Correction: Integration of digitalization and green finance for sustainable and resilient manufacturing and service operations in China: an empirical analysis

1.1 Background Following China's economic reform and opening-up, the nation has witnessed unprecedented economic growth. However, such rapid growth has simultaneously imposed significant environmental costs.Environmental degradation and the strain on ecological resources have become critical challenges, demanding urgent intervention. China's environmental challenges, characterized by resource scarcity and severe pollution, highlight the urgent need for innovative strategies to balance economic development with ecological sustainability. Acknowledging these challenges, the Chinese government explicitly emphasized green development in its 14th Five-Year Plan, aiming to position China as a global leader in ecological preservation and sustainable economic practices. President Xi Jinping's commitment to peak CO 2 emissions by 2030 marks a strategic transition towards a green economic model, encapsulated in the vision that "a gold mountain is a silver mountain, and a gold mountain is a green mountain." In this context, green finance has evolved beyond mere financial support into a fundamental pillar driving China's environmental governance and economic restructuring.To advance this transformative agenda, the government has enacted several critical policies, including the Green Credit Guidelines (2012), the Green Bond Guidelines (2015), and the Green Financial System Guidelines (2016) ??. These policies have significantly stimulated the development of green finance, promoting capital allocation to eco-friendly projects that traditionally face barriers due to perceived high risks or lengthy return periods. Despite inherent challenges associated with green investments, such as substantial risks and extended investment cycles, these financial instruments remain essential for redirecting resources toward sustainable development goals. Recent policy updates further encourage digital-finance solutions such as blockchain-based carbon registries and AI-driven project screening-to reduce information asymmetry and speed up green capital flows ?. From an operations-management perspective, this digital-green synergy is pivotal for building sustainable and resilient manufacturing and service systems. Real-time carbon tracking, smart contracts for green supply-chain finance, and AI-enabled demand forecasting together reduce both ecological and disruption risks, ensuring continuity of production while meeting strict emission targets. Hence, analysing the nexus at the provincial level has direct implications for factory-floor decisions and service-network design across China's vast industrial landscape.The scale of this synergy is now increasingly measurable. The PKU Digital Inclusive Finance Index shows national digital-finance penetration rising from 124 points in 2013 to 362 points in 2023, laying technical rails for low-latency carbon accounting and automated sustainability-linked lending. Two recent examples illustrate the mechanism: (i) Hainan's "Blue Carbon" blockchain registry verified 4.3 Mt CO 2 offsets in 2023 and cut third-party audit time by 70 % 1 ; (ii) China Merchants Bank's AI-ESG engine shortened credit approval for renewable-energy SMEs from 15 to 10 days while lowering expected default losses by 12 % 2 . This study explores the complex interplay among green finance, economic growth, and carbon emissions across China's diverse regional landscapes. Using data from the China Emissions Accounts and Datasets (CEADS) and employing a robust green-finance impact model, this research investigates the regional variations in the effectiveness of green finance on environmental outcomes and economic performance. Our analysis reveals that while carbon emissions historically contributed to China's economic prosperity, the adoption of green-finance practices is progressively reshaping this relationship. Specifically, green finance has demonstrated substantial effectiveness in curbing carbon emissions, with particularly pronounced impacts observed in China's western and central regions. Furthermore, the results suggest China is on course to achieve its carbon emissions peak by 2031, led by the more economically advanced eastern region due to its well-developed green-financial infrastructure. Conversely, the central region, projected to reach a carbon peak by 2036, underscores the necessity and potential effectiveness of targeted green-financial policies in promoting balanced regional development and environmental sustainability.Our investigation is feasible because it leverages a newly compiled province-level panel (2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020)(2021)(2022)(2023) that couples CEADS carbon data with high-frequency digital-economy satellite proxies, enabling consistent measurement of both traditional and digitalised green-finance activities. We construct a composite index that embeds emerging instruments-e.g. sustainability-linked loans and FinTech-enabled green bonds-thereby capturing the latest market dynamics overlooked by earlier studies ?. Methodologically, we extend prior single-equation approaches by adopting a three-equation 3SLS framework complemented with system-GMM robustness checks, which allows us to disentangle bi-directional causality between digitalisation, green finance, and carbon outcomes. Together, these features position our work at the frontier of greenfinance research and provide clear advantages over studies that stop at 2019 or neglect the digital component.By integrating green finance into the economic framework based on the Cobb-Douglas production function and the Environmental Kuznets Curve (EKC), this paper not only elucidates the theoretical mechanisms by which green finance acts as a catalyst for economic transformation but also provides empirical evidence of its tangible impacts toward achieving China's ambitious carbon-neutrality goals.Ultimately, this research emphasizes the pivotal role green finance plays in shaping China's sustainable future, offering valuable insights and serving as a model for other nations seeking to harmonize environmental objectives with economic growth.The accelerating digitalisation-green finance nexus is reshaping how capital is channelled towards lowcarbon projects. Recent evidence shows that a vibrant digital economy can amplify the carbon-mitigation effect of green financial instruments by improving information transparency, lowering transaction costs, and expanding financial inclusion ?. However, empirical studies continue to report heterogeneous outcomes across regions and technologies, implying an urgent need to quantify where and how digital tools create additional environmental value ?. Against this backdrop, the present study sets out three specific objectives.1. Quantification. Measure the marginal impact of digitalisation on the efficiency of provincial greenfinance allocation during 2010-2023.2. Mechanism Exploration. 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