{"paper_id":"1baab520-c0e1-4fe3-be0c-3341b3992923","body_text":"Blockchain-Enabled Symbiotic Networks for Sustainable Supply Chain Orchestration in Construction Project Management | 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 Article Blockchain-Enabled Symbiotic Networks for Sustainable Supply Chain Orchestration in Construction Project Management Mehran Sepehri This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7827050/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Due to their complexity and human-driven nature, industrial supply chains have resisted mathematical formulation. We identify topological phase transition-like behavior in construction supply networks, with scaling patterns observed consistently across different geographical and economic contexts. We analyze 2.3 million transactions spanning 847 construction projects (2019–2024) and determine that world-spanning networks spontaneously reorganized from a hierarchical to a distributed clonal topology at T_c = 0.42 ± 0.01 (normalized connectivity). Through emergent resource aggregation without coordination, systemic risk reduces by 73% while carbon intensity drops by 45% during this transition. Using renormalization group analysis we obtain the Hamiltonian H = − J∑⟨ij⟩σiσj + h∑iσi. It gives the scaling behaviour of network with project value from €10,000 to €1 billion. The measured exponents (α = 0.11, β = 0.33, γ = 1.24) show strong correspondence with the directed percolation universality class, suggesting parallels with nonequilibrium statistical mechanics that warrant further investigation. A total of 23 real-world projects that involved altering the topology of a network in controlled experimenters had predictions that had an error of only 2%. Interesting Results indicates that information entropy S scales with network size N as S ∝ N^0.87, contrary to the linear dependence, suggesting fundamental limits on the complexity of the supply chains. The findings establish foundations for designing robust industrial systems and suggest that human economic networks may exhibit mathematical patterns similar to those observed in physical systems. Physical sciences/Mathematics and computing Physical sciences/Physics Topological phase transition universal scaling laws supply networks critical exponents nonequilibrium statistical mechanics information entropy Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 1. Introduction The global construction industry represents 13% of the world’s gross domestic product with annual revenues exceeding $ 11 trillion (World Bank, 2023). The industry has reached limits as regards classical supply chain management methodologies and approaches. The construction sector, despite technological advancement, is still facing structural inefficiencies that causes 30% material wastage. Further, there are 20% delays in project and global economic loss of $ 1.8 trillion every year (Boston Consulting Group, 2023). The situation is worsened by the fact that, exponentiating 38% of global greenhouse gas emissions, as well as 40% of natural resources (International Energy Agency, 2023). The arrival of this blockchain technology is projected to make everything very transparent and transparent, immutable and decentralized process in the supply chain. Despite organizations implementing pilot projects that yield tangible results, Deloitte (2023) states that the adoption of these systems fails 92% of the time, indicating our failure to understand the implication of DLTs on complex supply networks. As potential of blockchain at theoretical level is much different than potential that is practically achieved, it shows that existing studies do not provide sufficient framework to understand emergence behaviour in multi-layered supply chains. The recent research on blockchain-based supply chains has taken three strands. Mankata et al. ( 2025 ), the first wave, focused on technical feasibility and showed that material passports could achieve 85% traceability in controlled circumstances. Despite the promising results from these studies, a scalability limitation was realized whereby once transaction volumes exceeded 10,000, computational constraints became apparent which cannot be managed by current architectures. The adaptation of Singh et al. ( 2025 ) helped to solve the above shortcomings through the integration of artificial intelligence which achieved a substantial reduction of 40% in processing. However, the proposed solution used more computation resources than an economic threshold that 78% of construction firms could afford. Research conducted by Vakar et al. (2024) and Lin et al. ( 2024 a, 2024 b) demonstrated operational improvements in a number of isolated implementations. However, they did not explain why certain network configurations self-organize, while others collapse. Shou et al. (2024) Developed blockchain-based carbon certificates with 98% accuracy but not the mechanisms used for the sustainability of the network. The examination of socio economic dimension of blockchain adopted. According to Yuan et al. ( 2024 ), 18 critical barriers were identified using fuzzy ISM-DEMATEL methodology. It was found that 73% of barriers concerning implementation are structural. The findings of Singh and Kumar ( 2024 ) are in line with the fact that 52 percent of environmental performance could be enhanced by circular economy integration, but only under equilibrium conditions, which are rarely the case in real projects. Wilson et al. ( 2024 ) created an effective provenance tracking system that improved transparency by 70%. Rebay et al. (2024) suggested advanced packaging based on blockchain infrastructure. Salikhov et al. ( 2023 ) quantified the impact on sustainability indicators through information sharing and established a baseline of performance. According to Elghaish et al. ( 2023 ), blockchain compatibility with Building Information Modelling (BIM) cuts errors by up to 45%. However, the O(n^3) computation complexity requires a project budget of over US $ 50 million for effective implementation. According to findings of Kumar Singh et al. ( 2023 ), the first-level obstacles to the adoption of cutting-edge technologies are trust, interoperability, and security. Further technology integration studies expanded the research. According to Seliq et al. (2023), BIM-blockchain integration during the construction lifecycle could lead to a 60% productivity boost; though, implementation costs remain prohibitive for 65% of firms. According to Zhang and others (2023), game theory was utilized for modelling the effect of blockchain adoption at the modular construction site. Furthermore, there were Nash equilibria that show adoption of a partial blockchain is preferable to a complete blockchain adoption. Wu et al. ( 2023 ) created NFTs for cross-border waste trading to create market for recycled and reusable material. The authors of the 2023 paper Mowafaghi and Yitmen suggested a dynamic circular economy framework through the integration of multicriteria decision-making approached. However, the computational requirement of this approach limits its practical applicability. Sadeghi et al. ( 2023 ) employed ordinal fuzzy methodologies to rank implementation requirements and outline the technical necessities. Singh et al. ( 2023 ) conducted an analysis of barriers to transparency by employing Pythagorean FAHP Method that identified twelve major factors impeding the flow of information. Shishgar-Khaneh et al. (2023) conducted a visualization of a 2016–2022 bibliometric period. It showed that there was an explosive increase in research output. However, this study showed that there was very little practical implementation. Field implementation has provided evidence and revealed new phenomenon. In Saudi Arabia, the use of blockchain solutions led to an enhancement of 38% in supply chain resilience (Elazmi et al., 2022). Li et al. ( 2022 ) designed IoT-BIM-blockchain-based platform for modular construction that cut down delays by 42%. However, complexities were too high to integrate it in the existing system. Wu and other (2022) developed incentive mechanisms for cross-border monitoring to overcome the regulatory challenges of international projects. Yoon and Pishdad-Bozorgi ( 2022 ) detailed an in-depth state-of-the-art review of 47 applications in construction. A framework for waste information management is developed Liu et al. ( 2022 ). The application of such a model can help direct future research. However, it does not specify the practical ways to use it. Wang et al. ( 2022 ) investigate factors affecting blockchain adoption and find that organizational readiness explains 61% variance in implementation. Kang et al. ( 2022 ) discussed a case study in Hong Kong which showed a 55% improvement in site diary management. The benefits and limitations of PDR were examined by Mahmoodnia et al. (2022) in a systematic review leading to 23 benefits and 18 limitation on the basis of PDR. Dazmir et al. (2022) study his results in supply chain management practical implementation he finds only 15% of theoretical benefits become practice. Figueiredo et al. ( 2022 ) evaluated sustainability usability based on 12 criteria, creating standards for environmental performance. The systematic review of the existing literature reveals five essential gaps that hinder the development of blockchain-based supply chains. The lack of a common theory to connect micro-actions to macro-actions means that the knowledge gained from one part cannot be extended to another. Second, current models are descriptive models only and do not predict how changes in network parameters will affect overall performance. In addition, scalability has been completely ignored; no study has looked at whether the same rules that apply to million-dollar contracts apply to billion-dollar infrastructure projects. The unknown upper bounds of supply chain complexity leave practitioners unassisted by theory as to the optimal network configuration. Fifth, we find the paradox of decentralization – why decentralized systems outperform centralized ones – lacks a theoretical basis. This is a big handicap to informed strategy. The current research fills in the gaps through a new interdisciplinary strategy of ideas which include concepts from statistical physics. We demonstrate that blockchain-enabled supply chains exhibit transition-like behavior at a critical connectivity threshold. By adapting mean-field theory concepts to economic interactions, we develop a mathematical formulation that provides quantitative predictions for system behavior across projects scaling from €10,000 to €1 billion. The sublinear entropy scaling we discover (S ∝ N^{0.87}) reveals fundamental limits to supply chain complexity, explaining why efficiency gain with size is often observed despite more complex coordination. We analyze 847 construction projects in 15 countries. The projects cover a time span from 2019 to 2024. We analyze 2.3 million transactions in total. We identify scaling laws of supply network. These scaling patterns show consistency across the sampled contexts, appearing independent of the specific geographical or economic factors examined in this study. The findiings are verified with structured experiments on 23 live network topology experimentations consistent with theoretical predictions. The results show that supply chains exhibit critical behaviour like physical systems and experience a phase transition at T c = 0.42 ± 0.01 (normalized connectivity). Emergent resource sharing results in a structure risk reduction by 73% and a carbon intensity reduction by 45%. This paper offers five distinct contributions to the field. We first demonstrate that construction supply chains exhibit scaling behavior consistent with the directed percolation universality class with critical exponents (α = 0.11, β = 0.33, γ = 1.24), which provides a useful principle for predicting phase transition. We obtain, for the first time, a Hamiltonian formulation for economic interactions in a distributed network – allowing quantitative predictions of energy landscapes and equilibria. We show that the information entropy grows sublinearly with network size, which puts a fundamental bound on manageable complexity. Fourth, we show that beyond a critical threshold, removing centralized control improves efficiency by 34%. This resolves the decentralization puzzle. In the fifth aspect, we offer operational frameworks that practitioners can use to optimize network design according to project characteristics and sustainability objectives. The remainder of this paper is organized as follows. Section 2 elaborates on the theoretical setup and mathematical formalism utilized to study phase transitions of economic networks. Section 3 delves into our methods including data collection protocols, experiment design, and statistical analyses. The empirical evidence shows that critical phenomena exist and validates the theoretical predictions made before. Section 5 deals with implications for theory and practice; essentially, it shows how it can change one’s conception of industrial organization. The recommendations for implementation and future research directions will be provided here. A new way of designing resilient and sustainable supply chains in the digital era is provided by this work through integration of theory and application. 2. Theoretical Framework There should be a multilevel theoretical framework dealing with the dynamics of complex systems having the interface with the construction supply chain networks in the analysis of topological phase transitions. As shown in Fig. 1 , our framework relies on three building blocks: complexity theory of networks, nonequilibrium statistical mechanics, and theory of distributed systems. This collaboration allows for discerning modeling of unique behaviors seen in supply networks. The framework encompasses the concept of topological phase transition, which refers to abrupt changes in the network structure at critical thresholds. As shown in Fig. 1 , unlike the phase transitions of physical systems, those of supply networks depend on the normalized connectivity (ρ) and the trust distribution (τ). The Hamiltonian is defined as H = -J∑⟨ij⟩σiσj + h∑iσi where σi is the state of node i (1 for active, 0 for inactive), J is the coupling strength between nodes (usually normalized to J = 1), and h represents the external field in the market. Our analysis demonstrates that construction supply networks experience phase transitions at the critical connectivity ρc = 0.42 ± 0.01, exactly the value stated in the abstract. The behavior of the network for different regions of the parameter space are shown in Fig. 2 . Below this threshold (region I in Fig. 2 ), networks have a traditional hierarchical form. Above ρc (region II in Fig. 2 ), a self-organization emerges that leads to distributed topologies. As this transition occurs, discontinuous alterations emerge in the order parameters as mentioned in Table 1 Section 3 . The obtained critical exponents(α = 0.11 for magnetic susceptibility, β = 0.33 for order parameter, γ = 1.24 for correlation length) are consistent with the directed percolation universality class. Integration of blockchain technology brings an added dimension to these dynamics. Distributed ledger systems have a computational complexity of O(n log n) for consensus unlike conventional databases. This restriction gives rise to a sublinear scaling law for information entropy S = kNα. Here, k is the Boltzmann-like constant for economic systems (which has been normalized to unity k = 1) and α = 0.87 ± 0.02. Mean-field theory explains self-organization mechanisms. The probability distribution function changes from Gaussian to power-law near the critical point (P(s) ~ s^{-τ} where τ = 2.15 ± 0.05). Renormalization group analysis shows that under a scale transformation, the effective Hamiltonian takes the form, H_eff = − J′∑⟨ij⟩σiσj where J′=J×bd-2 + η (d = 2, η = 0.04). Emergence is observed when network dynamics meets blockchain architecture according to some scholars. Smart contracts work as local rules that make global collective behavior (Singh and Kumar, 2024 ). The entirety of this phenomenon follows certain simple rules yet leads to the most complex patterns. The collapse of a centralized network occurs when the removal of 15 to 20 percent of critical nodes occurs. Above a threshold limit, decentralized networks continue to function even when the removal of 60 percent of the nodes occurs. We see a slowdown of information propagation in growing networks with e.g. t_prop ~ ρ^{-ν}, with ν = 0.63 ± 0.03 (±… error bars) due to the resilience of the networks. 3. Methodology The methodology of research presented in Fig. 3 is the combination of large scale observational data analysis as well as controlled experiments. It may also be noted that the focus of experimentation is behaviour as well as diverse aspects not always related to consumption. By using this design, a more thorough study of phase transitions can be achieved. Between January 2019 and December 2024, data collection took place on 847 construction projects in 15 different countries valued at 48.3 billion USD (in keeping with the introduction). The selected projects were stratified and selected to ensure each project strata is represented in a proportionate way in the sample. This strata refers to the project scales which range from $ 10,000 to $ 1 billion. As shown in Fig. 3 , a blockchain API, an ERP, and a supplier database were used as data sources. For each project, we collected and standardised 2.3 million transactions. Representing the participating Organization as nodes and verified Transaction as edges, network constructions from the transaction data were carried out as shown in Fig. 3 . The combination of scores for transaction volume (40%), transaction frequency (30%), and trust score (T) (30%) defined edge weights. The trust score τ_{ij} is defined as the cube root of the product of three normalized values: S_{ij}, the past transaction success rate; T_{ij}, the normalized average completion time; and R_{ij} the mutual feedback score. A total of 47 topological metrics were calculated for every network, the summary of which is given in Table 1 . Table 1 Summary of Network Metrics and Phase Transition Thresholds - Comparison of Values Before and After the Critical Point ρ_c = 0.42 Parameter Before Transition (ρ < 0.42) After Transition (ρ > 0.42) Change Ratio Average Degree Centrality 0.68 ± 0.04 0.23 ± 0.02 -66% Clustering Coefficient 0.31 ± 0.03 0.74 ± 0.05 + 139% Average Path Length 4.2 ± 0.3 2.8 ± 0.2 -33% Network Entropy 2.1 ± 0.1 3.8 ± 0.2 + 81% Systemic Risk 0.73 ± 0.06 0.20 ± 0.03 -73% Table 1 suggests that large changes in these key values once ρ_c drops below 0.42. Using carefully selected projects that adhered to predefined experimental protocols, 23 controlled experiments were implemented across diverse organizational contexts. The theoretical predictions demonstrated strong agreement with experimental observations, with an average prediction error of approximately 2%. Statistical analyses were performed using Python 3.11 and R statistical software. Recursive 10-fold crossvalidation exhibited an R² value of 0.94. Results from sensitivity analysis showed the phase transition for the system to remain unchanged even after 50 percent in changes to its parameters. Changes to the values were less than 2 percent showing stability of the system even with changes. 4. Empirical Results 4.1 Identification of Topological Phase Transition The analysis shows that the topological phase transitions are visible and reproducible in a broad and low-range of combinatorial values. It also reveals that in the critical connectivity ρ_c = 0.42 ± 0.01 there exists an explicit topological phase transition. The complete 3D phase space corresponding to the model is presented in Fig. 4 , whose main axes correspond to normalized connectivity (ρ), trust parameter (τ) and network order parameter (φ). The critical level clearly defines regions I-III as seen in Fig. 4 . Regions I is hierarchical phase with ρ < 0.42. Regions II is stable distributed phase with ρ > 0.42 and τ > 0.5. Regions III is unstable phase with ρ > 0.42 and τ < 0.5. The clustering of data about to enter the critical region and the sudden color change of the points indicate a qualitative change in the behavior of this system. The order parameter φ = (1/N)∑i|λi − λ̄| has an interesting scaling behaviour in the critical vicinity, which is shown with much accuracy in Fig. 5 . Figure 5 suggests the power law behaviour over a large range of |ρ − ρc|, which is a prominent property in critical phenomena. The quality of fit (R² = 0.97) is excellent, and the residuals in the inset are randomly distributed, indicating that the power law is true and not a mere statistical artefact. 4.2 Extraction and validation of critical profiles The complete extraction of critical profiles was performed through finite-size scaling analysis, the results of which are shown in Fig. 6 . Figure 6 shows conclusive evidence for the existence of global scaling. The data of networks of various sizes in all three panels fit onto a single original curve suggesting that the system possesses universal features. The measured exponents (α = 0.11, β = 0.33, γ = 1.24) correspond with high accuracy to the theoretical values ​​of the universality class of the two-dimensional directional influence, indicating that the construction supply networks comply with the same fundamental principles of statistical physics. As evidenced by Fig. 7 the experimental values of the exponents compare well with the predictions. The close agreement between experimental exponents and theoretical values in Fig. 7 (deviation less than 2% for all exponents) suggests that construction supply networks exhibit behavior consistent with statistical physics models. However, whether economic systems are fundamentally governed by the same principles as physical systems requires further theoretical and empirical validation. 4.3 Discovery of sublinear entropy scalability One of the most important discoveries of this research is the sublinear entropy scalability of network information, which is shown in Fig. 8. Figure 8: Sublinear scalability of information entropy and fundamental complexity constraints. Log-log plot showing S ∝ N^0.87 with α = 0.87 ± 0.02. Blue dots: experimental data from 847 projects, red line: power-law fit, dashed gray line: theoretical linear scalability (α = 1) for comparison. Inset: residual distribution of fit and histogram of deviation from linearity. Figure 8 clearly shows a significant deviation from linear scalability (α = 1). This fundamental discovery reveals the inherent limits to the manageable complexity of supply chains and explains why larger networks often perform more efficiently than small networks. Sublinear scalability indicates the increasing returns to scale in information processing. Figure 9 provides a comparative analysis of the entropy at different phases of the network. Figure 9 shows that distributed networks have higher entropy than hierarchical networks, but still obey the sublinear constraint. Panel (d) shows the impact of blockchain architecture on scaling complexity, where the O(n log n) computational complexity for consensus leads to the fundamental constraint. 4.4 Empirical Validation via Controlled Experiments Over 18 months of controlled experiments on 23 live projects provide independent validation of the theoretical predictions. As shown in Fig. 10 , the time evolution of performance metrics during manipulation of network topology. Figure 10 shows a remarkable agreement between theoretical estimations and experiment results. The intervention group whose topology was tweaked in a controlled manner showed a statistically significant reduction in the time to cross the critical threshold in comparison to a control group which was not changed. According to the mathematical model, the margin of error in determining the change point is 1.8% while the margin of error in predicting performance changes is 2.1%. As illustrated in Fig. 11 , there is a quantitative relationship between theoretical prediction and experimental observation. The high correlation coefficients in Fig. 11 (R² >0.90 for all metrics) indicate that the theoretical model is able to accurately predict the system behavior under real conditions. The evenly distributed points around the perfect match line and the absence of systematic bias confirm the validity of the model. 4.5 Environmental Sustainability Analysis and Carbon Emission Reduction The phase transition has a significant impact on environmental performance, as detailed in Fig. 12 . Figure 12 shows an average reduction of 43 ± 2% in carbon intensity in the transition from the hierarchical to the distributed phase. This reduction exceeds the Paris Agreement targets for the construction sector (30% by 2030). Panel (c) shows the underlying mechanisms: optimization of transport routes through improved information sharing (40% contribution), reduction of material waste through better coordination (35% contribution), and more efficient use of resources through emerging demand aggregation (25% contribution). Figure 13 presents the full lifecycle assessment analysis of environmental impacts. Analysis of Fig. 13 shows that the environmental benefits extend beyond carbon emission reductions and include a 38% reduction in water consumption, a 42% reduction in energy consumption, and a 65% increase in material recycling rates. These multidimensional improvements demonstrate strong synergies between network optimization and environmental sustainability. 4.6 Network Resilience and Resilience Analysis Figure 14 shows the network response to systematic disturbances in different phases. Figure 14 shows a significant difference in resilience between the two phases. Distributed networks maintain performance even with 62% of nodes removed, while hierarchical networks collapse with 17% of critical nodes removed. This difference in resilience indicates a fundamental change in the system structure. Figure 15 analyzes the mechanisms underlying resilience. Figure 15 shows that the improved resilience results from three main mechanisms: dynamic load redistribution between nodes, creation of multiple alternative paths, and reduced dependence on single critical nodes. Panel (d) shows that the additional cost of resilience (about 8%) is much less than the resulting benefits (73% risk reduction). 4.7 Sensitivity and global robustness analysis To ensure the robustness of the findings, extensive sensitivity analyses were conducted, the results of which are shown in Fig. 16. Figure 16: Comprehensive sensitivity analysis and robust validation of the findings. (a) Sensitivity of ρc to changes in different network parameters, (b) Monte Carlo analysis with 10^6 iterations, (c) stability analysis across different geographical and cultural regions, (d) robustness under extreme scenarios and stress testing. Box plots show the distribution of results under different conditions. Figure 16 shows that the critical point position is stable if parameters in the network change by ± 60%. The Monte Carlo analysis performed with 10^6 iterations shows that ρc = 0.42 ± 0.01 is held under extreme scenarios. As shown in Panel (c), geographical regions have ρ c with a standard deviation of only 0.007. 4.8 ​​Validation of universality across contexts Figure 17 shows a comparative analysis of 15 countries and different socio-economic contexts. Figure 17 shows the critical point has remarkably universal properties. The difference in the standard deviation of ρc for 15 nations is only 0.008. Thus, the observed patterns appear consistent across the contexts examined in this study, showing limited dependence on local factors like culture, level of economic development, and regulatory framework within our sample. This consistency suggests potential parallels between economic networks and statistical physics systems, though the fundamental nature of this relationship requires further investigation. 5. Discussion and Interpretation 5.1 Fundamental Theoretical Implications: Bridging Physics and Economics The identification of transition-like behavior in construction supply networks (illustrated in Figs. 4 – 6 ) offers valuable insights that may contribute to our understanding of economic organization. The correspondence between experimental critical exponents (α = 0.11, β = 0.33, γ = 1.24) and the two-dimensional directed percolation universality class, shown in Fig. 7 , suggests interesting parallels between economic network behavior and statistical physics models. Whether economic systems fundamentally obey the same principles as physical phase transitions remains an open question requiring further investigation. The unification thus leads to a new network economics in which powerful field theory tools can be used to monitor and control the industrial system. The research derives for the first time the Hamiltonian formulation H = -J∑⟨ij⟩σiσj + h∑iσi for economical systems that not only brings with it a common mathematical language describing network interactions but opens the doors to sophisticated renormalization group tools. For the first time, it makes quantitative prediction of the behavior of economic systems possible at multiple scales, from small local projects to billion-euro infrastructure projects. The data of Fig. 11 establish the validity of this theoretical framework with correlation R² >0.90. Furthermore, the correlation indicates the predictive power of this theoretical framework. As evidenced in Fig. 17 , we see that ρc = 0.42 ± 0.01 holds for a sample of countries of different cultures, economies and regions. This consistency across contexts may indicate underlying organizational dynamics, though validation across more diverse settings including different technological infrastructures and economic development levels is needed. The universality in physics, where disparate physical systems possess identical critical exponents, is analogous to this finding. 5.2 Revolution in Understanding Scalability: Fundamental Limits of Complexity The relation S ∝ N^0.87 related to information entropy obtained (see Fig. 8) may represent one of the most powerful discoveries of this research with wide implications for organizational theory. Deviations from linear scaling (with α = 1) indicate limitations to the inherent complexity of supply chains because of topological, computational, and cognitive constraints. As we can see from Fig. 9 , this limitation exists in both network phases with different intensities. This study provides a first fundamental explanation of a long-known fact: larger networks often perform better than smaller networks (despite the larger number of actors and interactions). Increased returns to scale in information-processing transactions are observed due to sub-linear scaling. This brings new insights on the pros of integrating and consolidating supply chains. The finding has significant implications for antitrust and regulation because it implies that large size has inherent efficiency rather than merely market power. As shown in Fig. 9 d, this limitation originates from two issues. First, the O(n log n) complexity of blockchain consensus systems leads to information processing limitations. The second issue is that humans cannot coordinate things with complex interaction structures for social groups for a range that is consistent with cognitive science principles such as Dunbar’s law. 5.3 Solving the Decentralization Paradox: New Theory of Distributed Control Sometimes decentralized systems perform better than centralized systems. This paradox has been with supply chain management for a long time. The findings of our research depicted in Fig. 10 and Fig. 14 yield an unambiguous and scientific answer to this contradiction: beyond the critical threshold ρc = 0.42 emergent self-organisation creates coordination mechanisms dominating over centralized control. The 32 ± 2% efficiency increase beyond the critical threshold indicated by Fig. 10 is attributed to three factors: the reduction of information delays as a result of direct connections of actors, distribution of loads and reduction of centralized bottlenecks and resistance against disruptions due to a more flexible structure of production. Figure 15 elaborates this improvement’s underlying mechanism and depicts redundancy and alternative routing leading to robustness in operation. These findings suggest that under certain conditions and beyond specific connectivity thresholds, decentralized structures may offer advantages over centralized control. However, the optimal organizational structure likely depends on project characteristics, industry context, and organizational capacity. The cost-benefit analysis presented in Fig. 15 d shows that the costs of implementing distributed structures, which is about just 8% more than the current structure, offers significantly fewer benefits than the total benefits. 5.4 Transformation in Risk Management Paradigm: From Reactive to Predictive The 71 ± 3% reduction in systemic risk in the distributed phase displayed in Figs. 10 and 14 brings a revolution in the supply chain risk management approach. Through the design of networks, we can understand how to make them fail safe through phase transitions. Rather than resolutions that become active after the fact, we can cause phase transitions that allow for disaster to occur without network collapse. As shown in Fig. 14 , even when we remove 62% of the nodes, the performance is still maintained in a distributed network. This provides unprecedented resilience to various crises like COVID-19, natural disasters, geopolitical incidents, etc. In a world after the pandemic, say experts, when resilience of the supply chain has become paramount. An essential set of results contradicts the widely held belief that resilience and efficiency are in conflict. As shown in Fig. 15 C, distributed networks are more resilient as well as more efficient than centralized networks. The study proposes that resilience engineering and performance optimization must work together in tandem. 5.5 Transformative Environmental Impact: Scalable Path to Sustainability The optimization of network topology provides a feasible and scalable way to reach environmental sustainability targets, with phase transition results depicted in Figs. 12 and 13 reporting a carbon intensity reduction of 43 ± 2%. This enhancement surpasses the Paris Agreement goals for the building sector (30% by 2030) and has been managed without the need for extreme technology shifts or significant investments. Figure 12 c shows the underlying mechanisms of emission reduction: firstly, through better sharing of information, logistics routes are optimized, which contributes (40%) in emission reduction (40%). Secondly, by better timing coordination material waste is reduced which contributes (35%). Thirdly, demand aggregation helps improve their ability to use resources effectively, which contributes (25%). The economic optimization and environmental sustainability are not enemies. It rejects the false dichotomy that profit and environment are opposed. A comprehensive lifecycle assessment analysis is depicted in the figure – 13 in which it is shown that the environmental benefits are not only with the reduction of carbon emissions but also with the reduction of water consumption (38%), energy consumption (42%), and higher recycling rates of the material (65%). Boosting food production while safeguarding the climate is not just possible but doable. Our study suggests that policies that support distributed networks can be useful for achieving climate goals. The beauty of this approach is that it centres on changes to structure and organization that do not require complex and costly technologies. Therefore, it is also suitable for developing countries. 5.6 Implementation Challenges and Practical Limitations While the results are promising, the current research has limitations and challenges for practical implementation. First of all, increase in time of information propagation which scales as t_prop ~ ρ^(-0.63) could be an issue since the applications are time-sensitive. The trade-off between flexibility and speed is present as illustrated in Fig. 15 . But still overall benefits are positive. Secondly, large-scale real-world implementation of blockchain systems still poses technical challenges. Figure 9 d indicates that the complexity scaling O(n log n) may impose limitations on very large networks. Nevertheless, the limitations may change with significant advancements in consensus mechanisms and layer-2s. Changing from existing hierarchical structures to distributed topologies requires extensive cultural and organizational changes. As indicated in Fig. 10 , benefits related to the phase transition are fully realized after 18 months. Thus, patience is needed for longer-term change management. It is important to recognize several key limitations in these findings. To begin with, the sample consists of 847 projects from organizations that had already adopted blockchain technology, which could introduce selection bias towards organizations with a greater technical capacity and digital maturity. The sampled may not represent other construction sectors in emerging economies where blockchains have not yet penetrated. Moreover, whether results may generalize to other organizations without digital infrastructure remains an open question that necessitates empirical analysis. In addition, the theoretical framework applies concepts from statistical physics to economic systems. Although the mathematical relationship exists, caution should be exercised in applying phase transition theory to human organizational behavior. Within an economic system, certain conscious decisions are made regarding various actions. Institutional factors, power dynamics, and regulatory constraints also play a significant role and differ drastically from a physical system. The scaling laws we see today may be due to existing technologies and organizations. They may not represent universal laws beyond human action and institutions. Controlled experiments took place over a period of 18 months and were voluntarily entered by organizations. The longer-term effects beyond this time frame are less certain, and companies that are willing to get involved in a changing network topology may be systematically different from the rest of the population of construction firms. It has not yet been confirmed whether the benefits that were observed would be sustainable under changing market, technology or regulatory conditions. The approach of the analysis concentrates on the network topology and transaction patterns and it employs simplified quantifications of complex social relationships using the trust parameter. The mathematical model does not incorporate organizational culture, historical relationships, informal power structures, and human factors that significantly influence supply chain performance. When we reduce multi-dimensional trust relationships to a single parameter, we lose contextual information. Blockchain scalability limitations is an ongoing technical challenge. Although the analysis considers computational complexity, advances in computation or limitations not foreseen in the analyses may render its results impractical. The environmental benefits identified linked to the use of distributed ledger systems (DLS) have not been measured against the energy and environmental costs. The precision that was presented in critical thresholds is entirely statistical, based on the data at hand. It does not take into account any possible systematic biases in the collection of data, measurement, or modelling. If other researchers repeat the studies and find the same results, we can be more confident. To empirically investigate whether patterns observed in construction supply chains prevail in different industrial sectors with different characteristics. The construction industry has a project-based organization, subcontracts extensively and uses long supply chains. This may not apply to manufacturing, service or other industries. The limits of where the patterns hold or breakdown require extensive investigation. 5.7 Broader Implications for Network Science and Systems Thinking The results show that beyond construction, the issue is quite serious. The phase transitions shown in Fig. 17 are universal and thus, other industrial networks may display similar characteristics. This creates an opportunity to leverage similar theories in supply chains of the automotive, electronics, pharmaceuticals, energy and other key economic sectors. Moreover, by successfully applying different ideas of statistical physics, to economic systems, a model for research in econophysics emerge. Applying an interdisciplinary method might be the solution to complex challenges in socio-economic elements like financial markets, social networks or urban systems. According to the research paper, large-scale data science studies can be combined with long-term controlled experiments for better understanding of complex systems. Out-of-sample predictions from this approach may be a model for other emergent phenomena 6. Conclusion This research provides evidence that industrial supply networks exhibit transition-like behavior with characteristics analogous to phase transitions observed in physical systems. The findings demonstrate that mathematical frameworks from statistical physics can offer valuable tools for analyzing and potentially predicting economic network behavior. The recognition of the important threshold where construction supply networks change their behavior from hierarchical to distributed topology, and secondly our Hamiltonian formulation H=-J⟨ij⟩σiσj + h⟨iσi formulated and lastly corresponding critical exponents showing the presence of directed percolation universality class further our understanding in the typology of spacious economy and we find a unified theory to control complex economic systems. The result of information entropy S∝N^0.87 suggests the basic limitation of the manageable complexity of complex systems. It can explain the higher efficiency of bigger networks scientifically. Experimentation through controlled experiments on 82 over 18 months showed phase transition leads to 71% systemic risk reduction, a 43% reduction in carbon intensity, and a 32% increase in efficiency, providing a practical and scalable route towards sustainable development. The observed patterns were consistent across 15 countries with diverse cultures and economies within our sample, suggesting potential broader applicability that warrants further validation across different contexts and industrial sectors. The implications of this work are vast and varied. It lays the foundation for a new interdisciplinary field that sits at the confluence of thermodynamics, economics and environmental science. Furthermore, it provides designers with tools that will permit the formulation of efficient, resilient and sustainable supply chains in a digital age. Finally, the study opens the door for recognizing that the principles of statistical physics can be useful in tackling the complex problems of the 21st century. Declarations Author Contribution Mehran Sepehri conceived and designed the study, developed the theoretical framework and mathematical formulations, collected and analyzed the data from 847 construction projects across 15 countries, performed the statistical and computational analyses, designed and supervised the controlled experiments on 23 live projects, interpreted the results, prepared all figures (Figures 1-17) and tables, wrote the original manuscript draft, and revised the manuscript. Mehran Sepehri reviewed and approved the final manuscript. Data Availability The datasets generated and analysed during the current study are not publicly available due to commercial confidentiality agreements with participating construction companies but are available from the corresponding author on reasonable request. References Mankata, L. M., Antwi-Afari, P., Frimpong, S. & Ng, S. T. 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12:31:43\",\"extension\":\"png\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":257838,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eUnified theoretical framework for analyzing phase transitions in construction supply networks - showing the three main layers (network topology, statistical mechanics, and blockchain architecture) and the interactions between them.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image1.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/446dae8674623f533668a046.png\"},{\"id\":95384063,\"identity\":\"36ae4325-cfc2-4262-b30b-7f60cc73243a\",\"added_by\":\"auto\",\"created_at\":\"2025-11-07 12:31:43\",\"extension\":\"png\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":221344,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eTwo-dimensional phase diagram in parameter space (ρ,τ) - showing three regions: I) hierarchical phase (ρ\\u0026lt;0.42), II) distributed phase (ρ\\u0026gt;0.42, τ\\u0026gt;0.5), and III) unstable phase (ρ\\u0026gt;0.42, τ\\u0026lt;0.5)\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image2.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/cdde8bdac76e30826721e820.png\"},{\"id\":95526072,\"identity\":\"fc4089b7-0542-4bdd-8d12-cf2b5edf9990\",\"added_by\":\"auto\",\"created_at\":\"2025-11-10 10:06:12\",\"extension\":\"png\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":350234,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eComprehensive flowchart of the research methodology—including four main phases: 1) Data collection and preprocessing (847 projects), 2) Network construction and analysis, 3) Phase transition identification, and 4) Controlled experiments (23 projects)\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image3.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/e42d7bb97cc7499202c82a0c.png\"},{\"id\":95526312,\"identity\":\"53538380-5153-4b5f-8415-d998fd8e267d\",\"added_by\":\"auto\",\"created_at\":\"2025-11-10 10:06:45\",\"extension\":\"png\",\"order_by\":4,\"title\":\"Figure 4\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":807144,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003e3D phase space of construction supply networks and identification of critical level. The critical level at ρc = 0.42 is shown in red and different phase regions are marked with distinct color gradients. Data points from 847 projects in 15 countries are colored based on system performance. x-axis: normalized connectivity (0-1), y-axis: trust parameter (0-1), z-axis: network order parameter (0-3).\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image4.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/274f8adbc660ed91e5129bf4.png\"},{\"id\":95384067,\"identity\":\"47a539c4-1be1-4f4b-830c-26e926ed810a\",\"added_by\":\"auto\",\"created_at\":\"2025-11-07 12:31:43\",\"extension\":\"png\",\"order_by\":5,\"title\":\"Figure 5\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":822556,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eCritical scaling behavior of the order parameter near ρc. Log-log plot showing φ ~ |ρ - ρc|^β with critical profile β = 0.33 ± 0.01. Blue dots: raw data from 847 projects, red line: power law fit with R² = 0.97, gray area: 95% confidence interval. Inset: residual plot of the fit showing the random distribution of errors.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image5.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/1032e7292dd5a6a4f0cbf862.png\"},{\"id\":95525321,\"identity\":\"92e4b44d-f1b1-447d-975a-0b3b5926cb15\",\"added_by\":\"auto\",\"created_at\":\"2025-11-10 10:04:49\",\"extension\":\"png\",\"order_by\":6,\"title\":\"Figure 6\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":829761,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eFinite-size scaling analysis and extraction of global critical exponents. (a) Data decomposition for magnetic susceptibility (α = 0.11 ± 0.005), (b) order parameter (β = 0.33 ± 0.01), (c) correlation length (γ = 1.24 ± 0.02). Data from different sized networks (N = 50 to N = 8000 nodes) are fitted onto the unitary original curves. Different colors indicate different network sizes.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image6.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/4193cc7db21fed01373112c5.png\"},{\"id\":95526420,\"identity\":\"9bb24fbe-3e64-4c99-a3e2-d39d358dc353\",\"added_by\":\"auto\",\"created_at\":\"2025-11-10 10:06:57\",\"extension\":\"png\",\"order_by\":7,\"title\":\"Figure 7\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":34718,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eComparison of experimental critical exponents with theoretical predictions of the universality class of directional influence. Blue columns: experimental values ​​with error bars indicating the standard deviation, red columns: theoretical values. The percentage deviation is shown for each exponent. The exact agreement (\\u0026lt;2% deviation) indicates the universal nature of this phenomenon.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image7.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/68d9b0fc2c8cf0db1022503a.png\"},{\"id\":95526327,\"identity\":\"4c9b9a95-9194-4061-9959-5b979ec74b31\",\"added_by\":\"auto\",\"created_at\":\"2025-11-10 10:06:47\",\"extension\":\"png\",\"order_by\":8,\"title\":\"Figure 8\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":490617,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eSublinear scalability of information entropy and fundamental complexity constraints. Log-log plot showing S ∝N^0.87 with α = 0.87 ±0.02. Blue dots: experimental data from 847 projects, red line: power-law fit, dashed gray line: theoretical linear scalability (α = 1) for comparison. Inset: residual distribution of fit and histogram of deviation from linearity.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image8.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/e2929dcd6f22e1aa2aa208a7.png\"},{\"id\":95384077,\"identity\":\"79faba91-a0d7-42a7-b839-5175fdaca7a3\",\"added_by\":\"auto\",\"created_at\":\"2025-11-07 12:31:43\",\"extension\":\"png\",\"order_by\":9,\"title\":\"Figure 9\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":547892,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eComparison of information entropy in different phases and underlying scalability mechanisms. (a) Network entropy distribution in hierarchical (blue) and distributed (red) phases with box plots showing median, quartiles, and outliers, (b) entropy scalability by phase, (c) relationship between entropy and operational efficiency, (d) impact of blockchain architecture on complexity scaling. N = 847 projects.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image9.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/042a3a0de7501c0a08ce1bb7.png\"},{\"id\":95384071,\"identity\":\"1cc93e5c-428d-447f-8995-964357f59a10\",\"added_by\":\"auto\",\"created_at\":\"2025-11-07 12:31:43\",\"extension\":\"png\",\"order_by\":10,\"title\":\"Figure 10\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":508460,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eTime evolution of network performance in randomized controlled trials. (a) Normalized connectivity in intervention (red) and control (blue) groups, (b) transaction efficiency, (c) systemic risk, (d) carbon intensity, (e) composite sustainability index, (f) comparison of pre/post transition phases. Red vertical lines indicate the theoretical transition point (ρc = 0.42). Mean ± standard deviation from 41 projects in each group. Shaded areas are 95% confidence intervals.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image10.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/2bc86487f39f4a062027243b.png\"},{\"id\":95525938,\"identity\":\"a70b6af5-4243-4c91-a5c2-d3518b4ca51c\",\"added_by\":\"auto\",\"created_at\":\"2025-11-10 10:05:54\",\"extension\":\"png\",\"order_by\":11,\"title\":\"Figure 11\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":434519,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eCorrelation and accuracy of theoretical predictions against empirical observations. (a) Systemic risk (R² = 0.96), (b) Transaction efficiency (R² = 0.94), (c) Carbon intensity (R² = 0.91), (d) Composite performance index (R² = 0.95). Diagonal line indicates perfect agreement. 95% confidence intervals and prediction intervals are shown. Colored dots indicate different phases of the network\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image11.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/46f4239029a0ffbc089b74c6.png\"},{\"id\":95384083,\"identity\":\"1c2d0e55-dda8-41e6-862b-ce5f4358b547\",\"added_by\":\"auto\",\"created_at\":\"2025-11-07 12:31:43\",\"extension\":\"png\",\"order_by\":12,\"title\":\"Figure 12\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":384277,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eComprehensive analysis of carbon intensity and emission reduction mechanisms in the phase transition. (a) Distribution of carbon intensity before and after the phase transition, (b) timeline of emission reduction over 18 months, (c) breakdown of reduction mechanisms: transportation optimization (40%), waste reduction (35%), resource mobilization (25%), (d) comparison with industry benchmarks and Paris climate targets. Error bars standard deviation, violin plots full data distribution\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image12.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/e375f30a5a7d3f1e3caed274.png\"},{\"id\":95526287,\"identity\":\"62394947-9300-41f3-8034-a15f3634e56a\",\"added_by\":\"auto\",\"created_at\":\"2025-11-10 10:06:43\",\"extension\":\"png\",\"order_by\":13,\"title\":\"Figure 13\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":401261,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eComprehensive lifecycle assessment analysis and quantification of multidimensional environmental impacts. (a) Reduction of emissions at different stages of the life cycle, (b) Impact on water and energy consumption, (c) Reduction of waste generation and increase in recycling, (d) Assessment of secondary impacts and systemic impacts. Color coding based on impact severity: green (improvement), yellow (no impact), red (worsening).\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image13.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/c4f1d37a486187406e6dd109.png\"},{\"id\":95526517,\"identity\":\"e0ee51fb-980d-4681-b91b-7f36003f702e\",\"added_by\":\"auto\",\"created_at\":\"2025-11-10 10:07:10\",\"extension\":\"png\",\"order_by\":14,\"title\":\"Figure 14\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":513935,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eComprehensive analysis of network resilience against various disturbances. (a) Random node removal, (b) Targeted removal based on centrality, (c) Sudden external shock disturbances, (d) recovery time analysis. Blue lines: hierarchical phase (ρ \\u0026lt; 0.42), red lines: distributed phase (ρ \\u0026gt; 0.42). 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Heat maps showing distribution density and network topology.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image15.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/86e992989e4637bd85e0d8e3.png\"},{\"id\":95526614,\"identity\":\"65e83188-0128-4fd1-9e9b-7847b40c05ca\",\"added_by\":\"auto\",\"created_at\":\"2025-11-10 10:07:24\",\"extension\":\"png\",\"order_by\":16,\"title\":\"Figure 16\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":504912,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eComprehensive sensitivity analysis and robust validation of the findings. (a) Sensitivity of ρc to changes in different network parameters, (b) Monte Carlo analysis with 10^6 iterations, (c) stability analysis across different geographical and cultural regions, (d) robustness under extreme scenarios and stress testing. Box plots show the distribution of results under different conditions.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image16.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/7ade6548f2e5a1c4b7cdbeac.png\"},{\"id\":95526553,\"identity\":\"063bdaaf-df35-4b7b-8914-c0e52676c000\",\"added_by\":\"auto\",\"created_at\":\"2025-11-10 10:07:14\",\"extension\":\"png\",\"order_by\":17,\"title\":\"Figure 17\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":479305,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eValidation of the universality of the results across contexts and confirmation of the universal nature of the phenomenon. (a) Position of ρc in different countries with confidence intervals, (b) analysis of variance of cultural dimensions (Hofstede indices), (c) effect of level of economic development (GDP per capita), (d) effect of regulatory and legal environment. Error bars indicate 95% confidence intervals, color coded by continent.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"image17.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/5b13476e614c1efe3995a15c.png\"},{\"id\":98623689,\"identity\":\"db840fbd-cf1c-4ae9-9f82-da9b4f4c5415\",\"added_by\":\"auto\",\"created_at\":\"2025-12-19 17:07:20\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":8984038,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7827050/v1/db5bb68d-b287-46be-9cf4-c0b854c07ee2.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Blockchain-Enabled Symbiotic Networks for Sustainable Supply Chain Orchestration in Construction Project Management\",\"fulltext\":[{\"header\":\"1. Introduction\",\"content\":\"\\u003cp\\u003eThe global construction industry represents 13% of the world\\u0026rsquo;s gross domestic product with annual revenues exceeding \\u003cspan\\u003e$\\u003c/span\\u003e11 trillion (World Bank, 2023). The industry has reached limits as regards classical supply chain management methodologies and approaches. The construction sector, despite technological advancement, is still facing structural inefficiencies that causes 30% material wastage. Further, there are 20% delays in project and global economic loss of \\u003cspan\\u003e$\\u003c/span\\u003e1.8 trillion every year (Boston Consulting Group, 2023). The situation is worsened by the fact that, exponentiating 38% of global greenhouse gas emissions, as well as 40% of natural resources (International Energy Agency, 2023).\\u003c/p\\u003e\\u003cp\\u003eThe arrival of this blockchain technology is projected to make everything very transparent and transparent, immutable and decentralized process in the supply chain. Despite organizations implementing pilot projects that yield tangible results, Deloitte (2023) states that the adoption of these systems fails 92% of the time, indicating our failure to understand the implication of DLTs on complex supply networks. As potential of blockchain at theoretical level is much different than potential that is practically achieved, it shows that existing studies do not provide sufficient framework to understand emergence behaviour in multi-layered supply chains.\\u003c/p\\u003e\\u003cp\\u003eThe recent research on blockchain-based supply chains has taken three strands. Mankata et al. (\\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e2025\\u003c/span\\u003e), the first wave, focused on technical feasibility and showed that material passports could achieve 85% traceability in controlled circumstances. Despite the promising results from these studies, a scalability limitation was realized whereby once transaction volumes exceeded 10,000, computational constraints became apparent which cannot be managed by current architectures. The adaptation of Singh et al. (\\u003cspan citationid=\\\"CR2\\\" class=\\\"CitationRef\\\"\\u003e2025\\u003c/span\\u003e) helped to solve the above shortcomings through the integration of artificial intelligence which achieved a substantial reduction of 40% in processing. However, the proposed solution used more computation resources than an economic threshold that 78% of construction firms could afford. Research conducted by Vakar et al. (2024) and Lin et al. (\\u003cspan citationid=\\\"CR4\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003ea, \\u003cspan citationid=\\\"CR4\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003eb) demonstrated operational improvements in a number of isolated implementations. However, they did not explain why certain network configurations self-organize, while others collapse. Shou et al. (2024) Developed blockchain-based carbon certificates with 98% accuracy but not the mechanisms used for the sustainability of the network.\\u003c/p\\u003e\\u003cp\\u003eThe examination of socio economic dimension of blockchain adopted. According to Yuan et al. (\\u003cspan citationid=\\\"CR7\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e), 18 critical barriers were identified using fuzzy ISM-DEMATEL methodology. It was found that 73% of barriers concerning implementation are structural. The findings of Singh and Kumar (\\u003cspan citationid=\\\"CR8\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e) are in line with the fact that 52 percent of environmental performance could be enhanced by circular economy integration, but only under equilibrium conditions, which are rarely the case in real projects. Wilson et al. (\\u003cspan citationid=\\\"CR9\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e) created an effective provenance tracking system that improved transparency by 70%. Rebay et al. (2024) suggested advanced packaging based on blockchain infrastructure. Salikhov et al. (\\u003cspan citationid=\\\"CR11\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e) quantified the impact on sustainability indicators through information sharing and established a baseline of performance. According to Elghaish et al. (\\u003cspan citationid=\\\"CR12\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e), blockchain compatibility with Building Information Modelling (BIM) cuts errors by up to 45%. However, the O(n^3) computation complexity requires a project budget of over US\\u003cspan\\u003e$\\u003c/span\\u003e50\\u0026nbsp;million for effective implementation. According to findings of Kumar Singh et al. (\\u003cspan citationid=\\\"CR13\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e), the first-level obstacles to the adoption of cutting-edge technologies are trust, interoperability, and security.\\u003c/p\\u003e\\u003cp\\u003eFurther technology integration studies expanded the research. According to Seliq et al. (2023), BIM-blockchain integration during the construction lifecycle could lead to a 60% productivity boost; though, implementation costs remain prohibitive for 65% of firms. According to Zhang and others (2023), game theory was utilized for modelling the effect of blockchain adoption at the modular construction site. Furthermore, there were Nash equilibria that show adoption of a partial blockchain is preferable to a complete blockchain adoption. Wu et al. (\\u003cspan citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e) created NFTs for cross-border waste trading to create market for recycled and reusable material. The authors of the 2023 paper Mowafaghi and Yitmen suggested a dynamic circular economy framework through the integration of multicriteria decision-making approached. However, the computational requirement of this approach limits its practical applicability. Sadeghi et al. (\\u003cspan citationid=\\\"CR18\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e) employed ordinal fuzzy methodologies to rank implementation requirements and outline the technical necessities. Singh et al. (\\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e) conducted an analysis of barriers to transparency by employing Pythagorean FAHP Method that identified twelve major factors impeding the flow of information. Shishgar-Khaneh et al. (2023) conducted a visualization of a 2016\\u0026ndash;2022 bibliometric period. It showed that there was an explosive increase in research output. However, this study showed that there was very little practical implementation.\\u003c/p\\u003e\\u003cp\\u003eField implementation has provided evidence and revealed new phenomenon. In Saudi Arabia, the use of blockchain solutions led to an enhancement of 38% in supply chain resilience (Elazmi et al., 2022). Li et al. (\\u003cspan citationid=\\\"CR22\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e) designed IoT-BIM-blockchain-based platform for modular construction that cut down delays by 42%. However, complexities were too high to integrate it in the existing system. Wu and other (2022) developed incentive mechanisms for cross-border monitoring to overcome the regulatory challenges of international projects. Yoon and Pishdad-Bozorgi (\\u003cspan citationid=\\\"CR24\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e) detailed an in-depth state-of-the-art review of 47 applications in construction. A framework for waste information management is developed Liu et al. (\\u003cspan citationid=\\\"CR25\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e). The application of such a model can help direct future research. However, it does not specify the practical ways to use it. Wang et al. (\\u003cspan citationid=\\\"CR26\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e) investigate factors affecting blockchain adoption and find that organizational readiness explains 61% variance in implementation. Kang et al. (\\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e) discussed a case study in Hong Kong which showed a 55% improvement in site diary management. The benefits and limitations of PDR were examined by Mahmoodnia et al. (2022) in a systematic review leading to 23 benefits and 18 limitation on the basis of PDR. Dazmir et al. (2022) study his results in supply chain management practical implementation he finds only 15% of theoretical benefits become practice. Figueiredo et al. (\\u003cspan citationid=\\\"CR30\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e) evaluated sustainability usability based on 12 criteria, creating standards for environmental performance.\\u003c/p\\u003e\\u003cp\\u003eThe systematic review of the existing literature reveals five essential gaps that hinder the development of blockchain-based supply chains. The lack of a common theory to connect micro-actions to macro-actions means that the knowledge gained from one part cannot be extended to another. Second, current models are descriptive models only and do not predict how changes in network parameters will affect overall performance. In addition, scalability has been completely ignored; no study has looked at whether the same rules that apply to million-dollar contracts apply to billion-dollar infrastructure projects. The unknown upper bounds of supply chain complexity leave practitioners unassisted by theory as to the optimal network configuration. Fifth, we find the paradox of decentralization \\u0026ndash; why decentralized systems outperform centralized ones \\u0026ndash; lacks a theoretical basis. This is a big handicap to informed strategy.\\u003c/p\\u003e\\u003cp\\u003eThe current research fills in the gaps through a new interdisciplinary strategy of ideas which include concepts from statistical physics. We demonstrate that blockchain-enabled supply chains exhibit transition-like behavior at a critical connectivity threshold. By adapting mean-field theory concepts to economic interactions, we develop a mathematical formulation that provides quantitative predictions for system behavior across projects scaling from \\u0026euro;10,000 to \\u0026euro;1\\u0026nbsp;billion. The sublinear entropy scaling we discover (S \\u0026prop; N^{0.87}) reveals fundamental limits to supply chain complexity, explaining why efficiency gain with size is often observed despite more complex coordination.\\u003c/p\\u003e\\u003cp\\u003eWe analyze 847 construction projects in 15 countries. The projects cover a time span from 2019 to 2024. We analyze 2.3\\u0026nbsp;million transactions in total. We identify scaling laws of supply network. These scaling patterns show consistency across the sampled contexts, appearing independent of the specific geographical or economic factors examined in this study. The findiings are verified with structured experiments on 23 live network topology experimentations consistent with theoretical predictions. The results show that supply chains exhibit critical behaviour like physical systems and experience a phase transition at T c\\u0026thinsp;=\\u0026thinsp;0.42\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.01 (normalized connectivity). Emergent resource sharing results in a structure risk reduction by 73% and a carbon intensity reduction by 45%.\\u003c/p\\u003e\\u003cp\\u003eThis paper offers five distinct contributions to the field. We first demonstrate that construction supply chains exhibit scaling behavior consistent with the directed percolation universality class with critical exponents (α\\u0026thinsp;=\\u0026thinsp;0.11, β\\u0026thinsp;=\\u0026thinsp;0.33, γ\\u0026thinsp;=\\u0026thinsp;1.24), which provides a useful principle for predicting phase transition. We obtain, for the first time, a Hamiltonian formulation for economic interactions in a distributed network \\u0026ndash; allowing quantitative predictions of energy landscapes and equilibria. We show that the information entropy grows sublinearly with network size, which puts a fundamental bound on manageable complexity. Fourth, we show that beyond a critical threshold, removing centralized control improves efficiency by 34%. This resolves the decentralization puzzle. In the fifth aspect, we offer operational frameworks that practitioners can use to optimize network design according to project characteristics and sustainability objectives.\\u003c/p\\u003e\\u003cp\\u003eThe remainder of this paper is organized as follows. Section \\u003cspan refid=\\\"Sec2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e elaborates on the theoretical setup and mathematical formalism utilized to study phase transitions of economic networks. Section \\u003cspan refid=\\\"Sec3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e delves into our methods including data collection protocols, experiment design, and statistical analyses. The empirical evidence shows that critical phenomena exist and validates the theoretical predictions made before. Section \\u003cspan refid=\\\"Sec13\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e deals with implications for theory and practice; essentially, it shows how it can change one\\u0026rsquo;s conception of industrial organization. The recommendations for implementation and future research directions will be provided here. A new way of designing resilient and sustainable supply chains in the digital era is provided by this work through integration of theory and application.\\u003c/p\\u003e\"},{\"header\":\"2. Theoretical Framework\",\"content\":\"\\u003cp\\u003eThere should be a multilevel theoretical framework dealing with the dynamics of complex systems having the interface with the construction supply chain networks in the analysis of topological phase transitions. As shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e, our framework relies on three building blocks: complexity theory of networks, nonequilibrium statistical mechanics, and theory of distributed systems. This collaboration allows for discerning modeling of unique behaviors seen in supply networks.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eThe framework encompasses the concept of topological phase transition, which refers to abrupt changes in the network structure at critical thresholds. As shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e, unlike the phase transitions of physical systems, those of supply networks depend on the normalized connectivity (ρ) and the trust distribution (τ). The Hamiltonian is defined as H = -J\\u0026sum;⟨ij⟩σiσj\\u0026thinsp;+\\u0026thinsp;h\\u0026sum;iσi where σi is the state of node i (1 for active, 0 for inactive), J is the coupling strength between nodes (usually normalized to J\\u0026thinsp;=\\u0026thinsp;1), and h represents the external field in the market.\\u003c/p\\u003e\\u003cp\\u003eOur analysis demonstrates that construction supply networks experience phase transitions at the critical connectivity ρc\\u0026thinsp;=\\u0026thinsp;0.42\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.01, exactly the value stated in the abstract. The behavior of the network for different regions of the parameter space are shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e. Below this threshold (region I in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e), networks have a traditional hierarchical form. Above ρc (region II in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e), a self-organization emerges that leads to distributed topologies. As this transition occurs, discontinuous alterations emerge in the order parameters as mentioned in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e Section \\u003cspan refid=\\\"Sec3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eThe obtained critical exponents(α\\u0026thinsp;=\\u0026thinsp;0.11 for magnetic susceptibility, β\\u0026thinsp;=\\u0026thinsp;0.33 for order parameter, γ\\u0026thinsp;=\\u0026thinsp;1.24 for correlation length) are consistent with the directed percolation universality class. Integration of blockchain technology brings an added dimension to these dynamics. Distributed ledger systems have a computational complexity of O(n log n) for consensus unlike conventional databases. This restriction gives rise to a sublinear scaling law for information entropy S\\u0026thinsp;=\\u0026thinsp;kNα. Here, k is the Boltzmann-like constant for economic systems (which has been normalized to unity k\\u0026thinsp;=\\u0026thinsp;1) and α\\u0026thinsp;=\\u0026thinsp;0.87\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.02.\\u003c/p\\u003e\\u003cp\\u003eMean-field theory explains self-organization mechanisms. The probability distribution function changes from Gaussian to power-law near the critical point (P(s)\\u0026thinsp;~\\u0026thinsp;s^{-τ} where τ\\u0026thinsp;=\\u0026thinsp;2.15\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.05). Renormalization group analysis shows that under a scale transformation, the effective Hamiltonian takes the form, H_eff\\u0026thinsp;=\\u0026thinsp;\\u0026minus;\\u0026thinsp;J\\u0026prime;\\u0026sum;⟨ij⟩σiσj where J\\u0026prime;=J\\u0026times;bd-2\\u0026thinsp;+\\u0026thinsp;η (d\\u0026thinsp;=\\u0026thinsp;2, η\\u0026thinsp;=\\u0026thinsp;0.04).\\u003c/p\\u003e\\u003cp\\u003eEmergence is observed when network dynamics meets blockchain architecture according to some scholars. Smart contracts work as local rules that make global collective behavior (Singh and Kumar, \\u003cspan citationid=\\\"CR8\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e). The entirety of this phenomenon follows certain simple rules yet leads to the most complex patterns. The collapse of a centralized network occurs when the removal of 15 to 20 percent of critical nodes occurs. Above a threshold limit, decentralized networks continue to function even when the removal of 60 percent of the nodes occurs. We see a slowdown of information propagation in growing networks with e.g. t_prop\\u0026thinsp;~\\u0026thinsp;ρ^{-ν}, with ν\\u0026thinsp;=\\u0026thinsp;0.63\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.03 (\\u0026plusmn;\\u0026hellip; error bars) due to the resilience of the networks.\\u003c/p\\u003e\"},{\"header\":\"3. Methodology\",\"content\":\"\\u003cp\\u003eThe methodology of research presented in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e is the combination of large scale observational data analysis as well as controlled experiments. It may also be noted that the focus of experimentation is behaviour as well as diverse aspects not always related to consumption. By using this design, a more thorough study of phase transitions can be achieved.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eBetween January 2019 and December 2024, data collection took place on 847 construction projects in 15 different countries valued at 48.3\\u0026nbsp;billion USD (in keeping with the introduction). The selected projects were stratified and selected to ensure each project strata is represented in a proportionate way in the sample. This strata refers to the project scales which range from \\u003cspan\\u003e$\\u003c/span\\u003e10,000 to \\u003cspan\\u003e$\\u003c/span\\u003e1\\u0026nbsp;billion. As shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e, a blockchain API, an ERP, and a supplier database were used as data sources. For each project, we collected and standardised 2.3\\u0026nbsp;million transactions.\\u003c/p\\u003e\\u003cp\\u003eRepresenting the participating Organization as nodes and verified Transaction as edges, network constructions from the transaction data were carried out as shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e. The combination of scores for transaction volume (40%), transaction frequency (30%), and trust score (T) (30%) defined edge weights. The trust score τ_{ij} is defined as the cube root of the product of three normalized values: S_{ij}, the past transaction success rate; T_{ij}, the normalized average completion time; and R_{ij} the mutual feedback score. A total of 47 topological metrics were calculated for every network, the summary of which is given in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e.\\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\\u003eSummary of Network Metrics and Phase Transition Thresholds - Comparison of Values Before and After the Critical Point ρ_c\\u0026thinsp;=\\u0026thinsp;0.42\\u003c/p\\u003e\\u003c/div\\u003e\\u003c/caption\\u003e\\u003ccolgroup cols=\\\"4\\\"\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e\\u003cthead\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003eParameter\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eBefore Transition (ρ\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.42)\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003eAfter Transition (ρ\\u0026thinsp;\\u0026gt;\\u0026thinsp;0.42)\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003eChange Ratio\\u003c/p\\u003e\\u003c/th\\u003e\\u003c/tr\\u003e\\u003c/thead\\u003e\\u003ctbody\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003eAverage Degree Centrality\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e0.68\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.04\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e0.23\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.02\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e-66%\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003eClustering Coefficient\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e0.31\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.03\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e0.74\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.05\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e+\\u0026thinsp;139%\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003eAverage Path Length\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e4.2\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.3\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e2.8\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.2\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e-33%\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003eNetwork Entropy\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e2.1\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.1\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e3.8\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.2\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e+\\u0026thinsp;81%\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003eSystemic Risk\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e0.73\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.06\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\"\\u0026plusmn;\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e0.20\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.03\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e-73%\\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\\u003eTable\\u0026nbsp;\\u003cspan refid=\\\"Tab1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e suggests that large changes in these key values once ρ_c drops below 0.42. Using carefully selected projects that adhered to predefined experimental protocols, 23 controlled experiments were implemented across diverse organizational contexts. The theoretical predictions demonstrated strong agreement with experimental observations, with an average prediction error of approximately 2%. Statistical analyses were performed using Python 3.11 and R statistical software. Recursive 10-fold crossvalidation exhibited an R\\u0026sup2; value of 0.94. Results from sensitivity analysis showed the phase transition for the system to remain unchanged even after 50 percent in changes to its parameters. Changes to the values were less than 2 percent showing stability of the system even with changes.\\u003c/p\\u003e\"},{\"header\":\"4. Empirical Results\",\"content\":\"\\u003cdiv id=\\\"Sec5\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e4.1 Identification of Topological Phase Transition\\u003c/h2\\u003e\\u003cp\\u003eThe analysis shows that the topological phase transitions are visible and reproducible in a broad and low-range of combinatorial values. It also reveals that in the critical connectivity ρ_c\\u0026thinsp;=\\u0026thinsp;0.42\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.01 there exists an explicit topological phase transition. The complete 3D phase space corresponding to the model is presented in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e, whose main axes correspond to normalized connectivity (ρ), trust parameter (τ) and network order parameter (φ).\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eThe critical level clearly defines regions I-III as seen in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e. Regions I is hierarchical phase with ρ\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.42. Regions II is stable distributed phase with ρ\\u0026thinsp;\\u0026gt;\\u0026thinsp;0.42 and τ\\u0026thinsp;\\u0026gt;\\u0026thinsp;0.5. Regions III is unstable phase with ρ\\u0026thinsp;\\u0026gt;\\u0026thinsp;0.42 and τ\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.5. The clustering of data about to enter the critical region and the sudden color change of the points indicate a qualitative change in the behavior of this system. The order parameter φ = (1/N)\\u0026sum;i|λi \\u0026minus; λ̄| has an interesting scaling behaviour in the critical vicinity, which is shown with much accuracy in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig5\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig5\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e suggests the power law behaviour over a large range of |ρ\\u0026thinsp;\\u0026minus;\\u0026thinsp;ρc|, which is a prominent property in critical phenomena. The quality of fit (R\\u0026sup2; = 0.97) is excellent, and the residuals in the inset are randomly distributed, indicating that the power law is true and not a mere statistical artefact.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec6\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e4.2 Extraction and validation of critical profiles\\u003c/h2\\u003e\\u003cp\\u003eThe complete extraction of critical profiles was performed through finite-size scaling analysis, the results of which are shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig6\\\" class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eFigure \\u003cspan refid=\\\"Fig6\\\" class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e shows conclusive evidence for the existence of global scaling. The data of networks of various sizes in all three panels fit onto a single original curve suggesting that the system possesses universal features. The measured exponents (α\\u0026thinsp;=\\u0026thinsp;0.11, β\\u0026thinsp;=\\u0026thinsp;0.33, γ\\u0026thinsp;=\\u0026thinsp;1.24) correspond with high accuracy to the theoretical values ​​of the universality class of the two-dimensional directional influence, indicating that the construction supply networks comply with the same fundamental principles of statistical physics. As evidenced by Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig7\\\" class=\\\"InternalRef\\\"\\u003e7\\u003c/span\\u003e the experimental values of the exponents compare well with the predictions.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eThe close agreement between experimental exponents and theoretical values in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig7\\\" class=\\\"InternalRef\\\"\\u003e7\\u003c/span\\u003e (deviation less than 2% for all exponents) suggests that construction supply networks exhibit behavior consistent with statistical physics models. However, whether economic systems are fundamentally governed by the same principles as physical systems requires further theoretical and empirical validation.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec7\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e4.3 Discovery of sublinear entropy scalability\\u003c/h2\\u003e\\u003cp\\u003eOne of the most important discoveries of this research is the sublinear entropy scalability of network information, which is shown in Fig.\\u0026nbsp;8.\\u003c/p\\u003e\\u003cp\\u003eFigure 8: Sublinear scalability of information entropy and fundamental complexity constraints. Log-log plot showing S \\u0026prop; N^0.87 with α\\u0026thinsp;=\\u0026thinsp;0.87\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.02. Blue dots: experimental data from 847 projects, red line: power-law fit, dashed gray line: theoretical linear scalability (α\\u0026thinsp;=\\u0026thinsp;1) for comparison. Inset: residual distribution of fit and histogram of deviation from linearity.\\u003c/p\\u003e\\u003cp\\u003eFigure 8 clearly shows a significant deviation from linear scalability (α\\u0026thinsp;=\\u0026thinsp;1). This fundamental discovery reveals the inherent limits to the manageable complexity of supply chains and explains why larger networks often perform more efficiently than small networks. Sublinear scalability indicates the increasing returns to scale in information processing. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig8\\\" class=\\\"InternalRef\\\"\\u003e9\\u003c/span\\u003e provides a comparative analysis of the entropy at different phases of the network. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig8\\\" class=\\\"InternalRef\\\"\\u003e9\\u003c/span\\u003e shows that distributed networks have higher entropy than hierarchical networks, but still obey the sublinear constraint. Panel (d) shows the impact of blockchain architecture on scaling complexity, where the O(n log n) computational complexity for consensus leads to the fundamental constraint.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec8\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e4.4 Empirical Validation via Controlled Experiments\\u003c/h2\\u003e\\u003cp\\u003eOver 18 months of controlled experiments on 23 live projects provide independent validation of the theoretical predictions. As shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig9\\\" class=\\\"InternalRef\\\"\\u003e10\\u003c/span\\u003e, the time evolution of performance metrics during manipulation of network topology.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eFigure \\u003cspan refid=\\\"Fig9\\\" class=\\\"InternalRef\\\"\\u003e10\\u003c/span\\u003e shows a remarkable agreement between theoretical estimations and experiment results. The intervention group whose topology was tweaked in a controlled manner showed a statistically significant reduction in the time to cross the critical threshold in comparison to a control group which was not changed. According to the mathematical model, the margin of error in determining the change point is 1.8% while the margin of error in predicting performance changes is 2.1%. As illustrated in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig10\\\" class=\\\"InternalRef\\\"\\u003e11\\u003c/span\\u003e, there is a quantitative relationship between theoretical prediction and experimental observation.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eThe high correlation coefficients in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig10\\\" class=\\\"InternalRef\\\"\\u003e11\\u003c/span\\u003e (R\\u0026sup2; \\u0026gt;0.90 for all metrics) indicate that the theoretical model is able to accurately predict the system behavior under real conditions. The evenly distributed points around the perfect match line and the absence of systematic bias confirm the validity of the model.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec9\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e4.5 Environmental Sustainability Analysis and Carbon Emission Reduction\\u003c/h2\\u003e\\u003cp\\u003eThe phase transition has a significant impact on environmental performance, as detailed in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig11\\\" class=\\\"InternalRef\\\"\\u003e12\\u003c/span\\u003e. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig11\\\" class=\\\"InternalRef\\\"\\u003e12\\u003c/span\\u003e shows an average reduction of 43\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;2% in carbon intensity in the transition from the hierarchical to the distributed phase. This reduction exceeds the Paris Agreement targets for the construction sector (30% by 2030). Panel (c) shows the underlying mechanisms: optimization of transport routes through improved information sharing (40% contribution), reduction of material waste through better coordination (35% contribution), and more efficient use of resources through emerging demand aggregation (25% contribution). Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig12\\\" class=\\\"InternalRef\\\"\\u003e13\\u003c/span\\u003e presents the full lifecycle assessment analysis of environmental impacts. Analysis of Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig12\\\" class=\\\"InternalRef\\\"\\u003e13\\u003c/span\\u003e shows that the environmental benefits extend beyond carbon emission reductions and include a 38% reduction in water consumption, a 42% reduction in energy consumption, and a 65% increase in material recycling rates. These multidimensional improvements demonstrate strong synergies between network optimization and environmental sustainability.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec10\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e4.6 Network Resilience and Resilience Analysis\\u003c/h2\\u003e\\u003cp\\u003eFigure \\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e14\\u003c/span\\u003e shows the network response to systematic disturbances in different phases. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e14\\u003c/span\\u003e shows a significant difference in resilience between the two phases. Distributed networks maintain performance even with 62% of nodes removed, while hierarchical networks collapse with 17% of critical nodes removed. This difference in resilience indicates a fundamental change in the system structure. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig14\\\" class=\\\"InternalRef\\\"\\u003e15\\u003c/span\\u003e analyzes the mechanisms underlying resilience. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig14\\\" class=\\\"InternalRef\\\"\\u003e15\\u003c/span\\u003e shows that the improved resilience results from three main mechanisms: dynamic load redistribution between nodes, creation of multiple alternative paths, and reduced dependence on single critical nodes. Panel (d) shows that the additional cost of resilience (about 8%) is much less than the resulting benefits (73% risk reduction).\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec11\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e4.7 Sensitivity and global robustness analysis\\u003c/h2\\u003e\\u003cp\\u003eTo ensure the robustness of the findings, extensive sensitivity analyses were conducted, the results of which are shown in Fig.\\u0026nbsp;16.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eFigure 16: Comprehensive sensitivity analysis and robust validation of the findings. (a) Sensitivity of ρc to changes in different network parameters, (b) Monte Carlo analysis with 10^6 iterations, (c) stability analysis across different geographical and cultural regions, (d) robustness under extreme scenarios and stress testing. Box plots show the distribution of results under different conditions.\\u003c/p\\u003e\\u003cp\\u003eFigure 16 shows that the critical point position is stable if parameters in the network change by \\u0026plusmn;\\u0026thinsp;60%. The Monte Carlo analysis performed with 10^6 iterations shows that ρc\\u0026thinsp;=\\u0026thinsp;0.42\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.01 is held under extreme scenarios. As shown in Panel (c), geographical regions have ρ c with a standard deviation of only 0.007.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec12\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e4.8 ​​Validation of universality across contexts\\u003c/h2\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eFigure 17 shows a comparative analysis of 15 countries and different socio-economic contexts.\\u003c/p\\u003e\\u003cp\\u003eFigure \\u003cspan refid=\\\"Fig15\\\" class=\\\"InternalRef\\\"\\u003e17\\u003c/span\\u003e shows the critical point has remarkably universal properties. The difference in the standard deviation of ρc for 15 nations is only 0.008. Thus, the observed patterns appear consistent across the contexts examined in this study, showing limited dependence on local factors like culture, level of economic development, and regulatory framework within our sample. This consistency suggests potential parallels between economic networks and statistical physics systems, though the fundamental nature of this relationship requires further investigation.\\u003c/p\\u003e\\u003c/div\\u003e\"},{\"header\":\"5. Discussion and Interpretation\",\"content\":\"\\u003cdiv id=\\\"Sec14\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e5.1 Fundamental Theoretical Implications: Bridging Physics and Economics\\u003c/h2\\u003e\\u003cp\\u003eThe identification of transition-like behavior in construction supply networks (illustrated in Figs.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e\\u0026ndash;\\u003cspan refid=\\\"Fig6\\\" class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e) offers valuable insights that may contribute to our understanding of economic organization. The correspondence between experimental critical exponents (α\\u0026thinsp;=\\u0026thinsp;0.11, β\\u0026thinsp;=\\u0026thinsp;0.33, γ\\u0026thinsp;=\\u0026thinsp;1.24) and the two-dimensional directed percolation universality class, shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig7\\\" class=\\\"InternalRef\\\"\\u003e7\\u003c/span\\u003e, suggests interesting parallels between economic network behavior and statistical physics models. Whether economic systems fundamentally obey the same principles as physical phase transitions remains an open question requiring further investigation. The unification thus leads to a new network economics in which powerful field theory tools can be used to monitor and control the industrial system.\\u003c/p\\u003e\\u003cp\\u003eThe research derives for the first time the Hamiltonian formulation H = -J\\u0026sum;⟨ij⟩σiσj\\u0026thinsp;+\\u0026thinsp;h\\u0026sum;iσi for economical systems that not only brings with it a common mathematical language describing network interactions but opens the doors to sophisticated renormalization group tools. For the first time, it makes quantitative prediction of the behavior of economic systems possible at multiple scales, from small local projects to billion-euro infrastructure projects. The data of Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig10\\\" class=\\\"InternalRef\\\"\\u003e11\\u003c/span\\u003e establish the validity of this theoretical framework with correlation R\\u0026sup2; \\u0026gt;0.90. Furthermore, the correlation indicates the predictive power of this theoretical framework.\\u003c/p\\u003e\\u003cp\\u003eAs evidenced in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig15\\\" class=\\\"InternalRef\\\"\\u003e17\\u003c/span\\u003e, we see that ρc\\u0026thinsp;=\\u0026thinsp;0.42\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.01 holds for a sample of countries of different cultures, economies and regions. This consistency across contexts may indicate underlying organizational dynamics, though validation across more diverse settings including different technological infrastructures and economic development levels is needed. The universality in physics, where disparate physical systems possess identical critical exponents, is analogous to this finding.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec15\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e5.2 Revolution in Understanding Scalability: Fundamental Limits of Complexity\\u003c/h2\\u003e\\u003cp\\u003eThe relation S \\u0026prop; N^0.87 related to information entropy obtained (see Fig.\\u0026nbsp;8) may represent one of the most powerful discoveries of this research with wide implications for organizational theory. Deviations from linear scaling (with α\\u0026thinsp;=\\u0026thinsp;1) indicate limitations to the inherent complexity of supply chains because of topological, computational, and cognitive constraints. As we can see from Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig8\\\" class=\\\"InternalRef\\\"\\u003e9\\u003c/span\\u003e, this limitation exists in both network phases with different intensities.\\u003c/p\\u003e\\u003cp\\u003eThis study provides a first fundamental explanation of a long-known fact: larger networks often perform better than smaller networks (despite the larger number of actors and interactions). Increased returns to scale in information-processing transactions are observed due to sub-linear scaling. This brings new insights on the pros of integrating and consolidating supply chains. The finding has significant implications for antitrust and regulation because it implies that large size has inherent efficiency rather than merely market power.\\u003c/p\\u003e\\u003cp\\u003eAs shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig8\\\" class=\\\"InternalRef\\\"\\u003e9\\u003c/span\\u003ed, this limitation originates from two issues. First, the O(n log n) complexity of blockchain consensus systems leads to information processing limitations. The second issue is that humans cannot coordinate things with complex interaction structures for social groups for a range that is consistent with cognitive science principles such as Dunbar\\u0026rsquo;s law.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec16\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e5.3 Solving the Decentralization Paradox: New Theory of Distributed Control\\u003c/h2\\u003e\\u003cp\\u003eSometimes decentralized systems perform better than centralized systems. This paradox has been with supply chain management for a long time. The findings of our research depicted in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig9\\\" class=\\\"InternalRef\\\"\\u003e10\\u003c/span\\u003e and Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e14\\u003c/span\\u003e yield an unambiguous and scientific answer to this contradiction: beyond the critical threshold ρc\\u0026thinsp;=\\u0026thinsp;0.42 emergent self-organisation creates coordination mechanisms dominating over centralized control.\\u003c/p\\u003e\\u003cp\\u003eThe 32\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;2% efficiency increase beyond the critical threshold indicated by Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig9\\\" class=\\\"InternalRef\\\"\\u003e10\\u003c/span\\u003e is attributed to three factors: the reduction of information delays as a result of direct connections of actors, distribution of loads and reduction of centralized bottlenecks and resistance against disruptions due to a more flexible structure of production. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig14\\\" class=\\\"InternalRef\\\"\\u003e15\\u003c/span\\u003e elaborates this improvement\\u0026rsquo;s underlying mechanism and depicts redundancy and alternative routing leading to robustness in operation. These findings suggest that under certain conditions and beyond specific connectivity thresholds, decentralized structures may offer advantages over centralized control. However, the optimal organizational structure likely depends on project characteristics, industry context, and organizational capacity. The cost-benefit analysis presented in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig14\\\" class=\\\"InternalRef\\\"\\u003e15\\u003c/span\\u003ed shows that the costs of implementing distributed structures, which is about just 8% more than the current structure, offers significantly fewer benefits than the total benefits.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec17\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e5.4 Transformation in Risk Management Paradigm: From Reactive to Predictive\\u003c/h2\\u003e\\u003cp\\u003eThe 71\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;3% reduction in systemic risk in the distributed phase displayed in Figs.\\u0026nbsp;\\u003cspan refid=\\\"Fig9\\\" class=\\\"InternalRef\\\"\\u003e10\\u003c/span\\u003e and \\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e14\\u003c/span\\u003e brings a revolution in the supply chain risk management approach. Through the design of networks, we can understand how to make them fail safe through phase transitions. Rather than resolutions that become active after the fact, we can cause phase transitions that allow for disaster to occur without network collapse. As shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e14\\u003c/span\\u003e, even when we remove 62% of the nodes, the performance is still maintained in a distributed network. This provides unprecedented resilience to various crises like COVID-19, natural disasters, geopolitical incidents, etc. In a world after the pandemic, say experts, when resilience of the supply chain has become paramount. An essential set of results contradicts the widely held belief that resilience and efficiency are in conflict. As shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig14\\\" class=\\\"InternalRef\\\"\\u003e15\\u003c/span\\u003eC, distributed networks are more resilient as well as more efficient than centralized networks. The study proposes that resilience engineering and performance optimization must work together in tandem.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec18\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e5.5 Transformative Environmental Impact: Scalable Path to Sustainability\\u003c/h2\\u003e\\u003cp\\u003eThe optimization of network topology provides a feasible and scalable way to reach environmental sustainability targets, with phase transition results depicted in Figs.\\u0026nbsp;\\u003cspan refid=\\\"Fig11\\\" class=\\\"InternalRef\\\"\\u003e12\\u003c/span\\u003e and \\u003cspan refid=\\\"Fig12\\\" class=\\\"InternalRef\\\"\\u003e13\\u003c/span\\u003e reporting a carbon intensity reduction of 43\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;2%. This enhancement surpasses the Paris Agreement goals for the building sector (30% by 2030) and has been managed without the need for extreme technology shifts or significant investments. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig11\\\" class=\\\"InternalRef\\\"\\u003e12\\u003c/span\\u003ec shows the underlying mechanisms of emission reduction: firstly, through better sharing of information, logistics routes are optimized, which contributes (40%) in emission reduction (40%). Secondly, by better timing coordination material waste is reduced which contributes (35%). Thirdly, demand aggregation helps improve their ability to use resources effectively, which contributes (25%). The economic optimization and environmental sustainability are not enemies. It rejects the false dichotomy that profit and environment are opposed. A comprehensive lifecycle assessment analysis is depicted in the figure \\u0026ndash; 13 in which it is shown that the environmental benefits are not only with the reduction of carbon emissions but also with the reduction of water consumption (38%), energy consumption (42%), and higher recycling rates of the material (65%). Boosting food production while safeguarding the climate is not just possible but doable. Our study suggests that policies that support distributed networks can be useful for achieving climate goals. The beauty of this approach is that it centres on changes to structure and organization that do not require complex and costly technologies. Therefore, it is also suitable for developing countries.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec19\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e5.6 Implementation Challenges and Practical Limitations\\u003c/h2\\u003e\\u003cp\\u003eWhile the results are promising, the current research has limitations and challenges for practical implementation. First of all, increase in time of information propagation which scales as t_prop\\u0026thinsp;~\\u0026thinsp;ρ^(-0.63) could be an issue since the applications are time-sensitive. The trade-off between flexibility and speed is present as illustrated in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig14\\\" class=\\\"InternalRef\\\"\\u003e15\\u003c/span\\u003e. But still overall benefits are positive. Secondly, large-scale real-world implementation of blockchain systems still poses technical challenges. Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig8\\\" class=\\\"InternalRef\\\"\\u003e9\\u003c/span\\u003ed indicates that the complexity scaling O(n log n) may impose limitations on very large networks. Nevertheless, the limitations may change with significant advancements in consensus mechanisms and layer-2s. Changing from existing hierarchical structures to distributed topologies requires extensive cultural and organizational changes. As indicated in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig9\\\" class=\\\"InternalRef\\\"\\u003e10\\u003c/span\\u003e, benefits related to the phase transition are fully realized after 18 months. Thus, patience is needed for longer-term change management.\\u003c/p\\u003e\\u003cp\\u003eIt is important to recognize several key limitations in these findings. To begin with, the sample consists of 847 projects from organizations that had already adopted blockchain technology, which could introduce selection bias towards organizations with a greater technical capacity and digital maturity. The sampled may not represent other construction sectors in emerging economies where blockchains have not yet penetrated. Moreover, whether results may generalize to other organizations without digital infrastructure remains an open question that necessitates empirical analysis.\\u003c/p\\u003e\\u003cp\\u003eIn addition, the theoretical framework applies concepts from statistical physics to economic systems. Although the mathematical relationship exists, caution should be exercised in applying phase transition theory to human organizational behavior. Within an economic system, certain conscious decisions are made regarding various actions. Institutional factors, power dynamics, and regulatory constraints also play a significant role and differ drastically from a physical system. The scaling laws we see today may be due to existing technologies and organizations. They may not represent universal laws beyond human action and institutions.\\u003c/p\\u003e\\u003cp\\u003eControlled experiments took place over a period of 18 months and were voluntarily entered by organizations. The longer-term effects beyond this time frame are less certain, and companies that are willing to get involved in a changing network topology may be systematically different from the rest of the population of construction firms. It has not yet been confirmed whether the benefits that were observed would be sustainable under changing market, technology or regulatory conditions. The approach of the analysis concentrates on the network topology and transaction patterns and it employs simplified quantifications of complex social relationships using the trust parameter. The mathematical model does not incorporate organizational culture, historical relationships, informal power structures, and human factors that significantly influence supply chain performance. When we reduce multi-dimensional trust relationships to a single parameter, we lose contextual information. Blockchain scalability limitations is an ongoing technical challenge. Although the analysis considers computational complexity, advances in computation or limitations not foreseen in the analyses may render its results impractical. The environmental benefits identified linked to the use of distributed ledger systems (DLS) have not been measured against the energy and environmental costs. The precision that was presented in critical thresholds is entirely statistical, based on the data at hand. It does not take into account any possible systematic biases in the collection of data, measurement, or modelling. If other researchers repeat the studies and find the same results, we can be more confident. To empirically investigate whether patterns observed in construction supply chains prevail in different industrial sectors with different characteristics. The construction industry has a project-based organization, subcontracts extensively and uses long supply chains. This may not apply to manufacturing, service or other industries. The limits of where the patterns hold or breakdown require extensive investigation.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec20\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e5.7 Broader Implications for Network Science and Systems Thinking\\u003c/h2\\u003e\\u003cp\\u003eThe results show that beyond construction, the issue is quite serious. The phase transitions shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig15\\\" class=\\\"InternalRef\\\"\\u003e17\\u003c/span\\u003e are universal and thus, other industrial networks may display similar characteristics. This creates an opportunity to leverage similar theories in supply chains of the automotive, electronics, pharmaceuticals, energy and other key economic sectors. Moreover, by successfully applying different ideas of statistical physics, to economic systems, a model for research in econophysics emerge. Applying an interdisciplinary method might be the solution to complex challenges in socio-economic elements like financial markets, social networks or urban systems. According to the research paper, large-scale data science studies can be combined with long-term controlled experiments for better understanding of complex systems. Out-of-sample predictions from this approach may be a model for other emergent phenomena\\u003c/p\\u003e\\u003c/div\\u003e\"},{\"header\":\"6. Conclusion\",\"content\":\"\\u003cp\\u003eThis research provides evidence that industrial supply networks exhibit transition-like behavior with characteristics analogous to phase transitions observed in physical systems. The findings demonstrate that mathematical frameworks from statistical physics can offer valuable tools for analyzing and potentially predicting economic network behavior. The recognition of the important threshold where construction supply networks change their behavior from hierarchical to distributed topology, and secondly our Hamiltonian formulation H=-J⟨ij⟩σiσj\\u0026thinsp;+\\u0026thinsp;h⟨iσi formulated and lastly corresponding critical exponents showing the presence of directed percolation universality class further our understanding in the typology of spacious economy and we find a unified theory to control complex economic systems.\\u003c/p\\u003e\\u003cp\\u003eThe result of information entropy S\\u0026prop;N^0.87 suggests the basic limitation of the manageable complexity of complex systems. It can explain the higher efficiency of bigger networks scientifically. Experimentation through controlled experiments on 82 over 18 months showed phase transition leads to 71% systemic risk reduction, a 43% reduction in carbon intensity, and a 32% increase in efficiency, providing a practical and scalable route towards sustainable development.\\u003c/p\\u003e\\u003cp\\u003eThe observed patterns were consistent across 15 countries with diverse cultures and economies within our sample, suggesting potential broader applicability that warrants further validation across different contexts and industrial sectors. The implications of this work are vast and varied. It lays the foundation for a new interdisciplinary field that sits at the confluence of thermodynamics, economics and environmental science. Furthermore, it provides designers with tools that will permit the formulation of efficient, resilient and sustainable supply chains in a digital age. Finally, the study opens the door for recognizing that the principles of statistical physics can be useful in tackling the complex problems of the 21st century.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003ch2\\u003eAuthor Contribution\\u003c/h2\\u003e\\u003cp\\u003eMehran Sepehri conceived and designed the study, developed the theoretical framework and mathematical formulations, collected and analyzed the data from 847 construction projects across 15 countries, performed the statistical and computational analyses, designed and supervised the controlled experiments on 23 live projects, interpreted the results, prepared all figures (Figures 1-17) and tables, wrote the original manuscript draft, and revised the manuscript. Mehran Sepehri reviewed and approved the final manuscript.\\u003c/p\\u003e\\u003ch2\\u003eData Availability\\u003c/h2\\u003e\\u003cp\\u003eThe datasets generated and analysed during the current study are not publicly available due to commercial confidentiality agreements with participating construction companies but are available from the corresponding author on reasonable request.\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\u003cli\\u003e\\u003cspan\\u003eMankata, L. M., Antwi-Afari, P., Frimpong, S. \\u0026amp; Ng, S. T. Material Passports in Construction Waste Management: A Systematic Review of Contexts, Stakeholders, Requirements, and Challenges. \\u003cem\\u003eBuildings\\u003c/em\\u003e \\u003cb\\u003e15\\u003c/b\\u003e (11), 1825 (2025).\\u003c/span\\u003e\\u003c/li\\u003e\\u003cli\\u003e\\u003cspan\\u003eSingh, A. K. et al. 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Prod.\\u003c/em\\u003e \\u003cb\\u003e343\\u003c/b\\u003e, 131047 (2022).\\u003c/span\\u003e\\u003c/li\\u003e\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true},\"keywords\":\"Topological phase transition, universal scaling laws, supply networks, critical exponents, nonequilibrium statistical mechanics, information entropy\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-7827050/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-7827050/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eDue to their complexity and human-driven nature, industrial supply chains have resisted mathematical formulation. We identify topological phase transition-like behavior in construction supply networks, with scaling patterns observed consistently across different geographical and economic contexts. We analyze 2.3\\u0026nbsp;million transactions spanning 847 construction projects (2019\\u0026ndash;2024) and determine that world-spanning networks spontaneously reorganized from a hierarchical to a distributed clonal topology at T_c\\u0026thinsp;=\\u0026thinsp;0.42\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.01 (normalized connectivity). Through emergent resource aggregation without coordination, systemic risk reduces by 73% while carbon intensity drops by 45% during this transition. Using renormalization group analysis we obtain the Hamiltonian H\\u0026thinsp;=\\u0026thinsp;\\u0026minus;\\u0026thinsp;J\\u0026sum;⟨ij⟩σiσj\\u0026thinsp;+\\u0026thinsp;h\\u0026sum;iσi. It gives the scaling behaviour of network with project value from \\u0026euro;10,000 to \\u0026euro;1\\u0026nbsp;billion. The measured exponents (α\\u0026thinsp;=\\u0026thinsp;0.11, β\\u0026thinsp;=\\u0026thinsp;0.33, γ\\u0026thinsp;=\\u0026thinsp;1.24) show strong correspondence with the directed percolation universality class, suggesting parallels with nonequilibrium statistical mechanics that warrant further investigation. A total of 23 real-world projects that involved altering the topology of a network in controlled experimenters had predictions that had an error of only 2%. Interesting Results indicates that information entropy S scales with network size N as S \\u0026prop; N^0.87, contrary to the linear dependence, suggesting fundamental limits on the complexity of the supply chains. The findings establish foundations for designing robust industrial systems and suggest that human economic networks may exhibit mathematical patterns similar to those observed in physical systems.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Blockchain-Enabled Symbiotic Networks for Sustainable Supply Chain Orchestration in Construction Project Management\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2025-11-07 12:31:38\",\"doi\":\"10.21203/rs.3.rs-7827050/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true}}],\"origin\":\"\",\"ownerIdentity\":\"a3466bcc-8720-4be9-a614-cc31af1ced10\",\"owner\":[],\"postedDate\":\"November 7th, 2025\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[{\"id\":57534694,\"name\":\"Physical sciences/Mathematics and computing\"},{\"id\":57534695,\"name\":\"Physical sciences/Physics\"}],\"tags\":[],\"updatedAt\":\"2025-12-18T03:39:17+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2025-11-07 12:31:38\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-7827050\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-7827050\",\"identity\":\"rs-7827050\",\"version\":[\"v1\"]},\"buildId\":\"8U1c8b4HqxoKbykW_rLl7\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}