Research institutions compete for funding, talent and reputation. This competition is not a market distortion but a deliberate feature of research systems designed to allocate scarce resources to the most productive groups [16]. Competition creates demand for information asymmetries: institutions that can identify emerging research strengths more rapidly than and prior to their competitors, benchmark their performance more precisely, or anticipate funder priorities more accurately gain a structural advantage. This mechanism leads to the creation of centres of excellence and a varied landscape with specialisms. This dynamic is analogous to the knowledge spillovers that Jaffe [32] demonstrated in industrial R&D: structured data about who is doing what research, is the mechanism through which competitive intelligence flows, and actors who can access and interpret that data more effectively gain a systematic advantage.

This demand is not served by raw open data. It is served by refined, contextualised analytical products that transform the scholarly record into strategic intelligence. University research offices invest in benchmarking tools not because they object to openness but because their competitive environment rewards the ability to extract actionable insight faster and more accurately than other actors. The data they need is not merely accessible in the FAIR sense [69]—it must be Findable, Interoperable and Reusable in a specific institutional context, which currently requires curation and enrichment beyond what open provision typically delivers.

An increasingly important driver is the emerging ecosystem of research translation partnerships between academic and commercial organisations. The translation of basic research into application—what Stokes [62] mapped as “use-inspired basic research”—requires both parties to understand the alignment of their respective capabilities. In what Adams [3] has characterised as the “fourth age of research,” where the dominant mode of production is international collaboration, the data infrastructure required to support translation must be correspondingly global and interlinked. Which research groups are working on problems relevant to a company’s R&D pipeline? Which institutions have the expertise and infrastructure to support a translational challenge? These questions require high-quality data on research capabilities that goes beyond publication counts: entity-resolved researcher profiles, institutionally contextualised output data, patent-to-publication linkage, clinical trial mapping and funding flow analysis—all at a quality sufficient to support investment decisions [55].

Research-intensive industries—biomedical and pharmaceutical most prominently, but also automotive, engineering, agrichemical, petrochemical and financial, to name just a few—conduct substantial research programmes and depend on the scholarly record for competitive intelligence, prior art analysis and strategic planning. Their data needs differ from those of academic users in important respects: they require data at a granularity and domain specificity that reflects their particular R&D portfolios; they are willing to pay for quality because the decisions that depend on it have direct financial consequences; and they often require integration across scholarly and non-scholarly sources—patents, regulatory filings, clinical trial registrations, market data—that falls outside the scope of what open scholarly infrastructure was designed to provide. Even at the national policy level, analyses demonstrating that research impact is driven primarily by international collaboration rather than domestic performance [2] require data structured and refined to a quality that supports robust interpretation [64]—a quality level that raw open metadata does not yet consistently deliver.

The sectoral annulus model introduced above can be made more precise by attending carefully to the geometry of the diagram (Fig. 2). Each data-type segment has two independent visual properties: its radial position (how far from the centre both the inner and outer arcs sit) and its thickness (the gap between the inner and outer arcs). Together, these encode a surprisingly rich set of inferences about the state of a data type in the knowledge ecosystem.

The radial position of a segment captures the total structuring investment and ecosystem development for that data type. If both arcs are close to the centre, the data type is either embryonic (nobody has invested much in structuring it because demand has not yet materialised) or inherently limited in scope (the information content is bounded and does not require deep development). If both arcs are far from the centre, the data type has a well-developed ecosystem with significant structuring effort and mature systems. Radial position is not, however, purely about demand: a data type may be close to the centre either because there is little interest in it or because the cost of mining it is prohibitively high despite significant latent demand. The distinction matters for governance: the first case requires no intervention, while the second may require public investment or standards development to unlock the latent value.

The thickness of a segment represents the commercial opportunity—the gap between what is openly available and what has been structured at the frontier. A thick segment indicates a large space in which commercial refinement can operate. A thin segment indicates that open provision is close to the frontier, leaving little room for commercial differentiation.

These two properties interact to create four characteristic configurations:

1. A segment that is thin and close to the centre represents a data type that is low-cost to produce, for which adequate systems are in place, and where little innovation is required. Structured peer review metadata might currently fall into this category—some data exists, but neither demand nor production investment is deep.

2. A segment that is thin and far from the centre represents the success case: mature systems, good standards, and open provision that has caught up with the frontier. Basic bibliographic metadata with DOIs is approaching this state. The annulus has been compressed by standards adoption and collective disclosure through Crossref.

3. A segment that is thick and close to the centre represents either gatekeeping (significant structuring has occurred but little is openly available) or an embryonic field where the data are expensive and difficult to mine. The legacy Web of Science model exemplified a gatekeeping pattern: the inner arc was very close to the centre (almost nothing open) while the outer arc was moderately distant (substantial commercial product). This makes sense during the initial development of a new data source such as the Web of Science. In the 1950s the data were not diverse, it was hard to mine and hence a homogeneous annulus would be an appropriate representation similar to Figure 1). The openness boundary can be shrunk to the centre with the annulus becoming a fully filled circle as there was essentially no open data—the cost of production precluded that option at that time—the data were excessively expensive to mine. Indeed, so expensive was it to mine data that it was only Garfield’s critical realisation was that citations were Pareto distributed [11, 21] that made it financially tractable to construct an index [47, 71]. For more recent emerging data types like AI disclosure, modern technologies automatically set the boundaries differently—the thickness reflects tends to be closer to the market expectation of the production cost.

4. A segment that is thick and far from the centre indicates a data type with extensive development at the frontier and a substantial commercial zone, but also a meaningful open core. Domain-specific enrichment—pharmaceutical patent-to-publication linkage, translational alignment data, institutional analytics—sits here. The thickness reflects the genuine cost of refinement at the quality levels that demanding users require.

Several additional inferences follow from this geometry. First, the ratio of the inner radius to the outer radius for each segment yields a natural openness ratio—the proportion of total structuring effort that is openly available. A ratio approaching one indicates near-complete openness for a mature data type. A ratio close to zero indicates that most structured data remains behind a commercial boundary. This ratio is a useful diagnostic for governance: one might argue that for data types essential to basic research management, the openness ratio should be above some threshold, even if the absolute frontier extends further for specialised users.

Second, the diagram should be understood as a snapshot of a dynamic system. The trajectory of each segment is as important as its current position. A segment in which both arcs are moving outward indicates a dynamic, maturing data type—new structuring is occurring and new data is becoming open. A segment in which the outer arc moves outward while the inner arc remains stationary represents increasing commercial development without corresponding openness gains—a pattern that should raise governance concerns. A segment in which the inner arc is catching up with the outer represents active commoditisation. And a segment in which neither arc moves is stagnant.

Third, there is a structural constraint that the diagram makes visible: the inner boundary (or openness boundary) can never move outward faster than the outer boundary (the structuring frontier) in the long run, because data cannot be made openly available until it has been structured. Open provision is bounded above by total structuring effort. This has a crucial implication for the argument of this paper. In domains where no one is investing in frontier structuring—because there is no commercial incentive and no public funding—the inner boundary stalls too. The annulus does not merely describe the commercial gap; it describes the investment incentive. An annulus that is too thin removes the economic incentive for frontier structuring, which in turn slows the outward movement of the inner boundary. This is the strongest version of the argument that the annulus is functional: without sufficient annulus width, the entire system—including the open core—advances more slowly.

Fourth, there is an important category of cases in which the inner arc is further out than market forces alone would produce. This represents deliberate intervention—a mandate, a philanthropic investment, or a strategic commercial decision to make data open beyond what the natural economics would deliver. The Dimensions free tier and BigQuery access [24, 28] represent strategic commercial decisions to push the inner boundary outward. OpenAlex [58] represents philanthropic funding achieving a similar effect. The Barcelona Declaration [9] is, in effect, an attempt to create coordinated pressure to push the inner boundary outward across many data types simultaneously. The inner boundary is not solely determined by production cost—it is also shaped by values, strategy and governance choices.

A consideration that cuts across the three demand drivers and the geometric analysis above concerns the equity implications of how the annulus is structured. In a world where AI can be used to enhance and enrich base-level data, institutions with computational resources, technical talent and data science capacity can run their own enhancement pipelines—resolving affiliations, classifying output, identifying collaboration opportunities. Institutions in under-resourced settings cannot. The data is nominally open, but the capacity to extract value from it is profoundly unequal.

This creates a strong case for centralised provision at accessible cost. If each institution must independently enhance its own data, the gap between rich and poor institutions widens. If intermediaries—whether commercial or community [24]—produce enhanced, trustworthy data that everyone can agree is a source of “truth” for certain evaluative activities at a consistent quality standard, the baseline rises for everyone. The centralised model is not just more computationally efficient; it is more equitable, because it sets a floor below which no institution needs to fall [15]. Lane [40] has articulated this principle forcefully in the context of public data systems: Data infrastructure should be designed so that access does not depend on insider knowledge or privileged networks, because “unless a researcher is able to tap into a network of cognoscenti, they would not know about the data, or not know how to use it” [39]. The same logic applies to scholarly metadata: the open core must be not merely technically accessible but practically usable by institutions at all resource levels. Adams, Gurney, Hook and Leydesdorff [1] have demonstrated what structured data can reveal about collaboration patterns in Africa—analyses that would be impossible without the kind of institutionally resolved, openly available metadata that the inner circle of the annulus is designed to provide. More recently Pinfield [54] argues that nominal openness isn’t sufficient when the capacity to extract value from open data is unequally distributed.

The governance implication is that public investment should focus on ensuring that the baseline of structured data available to all institutions is as high as possible—not on eliminating the annulus entirely. The annulus above the baseline serves differentiated demand from users who can afford to pay for frontier refinement. The baseline—the inner circle—serves the equity function of ensuring that under-resourced institutions are not excluded from the structured data they need for competent research management and strategic decision-making. In some sense, this constitutes a modern form of institution building—in this case not research-performing institutions but rather social institutions that define norms and expectations of data, its quality and its uses.

Consider a single segment of the annulus at a given point in time. Let ri denote the inner radius (the openness boundary) and ro the outer radius (the structuring frontier). The annulus width is w=ro−ri and the openness ratio is ρ=ri/ro.

It is helpful to define the value and cost functions in an order that parallels how data enter the system: structuring first, and open provision as an overlay on structured data. We therefore begin with the total value and cost of structuring, and then introduce separately the additional welfare and different cost profile associated with making part of the structured data openly available.

Value of structuring. Let V​(ro) denote the total value, to all users, of having data structured up to frontier level ro, evaluated at whatever access terms apply (paywalled, tiered or free). V is increasing and concave in ro: deeper structuring yields diminishing returns as progressively more specialised data types are brought into the structured domain.

Cost of structuring. Let C​(ro) denote the full cost of producing and sustaining structure up to level ro—entity resolution, disambiguation, classification, and the ongoing stewardship required to keep the structured representation current as the underlying record evolves [18, 10]. C is increasing and convex: the easy structuring tasks (for example, applying DOIs, resolving common institutional names) are accomplished first, and each additional unit of frontier structuring requires more domain expertise, more validation and continuing maintenance. We do not separate production from maintenance because they are incurred jointly and scale together with ro.

Openness premium. Let B​(ri) denote the additional welfare gain from making the range [0,ri] openly available rather than providing it on restricted terms—the equity, access and knowledge-spillover premium that openness is incremental to the value captured in V. B is increasing and concave in ri: the first units of open provision (basic bibliographic metadata, core identifiers) have enormous marginal value because they set a floor for all institutions, while later units have diminishing marginal impact. This is where the equity argument of Sec. III.5 enters formally—the social weight on the early units of B is high because they serve under-resourced institutions that would otherwise be excluded [61].

Cost of the openness overlay. Let M​(ri) denote the additional cost of running the openness overlay on the range [0,ri]: data standardisation and governance, free distribution at scale, community oversight, and the persistence and preservation guarantees that openness requires. M is increasing in ri and is subject to external pressures that may raise it exogenously—the AI-harvesting cost inflation documented by Crossref [23] enters through M rather than C.

Under this decomposition, paywalled data inside the annulus incurs C but not M; open-core data incurs both. The social welfare function is then

W = V​(r_o) + B​(r_i) − C​(r_o) − M​(r_i).         (1)

This is subject to a sustainability constraint: the system must be financially viable. In general, revenue depends on both boundaries, since deeper frontier refinement commands higher marginal revenue per unit of width than shallow refinement of commoditised data. The appropriate object is therefore R​(ri,ro). Within a single segment of the annulus, where the radial range is narrow, revenue is locally well approximated as a function of width alone, and we write R​(w) with the understanding that this is a local reduction. We return to this point in Sec. IV.3. Revenue plus any public subsidy S must cover the costs:

R​(w) + S ≥ C​(r_o) + M​(r_i).         (2)

The constrained optimisation yields first-order conditions that characterise the optimal boundaries. For the inner boundary,

B′​(r_i) = (1 + λ) ​[M′​(r_i) + R′​(w)],         (3)

and for the outer boundary,

V′​(r_o) = (1 + λ) ​[C′​(r_o) − R′​(w)],         (4)

where λ≥0 is the shadow price of the sustainability constraint and a dash implies the derivative of the function with respect to its natural variable, thus B′​(ri)=d​B/d​ri. λ measures the social welfare gained from relaxing the constraint by one unit—for example, through an incremental unit of public subsidy. When revenue plus subsidy more than covers costs, the constraint does not bind and λ=0; the first-order conditions reduce to the unconstrained conditions B′​(ri)=M′​(ri)+R′​(w) and V′​(ro)=C′​(ro)−R′​(w). When the constraint binds tightly, λ is large and the annulus must do more of the work of sustaining the system.

The first-order conditions have a direct intuitive reading. Equation (3) states that the marginal social value of expanding the open core, B′​(ri), should equal the marginal cost of doing so—directly, through the incremental cost of open provision, M′​(ri), and indirectly, through the revenue forgone by narrowing the annulus, R′​(w). The weight (1+λ) reflects the fact that, when money is tight, costs and forgone revenues count more heavily against social welfare. Equation (4) is the symmetric condition for the outer boundary: the marginal value of frontier structuring, V′​(ro), should equal the marginal structuring cost, C′​(ro), less the marginal revenue gained from widening the annulus, R′​(w), again weighted by the tightness of the financial constraint. Readers seeking a textbook treatment of the underlying constrained-welfare machinery will find the most relevant material in Stiglitz [61] and, at greater technical depth, in Atkinson and Stiglitz [8].

Figure 3 explores these conditions pictorially. Panel (a) plots net welfare W as a function of annulus width w, holding the outer boundary at its optimal level: the curve is an inverted-U with maximum at w∗. As w→0 the sustainability constraint binds and frontier investment becomes unsustainable; as w grows large the social benefit of openness is progressively forgone. The asymmetry of the curve is deliberate: the left shoulder reflects a discrete feasibility collapse (the constraint ceases to hold), while the right shoulder reflects a continuous opportunity cost (forgone units of B​(ri)). Panel (b) shows the boundaries ri and ro and the width w of the annulus.

Even without solving the optimisation for specific functional forms, the framework yields several qualitative predictions that are, in principle, testable.

Prediction 1: the optimal annulus width is wider where structuring costs are higher. When the marginal cost (i.e. the cost of obtaining an additional data point in a given set) of structuring data C′​(ro) is large, the sustainability constraint binds more tightly (higher λ), and more revenue from the annulus is needed to sustain frontier investment. This explains why the annulus persists for data types that require deep domain-specific enrichment (pharmaceutical patent linkage, translational alignment data) while narrowing for data types where AI has reduced structuring costs.

Prediction 2: the optimal width is narrower where the social benefit of openness is steep. When the marginal welfare gain (i.e. the welfare associated with making open an additional data point in a given data set) B′​(ri) is large—for data types essential to basic research management, where equity concerns dominate—the first-order condition (3) pushes ri outward, narrowing the annulus. This formalises the intuition that governance should prioritise high openness ratios for foundational data types.

Prediction 3: the optimal width shrinks as technology reduces structuring costs. As AI and standards adoption reduce C​(ro), the sustainability constraint loosens (lower λ), and the inner boundary can move outward. This is the formal version of the claim that technology compresses the annulus—but it also predicts that the compression is modulated by the shadow price, not automatic. There are a variety of assumptions implicit in this. Two of the most significant are that: i) the externalities associated with data labelling and the environmental impact of AI are negligible; ii) that algorithmic data improvement finds a systematic structure that allows context of data improvements to travel with metadata in a transparent manner.

Prediction 4: public subsidy is a substitute for annulus width. A larger S relaxes the sustainability constraint, allowing a thinner annulus at the same level of frontier investment. The Entrepreneurial State model [43] corresponds to the limiting case S→S∗ where subsidy fully replaces annulus revenue and w→0. The functional annulus model corresponds to moderate S and moderate w. The framework makes explicit what each model asks of the public purse. The risk of this model is that innovation may lack an appropriate efficiency moderator.

Prediction 5: an annulus that is too thin slows the entire system. This follows from the structural constraint that the inner boundary cannot advance faster than the outer boundary: ri≤ro at all times. If the annulus is compressed below the level at which frontier investment is sustainable (R​(w)+S<C​(ro)+M​(ri)), the outer boundary stalls—and with it, the inner boundary. Open provision is bounded above by frontier structuring. This is the formal expression of the argument that the annulus is functional: eliminating it does not merely reduce commercial revenue but reduces the rate at which the open core can expand.

The framework is structurally homologous to the Nordhaus optimal patent life derivation [50], but differs in two important respects. First, in the patent case, the deadweight loss arises from monopoly pricing during the exclusivity period—a dynamic that Jaffe and Lerner [31] have documented can lead to patent systems in which exclusivity periods bear little relationship to the investment required. In the annulus case, the analogous loss arises from restricted data access: institutions that cannot afford refined data make worse decisions than they would with full access, and the research ecosystem as a whole operates below its potential [7]. Second, patent life is uniform across all inventions within a jurisdiction. The optimal annulus width is a function of the data type’s characteristics—its structuring cost profile, its demand heterogeneity, and the social weight placed on open access to it. The framework does not yield a single optimal width but an optimal width function w∗​(C′,B′,V′,λ) that varies across segments of the annulus diagram. This is more complex than the patent case but also more realistic, since different data types in the scholarly ecosystem clearly operate under different economic conditions.

The framework has important limitations. First, the functional forms of B, V, C, M and R are not known empirically for any data type in the scholarly ecosystem; their estimation is itself a research programme (see Sec. IX). Second, the shadow price λ is not directly observable; proxies would need to be developed—for example, the ratio of unmet demand for open data to available public funding could serve as a coarse indicator of when the constraint binds tightly. Third, the reduction from R​(ri,ro) to R​(w) is a local approximation, valid within a single segment of the annulus where the radial range is narrow. Across segments, and at very different radial positions, revenue depends on the absolute level of structuring as well as on its differential from the open core, and the general form R​(ri,ro) is appropriate; the qualitative predictions of Sec. IV.2 are robust to this generalisation because they depend on signs of first and second derivatives rather than on the specific reduction to width. Fourth, the model is static: it characterises the optimal annulus at a point in time rather than the optimal trajectory of both boundaries. A dynamic extension—casting the problem as an optimal control problem with equations of motion for ri​(t) and ro​(t), driven by technological change and standards adoption—would be a natural next step, and would connect to the broader literature on the optimal timing of technology diffusion.

We note these limitations not to undermine the framework but to identify the empirical and theoretical work required to make it operational. Even in its current form, the framework provides something that the governance conversation around open research information has lacked: a formal language for reasoning about the trade-offs involved in setting the boundary, and a set of testable predictions about how the annulus should respond to changes in technology, demand and policy.

AI techniques—automated metadata extraction, entity resolution, semantic classification, citation parsing—have lowered the cost and increased the speed of basic data structuring. Tasks that previously required teams of manual curators can now be accomplished computationally at a fraction of the cost. This is unambiguously positive: it pushes the inner boundary of the annulus outward, expanding the volume of data that can be provided openly, with “appropriate provenance”.

Additionally, the distribution of benefit is uneven. AI is most powerful when applied to large, well-organised data collections. Actors who already hold substantial structured data assets gain disproportionate advantage because their existing assets provide training data, ground truth and computational context [60].

A less-discussed effect of AI is that it raises the quality threshold at which data refinement has commercial value. As basic structuring becomes commoditised through AI automation, the annulus does not disappear—it migrates to higher-order refinement tasks. The commercially valuable frontier moves from “can you structure this data at all?” to “can you structure it at a quality level that supports investment decisions, regulatory submissions or competitive strategy?”

This dynamic is familiar from other technology-intensive industries. In financial data, the commoditisation of basic market data did not eliminate the market for refined analytics; it created a new premium tier of algorithmic intelligence. In geospatial data, the availability of free satellite imagery did not eliminate demand for domain-specific analysis; it shifted the value frontier from data acquisition to data interpretation. The same pattern is visible in scholarly data.

AI also introduces a systemic quality risk that has received insufficient attention. When multiple actors independently use AI to enhance metadata without tracking the provenance and processing history of their enhancements, the result is not merely duplicated effort—it is a potential quality degradation. An AI-derived institutional affiliation that is contributed back into a shared system without its processing history becomes, for the next consumer, an apparently authoritative data point whose reliability cannot be assessed. If that consumer’s AI then builds on it, errors compound. Porter [56, 57] has articulated this risk clearly: AI enhancement of metadata without understanding or context can lead to poorer quality data, as downstream users do not understand the full processing and provenance of a piece of metadata that has been contributed to a centralised system without the details of its history.

This creates a system-level efficiency argument for centralised structured data intermediaries—whether open or commercial—that goes beyond the usual access debate. The intermediary exists not to restrict access but because centralised normalisation with provenance tracking is more efficient and more reliable than distributed rederivation without it. In an era of concern about computational carbon footprints, the duplication cost of many independent AIs repeatedly rederiving the same structured data—rather than consuming it from a maintained, provenanced central store—is itself a consideration.

The most developed case for public intervention in knowledge infrastructure is Mazzucato’s Entrepreneurial State [43], extended in her work on mission-oriented policy [44] and value theory [45]. Mazzucato argues that the state is not merely a passive corrector of market failures but an active co-creator of markets and technologies, and that publicly funded research constitutes a public investment whose returns should accrue to the public. Open knowledge infrastructure fits naturally into this framework: if public funding produces the research, the state should invest in the infrastructure required to make that research findable, usable and assessable as a public good. This argument has significant force. State investment has produced genuine public goods—from identifier infrastructure (ORCID, ROR) to national open science initiatives—and the Mazzucato framework provides the strongest theoretical justification for continued public investment in the open core of the annulus.

Moreover, the question of how to track and measure the returns on public investment in research infrastructure—which Lane, Owen-Smith and Weinberg [41] have recently addressed in the context of AI—is itself dependent on the kind of structured, linked metadata that the annulus model describes. The Entrepreneurial State cannot assess whether its investments are generating public value without the data infrastructure to measure outcomes, creating a recursive dependency: the state needs structured data to justify its investment in structured data.

But applying the Entrepreneurial State Model (ESM) to the full spectrum of data refinement needs creates difficulties that the annulus framework makes visible. The welfare framework in Sec. IV makes the trade-off explicit: the ESM corresponds to the limiting case in which public subsidy S fully replaces annulus revenue and the annulus width w approaches zero. This is logically coherent but practically demanding for three reasons.

First, cost allocation. In an idealised scenario, public institutions could centralise the refining process so as to avoid inefficiency and duplication of effort. However, in bearing the full cost of refining data to the quality levels required by pharmaceutical companies, venture capital firms and corporate R&D departments, the public subsidy flows disproportionately to private beneficiaries. This is not market creation—the canonical justification for the Entrepreneurial State—but public subsidy of private competitive intelligence [48]. The distinction matters: Mazzucato’s argument is strongest when the state creates infrastructure that enables private innovation (roads, internet protocols, basic research); it is weaker when the state produces the specific refined products that private actors would otherwise pay for.

Second, fiscal fragility. State funding is subject to political cycles and fiscal pressures, creating structural vulnerability. A knowledge infrastructure entirely dependent on public funding is exposed to exactly the kinds of budgetary shocks that the Mazzucato framework seeks to prevent in other domains. The history of state-funded data infrastructure is not reassuring: databases have been defunded, privatised, or allowed to decay when political attention shifts. The annulus model suggests a more resilient arrangement in which the open core is sustained by a combination of public investment and revenue from commercial frontier activity, diversifying the funding base rather than concentrating it in a single source.

Third, geopolitical risk. In a multipolar geopolitical environment, state-funded knowledge infrastructure carries risks of what Jasanoff [33] has termed divergent “civic epistemologies”—different political cultures’ ways of establishing what counts as reliable knowledge. A knowledge commons anchored to any particular state, or even a coalition of like-minded states, risks encoding particular epistemological assumptions into what presents itself as a universal infrastructure [15]. The concentration of infrastructure investment in the Global North has already produced a scholarly record with significant geographic biases; extending state-funded provision without addressing these structural biases may intensify rather than resolve the problem.

The annulus framework suggests a middle path: the Entrepreneurial State model is the right approach for the open core (foundational metadata, identifier infrastructure, the baseline that all institutions need), while the annulus provides the economic space for frontier refinement that serves differentiated demand and whose costs should not be socialised across the public purse. The governance challenge is ensuring that the boundary between these two zones is set in the public interest rather than by market power alone.

An alternative governance mechanism—one that has received less theoretical attention than it deserves—is already operating in part of the scholarly data ecosystem. Crossref, orignally as an industry collaboration among publishers and now expanding to be more inclusive in its membership, functions as a de facto boundary-setting institution for one zone of the annulus. When Crossref expands the scope of standard metadata disclosure—requiring, for example, that deposited records include reference lists, abstracts or ORCID identifiers—it effectively moves a data type from the annulus into the open baseline. This does not happen through state mandate or market competition but through collective agreement among the publishers of the underlying data.

This is a genuinely distinctive institutional mechanism. It is not state provision, not market dynamics, and not community self-organisation in the Ostrom [51] sense. It is collective disclosure by an organised industry body, and it has been remarkably effective at expanding the open core for data types that publishers already produce. Crossref has an increasingly diverse membership including publishers, research institutions, funders and governmental organisations. But the observation that Crossref has, without anyone having designed it for this purpose, become a boundary-setting mechanism for one part of the annulus raises an important question: under what conditions might similar mechanisms emerge for other data types? And might Crossref itself, with an appropriately expanded governance structure, play a broader role?

The Barcelona Declaration [9, 38] introduces a governance logic that is compatible with the functional annulus model. Rather than mandating specific data to be free, the Declaration frames openness as a civic obligation—what Porter [56, 57] has called “research information citizenship”—and distributes responsibility across producers, consumers and aggregators of metadata. Waltman [67] has argued that responsible research assessment requires open scholarly metadata—a position that the annulus framework refines: the question is not whether metadata should be open in principle, but which metadata types should be inside the open core at any given stage of the system’s maturation.

This framing is significant because it positions the Declaration not as a regulation but as a norm-setting body. In the same way that the scholarly community has developed informal norms about PhD embargoes and data sharing, the Barcelona Declaration could be the venue where the community develops norms about which data types should be inside the open core, what quality standards apply to open metadata, and what responsibilities different actors have in the production chain. The Declaration’s membership includes funders, institutions, and infrastructure providers—arguably the right constituency to develop these norms, though one could ask whether it should expand to include the corporate research users whose data needs shape part of the annulus.

Assessed against Ostrom’s [51] design principles for commons governance, the Barcelona Declaration framework has both strengths and gaps. It establishes boundaries and articulates proportional responsibilities. But it lacks effective monitoring of compliance, graduated sanctions for non-compliance, and formal conflict resolution mechanisms. The history of analogous declarations—the Budapest Open Access Initiative, DORA, Plan S—suggests that declarations without enforcement often fail to change institutional behaviour at scale [25, 70]. However, it is not necessary for there to be explicit, direct enforcement associated with these initiatives for them to be of value. Rather it is the engagement created by these approaches that engender change and new consensus in the policy environment. These initiatives do have each led to policy changes at institutional, local and national levels. Thus, ensuring that they provide inclusive mechanisms to host debate and strength their arguments to make them more potent in the policy arena would seem to be an important facet of their function.

The open access experience provides a brief but instructive parallel. Open access mandates attempted to collapse the annulus in scholarly publishing by requiring that publicly funded research be freely accessible. What followed was not the elimination of commercial logic but its displacement: article processing charges preserved publisher revenues while shifting their form, and in some analyses total costs to the research community increased, with the burden redistributed regressively [53, 35, 17, 13]. The annulus did not disappear; it migrated from access charges to publication charges while its structural function remained intact.

The annulus framework predicts this outcome: as long as there are genuine costs in the publication production system that exceed what can be funded through public subsidy alone, an annulus of some form will persist. The lesson for research metadata governance is that policy which treats the annulus as a pathology produces displacement rather than resolution. The functional annulus model avoids this trap by accepting the structural reality and focusing governance energy on the boundary conditions rather than on the elimination of commercial activity within the annulus.