives provides relevant methodologies [13, 57]. More broadly, the framework assumes that infrastructure resources are available and controllable by the operator subject to the physical and regulatory constraints modeled. This assumption may not hold in environments with strong external dependencies: a workload placed on infrastructure operated by a third-party cloud provider is subject to that provider’s scheduling policies, capacity allocation priorities, and jurisdictional obligations, which may override the operator’s sustainability and sovereignty requirements [54]. Incorporating such dependency constraints into the feasibility model requires extending the notion of a feasible sovereign operating region to account not only for physical and regulatory limits but also for contractual and legal boundaries on what the operator can unilaterally control. Formalizing this extension—mapping the space of actions available under diﬀerent infrastructure ownership and contractual structures—represents an important direction for future work at the intersection of infrastructure optimization and digital sovereignty. 8. Conclusion This paper introduced a sustainability-constrained workload orchestration framework for AI infrastructure. By treating carbon intensity, water availability, and power capacity as hard feasibility constraints rather than optimization objectives, the framework captures the regulatory and physical reality that certain environmental conditions are impermissible— not merely undesirable. By solving compute placement and optical network routing jointly, it resolves the green-but-far tension—the structural conﬂict between sustainability eligibility and latency admissibility—that decoupled approaches cannot represent as a constraint April 14, 2026

interaction. The Feasible Sovereign Operating Region provides a concrete, telemetry-grounded metric for sovereign AI capacity. Rather than measuring sovereignty through data localization or system ownership, the FSOR quantiﬁes the set of workloads that a given infrastructure can actually sustain under its physical and regulatory endowment. Scenario-based analysis shows that joint optimization consistently outperforms both unconstrained and computeonly baselines on environmental impact, while preserving latency guarantees for latencysensitive workloads. For the scenario sizes considered, all problem instances were solved to certiﬁed optimality within a ﬁve-minute telemetry cycle using an open-source MILP solver, conﬁrming operational tractability at these scales. Infeasibility events under water-stress conditions demonstrate that sustainability limits manifest as hard operational boundaries, providing operators with precise signals about the conditions under which sovereign AI operation is and is not feasible. These results reinforce the thesis that sovereignty in AI infrastructure is not a software property. It is an engineering outcome determined by the physical, environmental, and topological characteristics of the underlying system. Expanding sovereign AI capability requires coordinated investment in clean energy, eﬃcient cooling, and optical connectivity— alongside, but not replaced by, advances in compute technology. A region that neglects its infrastructure endowment cannot compensate through software optimization. The FSOR makes that boundary visible. References [1] International Energy Agency, Energy and AI, Tech. rep., IEA, Paris, licence: CC BY 4.0 (2025). URL https://www.iea.org/reports/energy-and-ai [2] D. Mytton, M. Ashtine, The ecology of artiﬁcial intelligence: energy, water, materials, and land limits of digital systems, Carbon Neutral Systems (Dec. 2025). doi:10.1007/ s44438-025-00018-8. URL https://link.springer.com/article/10.1007/s44438-025-00018-8 [3] D. Mytton, Data centre water consumption, npj Clean Water 4 (1) (2021) 11. doi: 10.1038/s41545-021-00101-w. URL https://doi.org/10.1038/s41545-021-00101-w [4] Y. Ye, T. Huang, Z. Shi, Y. Luo, X. Zhang, Artiﬁcial intelligence adoption for advancing energy justice: a multidimensional perspective, Scientiﬁc Reports (mar 2026). doi: 10.1038/s41598-026-38421-x. URL https://doi.org/10.1038/s41598-026-38421-x [5] B. W. Nkwawir, M. Ö. Kayalica, D. Ünal, A. C. Duman, H. S. Erden, Carbon-aware workload management in data centers: A multi-energy integration approach, in: Proceedings of the 16th ACM International Conference on Future Energy Systems (eApril 14, 2026

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Author biography Sergio Cruzes received his MSc. degree in electrical engineering from the University of São Paulo (EESC) with focus on optical communications, where he developed a prototype for video transmission over ﬁber optics using frequency modulation. He received his MBA degree in project management and technological innovation from FIPE Brazil in 2010. He currently works as an optical network engineer at Ciena Brazil, where his work spans optical transport, network automation, and the intersection of AI infrastructure April 14, 2026

with sustainable operations. He is the author of the IEEE Access paper “Telemetry and Agentic AI: Foundations for Optical Network Automation,” the IEEE paper “Failure Management Overview in Optical Networks,” the Optical Switching and Networking paper “Revolutionizing Optical Networks: The Integration and Impact of Large Language Models,” and the preprint “AI Infrastructure Sovereignty,”. His research interests include optical network automation, agentic AI architectures for network control, large language model applications in telecommunications, modern data center infrastructure and its physical constraints, AI infrastructure sovereignty and the role of environmental and topological endowments in determining regional AI capacity, high-spectral-eﬃciency coherent transmission systems, disaggregated optical networks, quality of transmission estimation, and failure management in optical networks.

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