Time as a Structural Barrier for a Circular Economy

Time as a Structural Barrier for a Circular Economy | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Time as a Structural Barrier for a Circular Economy JONAS GRAFSTRÖM This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8161933/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract Circular economy debates often acknowledge material lifespans and delays, but time is usually treated as a contextual issue rather than a structural barrier. The contribution is to reframe circular economy transitions as intertemporal processes by treating time as an endogenous structural barrier. A framework is developed that classifies goods into short-, medium-, and long-lived categories, demonstrating how lagged inflows and valuation biases suppress aggregate circularity even when technology improves. By making temporal mechanisms explicit, the analysis explains why indicators remain stagnant despite policy and efficiency gains. The contribution is to introduce time as an endogenous barrier, integrating insights from environmental and resource economics into circular economy theory and showing how delayed substitution shapes both firm investment and policy outcomes. Circular economy Material lifespans Intertemporal dynamics Structural barriers Resource recovery Figures Figure 1 1. Introduction Material recirculation and reuse in a circular economy (CE) does not occur instantaneously since goods have individual lifespans where some return for potential reuse/recycling within months, others after decades or a century (Eurostat, 2024 ). A food container may circulate in under a month (Sazdovski et al., 2022 ), a vehicle in twenty years (Held et al., 2021 ), and a building in fifty or more (Fahlstedt et al., 2024 ; Vollmers and Long, 2025 ). Barriers to a CE have been studied thought many aspects such as economical, technological, institutional and social (Kirchherr et al., 2018 ; Grafström and Aasma, 2022; Souza Piao et al., 2024 ; Gallego-Schmid et al., 2025 ) and geographical (Bourdin and Torre, 2025 ) yet describing time as a standalone variable has not been done. In much of the CE literature, time is treated as a contextual (e.g., “products last longer”) or practical issue. Time has not been absent from discussions of the circular economy. Concepts such as slowing resource loops (Vollmers and Long, 2025 ), extending product lifespans (Jerome and Ljunggren, 2025 ), and recognizing differences between short- and long-term strategies implicitly acknowledge that circularity unfolds over time (Bocken et al., 2016 ; Geissdoerfer et al., 2017 ). Recycling is often presented as an immediate loop-closing activity, while repair, remanufacturing, and design for longevity are viewed as long-horizon strategies with delayed benefits (Fullerton and He, 2024 ). There is a tension between short business cycles and longer ecological or material cycles (Timmers et al., 2024 ). Time as a barrier is under theorized and under researched. The purpose of the paper is to place time at the center of CE analysis and to demonstrate that it functions as a structural barrier. The paper theoretically formalizes how product lifespans, recovery rates, and historical inflows create delays in the substitution of primary- for secondary resources. Although, for example, both economics and industrial ecology recognize temporal aspects such as discounting, product lifespans, and lock-in, the circular economy literature has not treated time as a structural barrier in its own right. The core argument of the paper is that circularity at a given time, say t 0 ​, depends on decisions made in the past. Goods consumed at t 0 − τ i only reappear for recovery after their lifespan has elapsed, which means that current circular performance largely reflects lagged inflows rather than present effort. When long-lived goods dominate stocks, the relevant return point may lie far into the future, for instance at t n = t 0 + 50 in the case of buildings. In the interval between t 0 and t n ​, circularity indicators remain low even if recovery efficiency improves. As elaborated in Section 3.4, discounting further disadvantages long-lived strategies, since delayed benefits are heavily reduced in present-value terms (Hepburn and Koundouri, 2007 ). In economics, time has long been central to the analysis of investment, consumption, and policy. From Ramsey’s theory of saving (1928) to Fisher’s treatment of time preference (1930), and later work on irreversibility and delayed feedback (Arrow and Fisher, 1974 ; Pindyck, 1991 ; Gollier, 2012 ), the allocation of resources across time has been shown to structure welfare outcomes and policy evaluation. Similar principles apply to CE strategies, yet the explicit role of time has not been systematically incorporated into circular theory. The paper adopts a conceptual and analytical approach. It does not present new empirical data but instead develops stylized formalizations of temporal mechanisms that shape material recovery and circularity. Using simple dynamic expressions, it illustrates how lags, mismatches, and discounting effects arise from the interaction between product lifespans, recovery processes, and evaluation practices. Goods are separated into short-, medium-, and long-lived categories, which makes it possible to represent recovery flows across different temporal horizons. The main contribution is to reframe circular economy transitions as intertemporal processes by treating time as an endogenous (i.e., operating inside the system and actively shaping outcomes rather than being an external condition) structural barrier rather than a contextual factor. Existing literature often mentions that products last longer or that recycling is delayed, but time is rarely analyzed as a fundamental structural constraint. By formalizing temporal mechanisms, the paper clarifies why circularity indicators remain stagnant even when technology improves and policies are in place. The conceptual framework links circular economy analysis to long-standing insights from environmental and resource economics, where discounting, investment under uncertainty, and intertemporal allocation are central (Bretschger and Smulders, 2018 ). This connection helps to explain a puzzle in circular transitions: Under which conditions do lifespan distributions and recovery efficiencies keep the circularity ratio low despite policy effort and technical progress? By making time explicit, the paper provides both a theoretical foundation and policy relevance, showing that circularity evolves unevenly across temporal horizons and requires instruments that align with the time structure of material stocks 2. Time as a structural barrier in CE theory 2.1 Conceptual background: why time matters for circularity Circularity rates in the European Union, for example, have shown little movement over the past decade even though policies to promote it have been implemented. Figure 1 illustrates that the circularity rate in the European Union has remained largely stagnant between 2013 and 2023 across major material categories. Despite policy commitments and technological advances, secondary material use has not expanded significantly relative to total input demand. Time matters as a barrier for CE adoption because circularity, broadly speaking, depends on when materials return. Goods with different lifespans re-enter the economy non-simultaneously. The in- and outflow can be both calculated on by accountants in the firm and recognized by the factory workers. Even if today’s recovery technology is efficient some long-lived material stocks do not release materials for decades. For example, the approved plastics of today are maybe not the same as on a TV found in a barn in a summerhouse. Table 1 presents typical lifespans and return horizons for key material categories. Packaging can circulate back in weeks to under 2 years (Sazdovski et al., 2022 ). Textiles 2–5 years (Niinimäki et al., 2022). Consumer electronics return after 3–7 years. Vehicles circulate after 10–20 years (Held et al., 2021 ), and appliances after 7–15 years (Bakker et al., 2014 ). Buildings typically embed materials for 40–100 years, and infrastructure such as bridges and roads for 50–100 years. Industrial by-products such as slags and fly ash can re-enter loops continuously, with return times measured in weeks to years. The delay until substitution therefore ranges from less than a year for packaging to a century for infrastructure. Table 1 Materials, lifespans and circular strategies. Material / Sector Typical lifespan Strategy type(s) Loop time / return horizon Delay until circular benefit Recovery complexity Notes Packaging (plastics, glass, paper) Days – 2 years Recycling, reuse of containers Weeks to 1–2 years Immediate to moderate Low Fast return, large volumes Textiles (clothing, fabrics) 2–5 years Reuse, resale, repair, recycling 1–5 years Short to medium Low–medium Uncertain collection/reuse Consumer electronics (phones, laptops) 3–7 years Repair, resale, remanufacture, recycling 3–7 years Moderate Medium High obsolescence, logistics barriers Vehicles (cars, trucks) 10–20 years Remanufacture, component reuse, recycling 10–20 years Delayed Medium Recovery visible only after a decade Appliances / machinery 7–15 years Repair, remanufacture, recycling 7–15 years Medium to delayed Medium Modular design can shorten loops Buildings (residential, commercial) 40–100 years Design for longevity, component reuse, recycling 40–100 years Very delayed Medium–high Dominant in stocks, locked for generations Infrastructure (roads, bridges, utilities) 50–100 years Design for longevity, industrial symbiosis, recycling 50–100 years Very delayed High Extremely slow turnover Industrial by-products (slags, fly ash, residues) Continuous Industrial symbiosis, recycling Weeks to years Immediate if logistics exist High Rapid loops possible Recovery complexity refers to the difficulty of coordinating recovery flows across actors, technologies, and time horizons. Low complexity materials (e.g., packaging) return quickly and require limited coordination, whereas high complexity materials (e.g., infrastructure) involve multiple stakeholders, uncertain material quality, and a long time horizons before recovery become visible. Recovery always occurs with a delay, since secondary resources become available only once goods reach the end of their lifespan. During that waiting period, virgin extraction continues to dominate. The past further constrains the future. Historical inflows of long-lived goods determine when and how recovery will occur, so a housing boom today locks materials into stocks that will not return until late in the century. Economic evaluation adds another layer of disadvantage, since benefits that occur thirty to fifty years later are heavily discounted, which makes long-lived circular strategies appear less attractive than short-term measures such as recycling. 2.2 A theoretical view on how time affects economic decisions Economics has long treated time as a central structuring variable. From Ramsey's early treatment of intertemporal welfare (Ramsey, 1928 ) to Fisher’s work on time preference (Fisher, 1930 ), the allocation of resources across time has shaped how economists model investment, discount future outcomes, and evaluate long-run policy goals. In environmental economics, the incorporation of time has allowed for formal treatment of lagged feedback and delayed benefit features that play a critical role in the assessment of long-horizon problems such as climate change and resource depletion (Bretschger and Smulders, 2018 ). Several strands of economic theory inform how temporal features can be conceptualized. Böhm-Bawerk’s work in the late nineteenth century marked a step in bringing time explicitly into economic theory (Böhm-Bawerk, 1884). By differentiating between consumption goods and capital inputs across temporal stages, he provided a foundation for understanding why interest rates are positive. Böhm-Bawerk´s reasoning laid the groundwork for the concept of time preference, which later evolved into formal models of discounting used in macroeconomics and environmental economics. In parallel, Hotelling’s analysis of exhaustible resources (1931) demonstrated the long-term dynamics of economic activity. Property rights and predictable legal frameworks are key enablers in an economy since it enables exchange and long-term contracting (Hayek, 1945; North, 1990 ). Goods remain in use for decades, meaning that ownership and responsibility may not become relevant until far into the future. If rights are unclear, the passage of time intensifies the institutional barrier, as future actor’s face disputes over materials embedded long ago. Information problems also have a temporal dimension. Akerlof (1970) showed how quality uncertainty undermines markets for goods. In a circular setting, quality uncertainty is magnified by long delays. The quality of materials that will return in 20, 50, or 100 years cannot be credibly guaranteed at the time of production. And a hundred years from now what storage of information will it still be that works (likely not the floppy-disk or CD)? Investors might hesitate to commit to recovery capacity when the flow of information stretches across decades. What begins as a manageable information asymmetry today becomes more severe once the time lag is considered. Arrow and Fisher ( 1974 ) and Pindyck ( 1991 ) emphasized the value of waiting in settings where payoff is uncertain and irreversible, a logic directly applicable to long-horizon circular strategies such as product-as-a-service or modular design. The capital theory of investment—particularly under depreciation—suggests that systems with slow capital turnover, such as manufacturing assets or durable goods, may structurally resist rapid shifts (Hartwick, 1990 ; Berndt, 1991 ). A related perspective comes from vintage capital theory (Boucekkine et al., 2011 ), analyzing overlapping generations of capital goods shape production and investment dynamics (Johansen, 1959 ; Solow et al., 1966 ; Malcomson, 1975 ). Capital is not believed to be homogeneous but composed of “vintages” that embody different technologies and depreciation profiles. Circular systems display a comparable structure. Goods with short, medium, and long lifespans can be treated as vintages that coexist within the economy, each generating disposal flows on different time horizons (developed in section 3 ). Just as older vintages of capital constrain the speed of technological diffusion, long-lived material stocks constrain the speed of circular substitution. Even if newer goods are designed for high recoverability, the effective circularity of the system remains shaped by older vintages that persist in use. In parallel, models of delayed environmental feedback have drawn attention to the mismatch between cause and effect in ecological and economic systems (Wu et al., 2022 ). For example, the lag between greenhouse gas emissions and atmospheric accumulation has been used to justify declining discount rates in long-term policy assessments (Gollier, 2012 ; Cropper et al., 2014 ). Efforts to make the economy more circular may generate analogous mismatches. Delayed substitution effects, coordination time, or lifespan-based turnover can disconnect present investment from observable short-term gains, creating conditions where socially efficient outcomes are not aligned with private return expectations (Tessitore et al., 2023 ). Behavioral literature complements this economics structural view by emphasizing bounded rationality and present bias in economic decision-making (Tsoukis et al., 2025 ). Present bias means that near-term costs outweigh long-term benefits. Status quo bias and bounded rationality (Kahneman and Tversky, 1979; Samuelson and Zeckhauser, 1988 ) reduce the willingness to depart from established practices. When recovery strategies only deliver returns after decades, the psychological weight of delay could discourage adoption. Circularity based on repair, reuse, or longevity provides slow accumulating benefits, whereas short-lived recycling produces quick but limited gains. Empirical studies consistently show that consumers and firms underweight future benefits, especially when gains are uncertain, intangible, or distant (Laibson, 1997 ; Frederick et al., 2002 ). Path dependence and lock-in, as described in technology adoption models (Arthur, 1989 ), also interact with time. The QWERTY setting on the keyboard might not be the most efficient, but it will last. Long-lived assets such as infrastructure not only tie users to a given technology, but they also determine material flows for generations. Superior recovery methods may exist, yet their impact is deferred until current stocks or personnel are retired. Time therefore strengthens lock-in by extending its influence over long horizons and making transitions slower and more costly. Family firms can foster long term decision making but also be conservative and hindering change (Vollmers and Long, 2025 ). If a historic way has been practiced by your parents it might be harder to change that compared to being a CEO for a firm that you will leave in due time. The role of discounting itself has been widely debated in both environmental and climate economics (Conceição and Zhang, 2010 ). While standard models apply constant exponential discounting, alternative formulations have emerged to better reflect ethical and empirical concerns about intergenerational fairness and deep uncertainty (Stern, 2007 ; Heal, 2009 ). In the context of circular transitions, discounting interacts directly with the delayed return profiles described in the next section. If policy or capital markets heavily discount the future, slow-return circular strategies may appear inefficient even when their long-run benefits are substantial. Collective action problems have similarities with discounting mentioned above; they reinforce the structural role of time. Ostrom ( 1990 ) points out that when costs are concentrated in the present but benefits are dispersed across actors and over time, individual incentives misalign with collective welfare. In circular systems, the recovery of long-lived goods resembles such a dilemma: firms hesitate to invest early, since future material returns are uncertain and widely shared, even though coordinated commitment would raise long-term benefits. Time therefore interacts with institutional design, turning delayed benefits into a coordination challenge as well as an economic one. 3. Method and approach The methodological approach is initially analytical and conceptual rather than empirical. The purpose is to develop a stylized representation of how time functions as a structural barrier to circularity. The model builds on standard techniques in environmental and resource economics, where formal expressions are used to clarify dynamic relationships rather than to estimate them empirically. The equations therefore serve as heuristic devices—tools that expose how temporal mechanisms influence observable outcomes in circular systems. The model assumes that goods differ in their lifespans and that recovery processes introduce time lags between material inflows and outflows. Recovery efficiency, discounting, and synchronization costs are treated as endogenous parameters that jointly determine system-level circularity. Goods are grouped into three lifespan classes: short-, medium-, and long-lived, based on average return horizons found in the literature (Bakker et al., 2014 ; Held et al., 2021 ; Sazdovski et al., 2022 Niinimäki et al., 2022). Each class produces recovery flows at different points in time, creating asynchronous supply and demand for secondary materials. The analytical framework uses continuous-time notation to illustrate how stock–flow interactions evolve over time. Equations (1–13) formalize the relations among disposal flows, recovery efficiency, stock accumulation, and delayed substitution effects. The analysis proceeds in two steps. First, it identifies timing mismatches, recovery delays, and valuation biases as sources of temporal frictions. Second, it demonstrates how these frictions reduce observed circularity even under technological improvement. For the equation part no new data are collected; instead, the model operates as a conceptual simulation of intertemporal dynamics that connects economic reasoning about time with circular economy processes. The equations were developed through a combination of established economic theory and analytical reasoning (e.g., Varian, 1992; Acemoglu, 2008). The equation formulation draws upon foundational models in intertemporal and resource economics, where relationships between stocks, flows, and valuation over time have been formalized. The expressions were compared with equivalent representations in dynamic stock modeling and vintage capital theory (see Boucekkine et al., 2011 ). Conceptual validation was achieved through informal consultation with academic colleagues working in economics and circular economy research, whose feedback informed refinements in notation. The final equations were cross-checked against standard economic formulations of market processes and investment dynamics to confirm that they matched analytical logic rather than ad hoc assumptions. The equations used in the present analysis follow the standard structure of dynamic stock modelling: lifespans are represented as delayed outflows from earlier inflows, recovery efficiency evolves through time, and discount processes reflect intertemporal valuation. The formulation is consistent with the analytical approaches outlined in recent research on lifetime functions, temporal cohorts and hazard-based representations of stock turnover, including the treatment of age-specific and period-specific failure rates. Krych et al. ( 2025 ) provides explicit mathematical expressions for survival and hazard functions that serve as a reference point for lifetime-driven stock evolution. The approach taken here maintains that structure and applies it to the context of circularity analysis. 4. Formalizing the temporal dynamics of circularity The following sections introduce stylized equations to represent the temporal dynamics of recovery. The equation framework follows an analytical tradition established in earlier work on circularity barriers. Foundational inspiration is drawn from Grafström ( 2025a ) and Grafström et al. ( 2025b ). Those studies formalize dynamic constraints in metals and plastics systems. The present formulation adapts the underlying logic to a broader resource setting by translating core principles from that literature into a general representation of time dependent circularity. The structure used here aligns with the conceptual foundations outlined in those contributions and reflects an extension of their analytical approach. The intention is to integrate mechanisms already identified in previous research into a unified expression that clarifies how lifespans, recovery efficiency and delayed substitution interact across material systems. The equations are not predictive models but heuristic formalizations that clarify how delays, mismatches, and discounting influence circularity. Their role is to make explicit the structural effects of time that are otherwise described qualitatively in circular economy discussions. Section 4.1 formalizes timing mismatches and synchronization problems between disposal flows and current demand. Section 4.2 introduces lifespan classes: short-, medium-, and long-lived goods and shows how recovery dynamics differ across them. Section 4.3 links recovery flows to evolving material stocks and defines alternative measures of circularity. Section 4.4 incorporates discounting and delayed benefits to illustrate how economic evaluation systematically disadvantages long-lived strategies. 4.1 Timing sensitivity and storage as time-dependent barriers Circular recovery depends not only on efficiency but also on synchronization between disposal flows and current demand. Just in time and a CE does not go hand in hand, yet. Material recovery can stall due to poor synchronization. In Knoth et al., ( 2022 ), for example, architects, and contractors report that reclaimed components rarely appear when projects need them. Demolition schedules and disassembly lead times drift away from construction timelines or vice versa. Limited storage and rules (e.g., handling requirements) that tightly regulate waste storage, distance between stock and site add cost to every mismatch. Time is money and the combination turns viable material into an unattractive option for managers working under tight budgets and deadlines. It could be defined as a classic economic barrier but also one of time: $$\:\begin{array}{c}S\left(t\right)=R\left(t-\tau\:\right) \left(1\right)\end{array}$$ where S ( t ) is the secondary material available at time t , R ( t ) is the inflow generated by disassembly, and τ is the time required for demolition or deconstruction. The time lag means that what becomes available for reuse today reflects decisions made τ years ago. If demolition comes after new demand arises, supply arrives too late. If demolition occurs earlier, materials appear before there is a project that can use them. Demand for materials at time t can be written as D ( t ). The gap between what is needed and what is available is: $$\:\begin{array}{c}\varDelta\:\left(t\right)=D\left(t\right)-S\left(t\right) \left(2\right)\end{array}$$ If Δ(t) > 0, demand exceeds reclaimed supply, and new materials must fill the gap. If Δ(t) < 0, reclaimed materials arrive too early and sit unused. Perfect synchronization, Δ(t) = 0, is rare in practice. In most projects, mismatches dominate, which makes secondary inputs difficult to plan for within standard production schedules. For example, demolition schedules in construction rarely align with new material demand, which forces reliance on storage or virgin substitutes. A positive gap requires virgin extraction to fill the shortfall, whereas a negative gap requires storage or transport to manage early arrivals. The associated cost can be written as: $$\:\begin{array}{c}C\left(t\right)={c}_{s}\times\:max\left[0,S\left(t\right)\right]+{C}_{t}\times\:L, \left(3\right)\end{array}$$ where c s is the storage cost per unit, c t is the transport cost per unit, and L is the distance between stock and site. Even modest gaps between recovery and demand can create significant expenses. Storing large volumes or transporting them over long distances quickly erodes any savings from reuse. As a result, managers often find that reclaimed inputs become more costly than virgin materials once these timing-related frictions are accounted for. Equations 1–3 formalize reuse as a coordination problem between supply and demand. On the supply side, reclaimed materials enter the market only with a lag, since demolition and disassembly unfold over time and components become available only once the source asset reaches the end of its lifespan. On the demand side, production requires inputs according to its own schedule, largely independent of disposal flows. The result is a systematic disequilibrium: reclaimed supply often falls short when demand is high, and at other times exceeds requirements. Excess supply must be stored or transported, creating additional costs, whereas shortages require substitution with virgin inputs. Put differently, the effective supply curve for secondary materials is shifted forward in time relative to demand, which generates temporary surpluses and deficits. In economic terms, what may appear as a feasible technological option is converted into a binding cost condition once the temporal misalignment of supply and demand is considered. 4.2 Lifespan classes and recovery dynamics Goods differ greatly in how long they remain in use before returning to the economy. Now, let us for the sake of argument assume that material goods can be divided into three broad categories according to their expected duration of use. Class S (Short-lived): τ S ∼∈ [1–3] months, Class M (Medium-lived): τ M ∼∈ [1–20] years, and Class L (Long-lived): τ L ∼∈ [20–100] years. In formal terms: the disposal flow from class i at time t depends on what entered the economy τ i years earlier. Today’s recovery is yesterday’s inflow shifted forward by the lifespan of the good: $$\:\begin{array}{c}{DF}_{i}\left(t\right)={R}_{i}\left(t-{\tau\:}_{i}\right) \left(4\right)\end{array}$$ Let R ( t ) denote the inflow of raw material at time t , The disposal flow DF i ( t ) is determined by past inflows delayed by the average lifespan τ i . In other words, end-of-life flows observed today reflect production decisions made years or even decades earlier. Building on this, Eq. (5) introduces recovery efficiency. Disposal alone does not determine recovered supply; only the fraction that can be technically and economically recovered contributes to circularity. The recovered share of this disposal depends on the recovery rate γ i (t). The amount that is recirculated into the economy from class i is therefore: $$\:\begin{array}{c}{\varphi\:}_{i}\left(t\right)={\gamma\:}_{i}\left(t\right)\times\:{DF}_{i}\left(t\right) \left(5\right)\end{array}$$ The contribution of each class to circularity depends not only on its disposal flow but also on how much of that flow can be recovered. If recovery efficiency for class i is γ i , the recovered amount is γ i DF i (t) . Summing across all classes gives the total recovered input at time t . The circularity ratio is therefore: $$\:\begin{array}{c}C\left(t\right)=\frac{{\gamma\:}_{s}R\left(t-{\tau\:}_{s}\right)+{\gamma\:}_{m}R\left(t-{\tau\:}_{M}\right){+\gamma\:}_{L}R\left(t-{\tau\:}_{L}\right)}{R\left(t\right)} \left(6\right)\end{array}$$ Because the numerator reflects past inflows shifted forward by lifespans, while the denominator reflects current inflows, circularity indicators tend to stagnate when long-lived goods dominate stocks. This ratio shows why time matters for system-level outcomes. Short-lived goods generate visible substitution almost immediately. Medium-lived goods contribute only after a decade or two. Long-lived goods make little difference in the near term, even if recovery efficiency is high, because their inflows remain locked in the stock. If long-lived goods dominate total inflows, near-term circularity remains low regardless of improvements in recovery efficiency. The division into lifespan classes therefore illustrates a structural trap. Even as short-lived goods return quickly, they account for only a small share of total stocks. The bulk of material is embedded in long-lived assets, which means aggregate circularity indicators are weighted toward delayed flows. This explains why progress in recovery technology does not immediately translate into higher circularity at the system level. The responsiveness of circularity to an efficiency gain in class i can be written as: $$\:\begin{array}{c}\frac{\partial\:C\left(t\right)}{\partial\:{\gamma\:}_{i}}=\frac{R\left(t-{\tau\:}_{i}\right)}{R\left(t\right)}. \left(7\right)\end{array}$$ Short lifespans raise the ratio on the right. Long lifespans lower it. Gains therefore register quickly for short-lived goods and very slowly for long-lived assets. Disposal today reflects what was added to the stock τ i years ago. Circularity at any point in time is thus determined not only by present inflows and current recovery efficiency, but by yesterday’s inflows shifted forward by the lifespan of the good. Equations 4–7 make clear that secondary supply is always the shadow of past inflows. Short-lived goods re-enter the market quickly, so higher recovery rates translate into immediate outward shifts of effective supply. Medium-lived goods return only after a decade or more, which means today’s demand curve is still met largely by virgin inputs, regardless of technical recovery potential. Long-lived goods push this dynamic even further: the bulk of material embedded in buildings or infrastructure will not reappear for half a century, so efficiency gains in recovery remain locked into the future. In economic terms, the supply of secondary materials is intertemporal; it is governed less by current technology than by the time structure of past investment decisions. The circularity ratio therefore captures an intertemporal disequilibrium: demand is determined today, but supply is delivered with delays that can span generations. 4.3 Stocks, extraction, and an alternative circularity measure Circularity may fall in the short run even when recovery technology improves. The reason is that long-lived inflows expand total demand today but only return to recovery flows after several decades. This delay means that system circularity can stagnate or even decline despite higher recovery efficiency. Material stocks in each class ( M i ) evolve according to: $$\:\begin{array}{c}\frac{d{M}_{i}\left(t\right)}{dt}={R}_{i}\left(t\right)+{\varphi\:}_{i}\left(t\right)-{DF}_{i}\left(t\right) \left(8\right)\end{array}$$ where M i (t) is the stock of goods in class i∈{S, M, L}, R i (t) is new inflow, ϕ i (t) is recovered inflow, and DF i (t) is disposal flow. Since disposal is delayed by the lifespan τ i , the timing of returns depends on past inflows rather than current ones. Each flow’s return is therefore delayed and incomplete, depending on both its lifespan and the recovery system’s performance. Total raw material use is the sum over classes: $$\:\begin{array}{c}R\left(t\right)=\sum\:_{\varvec{i}\in\:\mathbf{S},\mathbf{M},\mathbf{L}}\left[{DF}_{i}\left(t\right)\times\:\left(1-{\gamma\:}_{i}\left(t\right)\right)\right] \left(9\right)\end{array}$$ where γi(t) is the recovery efficiency for class i . Today’s extraction is therefore the outcome of design and use decisions made in the past, shifted forward by product lifespans. It is also possible to define a disposal-based measure of circularity. The substitution share is: $$\:\begin{array}{c}\theta\:\left(t\right)=\frac{{\sum\:}_{i}{\varphi\:}_{i}\left(t\right)}{{\sum\:}_{i}{DF}_{i}\left(t\right)}=\frac{{\sum\:}_{i}{\gamma\:}_{i}\left(t\right)\times\:{R}_{i}\left(t-{\tau\:}_{i}\right)}{{\sum\:}_{i}{R}_{i}\left(t-{\tau\:}_{i}\right)} \left(10\right)\end{array}$$ This ratio captures the degree of circularity in the system at time t . Its value is determined jointly by the efficiency of recovery processes γ i ( t ), the profile of past inflows Ri ( t − τ i ), and the temporal mechanisms introduced by product lifespans τ i . As a result, system-wide circularity may stagnate or decline in the short run despite rising recovery efficiency when stocks are dominated by long-lived goods. Equations 8–10 emphasize that circularity is governed by stock–flow relations rather than instantaneous substitution. New inflows add to the stock of materials today, but the corresponding recovery flows emerge only after lifespans have elapsed. The system therefore carries a built-in delay: present extraction reflects past inflows shifted forward in time, not current design or efficiency alone. The consequence is that improvements in recovery technology may coincide with declining circularity indicators, since growing stocks of long-lived goods increase input demand without generating immediate returns. In economic terms, circularity at time t is an intertemporal outcome, shaped by the path of historical inflows, the temporal distribution of lifespans, and the discounting of delayed recovery. 4.4 Lags, discounting, and the evaluation of circular strategies The existence of time lags in material recovery has an additional consequence once economic evaluation is introduced. Benefits that arrive only after long delays are weighed less in present terms, which systematically disadvantages strategies aimed at long-lived goods. A building designed for recovery may release materials of high quality after fifty years, yet the value of that benefit is strongly reduced today. This creates a bias in favor of short-lived recovery, even when the long-term potential of long-lived assets is much larger. The effect of discounting can be expressed with a simple comparison. Suppose a strategy increases circularity by ΔC units per year. If the improvement is immediate, its present value under a social discount rate ρ is $$\:\begin{array}{c}{W}_{now}=\frac{\varDelta\:C}{\rho\:}. \left(11\right)\end{array}$$ If the same improvement is delayed by τ years, the present value becomes $$\:\begin{array}{c}{W}_{delay}=\frac{\varDelta\:C}{\rho\:}{e}^{-\rho\:t}. \left(12\right)\end{array}$$ The ratio of the two values is e −ρτ , which declines rapidly with both ρ and τ . At a discount rate of three percent, a benefit realised after forty years is worth less than one third of the same benefit obtained immediately. Private adoption decisions are subject to the same logic. Consider a project with a one-off cost Φ and a constant annual benefit b that begins only after a delay of τ . With discount rate r , the net present value is $$\:\begin{array}{c}V\left(\tau\:\right)=\frac{b}{r}{e}^{-\rho\:t}-\varPhi\: \left(13\right)\end{array}$$ Even when the project yields substantial long-run savings, the exponential decay in value with respect to τ makes adoption unattractive. The longer the delay, the less likely the project is to cross the investment threshold. Discounting amplifies the disadvantage of long-lived circular strategies, since their delayed benefits are given far lower present value than short-lived strategies, even when the ultimate returns are greater. Together, these layers demonstrate that time is not a peripheral issue but a structural barrier that slows CE transitions. Even with improving recovery technologies, the pace of progress remains tied to the temporal structure of stocks and the way benefits are valued across horizons. Equations 11–13 illustrate how discounting transforms delayed recovery into a structural disadvantage for long-lived goods. A benefit realized immediately retains most of its present value, but the same gain shifted decades into the future is sharply reduced once evaluated at any positive discount rate. From an economic standpoint, this introduces a systematic bias: projects aimed at long-lived assets appear less profitable, even when their eventual contribution is substantial. For private decision-makers, the option value of waiting becomes higher as delays lengthen, reducing incentives to invest in recovery capacity ahead of time. At the system level, this mechanism helps explain why circularity strategies cluster around short-lived goods, where returns are rapid and valuation losses minimal, and why sectors dominated by buildings or infrastructure struggle to attract comparable investment. Time, through the logic of discounting, thus acts as both an economic filter and a break on long-horizon circular strategies. 5 Result: connection to economic theory Section 4 can be brought together to show how time systematically constrains circularity. Table 2 summarizes section 4.1 – 4.4 and show how each temporal mechanism functions as a structural barrier. Table 2 Temporal mechanisms that create structural barriers to circular economy transitions. Temporal phenomenon How time creates the barrier Formal element Delayed recovery of materials Materials only re-enter after their lifespan has ended. For example, steel in a bridge built today will not be available until demolition several decades later, which means virgin steel continues to dominate current construction. \(\:S\left(t\right)=R\left(t-\tau\:\right),\) \(\:\varDelta\:\left(t\right)=D\left(t\right)-S\left(t\right)\) Timing mismatch between recovery and demand Recovered flows rarely coincide with the timing of new projects. A demolition may release timber months before a building is started, forcing storage or disposal, while the builder still purchases new wood. \(\:S\left(t\right)\:vs.\:D\left(t\right)\) Extra costs from poor timing When materials arrive too early or too late, they must be stored or moved. Large concrete components reclaimed from demolition may require long-term storage or costly transport to align with a future project, often erasing the financial advantage of reuse. \(\:C\left(t\right)={c}_{s}\times\:max\left[0,S\left(t\right)\right]+\) \(\:{C}_{t}\times\:L\) Different product lifespans Goods circulate at different speeds. A cotton shirt may return within two years, a car in fifteen, and a residential building only after half a century. Short-lived flows appear quickly but carry little weight in overall stocks, while long-lived flows dominate but remain locked for generations. \(\:{D}_{i}\left(t\right)={R}_{i}\left(t-{\tau\:}_{i}\right)\) Only partial recovery over time Not all discarded goods are usable when they return. A ten-year-old refrigerator may have recyclable metal, but plastics and electronics can be obsolete or degraded, limiting the recovery rate. \(\:{\varphi\:}_{i}\left(t\right)={\gamma\:}_{i}\left(t\right)\times\:{D}_{i}\left(t\right)\) Stagnant circularity Indicators remain flat when long-lived goods dominate. Even with better collection of textiles or packaging, overall circularity rates barely move if most material is tied up in buildings and infrastructure. \(\:C\left(t\right)\:=\frac{{\sum\:}_{i}{\gamma\:}_{i}{R}_{i}\left(t-{\tau\:}_{i}\right)}{R\left(t\right)}\) Speed of response to efficiency gains Efficiency improvements matter more in short loops. Better textile collection increases secondary supply almost immediately, but efficiency gains in construction will not show until buildings from the current boom reach end-of-life decades later. \(\:\frac{\partial\:C\left(t\right)}{\partial\:{\gamma\:}_{i}}=\frac{R\left(t-{\tau\:}_{i}\right)}{R\left(t\right)}\) Legacy of past material inflows Today’s consumption locks recovery for decades. For instance, copper installed in power grids during the 2020s will not return until late in the century, regardless of advances in recovery technology. \(\:\frac{d{M}_{i}\left(t\right)}{dt}={R}_{i}+{\varphi\:}_{i}-{D}_{i}\) Reduced value of future benefits Benefits that arrive far into the future lose present value. Designing a modular office building today may yield high-quality components in 40 years, yet investors discount that benefit so heavily that immediate recycling options appear more attractive. \(\:{W}_{delay}=\frac{\varDelta\:C}{\rho\:}{e}^{-\rho\:t}\) Delayed investment decisions Firms postpone investment until recovery flows are near. A company may plan to build a specialized plastics recycling facility but delay until volumes are sufficient, even if early action would generate higher long-run welfare. \(\:V\left(\tau\:\right)=\frac{b}{r}{e}^{-\rho\:t}-\varPhi\:\) The temporal mechanisms in Section 4 show that recovery flows arrive only after significant delays, as indicated in Eq. 4, that stocks expand long before disposal occurs, as indicated in Eq. 6, and that discounting lowers the value of distant returns, as indicated in Eq. 11. The same features generate collective action problems. In Ostrom’s framework (1990), the absence of institutions that align incentives leads to under provision of benefits that are dispersed across actors and over time. Applied to circular systems, firms face the option of waiting. Each actor prefers others to bear the cost of early investment in recovery infrastructure, since the eventual benefits will be shared but arrive decades later. Eq. 8 formalizes recovery efficiency as a function of investment timing, and Eq. 12 shows how delayed substitution limits near term gains. The outcome mirrors a failure of coordination. Several paradoxes follow. Improvement in recovery efficiency does not guarantee a rise in circularity in the short run, since relevant returns depend on past inflows for extended periods, as indicated in Eq. 5. Ambitious policy targets on five-year horizons generate limited movement when dominant stocks are long lived. Private investors face an option value of waiting even in cases where social welfare would increase with early action. Eq. 11 shows that valuation of future returns declines rapidly under discounting, which reduces the attractiveness of near-term investment. The apparent lack of progress is therefore consistent with a system governed by lags and valuation effects. Firm strategy benefits from aligning clocks. Procurement calendars can be coordinated with expected demolition windows through advanced purchase agreements and flexible specifications. In other sectors industrial symbiosis could be a way forward. Material exchanges with verified quality data reduce uncertainty when goods re-enter after long use. Contracts that recognize time value, for example by sharing storage and transport costs or by pricing options to call reclaimed stock later, can unlock adoption in sectors with volatile schedules. The temporal mechanisms represented in Equations 8–13 can be framed as a coordination game. Each firm faces the option to invest early in recovery infrastructure or to wait. As shown in Table 3 , the socially efficient outcome arises when both invest, since costs are shared and long-term recovery is secured. Yet the individually rational strategy is often to wait, since future benefits are delayed and discounted, while present costs are immediate. The result is a collective action problem in the Ostrom sense (1990): without institutional arrangements to align incentives, rational strategies produce under-investment in long-lived recovery capacity. Table 3 Payoff matrix: Invest in recovery infrastructure now vs. wait Firm A / Firm B Invest now Wait Invest now (5, 5) Both invest: infrastructure is built, costs are shared, future recovery is secured. (2, 6) A invests alone: A bears present costs, B free-rides on future shared benefits. Wait (6, 2) B invests alone: B bears present costs, A free-rides. (3, 3) Both wait: no early investment, circularity remains low, reliance on virgin inputs continues. The lifespan classes in Equations 4–7 parallel the structure of vintage capital theory (Johansen, 1959 ; Solow et al., 1966 ; Malcomson, 1975 ). In both cases, overlapping vintages coexist, with older stocks constraining the speed at which new technologies can influence outcomes. Just as older capital vintages slow technological diffusion in production models, long-lived goods in circular systems delay substitution and dampen the impact of improved recovery efficiency. The dynamics described in Equations 8–13 resemble the real options logic of investment under uncertainty (Arrow and Fisher, 1974 ; Pindyck, 1991 ). Since recovery from long-lived goods is delayed and uncertain, the value of committing capital today is reduced not only by discounting but also by the irreversibility of investment. Waiting preserves flexibility, while early action locks in costs without immediate returns. 6. Discussion: implications of time for circular transitions Time introduces both opportunities and constraints in circular transitions, one might say that there are two clocks of circularity at play. On the pro side, short-lived goods such as packaging or textiles demonstrate that rapid turnover allows technology and policy to translate quickly into measurable outcomes. Improvements in collection rates or recycling efficiency appear almost immediately in system indicators, and firms can capture near-term returns without facing long planning horizons. For policymakers, these sectors provide visible progress that can be achieved within electoral cycles, supporting credibility and accountability. On the contra-side, long-lived goods embody a different clock. Buildings, infrastructure, and capital equipment lock materials into use for decades, sometimes generations. From an intertemporal perspective, this means that even efficient recovery technologies cannot shift secondary supply until distant future dates. For private investors, the present value of those delayed benefits is sharply reduced once discounting is applied, reinforcing an incentive to wait before committing capital. For governments, the same delay undermines the effectiveness of short-term targets, since progress is structurally muted when long-lived stocks dominate. The temporal mechanisms in Section 4 show that recovery flows arrive only after significant delays, that stocks expand long before disposal occurs, and that discounting lowers the value of distant returns. These same features generate collective action problems. In Ostrom’s framework (1990), the absence of institutions that align incentives leads to under-provision of benefits that are dispersed across actors and over time. Applied to circular systems, firms face the option of waiting: each actor prefers others to bear the cost of early investment in recovery infrastructure, since the eventual benefits will be shared but arrive decades later. The equations formalize the intertemporal imbalance, and the outcome mirrors a coordination failure. Several paradoxes follow. Improvement in recovery efficiency does not guarantee a rise in circularity in the short run, since the relevant returns depend on past inflows, for some years at least. Ambitious policy targets on five-year horizons generate limited movement when dominant stocks are long-lived. Private investors face an option value of waiting even in cases where social welfare would increase with early action. The apparent lack of progress is therefore consistent with a system governed by lags and valuation effects. Firm strategy benefits from aligning clocks. Procurement calendars can be coordinated with expected demolition windows through advanced purchase agreements and flexible specifications. In other sectors industrial symbiosis could be a way forward. Material exchanges with verified quality data reduce uncertainty when goods re-enter after long use. Contracts that recognize time value, for example by sharing storage and transport costs or by pricing options to call reclaimed stock later, can unlock adoption in sectors with volatile schedules. Policy design gains from explicit time alignment. Short-lived sectors can support visible progress through high-frequency collection standards and minimum recycled content. Medium-lived sectors require stable rules that support remanufacturing, modular design, and access to spare parts for over a decade or more. Long-lived sectors benefit from design requirements for disassembly, building passports that preserve information over many years, public support for material banks, and demolition planning that treats end of life as a managed phase rather than an afterthought. Indicators that credit expected future substitution from assets already in service can help align political horizons with material horizons. The broader implication of this paper is straightforward. Circularity is an intertemporal allocation problem. Stocks reflect past choices, flows return on varied clocks, and evaluation rules favor near-term gains. Recognizing time as an endogenous barrier clarifies why observed progress can look flat despite policy and technological effort. A realistic transition path combines quick gains in fast loops with credible commitments that prepare slow loops for recovery many years ahead. The structural role of time creates intertemporal externalities: present actors extract and consume without accounting for how their choices constrain future recovery. Without corrective mechanisms, private incentives underweight long-run benefits, leading to underinvestment in design for longevity, modularity, and recovery capacity. Policy responses such as extended producer responsibility, material passports, or differentiated taxes can be understood as Pigouvian tools designed to internalize these temporal externalities. The analytical structure developed in the study advances circular economy research by introducing a formal treatment of time dependent mechanisms that shape system level circularity. Earlier frameworks have focused on technological conditions, material substitution and regulatory design, but limited attention has been given to the dynamic role of stock formation. The model provides an explicit representation of how goods with long lifespans influence observable outcomes by delaying return flows and creating asynchronous material cycles. The analytical expressions clarify how recovery efficiency, valuation patterns and stock accumulation interact over time and reveal structural barriers that remain in place even under favorable technological progress. The paper shows that circularity is influenced not only by the performance of recovery processes but also by the temporal structure of material systems. The contribution therefore lies in establishing a clear link between lifespan heterogeneity, delayed substitution and system level circularity. The formulation extends earlier work on dynamic material constraints by providing a general representation of time-based frictions that influence circularity indicators across sectors with pronounced stock accumulation. 7. Concluding remarks and directions for future research The novelty of the paper lies in integrating intertemporal economics into circular economy theory by making time an endogenous barrier rather than a contextual factor. By positioning time as a structural barrier, the analysis explains why circularity evolves unevenly across sectors and why short-term interventions often produce limited aggregate effects. The purpose of the paper has been to place time at the center of circular economy analysis and to show that it constitutes a structural barrier. The results demonstrate that recovery flows are never immediate but always delayed by product lifespans. The analysis clarified this dynamic through four cases: recovery lags, partial recirculation, aggregate circularity defined by past inflows, and the discounting of delayed benefits. Each case shows that time shapes outcomes as much as technology or institutions. The finding is that circularity is best understood as an intertemporal process. The implications are threefold. For policy, indicators must reflect recovery delays to avoid misleading assessments of progress. For practice, investment strategies must account for the long horizons associated with major material stocks. For research, further work is needed to measure lifespan distributions and to integrate time more explicitly into models of resource use and intertemporal choice. Recognizing time as endogenous rather than contextual provides a foundation for more realistic analysis and more durable strategies for circular transitions. The framework opens a range of theoretical extensions. One avenue is to explore stochastic lifespan distributions and uncertainty in recovery efficiency, linking the dynamics of circularity to models of irreversible investment. Another is to embed the analysis in overlapping generations settings, making explicit the intergenerational distribution of costs and benefits implied by long-lived stocks. Every product carries its own clock. A shirt comes back within a few years, a refrigerator after a decade, a bridge only when today’s students are retired. Markets respond to those clocks: supply of secondary materials arrives late, demand is always current, and the future is discounted. Circularity is therefore not a smooth loop but a staggered sequence of returns, shaped as much by time as by technology. Seeing the circular economy through this intertemporal lens reveals why progress is uneven and why strategies must be calibrated to the rhythms of material life. Why is circularity proceeding so slowly? Maybe it is because we have forgotten about time. Declarations Funding information Financial support from for FORMAS grant 2022-00635 - Barriers for a circular Swedish industry. The funder did not play any part in performing or planning this research. Responsibility for any remaining errors, however, resides solely with the author. Declaration of generative AI and AI-assisted technologies in the writing process. During the preparation of this work the author used ChatGPT to improve the language. After using this tool/service and to structure some of the equations, the author reviewed and edited the content as needed and take full responsibility for the content of the published article. Author Contribution I did it all. References Akerlof, G. A. (1978). The market for “lemons”: Quality uncertainty and the market mechanism. In Uncertainty in economics (pp. 235–251). Academic Press. Arrow, K. J., & Fisher, A. C. (1974). Environmental preservation, uncertainty, and irreversibility. Quarterly Journal of Economics , 88(2), 312–319. Arthur, W. B. (1989). Competing technologies, increasing returns, and lock-in by historical events. 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Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 21 Dec, 2025 Reviewers agreed at journal 11 Dec, 2025 Reviewers invited by journal 03 Dec, 2025 Editor assigned by journal 24 Nov, 2025 Submission checks completed at journal 22 Nov, 2025 First submitted to journal 20 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8161933","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":554620477,"identity":"3b911daa-7895-43d1-88b0-0b8c5411d40e","order_by":0,"name":"JONAS GRAFSTRÖM","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYBACxgYYi/kAmJLjI14LWwKYbczGRrR9UC2JbYS0MLf3Hvz4g6E2n7+N/fnjiopt6W3yPQaMPyrwOKznXLI0D8NxyxnHeAwbz5y5ndvGxmPAzHMGj5YZOQbSDAzHDBju9zA2NrZBtTC24dVi/PMHUIv8MfaHIC3pbEAtjD//4dViJsHDUGNgcIzBEKQlAaSFgbcBn1/OmFnzGBwwMAT6ZWbDmduGbWxpBYd5juHWYtjeY3zzR0Wdgdwx9gcfGypuy/MzH9748EcNHi1gFxgcRhU9gFsDA4M8hKrDp2YUjIJRMApGOgAAQZVOALsC8ycAAAAASUVORK5CYII=","orcid":"","institution":"LULEÅ UNIVERSITY OF TECHNOLOGY AND The Ratio Institute","correspondingAuthor":true,"prefix":"","firstName":"JONAS","middleName":"","lastName":"GRAFSTRÖM","suffix":""}],"badges":[],"createdAt":"2025-11-20 08:08:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8161933/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8161933/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":97670251,"identity":"23984b85-f7d7-409f-a4cf-2ac6a0074357","added_by":"auto","created_at":"2025-12-08 09:29:59","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77727,"visible":true,"origin":"","legend":"","description":"","filename":"9.0CirculartimeRNR.docx","url":"https://assets-eu.researchsquare.com/files/rs-8161933/v1/68f5f91455870d894338cf84.docx"},{"id":97670315,"identity":"cd696ec8-d6e4-4869-9a5c-e1ea7b841563","added_by":"auto","created_at":"2025-12-08 09:30:16","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2570,"visible":true,"origin":"","legend":"","description":"","filename":"c6922990b04d40f9803eef63ec8c2e41.json","url":"https://assets-eu.researchsquare.com/files/rs-8161933/v1/2c5825074db46289c9fd7f89.json"},{"id":97502172,"identity":"b3f21a2f-3cbb-4f5f-884e-e1a61ed51dd8","added_by":"auto","created_at":"2025-12-05 06:24:19","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":137660,"visible":true,"origin":"","legend":"","description":"","filename":"c6922990b04d40f9803eef63ec8c2e411enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-8161933/v1/0db1d97bf24773a5a36d97d5.xml"},{"id":97502176,"identity":"e2e15731-3fc1-4a13-9028-ed453598ded6","added_by":"auto","created_at":"2025-12-05 06:24:19","extension":"xml","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":135950,"visible":true,"origin":"","legend":"","description":"","filename":"c6922990b04d40f9803eef63ec8c2e411structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8161933/v1/7bae03a1a3bb84a5099f20f1.xml"},{"id":97502175,"identity":"1d642fa1-d558-418b-88f1-e86271ebad44","added_by":"auto","created_at":"2025-12-05 06:24:19","extension":"html","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":145776,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8161933/v1/3a300f04940b3678e31d3571.html"},{"id":97502171,"identity":"dc90d247-3175-4e3b-a27a-813ff019783b","added_by":"auto","created_at":"2025-12-05 06:24:19","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":51661,"visible":true,"origin":"","legend":"\u003cp\u003eCircularity rate by material categories (%), EU, 2013-2023. Source: Eurostat, (2024).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8161933/v1/4565ad7d1aaa5a52d22451ef.png"},{"id":97677735,"identity":"5b6358de-f1fe-4a44-8c3b-c44a124438b4","added_by":"auto","created_at":"2025-12-08 09:54:19","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1313501,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8161933/v1/4215dd8b-45e1-46a3-b609-2fd272ccbee9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Time as a Structural Barrier for a Circular Economy","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eMaterial recirculation and reuse in a circular economy (CE) does not occur instantaneously since goods have individual lifespans where some return for potential reuse/recycling within months, others after decades or a century (Eurostat, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). A food container may circulate in under a month (Sazdovski et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), a vehicle in twenty years (Held et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), and a building in fifty or more (Fahlstedt et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Vollmers and Long, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Barriers to a CE have been studied thought many aspects such as economical, technological, institutional and social (Kirchherr et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Grafstr\u0026ouml;m and Aasma, 2022; Souza Piao et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Gallego-Schmid et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) and geographical (Bourdin and Torre, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) yet describing time as a standalone variable has not been done. In much of the CE literature, time is treated as a contextual (e.g., \u0026ldquo;products last longer\u0026rdquo;) or practical issue.\u003c/p\u003e\u003cp\u003eTime has not been absent from discussions of the circular economy. Concepts such as slowing resource loops (Vollmers and Long, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), extending product lifespans (Jerome and Ljunggren, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), and recognizing differences between short- and long-term strategies implicitly acknowledge that circularity unfolds over time (Bocken et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Geissdoerfer et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Recycling is often presented as an immediate loop-closing activity, while repair, remanufacturing, and design for longevity are viewed as long-horizon strategies with delayed benefits (Fullerton and He, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). There is a tension between short business cycles and longer ecological or material cycles (Timmers et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Time as a barrier is under theorized and under researched.\u003c/p\u003e\u003cp\u003eThe purpose of the paper is to place time at the center of CE analysis and to demonstrate that it functions as a structural barrier. The paper theoretically formalizes how product lifespans, recovery rates, and historical inflows create delays in the substitution of primary- for secondary resources. Although, for example, both economics and industrial ecology recognize temporal aspects such as discounting, product lifespans, and lock-in, the circular economy literature has not treated time as a structural barrier in its own right.\u003c/p\u003e\u003cp\u003eThe core argument of the paper is that circularity at a given time, say \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e​, depends on decisions made in the past. Goods consumed at \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u003cem\u003e\u0026minus;\u0026thinsp;τ\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e only reappear for recovery after their lifespan has elapsed, which means that current circular performance largely reflects lagged inflows rather than present effort. When long-lived goods dominate stocks, the relevant return point may lie far into the future, for instance at \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003en\u003c/em\u003e\u003c/sub\u003e = \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e + 50 in the case of buildings. In the interval between t\u003csub\u003e0\u003c/sub\u003e and \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003en\u003c/em\u003e\u003c/sub\u003e​, circularity indicators remain low even if recovery efficiency improves. As elaborated in Section 3.4, discounting further disadvantages long-lived strategies, since delayed benefits are heavily reduced in present-value terms (Hepburn and Koundouri, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2007\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn economics, time has long been central to the analysis of investment, consumption, and policy. From Ramsey\u0026rsquo;s theory of saving (1928) to Fisher\u0026rsquo;s treatment of time preference (1930), and later work on irreversibility and delayed feedback (Arrow and Fisher, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1974\u003c/span\u003e; Pindyck, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e1991\u003c/span\u003e; Gollier, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), the allocation of resources across time has been shown to structure welfare outcomes and policy evaluation. Similar principles apply to CE strategies, yet the explicit role of time has not been systematically incorporated into circular theory.\u003c/p\u003e\u003cp\u003eThe paper adopts a conceptual and analytical approach. It does not present new empirical data but instead develops stylized formalizations of temporal mechanisms that shape material recovery and circularity. Using simple dynamic expressions, it illustrates how lags, mismatches, and discounting effects arise from the interaction between product lifespans, recovery processes, and evaluation practices. Goods are separated into short-, medium-, and long-lived categories, which makes it possible to represent recovery flows across different temporal horizons.\u003c/p\u003e\u003cp\u003eThe main contribution is to reframe circular economy transitions as intertemporal processes by treating time as an endogenous (i.e., operating inside the system and actively shaping outcomes rather than being an external condition) structural barrier rather than a contextual factor. Existing literature often mentions that products last longer or that recycling is delayed, but time is rarely analyzed as a fundamental structural constraint. By formalizing temporal mechanisms, the paper clarifies why circularity indicators remain stagnant even when technology improves and policies are in place.\u003c/p\u003e\u003cp\u003eThe conceptual framework links circular economy analysis to long-standing insights from environmental and resource economics, where discounting, investment under uncertainty, and intertemporal allocation are central (Bretschger and Smulders, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). This connection helps to explain a puzzle in circular transitions: Under which conditions do lifespan distributions and recovery efficiencies keep the circularity ratio low despite policy effort and technical progress?\u003c/p\u003e\u003cp\u003eBy making time explicit, the paper provides both a theoretical foundation and policy relevance, showing that circularity evolves unevenly across temporal horizons and requires instruments that align with the time structure of material stocks\u003c/p\u003e"},{"header":"2. Time as a structural barrier in CE theory","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Conceptual background: why time matters for circularity\u003c/h2\u003e\u003cp\u003eCircularity rates in the European Union, for example, have shown little movement over the past decade even though policies to promote it have been implemented. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates that the circularity rate in the European Union has remained largely stagnant between 2013 and 2023 across major material categories. Despite policy commitments and technological advances, secondary material use has not expanded significantly relative to total input demand.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTime matters as a barrier for CE adoption because circularity, broadly speaking, depends on when materials return. Goods with different lifespans re-enter the economy non-simultaneously. The in- and outflow can be both calculated on by accountants in the firm and recognized by the factory workers. Even if today\u0026rsquo;s recovery technology is efficient some long-lived material stocks do not release materials for decades. For example, the approved plastics of today are maybe not the same as on a TV found in a barn in a summerhouse.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents typical lifespans and return horizons for key material categories. Packaging can circulate back in weeks to under 2 years (Sazdovski et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Textiles 2\u0026ndash;5 years (Niinim\u0026auml;ki et al., 2022). Consumer electronics return after 3\u0026ndash;7 years. Vehicles circulate after 10\u0026ndash;20 years (Held et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), and appliances after 7\u0026ndash;15 years (Bakker et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Buildings typically embed materials for 40\u0026ndash;100 years, and infrastructure such as bridges and roads for 50\u0026ndash;100 years. Industrial by-products such as slags and fly ash can re-enter loops continuously, with return times measured in weeks to years. The delay until substitution therefore ranges from less than a year for packaging to a century for infrastructure.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eMaterials, lifespans and circular strategies.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaterial / Sector\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTypical lifespan\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStrategy type(s)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eLoop time / return horizon\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eDelay until circular benefit\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eRecovery complexity\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eNotes\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003ePackaging (plastics, glass, paper)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDays \u0026ndash; 2 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRecycling, reuse of containers\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eWeeks to 1\u0026ndash;2 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eImmediate to moderate\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eFast return, large volumes\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eTextiles (clothing, fabrics)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2\u0026ndash;5 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eReuse, resale, repair, recycling\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1\u0026ndash;5 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eShort to medium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eLow\u0026ndash;medium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eUncertain collection/reuse\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eConsumer electronics (phones, laptops)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3\u0026ndash;7 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRepair, resale, remanufacture, recycling\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3\u0026ndash;7 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eModerate\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eHigh obsolescence, logistics barriers\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eVehicles (cars, trucks)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e10\u0026ndash;20 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRemanufacture, component reuse, recycling\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e10\u0026ndash;20 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eDelayed\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eRecovery visible only after a decade\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eAppliances / machinery\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e7\u0026ndash;15 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRepair, remanufacture, recycling\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e7\u0026ndash;15 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMedium to delayed\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMedium\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eModular design can shorten loops\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eBuildings (residential, commercial)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e40\u0026ndash;100 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDesign for longevity, component reuse, recycling\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e40\u0026ndash;100 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eVery delayed\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMedium\u0026ndash;high\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eDominant in stocks, locked for generations\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eInfrastructure (roads, bridges, utilities)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e50\u0026ndash;100 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDesign for longevity, industrial symbiosis, recycling\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e50\u0026ndash;100 years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eVery delayed\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eExtremely slow turnover\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eIndustrial by-products (slags, fly ash, residues)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eContinuous\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eIndustrial symbiosis, recycling\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eWeeks to years\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eImmediate if logistics exist\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eHigh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eRapid loops possible\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eRecovery complexity refers to the difficulty of coordinating recovery flows across actors, technologies, and time horizons. Low complexity materials (e.g., packaging) return quickly and require limited coordination, whereas high complexity materials (e.g., infrastructure) involve multiple stakeholders, uncertain material quality, and a long time horizons before recovery become visible.\u003c/p\u003e\u003cp\u003eRecovery always occurs with a delay, since secondary resources become available only once goods reach the end of their lifespan. During that waiting period, virgin extraction continues to dominate. The past further constrains the future. Historical inflows of long-lived goods determine when and how recovery will occur, so a housing boom today locks materials into stocks that will not return until late in the century. Economic evaluation adds another layer of disadvantage, since benefits that occur thirty to fifty years later are heavily discounted, which makes long-lived circular strategies appear less attractive than short-term measures such as recycling.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 A theoretical view on how time affects economic decisions\u003c/h2\u003e\u003cp\u003eEconomics has long treated time as a central structuring variable. From Ramsey's early treatment of intertemporal welfare (Ramsey, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e1928\u003c/span\u003e) to Fisher\u0026rsquo;s work on time preference (Fisher, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1930\u003c/span\u003e), the allocation of resources across time has shaped how economists model investment, discount future outcomes, and evaluate long-run policy goals. In environmental economics, the incorporation of time has allowed for formal treatment of lagged feedback and delayed benefit features that play a critical role in the assessment of long-horizon problems such as climate change and resource depletion (Bretschger and Smulders, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eSeveral strands of economic theory inform how temporal features can be conceptualized. B\u0026ouml;hm-Bawerk\u0026rsquo;s work in the late nineteenth century marked a step in bringing time explicitly into economic theory (B\u0026ouml;hm-Bawerk, 1884). By differentiating between consumption goods and capital inputs across temporal stages, he provided a foundation for understanding why interest rates are positive. B\u0026ouml;hm-Bawerk\u0026acute;s reasoning laid the groundwork for the concept of time preference, which later evolved into formal models of discounting used in macroeconomics and environmental economics. In parallel, Hotelling\u0026rsquo;s analysis of exhaustible resources (1931) demonstrated the long-term dynamics of economic activity.\u003c/p\u003e\u003cp\u003eProperty rights and predictable legal frameworks are key enablers in an economy since it enables exchange and long-term contracting (Hayek, 1945; North, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1990\u003c/span\u003e). Goods remain in use for decades, meaning that ownership and responsibility may not become relevant until far into the future. If rights are unclear, the passage of time intensifies the institutional barrier, as future actor\u0026rsquo;s face disputes over materials embedded long ago.\u003c/p\u003e\u003cp\u003eInformation problems also have a temporal dimension. Akerlof (1970) showed how quality uncertainty undermines markets for goods. In a circular setting, quality uncertainty is magnified by long delays. The quality of materials that will return in 20, 50, or 100 years cannot be credibly guaranteed at the time of production. And a hundred years from now what storage of information will it still be that works (likely not the floppy-disk or CD)? Investors might hesitate to commit to recovery capacity when the flow of information stretches across decades. What begins as a manageable information asymmetry today becomes more severe once the time lag is considered.\u003c/p\u003e\u003cp\u003eArrow and Fisher (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1974\u003c/span\u003e) and Pindyck (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e1991\u003c/span\u003e) emphasized the value of waiting in settings where payoff is uncertain and irreversible, a logic directly applicable to long-horizon circular strategies such as product-as-a-service or modular design. The capital theory of investment\u0026mdash;particularly under depreciation\u0026mdash;suggests that systems with slow capital turnover, such as manufacturing assets or durable goods, may structurally resist rapid shifts (Hartwick, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1990\u003c/span\u003e; Berndt, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1991\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eA related perspective comes from vintage capital theory (Boucekkine et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2011\u003c/span\u003e), analyzing overlapping generations of capital goods shape production and investment dynamics (Johansen, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1959\u003c/span\u003e; Solow et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e1966\u003c/span\u003e; Malcomson, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1975\u003c/span\u003e). Capital is not believed to be homogeneous but composed of \u0026ldquo;vintages\u0026rdquo; that embody different technologies and depreciation profiles. Circular systems display a comparable structure. Goods with short, medium, and long lifespans can be treated as vintages that coexist within the economy, each generating disposal flows on different time horizons (developed in section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Just as older vintages of capital constrain the speed of technological diffusion, long-lived material stocks constrain the speed of circular substitution. Even if newer goods are designed for high recoverability, the effective circularity of the system remains shaped by older vintages that persist in use.\u003c/p\u003e\u003cp\u003eIn parallel, models of delayed environmental feedback have drawn attention to the mismatch between cause and effect in ecological and economic systems (Wu et al., \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). For example, the lag between greenhouse gas emissions and atmospheric accumulation has been used to justify declining discount rates in long-term policy assessments (Gollier, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Cropper et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Efforts to make the economy more circular may generate analogous mismatches. Delayed substitution effects, coordination time, or lifespan-based turnover can disconnect present investment from observable short-term gains, creating conditions where socially efficient outcomes are not aligned with private return expectations (Tessitore et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eBehavioral literature complements this economics structural view by emphasizing bounded rationality and present bias in economic decision-making (Tsoukis et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Present bias means that near-term costs outweigh long-term benefits. Status quo bias and bounded rationality (Kahneman and Tversky, 1979; Samuelson and Zeckhauser, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e1988\u003c/span\u003e) reduce the willingness to depart from established practices.\u003c/p\u003e\u003cp\u003eWhen recovery strategies only deliver returns after decades, the psychological weight of delay could discourage adoption. Circularity based on repair, reuse, or longevity provides slow accumulating benefits, whereas short-lived recycling produces quick but limited gains. Empirical studies consistently show that consumers and firms underweight future benefits, especially when gains are uncertain, intangible, or distant (Laibson, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Frederick et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2002\u003c/span\u003e).\u003c/p\u003e\u003cp\u003ePath dependence and lock-in, as described in technology adoption models (Arthur, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1989\u003c/span\u003e), also interact with time. The QWERTY setting on the keyboard might not be the most efficient, but it will last. Long-lived assets such as infrastructure not only tie users to a given technology, but they also determine material flows for generations. Superior recovery methods may exist, yet their impact is deferred until current stocks or personnel are retired. Time therefore strengthens lock-in by extending its influence over long horizons and making transitions slower and more costly.\u003c/p\u003e\u003cp\u003eFamily firms can foster long term decision making but also be conservative and hindering change (Vollmers and Long, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). If a historic way has been practiced by your parents it might be harder to change that compared to being a CEO for a firm that you will leave in due time.\u003c/p\u003e\u003cp\u003eThe role of discounting itself has been widely debated in both environmental and climate economics (Concei\u0026ccedil;\u0026atilde;o and Zhang, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). While standard models apply constant exponential discounting, alternative formulations have emerged to better reflect ethical and empirical concerns about intergenerational fairness and deep uncertainty (Stern, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Heal, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). In the context of circular transitions, discounting interacts directly with the delayed return profiles described in the next section. If policy or capital markets heavily discount the future, slow-return circular strategies may appear inefficient even when their long-run benefits are substantial.\u003c/p\u003e\u003cp\u003eCollective action problems have similarities with discounting mentioned above; they reinforce the structural role of time. Ostrom (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e1990\u003c/span\u003e) points out that when costs are concentrated in the present but benefits are dispersed across actors and over time, individual incentives misalign with collective welfare. In circular systems, the recovery of long-lived goods resembles such a dilemma: firms hesitate to invest early, since future material returns are uncertain and widely shared, even though coordinated commitment would raise long-term benefits. Time therefore interacts with institutional design, turning delayed benefits into a coordination challenge as well as an economic one.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Method and approach","content":"\u003cp\u003eThe methodological approach is initially analytical and conceptual rather than empirical. The purpose is to develop a stylized representation of how time functions as a structural barrier to circularity. The model builds on standard techniques in environmental and resource economics, where formal expressions are used to clarify dynamic relationships rather than to estimate them empirically. The equations therefore serve as heuristic devices\u0026mdash;tools that expose how temporal mechanisms influence observable outcomes in circular systems.\u003c/p\u003e\u003cp\u003eThe model assumes that goods differ in their lifespans and that recovery processes introduce time lags between material inflows and outflows. Recovery efficiency, discounting, and synchronization costs are treated as endogenous parameters that jointly determine system-level circularity. Goods are grouped into three lifespan classes: short-, medium-, and long-lived, based on average return horizons found in the literature (Bakker et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Held et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Sazdovski et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e Niinim\u0026auml;ki et al., 2022). Each class produces recovery flows at different points in time, creating asynchronous supply and demand for secondary materials.\u003c/p\u003e\u003cp\u003eThe analytical framework uses continuous-time notation to illustrate how stock\u0026ndash;flow interactions evolve over time. Equations\u0026nbsp;(1\u0026ndash;13) formalize the relations among disposal flows, recovery efficiency, stock accumulation, and delayed substitution effects. The analysis proceeds in two steps. First, it identifies timing mismatches, recovery delays, and valuation biases as sources of temporal frictions. Second, it demonstrates how these frictions reduce observed circularity even under technological improvement. For the equation part no new data are collected; instead, the model operates as a conceptual simulation of intertemporal dynamics that connects economic reasoning about time with circular economy processes.\u003c/p\u003e\u003cp\u003eThe equations were developed through a combination of established economic theory and analytical reasoning (e.g., Varian, 1992; Acemoglu, 2008). The equation formulation draws upon foundational models in intertemporal and resource economics, where relationships between stocks, flows, and valuation over time have been formalized. The expressions were compared with equivalent representations in dynamic stock modeling and vintage capital theory (see Boucekkine et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Conceptual validation was achieved through informal consultation with academic colleagues working in economics and circular economy research, whose feedback informed refinements in notation. The final equations were cross-checked against standard economic formulations of market processes and investment dynamics to confirm that they matched analytical logic rather than ad hoc assumptions.\u003c/p\u003e\u003cp\u003eThe equations used in the present analysis follow the standard structure of dynamic stock modelling: lifespans are represented as delayed outflows from earlier inflows, recovery efficiency evolves through time, and discount processes reflect intertemporal valuation. The formulation is consistent with the analytical approaches outlined in recent research on lifetime functions, temporal cohorts and hazard-based representations of stock turnover, including the treatment of age-specific and period-specific failure rates. Krych et al. (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) provides explicit mathematical expressions for survival and hazard functions that serve as a reference point for lifetime-driven stock evolution. The approach taken here maintains that structure and applies it to the context of circularity analysis.\u003c/p\u003e"},{"header":"4. Formalizing the temporal dynamics of circularity","content":"\u003cp\u003eThe following sections introduce stylized equations to represent the temporal dynamics of recovery. The equation framework follows an analytical tradition established in earlier work on circularity barriers. Foundational inspiration is drawn from Grafstr\u0026ouml;m (\u003cspan class=\"CitationRef\"\u003e2025a\u003c/span\u003e) and Grafstr\u0026ouml;m et al. (\u003cspan class=\"CitationRef\"\u003e2025b\u003c/span\u003e). Those studies formalize dynamic constraints in metals and plastics systems. The present formulation adapts the underlying logic to a broader resource setting by translating core principles from that literature into a general representation of time dependent circularity. The structure used here aligns with the conceptual foundations outlined in those contributions and reflects an extension of their analytical approach. The intention is to integrate mechanisms already identified in previous research into a unified expression that clarifies how lifespans, recovery efficiency and delayed substitution interact across material systems.\u003c/p\u003e\n\u003cp\u003eThe equations are not predictive models but heuristic formalizations that clarify how delays, mismatches, and discounting influence circularity. Their role is to make explicit the structural effects of time that are otherwise described qualitatively in circular economy discussions.\u003c/p\u003e\n\u003cp\u003eSection \u003cspan class=\"InternalRef\"\u003e4.1\u003c/span\u003e formalizes timing mismatches and synchronization problems between disposal flows and current demand. Section \u003cspan class=\"InternalRef\"\u003e4.2\u003c/span\u003e introduces lifespan classes: short-, medium-, and long-lived goods and shows how recovery dynamics differ across them. Section \u003cspan class=\"InternalRef\"\u003e4.3\u003c/span\u003e links recovery flows to evolving material stocks and defines alternative measures of circularity. Section \u003cspan class=\"InternalRef\"\u003e4.4\u003c/span\u003e incorporates discounting and delayed benefits to illustrate how economic evaluation systematically disadvantages long-lived strategies.\u003c/p\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n\u003ch2\u003e4.1 Timing sensitivity and storage as time-dependent barriers\u003c/h2\u003e\n\u003cp\u003eCircular recovery depends not only on efficiency but also on synchronization between disposal flows and current demand. Just in time and a CE does not go hand in hand, yet. Material recovery can stall due to poor synchronization. In Knoth et al., (\u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e), for example, architects, and contractors report that reclaimed components rarely appear when projects need them. Demolition schedules and disassembly lead times drift away from construction timelines or vice versa. Limited storage and rules (e.g., handling requirements) that tightly regulate waste storage, distance between stock and site add cost to every mismatch. Time is money and the combination turns viable material into an unattractive option for managers working under tight budgets and deadlines. It could be defined as a classic economic barrier but also one of time:\u003c/p\u003e\n\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equa\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}S\\left(t\\right)=R\\left(t-\\tau\\:\\right) \\left(1\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003eS\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) is the secondary material available at time \u003cem\u003et\u003c/em\u003e, \u003cem\u003eR\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) is the inflow generated by disassembly, and \u003cem\u003e\u0026tau;\u003c/em\u003e is the time required for demolition or deconstruction. The time lag means that what becomes available for reuse today reflects decisions made \u003cem\u003e\u0026tau;\u003c/em\u003e years ago. If demolition comes after new demand arises, supply arrives too late. If demolition occurs earlier, materials appear before there is a project that can use them.\u003c/p\u003e\n\u003cp\u003eDemand for materials at time \u003cem\u003et\u003c/em\u003e can be written as \u003cem\u003eD\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e). The gap between what is needed and what is available is:\u003c/p\u003e\n\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equb\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}\\varDelta\\:\\left(t\\right)=D\\left(t\\right)-S\\left(t\\right) \\left(2\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIf \u0026Delta;(t)\u0026thinsp;\u0026gt;\u0026thinsp;0, demand exceeds reclaimed supply, and new materials must fill the gap. If \u0026Delta;(t)\u0026thinsp;\u0026lt;\u0026thinsp;0, reclaimed materials arrive too early and sit unused. Perfect synchronization, \u0026Delta;(t)\u0026thinsp;=\u0026thinsp;0, is rare in practice. In most projects, mismatches dominate, which makes secondary inputs difficult to plan for within standard production schedules. For example, demolition schedules in construction rarely align with new material demand, which forces reliance on storage or virgin substitutes. A positive gap requires virgin extraction to fill the shortfall, whereas a negative gap requires storage or transport to manage early arrivals. The associated cost can be written as:\u003c/p\u003e\n\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equc\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}C\\left(t\\right)={c}_{s}\\times\\:max\\left[0,S\\left(t\\right)\\right]+{C}_{t}\\times\\:L, \\left(3\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e is the storage cost per unit, \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e is the transport cost per unit, and \u003cem\u003eL\u003c/em\u003e is the distance between stock and site. Even modest gaps between recovery and demand can create significant expenses. Storing large volumes or transporting them over long distances quickly erodes any savings from reuse. As a result, managers often find that reclaimed inputs become more costly than virgin materials once these timing-related frictions are accounted for.\u003c/p\u003e\n\u003cp\u003eEquations\u0026nbsp;1\u0026ndash;3 formalize reuse as a coordination problem between supply and demand. On the supply side, reclaimed materials enter the market only with a lag, since demolition and disassembly unfold over time and components become available only once the source asset reaches the end of its lifespan. On the demand side, production requires inputs according to its own schedule, largely independent of disposal flows. The result is a systematic disequilibrium: reclaimed supply often falls short when demand is high, and at other times exceeds requirements. Excess supply must be stored or transported, creating additional costs, whereas shortages require substitution with virgin inputs. Put differently, the effective supply curve for secondary materials is shifted forward in time relative to demand, which generates temporary surpluses and deficits. In economic terms, what may appear as a feasible technological option is converted into a binding cost condition once the temporal misalignment of supply and demand is considered.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n\u003ch2\u003e4.2 Lifespan classes and recovery dynamics\u003c/h2\u003e\n\u003cp\u003eGoods differ greatly in how long they remain in use before returning to the economy. Now, let us for the sake of argument assume that material goods can be divided into three broad categories according to their expected duration of use. Class S (Short-lived): \u003cem\u003e\u0026tau;\u003c/em\u003e\u003csub\u003e\u003cem\u003eS\u003c/em\u003e\u003c/sub\u003e\u0026sim;\u0026isin; [1\u0026ndash;3] months, Class M (Medium-lived): \u003cem\u003e\u0026tau;\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e\u0026sim;\u0026isin; [1\u0026ndash;20] years, and Class L (Long-lived): \u003cem\u003e\u0026tau;\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e\u0026sim;\u0026isin; [20\u0026ndash;100] years. In formal terms: the disposal flow from class \u003cem\u003ei\u003c/em\u003e at time \u003cem\u003et\u003c/em\u003e depends on what entered the economy \u003cem\u003e\u0026tau;\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e years earlier. Today\u0026rsquo;s recovery is yesterday\u0026rsquo;s inflow shifted forward by the lifespan of the good:\u003c/p\u003e\n\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equd\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{DF}_{i}\\left(t\\right)={R}_{i}\\left(t-{\\tau\\:}_{i}\\right) \\left(4\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eLet \u003cem\u003eR\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) denote the inflow of raw material at time \u003cem\u003et\u003c/em\u003e, The disposal flow \u003cem\u003eDF\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003et\u003c/em\u003e) is determined by past inflows delayed by the average lifespan \u003cem\u003e\u0026tau;\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e. In other words, end-of-life flows observed today reflect production decisions made years or even decades earlier.\u003c/p\u003e\n\u003cp\u003eBuilding on this, Eq.\u0026nbsp;(5) introduces recovery efficiency. Disposal alone does not determine recovered supply; only the fraction that can be technically and economically recovered contributes to circularity. The recovered share of this disposal depends on the recovery rate \u0026gamma;\u003csub\u003ei\u003c/sub\u003e(t). The amount that is recirculated into the economy from class \u003cem\u003ei\u003c/em\u003e is therefore:\u003c/p\u003e\n\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Eque\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{\\varphi\\:}_{i}\\left(t\\right)={\\gamma\\:}_{i}\\left(t\\right)\\times\\:{DF}_{i}\\left(t\\right) \\left(5\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe contribution of each class to circularity depends not only on its disposal flow but also on how much of that flow can be recovered.\u003c/p\u003e\n\u003cp\u003eIf recovery efficiency for class \u003cem\u003ei\u003c/em\u003e is \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e , the recovered amount is \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eDF\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(t)\u003c/em\u003e. Summing across all classes gives the total recovered input at time \u003cem\u003et\u003c/em\u003e. The circularity ratio is therefore:\u003c/p\u003e\n\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equf\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}C\\left(t\\right)=\\frac{{\\gamma\\:}_{s}R\\left(t-{\\tau\\:}_{s}\\right)+{\\gamma\\:}_{m}R\\left(t-{\\tau\\:}_{M}\\right){+\\gamma\\:}_{L}R\\left(t-{\\tau\\:}_{L}\\right)}{R\\left(t\\right)} \\left(6\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eBecause the numerator reflects past inflows shifted forward by lifespans, while the denominator reflects current inflows, circularity indicators tend to stagnate when long-lived goods dominate stocks. This ratio shows why time matters for system-level outcomes. Short-lived goods generate visible substitution almost immediately. Medium-lived goods contribute only after a decade or two. Long-lived goods make little difference in the near term, even if recovery efficiency is high, because their inflows remain locked in the stock. If long-lived goods dominate total inflows, near-term circularity remains low regardless of improvements in recovery efficiency.\u003c/p\u003e\n\u003cp\u003eThe division into lifespan classes therefore illustrates a structural trap. Even as short-lived goods return quickly, they account for only a small share of total stocks. The bulk of material is embedded in long-lived assets, which means aggregate circularity indicators are weighted toward delayed flows. This explains why progress in recovery technology does not immediately translate into higher circularity at the system level.\u003c/p\u003e\n\u003cp\u003eThe responsiveness of circularity to an efficiency gain in class \u003cem\u003ei\u003c/em\u003e can be written as:\u003c/p\u003e\n\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equg\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}\\frac{\\partial\\:C\\left(t\\right)}{\\partial\\:{\\gamma\\:}_{i}}=\\frac{R\\left(t-{\\tau\\:}_{i}\\right)}{R\\left(t\\right)}. \\left(7\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eShort lifespans raise the ratio on the right. Long lifespans lower it. Gains therefore register quickly for short-lived goods and very slowly for long-lived assets. Disposal today reflects what was added to the stock \u003cem\u003e\u0026tau;\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e years ago. Circularity at any point in time is thus determined not only by present inflows and current recovery efficiency, but by yesterday\u0026rsquo;s inflows shifted forward by the lifespan of the good.\u003c/p\u003e\n\u003cp\u003eEquations\u0026nbsp;4\u0026ndash;7 make clear that secondary supply is always the shadow of past inflows. Short-lived goods re-enter the market quickly, so higher recovery rates translate into immediate outward shifts of effective supply. Medium-lived goods return only after a decade or more, which means today\u0026rsquo;s demand curve is still met largely by virgin inputs, regardless of technical recovery potential. Long-lived goods push this dynamic even further: the bulk of material embedded in buildings or infrastructure will not reappear for half a century, so efficiency gains in recovery remain locked into the future. In economic terms, the supply of secondary materials is intertemporal; it is governed less by current technology than by the time structure of past investment decisions. The circularity ratio therefore captures an intertemporal disequilibrium: demand is determined today, but supply is delivered with delays that can span generations.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n\u003ch2\u003e4.3 Stocks, extraction, and an alternative circularity measure\u003c/h2\u003e\n\u003cp\u003eCircularity may fall in the short run even when recovery technology improves. The reason is that long-lived inflows expand total demand today but only return to recovery flows after several decades. This delay means that system circularity can stagnate or even decline despite higher recovery efficiency. Material stocks in each class (\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e) evolve according to:\u003c/p\u003e\n\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equh\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}\\frac{d{M}_{i}\\left(t\\right)}{dt}={R}_{i}\\left(t\\right)+{\\varphi\\:}_{i}\\left(t\\right)-{DF}_{i}\\left(t\\right) \\left(8\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(t)\u003c/em\u003e is the stock of goods in class i\u0026isin;{S, M, L}, \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(t)\u003c/em\u003e is new inflow, \u003cem\u003eϕ\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(t)\u003c/em\u003e is recovered inflow, and \u003cem\u003eDF\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(t)\u003c/em\u003e is disposal flow. Since disposal is delayed by the lifespan \u003cem\u003e\u0026tau;\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e , the timing of returns depends on past inflows rather than current ones.\u003c/p\u003e\n\u003cp\u003eEach flow\u0026rsquo;s return is therefore delayed and incomplete, depending on both its lifespan and the recovery system\u0026rsquo;s performance. Total raw material use is the sum over classes:\u003c/p\u003e\n\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equi\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}R\\left(t\\right)=\\sum\\:_{\\varvec{i}\\in\\:\\mathbf{S},\\mathbf{M},\\mathbf{L}}\\left[{DF}_{i}\\left(t\\right)\\times\\:\\left(1-{\\gamma\\:}_{i}\\left(t\\right)\\right)\\right] \\left(9\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003e\u0026gamma;i(t)\u003c/em\u003e is the recovery efficiency for class \u003cem\u003ei\u003c/em\u003e. Today\u0026rsquo;s extraction is therefore the outcome of design and use decisions made in the past, shifted forward by product lifespans. It is also possible to define a disposal-based measure of circularity. The substitution share is:\u003c/p\u003e\n\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equj\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}\\theta\\:\\left(t\\right)=\\frac{{\\sum\\:}_{i}{\\varphi\\:}_{i}\\left(t\\right)}{{\\sum\\:}_{i}{DF}_{i}\\left(t\\right)}=\\frac{{\\sum\\:}_{i}{\\gamma\\:}_{i}\\left(t\\right)\\times\\:{R}_{i}\\left(t-{\\tau\\:}_{i}\\right)}{{\\sum\\:}_{i}{R}_{i}\\left(t-{\\tau\\:}_{i}\\right)} \\left(10\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThis ratio captures the degree of circularity in the system at time \u003cem\u003et\u003c/em\u003e. Its value is determined jointly by the efficiency of recovery processes \u003cem\u003e\u0026gamma;\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003et\u003c/em\u003e), the profile of past inflows \u003cem\u003eRi\u003c/em\u003e(\u003cem\u003et\u0026thinsp;\u0026minus;\u0026thinsp;\u0026tau;\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e), and the temporal mechanisms introduced by product lifespans \u003cem\u003e\u0026tau;\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e. As a result, system-wide circularity may stagnate or decline in the short run despite rising recovery efficiency when stocks are dominated by long-lived goods.\u003c/p\u003e\n\u003cp\u003eEquations\u0026nbsp;8\u0026ndash;10 emphasize that circularity is governed by stock\u0026ndash;flow relations rather than instantaneous substitution. New inflows add to the stock of materials today, but the corresponding recovery flows emerge only after lifespans have elapsed. The system therefore carries a built-in delay: present extraction reflects past inflows shifted forward in time, not current design or efficiency alone. The consequence is that improvements in recovery technology may coincide with declining circularity indicators, since growing stocks of long-lived goods increase input demand without generating immediate returns. In economic terms, circularity at time \u003cem\u003et\u003c/em\u003e is an intertemporal outcome, shaped by the path of historical inflows, the temporal distribution of lifespans, and the discounting of delayed recovery.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n\u003ch2\u003e4.4 Lags, discounting, and the evaluation of circular strategies\u003c/h2\u003e\n\u003cp\u003eThe existence of time lags in material recovery has an additional consequence once economic evaluation is introduced. Benefits that arrive only after long delays are weighed less in present terms, which systematically disadvantages strategies aimed at long-lived goods. A building designed for recovery may release materials of high quality after fifty years, yet the value of that benefit is strongly reduced today. This creates a bias in favor of short-lived recovery, even when the long-term potential of long-lived assets is much larger.\u003c/p\u003e\n\u003cp\u003eThe effect of discounting can be expressed with a simple comparison. Suppose a strategy increases circularity by \u003cem\u003e\u0026Delta;C\u003c/em\u003e units per year. If the improvement is immediate, its present value under a social discount rate \u003cem\u003e\u0026rho;\u003c/em\u003e is\u003c/p\u003e\n\u003cdiv id=\"Equk\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equk\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{W}_{now}=\\frac{\\varDelta\\:C}{\\rho\\:}. \\left(11\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIf the same improvement is delayed by \u0026tau; years, the present value becomes\u003c/p\u003e\n\u003cdiv id=\"Equl\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equl\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{W}_{delay}=\\frac{\\varDelta\\:C}{\\rho\\:}{e}^{-\\rho\\:t}. \\left(12\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe ratio of the two values is \u003cem\u003ee\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026rho;\u0026tau;\u003c/em\u003e\u003c/sup\u003e, which declines rapidly with both \u003cem\u003e\u0026rho;\u003c/em\u003e and \u003cem\u003e\u0026tau;\u003c/em\u003e. At a discount rate of three percent, a benefit realised after forty years is worth less than one third of the same benefit obtained immediately.\u003c/p\u003e\n\u003cp\u003ePrivate adoption decisions are subject to the same logic. Consider a project with a one-off cost \u003cem\u003e\u0026Phi;\u003c/em\u003e and a constant annual benefit \u003cem\u003eb\u003c/em\u003e that begins only after a delay of \u003cem\u003e\u0026tau;\u003c/em\u003e. With discount rate \u003cem\u003er\u003c/em\u003e, the net present value is\u003c/p\u003e\n\u003cdiv id=\"Equm\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equm\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}V\\left(\\tau\\:\\right)=\\frac{b}{r}{e}^{-\\rho\\:t}-\\varPhi\\: \\left(13\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eEven when the project yields substantial long-run savings, the exponential decay in value with respect to \u003cem\u003e\u0026tau;\u003c/em\u003e makes adoption unattractive. The longer the delay, the less likely the project is to cross the investment threshold.\u003c/p\u003e\n\u003cp\u003eDiscounting amplifies the disadvantage of long-lived circular strategies, since their delayed benefits are given far lower present value than short-lived strategies, even when the ultimate returns are greater. Together, these layers demonstrate that time is not a peripheral issue but a structural barrier that slows CE transitions. Even with improving recovery technologies, the pace of progress remains tied to the temporal structure of stocks and the way benefits are valued across horizons.\u003c/p\u003e\n\u003cp\u003eEquations\u0026nbsp;11\u0026ndash;13 illustrate how discounting transforms delayed recovery into a structural disadvantage for long-lived goods. A benefit realized immediately retains most of its present value, but the same gain shifted decades into the future is sharply reduced once evaluated at any positive discount rate. From an economic standpoint, this introduces a systematic bias: projects aimed at long-lived assets appear less profitable, even when their eventual contribution is substantial. For private decision-makers, the option value of waiting becomes higher as delays lengthen, reducing incentives to invest in recovery capacity ahead of time. At the system level, this mechanism helps explain why circularity strategies cluster around short-lived goods, where returns are rapid and valuation losses minimal, and why sectors dominated by buildings or infrastructure struggle to attract comparable investment. Time, through the logic of discounting, thus acts as both an economic filter and a break on long-horizon circular strategies.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"5 Result: connection to economic theory","content":"\u003cp\u003eSection \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e4\u003c/span\u003e can be brought together to show how time systematically constrains circularity. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e summarizes section \u003cspan refid=\"Sec7\" class=\"InternalRef\"\u003e4.1\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Sec10\" class=\"InternalRef\"\u003e4.4\u003c/span\u003e and show how each temporal mechanism functions as a structural barrier.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eTemporal mechanisms that create structural barriers to circular economy transitions.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTemporal phenomenon\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHow time creates the barrier\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFormal element\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eDelayed recovery of materials\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMaterials only re-enter after their lifespan has ended. For example, steel in a bridge built today will not be available until demolition several decades later, which means virgin steel continues to dominate current construction.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\left(t\\right)=R\\left(t-\\tau\\:\\right),\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\left(t\\right)=D\\left(t\\right)-S\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eTiming mismatch between recovery and demand\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRecovered flows rarely coincide with the timing of new projects. A demolition may release timber months before a building is started, forcing storage or disposal, while the builder still purchases new wood.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\left(t\\right)\\:vs.\\:D\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eExtra costs from poor timing\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eWhen materials arrive too early or too late, they must be stored or moved. Large concrete components reclaimed from demolition may require long-term storage or costly transport to align with a future project, often erasing the financial advantage of reuse.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\left(t\\right)={c}_{s}\\times\\:max\\left[0,S\\left(t\\right)\\right]+\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{t}\\times\\:L\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eDifferent product lifespans\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eGoods circulate at different speeds. A cotton shirt may return within two years, a car in fifteen, and a residential building only after half a century. Short-lived flows appear quickly but carry little weight in overall stocks, while long-lived flows dominate but remain locked for generations.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{i}\\left(t\\right)={R}_{i}\\left(t-{\\tau\\:}_{i}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eOnly partial recovery over time\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNot all discarded goods are usable when they return. A ten-year-old refrigerator may have recyclable metal, but plastics and electronics can be obsolete or degraded, limiting the recovery rate.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varphi\\:}_{i}\\left(t\\right)={\\gamma\\:}_{i}\\left(t\\right)\\times\\:{D}_{i}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eStagnant circularity\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eIndicators remain flat when long-lived goods dominate. Even with better collection of textiles or packaging, overall circularity rates barely move if most material is tied up in buildings and infrastructure.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\left(t\\right)\\:=\\frac{{\\sum\\:}_{i}{\\gamma\\:}_{i}{R}_{i}\\left(t-{\\tau\\:}_{i}\\right)}{R\\left(t\\right)}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eSpeed of response to efficiency gains\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eEfficiency improvements matter more in short loops. Better textile collection increases secondary supply almost immediately, but efficiency gains in construction will not show until buildings from the current boom reach end-of-life decades later.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\partial\\:C\\left(t\\right)}{\\partial\\:{\\gamma\\:}_{i}}=\\frac{R\\left(t-{\\tau\\:}_{i}\\right)}{R\\left(t\\right)}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eLegacy of past material inflows\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eToday\u0026rsquo;s consumption locks recovery for decades. For instance, copper installed in power grids during the 2020s will not return until late in the century, regardless of advances in recovery technology.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{d{M}_{i}\\left(t\\right)}{dt}={R}_{i}+{\\varphi\\:}_{i}-{D}_{i}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eReduced value of future benefits\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBenefits that arrive far into the future lose present value. Designing a modular office building today may yield high-quality components in 40 years, yet investors discount that benefit so heavily that immediate recycling options appear more attractive.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{delay}=\\frac{\\varDelta\\:C}{\\rho\\:}{e}^{-\\rho\\:t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eDelayed investment decisions\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFirms postpone investment until recovery flows are near. A company may plan to build a specialized plastics recycling facility but delay until volumes are sufficient, even if early action would generate higher long-run welfare.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:V\\left(\\tau\\:\\right)=\\frac{b}{r}{e}^{-\\rho\\:t}-\\varPhi\\:\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe temporal mechanisms in Section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e4\u003c/span\u003e show that recovery flows arrive only after significant delays, as indicated in Eq.\u0026nbsp;4, that stocks expand long before disposal occurs, as indicated in Eq.\u0026nbsp;6, and that discounting lowers the value of distant returns, as indicated in Eq.\u0026nbsp;11. The same features generate collective action problems. In Ostrom\u0026rsquo;s framework (1990), the absence of institutions that align incentives leads to under provision of benefits that are dispersed across actors and over time. Applied to circular systems, firms face the option of waiting. Each actor prefers others to bear the cost of early investment in recovery infrastructure, since the eventual benefits will be shared but arrive decades later. Eq.\u0026nbsp;8 formalizes recovery efficiency as a function of investment timing, and Eq.\u0026nbsp;12 shows how delayed substitution limits near term gains. The outcome mirrors a failure of coordination.\u003c/p\u003e\u003cp\u003eSeveral paradoxes follow. Improvement in recovery efficiency does not guarantee a rise in circularity in the short run, since relevant returns depend on past inflows for extended periods, as indicated in Eq.\u0026nbsp;5. Ambitious policy targets on five-year horizons generate limited movement when dominant stocks are long lived. Private investors face an option value of waiting even in cases where social welfare would increase with early action. Eq.\u0026nbsp;11 shows that valuation of future returns declines rapidly under discounting, which reduces the attractiveness of near-term investment. The apparent lack of progress is therefore consistent with a system governed by lags and valuation effects.\u003c/p\u003e\u003cp\u003eFirm strategy benefits from aligning clocks. Procurement calendars can be coordinated with expected demolition windows through advanced purchase agreements and flexible specifications. In other sectors industrial symbiosis could be a way forward. Material exchanges with verified quality data reduce uncertainty when goods re-enter after long use. Contracts that recognize time value, for example by sharing storage and transport costs or by pricing options to call reclaimed stock later, can unlock adoption in sectors with volatile schedules.\u003c/p\u003e\u003cp\u003eThe temporal mechanisms represented in Equations 8\u0026ndash;13 can be framed as a coordination game. Each firm faces the option to invest early in recovery infrastructure or to wait. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the socially efficient outcome arises when both invest, since costs are shared and long-term recovery is secured. Yet the individually rational strategy is often to wait, since future benefits are delayed and discounted, while present costs are immediate. The result is a collective action problem in the Ostrom sense (1990): without institutional arrangements to align incentives, rational strategies produce under-investment in long-lived recovery capacity.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePayoff matrix: Invest in recovery infrastructure now vs. wait\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFirm A / Firm B\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eInvest now\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eWait\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eInvest now\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(5, 5) Both invest: infrastructure is built, costs are shared, future recovery is secured.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(2, 6) A invests alone: A bears present costs, B free-rides on future shared benefits.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eWait\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(6, 2) B invests alone: B bears present costs, A free-rides.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(3, 3) Both wait: no early investment, circularity remains low, reliance on virgin inputs continues.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe lifespan classes in Equations 4\u0026ndash;7 parallel the structure of vintage capital theory (Johansen, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1959\u003c/span\u003e; Solow et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e1966\u003c/span\u003e; Malcomson, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1975\u003c/span\u003e). In both cases, overlapping vintages coexist, with older stocks constraining the speed at which new technologies can influence outcomes. Just as older capital vintages slow technological diffusion in production models, long-lived goods in circular systems delay substitution and dampen the impact of improved recovery efficiency.\u003c/p\u003e\u003cp\u003eThe dynamics described in Equations 8\u0026ndash;13 resemble the real options logic of investment under uncertainty (Arrow and Fisher, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1974\u003c/span\u003e; Pindyck, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e1991\u003c/span\u003e). Since recovery from long-lived goods is delayed and uncertain, the value of committing capital today is reduced not only by discounting but also by the irreversibility of investment. Waiting preserves flexibility, while early action locks in costs without immediate returns.\u003c/p\u003e"},{"header":"6. Discussion: implications of time for circular transitions","content":"\u003cp\u003eTime introduces both opportunities and constraints in circular transitions, one might say that there are two clocks of circularity at play. On the pro side, short-lived goods such as packaging or textiles demonstrate that rapid turnover allows technology and policy to translate quickly into measurable outcomes. Improvements in collection rates or recycling efficiency appear almost immediately in system indicators, and firms can capture near-term returns without facing long planning horizons. For policymakers, these sectors provide visible progress that can be achieved within electoral cycles, supporting credibility and accountability.\u003c/p\u003e\u003cp\u003eOn the contra-side, long-lived goods embody a different clock. Buildings, infrastructure, and capital equipment lock materials into use for decades, sometimes generations. From an intertemporal perspective, this means that even efficient recovery technologies cannot shift secondary supply until distant future dates. For private investors, the present value of those delayed benefits is sharply reduced once discounting is applied, reinforcing an incentive to wait before committing capital. For governments, the same delay undermines the effectiveness of short-term targets, since progress is structurally muted when long-lived stocks dominate.\u003c/p\u003e\u003cp\u003eThe temporal mechanisms in Section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e4\u003c/span\u003e show that recovery flows arrive only after significant delays, that stocks expand long before disposal occurs, and that discounting lowers the value of distant returns. These same features generate collective action problems. In Ostrom\u0026rsquo;s framework (1990), the absence of institutions that align incentives leads to under-provision of benefits that are dispersed across actors and over time. Applied to circular systems, firms face the option of waiting: each actor prefers others to bear the cost of early investment in recovery infrastructure, since the eventual benefits will be shared but arrive decades later. The equations formalize the intertemporal imbalance, and the outcome mirrors a coordination failure.\u003c/p\u003e\u003cp\u003eSeveral paradoxes follow. Improvement in recovery efficiency does not guarantee a rise in circularity in the short run, since the relevant returns depend on past inflows, for some years at least. Ambitious policy targets on five-year horizons generate limited movement when dominant stocks are long-lived. Private investors face an option value of waiting even in cases where social welfare would increase with early action. The apparent lack of progress is therefore consistent with a system governed by lags and valuation effects.\u003c/p\u003e\u003cp\u003eFirm strategy benefits from aligning clocks. Procurement calendars can be coordinated with expected demolition windows through advanced purchase agreements and flexible specifications. In other sectors industrial symbiosis could be a way forward. Material exchanges with verified quality data reduce uncertainty when goods re-enter after long use. Contracts that recognize time value, for example by sharing storage and transport costs or by pricing options to call reclaimed stock later, can unlock adoption in sectors with volatile schedules.\u003c/p\u003e\u003cp\u003ePolicy design gains from explicit time alignment. Short-lived sectors can support visible progress through high-frequency collection standards and minimum recycled content. Medium-lived sectors require stable rules that support remanufacturing, modular design, and access to spare parts for over a decade or more. Long-lived sectors benefit from design requirements for disassembly, building passports that preserve information over many years, public support for material banks, and demolition planning that treats end of life as a managed phase rather than an afterthought. Indicators that credit expected future substitution from assets already in service can help align political horizons with material horizons.\u003c/p\u003e\u003cp\u003eThe broader implication of this paper is straightforward. Circularity is an intertemporal allocation problem. Stocks reflect past choices, flows return on varied clocks, and evaluation rules favor near-term gains. Recognizing time as an endogenous barrier clarifies why observed progress can look flat despite policy and technological effort. A realistic transition path combines quick gains in fast loops with credible commitments that prepare slow loops for recovery many years ahead.\u003c/p\u003e\u003cp\u003eThe structural role of time creates intertemporal externalities: present actors extract and consume without accounting for how their choices constrain future recovery. Without corrective mechanisms, private incentives underweight long-run benefits, leading to underinvestment in design for longevity, modularity, and recovery capacity. Policy responses such as extended producer responsibility, material passports, or differentiated taxes can be understood as Pigouvian tools designed to internalize these temporal externalities.\u003c/p\u003e\u003cp\u003eThe analytical structure developed in the study advances circular economy research by introducing a formal treatment of time dependent mechanisms that shape system level circularity. Earlier frameworks have focused on technological conditions, material substitution and regulatory design, but limited attention has been given to the dynamic role of stock formation. The model provides an explicit representation of how goods with long lifespans influence observable outcomes by delaying return flows and creating asynchronous material cycles. The analytical expressions clarify how recovery efficiency, valuation patterns and stock accumulation interact over time and reveal structural barriers that remain in place even under favorable technological progress. The paper shows that circularity is influenced not only by the performance of recovery processes but also by the temporal structure of material systems. The contribution therefore lies in establishing a clear link between lifespan heterogeneity, delayed substitution and system level circularity. The formulation extends earlier work on dynamic material constraints by providing a general representation of time-based frictions that influence circularity indicators across sectors with pronounced stock accumulation.\u003c/p\u003e"},{"header":"7. Concluding remarks and directions for future research","content":"\u003cp\u003eThe novelty of the paper lies in integrating intertemporal economics into circular economy theory by making time an endogenous barrier rather than a contextual factor. By positioning time as a structural barrier, the analysis explains why circularity evolves unevenly across sectors and why short-term interventions often produce limited aggregate effects. The purpose of the paper has been to place time at the center of circular economy analysis and to show that it constitutes a structural barrier. The results demonstrate that recovery flows are never immediate but always delayed by product lifespans.\u003c/p\u003e\u003cp\u003eThe analysis clarified this dynamic through four cases: recovery lags, partial recirculation, aggregate circularity defined by past inflows, and the discounting of delayed benefits. Each case shows that time shapes outcomes as much as technology or institutions. The finding is that circularity is best understood as an intertemporal process.\u003c/p\u003e\u003cp\u003eThe implications are threefold. For policy, indicators must reflect recovery delays to avoid misleading assessments of progress. For practice, investment strategies must account for the long horizons associated with major material stocks. For research, further work is needed to measure lifespan distributions and to integrate time more explicitly into models of resource use and intertemporal choice. Recognizing time as endogenous rather than contextual provides a foundation for more realistic analysis and more durable strategies for circular transitions.\u003c/p\u003e\u003cp\u003eThe framework opens a range of theoretical extensions. One avenue is to explore stochastic lifespan distributions and uncertainty in recovery efficiency, linking the dynamics of circularity to models of irreversible investment. Another is to embed the analysis in overlapping generations settings, making explicit the intergenerational distribution of costs and benefits implied by long-lived stocks.\u003c/p\u003e\u003cp\u003eEvery product carries its own clock. A shirt comes back within a few years, a refrigerator after a decade, a bridge only when today\u0026rsquo;s students are retired. Markets respond to those clocks: supply of secondary materials arrives late, demand is always current, and the future is discounted. Circularity is therefore not a smooth loop but a staggered sequence of returns, shaped as much by time as by technology. Seeing the circular economy through this intertemporal lens reveals why progress is uneven and why strategies must be calibrated to the rhythms of material life. Why is circularity proceeding so slowly? Maybe it is because we have forgotten about time.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding information\u003c/h2\u003e\n\u003cp\u003eFinancial support from for FORMAS grant 2022-00635 - Barriers for a circular Swedish industry. The funder did not play any part in performing or planning this research. Responsibility for any remaining errors, however, resides solely with the author.\u003c/p\u003e\n\u003ch2\u003eDeclaration of generative AI and AI-assisted technologies in the writing process.\u003c/h2\u003e\n\u003cp\u003eDuring the preparation of this work the author used ChatGPT to improve the language. After using this tool/service and to structure some of the equations, the author reviewed and edited the content as needed and take full responsibility for the content of the published article.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eI did it all.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAkerlof, G. A. (1978). The market for \u0026ldquo;lemons\u0026rdquo;: Quality uncertainty and the market mechanism. In \u003cem\u003eUncertainty in economics\u003c/em\u003e (pp. 235\u0026ndash;251). Academic Press.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eArrow, K. J., \u0026amp; Fisher, A. C. (1974). Environmental preservation, uncertainty, and irreversibility. \u003cem\u003eQuarterly Journal of Economics\u003c/em\u003e, 88(2), 312\u0026ndash;319.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eArthur, W. B. (1989). 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Fischer.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWu, Z., Liu, D., Mei, Y., Guo, S., Xiong, L., Liu, P., \u0026hellip; Zeng, Y. (2022). Delayed feedback between adaptive reservoir operation and environmental awareness within water supply-hydropower generation-environment nexus. \u003cem\u003eJournal of Cleaner Production\u003c/em\u003e, 345, 131181.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-industrial-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"44498","submissionUrl":"https://submission.springernature.com/new-submission/44498/3","title":"Journal of Industrial Ecology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Circular economy, Material lifespans, Intertemporal dynamics, Structural barriers, Resource recovery","lastPublishedDoi":"10.21203/rs.3.rs-8161933/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8161933/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCircular economy debates often acknowledge material lifespans and delays, but time is usually treated as a contextual issue rather than a structural barrier. The contribution is to reframe circular economy transitions as intertemporal processes by treating time as an endogenous structural barrier. A framework is developed that classifies goods into short-, medium-, and long-lived categories, demonstrating how lagged inflows and valuation biases suppress aggregate circularity even when technology improves. By making temporal mechanisms explicit, the analysis explains why indicators remain stagnant despite policy and efficiency gains. The contribution is to introduce time as an endogenous barrier, integrating insights from environmental and resource economics into circular economy theory and showing how delayed substitution shapes both firm investment and policy outcomes.\u003c/p\u003e","manuscriptTitle":"Time as a Structural Barrier for a Circular Economy","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-05 06:24:14","doi":"10.21203/rs.3.rs-8161933/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2025-12-21T12:21:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"283639179428827807786445167048458494613","date":"2025-12-11T09:52:44+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-03T10:49:00+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-24T15:37:30+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-22T08:11:14+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Industrial Ecology","date":"2025-11-20T07:58:07+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-industrial-ecology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"44498","submissionUrl":"https://submission.springernature.com/new-submission/44498/3","title":"Journal of Industrial Ecology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"aba27303-c1c7-482f-b769-a43d9d853461","owner":[],"postedDate":"December 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-01-12T14:54:00+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-05 06:24:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8161933","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8161933","identity":"rs-8161933","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}