Submitted:
15 June 2026
Posted:
17 June 2026
You are already at the latest version
Abstract
Keywords:
1. Introduction
1.1. Problem Statement
1.2. Research Hypothesis
1.3. Research Methodology

2. Foundations and Formalisation of the Transition
2.1. Baseline State
- Yt-1 is the baseline-state vector of performance variables;
- Xt-1 is the average innovation input variable;
- Ot-1 is the average innovation outcome variable;
- Pt-1 is the average innovation impact variable.
2.2. Advanced State
2.3. Transformation Engine Representing Connected Intelligence Couplings
- W is the weighted matrix of binary couplings of connected intelligence
- wHC, wHM, wCH, wCM, wMH, wMC are estimated weights
- xHC, xHM, xCH, xCM, xMH, xMC are measured KPI interaction effects metrics.
2.4. The Transition Model
- Y1ₜ, Y2ₜ, Y3ₜ, the three endogenous variables observed at time t;
- Y1,ₜ₋1, Y2,ₜ₋1, Y3,ₜ₋1, their one-period lagged values;
- W, the coefficient matrix, each lagged variable affects each current variable;
- b01, b02, b03 the intercept terms for each equation;
- wᵢⱼ (i,j = 1,2,3) the autoregressive coefficients corresponding to HC, HM, CH, CM, MH, MC binary couplings
- e1ₜ, e2ₜ, e3ₜ, the noise error terms at time t.
2.5. System Design and Selection of Variables
3. SmartGreenEcos: An Intelligent Environment for Manufacturing Ecosystems
3.1. The SmartGreenEcos Innovation Model
3.2. Selecting a Manufacturing Sector as Foundation of the Ecosystem
3.3. The Transformation Engine: Platforms and E-Services Actualising Binary Couplings
3.4. Indicators to Capture and Assess the Transition
4. The Dynamics of Intelligent Environments
4.1. Simulations with Synthetic Data: Creation of the Dataset

4.2. Simulation Analysis: Matrix Coefficients, Eigenvalues, and Eigenvectors
5. Discussion: Intelligent Environments and Ecosystemic Innovation
6. Conclusions
- the manufacturing ecosystem itself, including the industry sector, participating organisations, challenges, and transition objectives;
- digital platforms, e-services, and AI agents that support innovation in operations, skills, transactions, and product development; and
- human actors, experts, and personnel who implement and use these services and tools to transform the routines and innovation performance of companies.
Acknowledgments
References
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| Binary coupling interactions | Platform: Optimisation of operations | Platform: Capacity building | Platform: Transactions | Platform: Product development | Average normalised values |
|
xHC (H→C) Experts improve company operations, capabilities, transactions, products |
Number of company operations improved through expert advice | Number of company capabilities improved through expert advice | Number of company transactions improved through expert advice | Number of products improved through expert advice | Mean xHC value |
|
xHM (H→M) Experts improve digital or AI-supported operations, capabilities, transactions, products |
Number of digital or AI-supported operations improved through expert advice | Number of digital or AI capabilities improved through expert advice | Number of digital or AI-supported transactions improved through expert advice | Number of products with added digital or AI features improved through expert advice | Mean xHM value |
|
xCH (C→H) Collaborative settings improve expert-supported operations, capabilities, transactions, products |
Number of expert-supported operations improved through collaborative settings | Number of expert capabilities improved through collaborative settings | Number of expert-supported transactions improved through collaborative settings | Number of product ideas improved through collaborative settings | Mean xCH value |
|
xCM (C→M) Collaborative settings improve digital or AI-supported operations, capabilities, transactions, products |
Number of digital or AI-supported operations improved through collaborative settings | Number of digital or AI capabilities improved through collaborative settings | Number of digital or AI-supported transactions improved through collaborative settings | Number of products with added digital or AI features improved through collaborative settings | Mean xCM value |
|
xMH (M→H) Digital or AI agents improve expert-supported operations, capabilities, transactions, products |
Number of expert-supported operations improved through machine agents | Number of expert capabilities improved through machine agents | Number of expert-supported transactions improved through machine agents | Number of product ideas improved through machine agents | Mean xMH value |
|
xMC (M→C) Digital or AI agents improve company operations, capabilities, transactions, products |
Number of company operations improved through machine agents | Number of company capabilities improved through machine agents | Number of company transactions improved through machine agents | Number of products improved through machine agents | Mean xMC value |
|
Case ID |
Perturbed coefficient |
Coeff. value |
Yt1 | Yt2 | Yt3 | lambda 1 | lambda 2 | lambda 3 | v1.1 | v1.2 | v1.3 | v2.1 | v2.2 | v2.3 | v3.1 | v3.2 | v3.3 |
| 1 | w12 | 0.1 | 4.019744 | 1.627582 | 2.413552 | 0.2 | -0.1 | -0.1 | 0.57735 | 0.57735 | 0.57735 | -0.8165 | 0.408248 | 0.408248 | -0.16518 | -0.60989 | 0.775076 |
| 2 | w12 | 0.2 | 5.019744 | 1.627582 | 2.413552 | 0.230278 | -0.1 | -0.13028 | 0.677535 | 0.52007 | 0.52007 | -0.70711 | 1.67E-16 | 0.707107 | -0.85213 | 0.370046 | 0.370046 |
| 3 | w12 | 0.3 | 6.019744 | 1.627582 | 2.413552 | 0.256155 | -0.1 | -0.15616 | 0.74121 | 0.474662 | 0.474662 | -0.70711 | -5.6E-17 | 0.707107 | -0.87544 | 0.341762 | 0.341762 |
| 4 | w12 | 0.4 | 7.019744 | 1.627582 | 2.413552 | 0.279129 | -0.1 | -0.17913 | 0.784874 | 0.438162 | 0.438162 | -0.70711 | -1.7E-16 | 0.707107 | -0.89204 | 0.31958 | 0.31958 |
| 5 | w12 | 0.5 | 8.019744 | 1.627582 | 2.413552 | 0.3 | -0.1 | -0.2 | 0.816497 | 0.408248 | 0.408248 | -0.70711 | 5.55E-17 | 0.707107 | -0.90453 | 0.301511 | 0.301511 |
| 6 | w12 | 0.6 | 9.019744 | 1.627582 | 2.413552 | 0.319258 | -0.1 | -0.21926 | 0.840359 | 0.383274 | 0.383274 | -0.70711 | 1.11E-16 | 0.707107 | -0.91431 | 0.286386 | 0.286386 |
| 7 | w12 | 0.7 | 10.01974 | 1.627582 | 2.413552 | 0.337228 | -0.1 | -0.23723 | 0.858952 | 0.362078 | 0.362078 | -0.70711 | 1.67E-16 | 0.707107 | -0.92219 | 0.273462 | 0.273462 |
| 8 | w12 | 0.8 | 11.01974 | 1.627582 | 2.413552 | 0.354138 | -0.1 | -0.25414 | 0.873816 | 0.343835 | 0.343835 | -0.70711 | 0 | 0.707107 | -0.92869 | 0.262239 | 0.262239 |
| 9 | w12 | 0.9 | 12.01974 | 1.627582 | 2.413552 | 0.370156 | -0.1 | -0.27016 | 0.885952 | 0.32794 | 0.32794 | -0.70711 | 5.55E-17 | 0.707107 | -0.93414 | 0.252365 | 0.252365 |
| 10 | w12 | 1.0 | 13.01974 | 1.627582 | 2.413552 | 0.38541 | -0.1 | -0.28541 | 0.896033 | 0.313946 | 0.313946 | -0.70711 | 0 | 0.707107 | -0.93879 | 0.243583 | 0.243583 |
| 11 | w13 | 0.1 | 4.019744 | 1.627582 | 2.413552 | 0.2 | -0.1 | -0.1 | 0.57735 | 0.57735 | 0.57735 | -0.8165 | 0.408248 | 0.408248 | -0.16518 | -0.60989 | 0.775076 |
| 12 | w13 | 0.2 | 5.019744 | 1.627582 | 2.413552 | 0.230278 | -0.1 | -0.13028 | 0.677535 | 0.52007 | 0.52007 | 0.707107 | -0.70711 | -5.6E-17 | -0.85213 | 0.370046 | 0.370046 |
| 13 | w13 | 0.3 | 6.019744 | 1.627582 | 2.413552 | 0.256155 | -0.1 | -0.15616 | 0.74121 | 0.474662 | 0.474662 | 0.707107 | -0.70711 | 0 | -0.87544 | 0.341762 | 0.341762 |
| 14 | w13 | 0.4 | 7.019744 | 1.627582 | 2.413552 | 0.279129 | -0.1 | -0.17913 | 0.784874 | 0.438162 | 0.438162 | 0.707107 | -0.70711 | 5.55E-17 | -0.89204 | 0.31958 | 0.31958 |
| 15 | w13 | 0.5 | 8.019744 | 1.627582 | 2.413552 | 0.3 | -0.1 | -0.2 | 0.816497 | 0.408248 | 0.408248 | 0.707107 | -0.70711 | 1.11E-16 | -0.90453 | 0.301511 | 0.301511 |
| 16 | w13 | 0.6 | 9.019744 | 1.627582 | 2.413552 | 0.319258 | -0.1 | -0.21926 | 0.840359 | 0.383274 | 0.383274 | 0.707107 | -0.70711 | 5.55E-17 | -0.91431 | 0.286386 | 0.286386 |
| 17 | w13 | 0.7 | 10.01974 | 1.627582 | 2.413552 | 0.337228 | -0.1 | -0.23723 | 0.858952 | 0.362078 | 0.362078 | 0.707107 | -0.70711 | -1.7E-16 | -0.92219 | 0.273462 | 0.273462 |
| 18 | w13 | 0.8 | 11.01974 | 1.627582 | 2.413552 | 0.354138 | -0.1 | -0.25414 | 0.873816 | 0.343835 | 0.343835 | 0.707107 | -0.70711 | 1.11E-16 | -0.92869 | 0.262239 | 0.262239 |
| 19 | w13 | 0.9 | 12.01974 | 1.627582 | 2.413552 | 0.370156 | -0.1 | -0.27016 | 0.885952 | 0.32794 | 0.32794 | 0.707107 | -0.70711 | -1.7E-16 | -0.93414 | 0.252365 | 0.252365 |
| 20 | w13 | 1.0 | 13.01974 | 1.627582 | 2.413552 | 0.38541 | -0.1 | -0.28541 | 0.896033 | 0.313946 | 0.313946 | 0.707107 | -0.70711 | -5.6E-17 | -0.93879 | 0.243583 | 0.243583 |
| 21 | w13 | 0.1 | 4.019744 | 1.627582 | 2.413552 | 0.2 | -0.1 | -0.1 | 0.57735 | 0.57735 | 0.57735 | -0.8165 | 0.408248 | 0.408248 | -0.16518 | -0.60989 | 0.775076 |
| 22 | w21 | 0.2 | 4.019744 | 2.627582 | 2.413552 | 0.230278 | -0.1 | -0.13028 | 0.52007 | 0.677535 | 0.52007 | 2.78E-16 | -0.70711 | 0.707107 | 0.370046 | -0.85213 | 0.370046 |
| 23 | w21 | 0.3 | 4.019744 | 3.627582 | 2.413552 | 0.256155 | -0.1 | -0.15616 | 0.474662 | 0.74121 | 0.474662 | -2.8E-16 | -0.70711 | 0.707107 | 0.341762 | -0.87544 | 0.341762 |
| 24 | w21 | 0.4 | 4.019744 | 4.627582 | 2.413552 | 0.279129 | -0.1 | -0.17913 | 0.438162 | 0.784874 | 0.438162 | -2.8E-16 | -0.70711 | 0.707107 | 0.31958 | -0.89204 | 0.31958 |
| 25 | w21 | 0.5 | 4.019744 | 5.627582 | 2.413552 | 0.3 | -0.1 | -0.2 | 0.408248 | 0.816497 | 0.408248 | -2.3E-16 | -0.70711 | 0.707107 | 0.301511 | -0.90453 | 0.301511 |
| 26 | w21 | 0.6 | 4.019744 | 6.627582 | 2.413552 | 0.319258 | -0.1 | -0.21926 | -0.38327 | -0.84036 | -0.38327 | -3E-16 | -0.70711 | 0.707107 | -0.28639 | 0.914312 | -0.28639 |
| 27 | w21 | 0.7 | 4.019744 | 7.627582 | 2.413552 | 0.337228 | -0.1 | -0.23723 | -0.36208 | -0.85895 | -0.36208 | -2.5E-16 | -0.70711 | 0.707107 | -0.27346 | 0.922191 | -0.27346 |
| 28 | w21 | 0.8 | 4.019744 | 8.627582 | 2.413552 | 0.354138 | -0.1 | -0.25414 | -0.34384 | -0.87382 | -0.34384 | -1.6E-16 | -0.70711 | 0.707107 | -0.26224 | 0.928688 | -0.26224 |
| 29 | w21 | 0.9 | 4.019744 | 9.627582 | 2.413552 | 0.370156 | -0.1 | -0.27016 | 0.32794 | 0.885952 | 0.32794 | 8.78E-17 | -0.70711 | 0.707107 | 0.252365 | -0.93414 | 0.252365 |
| 30 | w21 | 1.0 | 4.019744 | 10.62758 | 2.413552 | 0.38541 | -0.1 | -0.28541 | -0.31395 | -0.89603 | -0.31395 | -5.3E-17 | -0.70711 | 0.707107 | -0.24358 | 0.938794 | -0.24358 |
| 31 | w23 | 0.1 | 4.019744 | 1.627582 | 2.413552 | 0.2 | -0.1 | -0.1 | 0.57735 | 0.57735 | 0.57735 | -0.8165 | 0.408248 | 0.408248 | -0.16518 | -0.60989 | 0.775076 |
| 32 | w23 | 0.2 | 4.019744 | 2.627582 | 2.413552 | 0.230278 | -0.1 | -0.13028 | -0.52007 | -0.67753 | -0.52007 | -0.70711 | 0.707107 | -9E-17 | 0.370046 | -0.85213 | 0.370046 |
| 33 | w23 | 0.3 | 4.019744 | 3.627582 | 2.413552 | 0.256155 | -0.1 | -0.15616 | -0.47466 | -0.74121 | -0.47466 | -0.70711 | 0.707107 | -1.2E-16 | 0.341762 | -0.87544 | 0.341762 |
| 34 | w23 | 0.4 | 4.019744 | 4.627582 | 2.413552 | 0.279129 | -0.1 | -0.17913 | -0.43816 | -0.78487 | -0.43816 | -0.70711 | 0.707107 | 8.39E-17 | 0.31958 | -0.89204 | 0.31958 |
| 35 | w23 | 0.5 | 4.019744 | 5.627582 | 2.413552 | 0.3 | -0.1 | -0.2 | -0.40825 | -0.8165 | -0.40825 | -0.70711 | 0.707107 | 5.3E-16 | 0.301511 | -0.90453 | 0.301511 |
| 36 | w23 | 0.6 | 4.019744 | 6.627582 | 2.413552 | 0.319258 | -0.1 | -0.21926 | -0.38327 | -0.84036 | -0.38327 | -0.70711 | 0.707107 | -2.4E-16 | 0.286386 | -0.91431 | 0.286386 |
| 37 | w23 | 0.7 | 4.019744 | 7.627582 | 2.413552 | 0.337228 | -0.1 | -0.23723 | -0.36208 | -0.85895 | -0.36208 | -0.70711 | 0.707107 | 1.72E-16 | 0.273462 | -0.92219 | 0.273462 |
| 38 | w23 | 0.8 | 4.019744 | 8.627582 | 2.413552 | 0.354138 | -0.1 | -0.25414 | -0.34384 | -0.87382 | -0.34384 | -0.70711 | 0.707107 | -9.7E-17 | 0.262239 | -0.92869 | 0.262239 |
| 39 | w23 | 0.9 | 4.019744 | 9.627582 | 2.413552 | 0.370156 | -0.1 | -0.27016 | -0.32794 | -0.88595 | -0.32794 | -0.70711 | 0.707107 | 9.76E-17 | 0.252365 | -0.93414 | 0.252365 |
| 40 | w23 | 1.0 | 4.019744 | 10.62758 | 2.413552 | 0.38541 | -0.1 | -0.28541 | -0.31395 | -0.89603 | -0.31395 | -0.70711 | 0.707107 | 5.44E-17 | 0.243583 | -0.93879 | 0.243583 |
| 41 | w31 | 0.1 | 4.019744 | 1.627582 | 2.413552 | 0.2 | -0.1 | -0.1 | 0.57735 | 0.57735 | 0.57735 | -0.8165 | 0.408248 | 0.408248 | -0.16518 | -0.60989 | 0.775076 |
| 42 | w31 | 0.2 | 4.019744 | 1.627582 | 3.413552 | 0.230278 | -0.1 | -0.13028 | 0.52007 | 0.52007 | 0.677535 | -1.1E-16 | -0.70711 | 0.707107 | 0.370046 | 0.370046 | -0.85213 |
| 43 | w31 | 0.3 | 4.019744 | 1.627582 | 4.413552 | 0.256155 | -0.1 | -0.15616 | 0.474662 | 0.474662 | 0.74121 | -5.6E-17 | -0.70711 | 0.707107 | 0.341762 | 0.341762 | -0.87544 |
| 44 | w31 | 0.4 | 4.019744 | 1.627582 | 5.413552 | 0.279129 | -0.1 | -0.17913 | 0.438162 | 0.438162 | 0.784874 | -7E-17 | -0.70711 | 0.707107 | 0.31958 | 0.31958 | -0.89204 |
| 45 | w31 | 0.5 | 4.019744 | 1.627582 | 6.413552 | 0.3 | -0.1 | -0.2 | 0.408248 | 0.408248 | 0.816497 | -1.2E-16 | -0.70711 | 0.707107 | 0.301511 | 0.301511 | -0.90453 |
| 46 | w31 | 0.6 | 4.019744 | 1.627582 | 7.413552 | 0.319258 | -0.1 | -0.21926 | 0.383274 | 0.383274 | 0.840359 | 2.98E-16 | -0.70711 | 0.707107 | 0.286386 | 0.286386 | -0.91431 |
| 47 | w31 | 0.7 | 4.019744 | 1.627582 | 8.413552 | 0.337228 | -0.1 | -0.23723 | 0.362078 | 0.362078 | 0.858952 | -1.8E-17 | -0.70711 | 0.707107 | 0.273462 | 0.273462 | -0.92219 |
| 48 | w31 | 0.8 | 4.019744 | 1.627582 | 9.413552 | 0.354138 | -0.1 | -0.25414 | 0.343835 | 0.343835 | 0.873816 | -1.1E-16 | -0.70711 | 0.707107 | 0.262239 | 0.262239 | -0.92869 |
| 49 | w31 | 0.9 | 4.019744 | 1.627582 | 10.41355 | 0.370156 | -0.1 | -0.27016 | 0.32794 | 0.32794 | 0.885952 | 7.02E-17 | -0.70711 | 0.707107 | 0.252365 | 0.252365 | -0.93414 |
| 50 | w31 | 1.0 | 4.019744 | 1.627582 | 11.41355 | 0.38541 | -0.1 | -0.28541 | 0.313946 | 0.313946 | 0.896033 | -5.3E-17 | -0.70711 | 0.707107 | 0.243583 | 0.243583 | -0.93879 |
| 51 | w32 | 0.1 | 4.019744 | 1.627582 | 2.413552 | 0.2 | -0.1 | -0.1 | 0.57735 | 0.57735 | 0.57735 | -0.8165 | 0.408248 | 0.408248 | -0.16518 | -0.60989 | 0.775076 |
| 52 | w32 | 0.2 | 4.019744 | 1.627582 | 3.413552 | 0.230278 | -0.1 | -0.13028 | -0.52007 | -0.52007 | -0.67753 | -0.70711 | -8.8E-16 | 0.707107 | -0.37005 | -0.37005 | 0.852134 |
| 53 | w32 | 0.3 | 4.019744 | 1.627582 | 4.413552 | 0.256155 | -0.1 | -0.15616 | -0.47466 | -0.47466 | -0.74121 | -0.70711 | 1.36E-16 | 0.707107 | -0.34176 | -0.34176 | 0.875441 |
| 54 | w32 | 0.4 | 4.019744 | 1.627582 | 5.413552 | 0.279129 | -0.1 | -0.17913 | -0.43816 | -0.43816 | -0.78487 | -0.70711 | -1.9E-16 | 0.707107 | -0.31958 | -0.31958 | 0.892041 |
| 55 | w32 | 0.5 | 4.019744 | 1.627582 | 6.413552 | 0.3 | -0.1 | -0.2 | -0.40825 | -0.40825 | -0.8165 | -0.70711 | 1.35E-17 | 0.707107 | -0.30151 | -0.30151 | 0.904534 |
| 56 | w32 | 0.6 | 4.019744 | 1.627582 | 7.413552 | 0.319258 | -0.1 | -0.21926 | -0.38327 | -0.38327 | -0.84036 | -0.70711 | 5.35E-17 | 0.707107 | -0.28639 | -0.28639 | 0.914312 |
| 57 | w32 | 0.7 | 4.019744 | 1.627582 | 8.413552 | 0.337228 | -0.1 | -0.23723 | -0.36208 | -0.36208 | -0.85895 | -0.70711 | 5.3E-17 | 0.707107 | -0.27346 | -0.27346 | 0.922191 |
| 58 | w32 | 0.8 | 4.019744 | 1.627582 | 9.413552 | 0.354138 | -0.1 | -0.25414 | -0.34384 | -0.34384 | -0.87382 | -0.70711 | -3.9E-17 | 0.707107 | -0.26224 | -0.26224 | 0.928688 |
| 59 | w32 | 0.9 | 4.019744 | 1.627582 | 10.41355 | 0.370156 | -0.1 | -0.27016 | -0.32794 | -0.32794 | -0.88595 | -0.70711 | -1E-16 | 0.707107 | -0.25236 | -0.25236 | 0.934144 |
| 60 | w32 | 1.0 | 4.019744 | 1.627582 | 11.41355 | 0.38541 | -0.1 | -0.28541 | -0.31395 | -0.31395 | -0.89603 | -0.70711 | 0 | 0.707107 | -0.24358 | -0.24358 | 0.938794 |
| Matrix coefficients | v1.1 | v1.2 | v1.3 | v2.1 | v2.2 | v2.3 | v3.1 | v3.2 | v3.3 |
| w12 (wHC xHC) | 0.933 | -0.974 | -0.974 | 0.522 | -0.522 | 0.522 | -0.614 | 0.401 | -0.719 |
| w13 (wHM xHM) | 0.933 | -0.974 | -0.974 | 0.522 | 0.522 | -0.522 | -0.614 | 0.401 | -0.719 |
| w21 (wCH xCH) | -0.974 | 0.933 | -0.974 | 0.522 | -0.680 | 0.517 | 0.280 | -0.732 | -0.719 |
| w23 (wCM xCM) | -0.974 | 0.933 | -0.974 | 0.522 | 0.522 | -0.522 | 0.280 | -0.732 | -0.719 |
| w31 (wMH xMH) | -0.974 | -0.974 | 0.933 | 0.522 | -0.294 | 0.052 | 0.214 | 0.797 | 0.888 |
| w32 (wMC xMC) | -0.974 | -0.974 | 0.933 | 0.522 | -0.522 | 0.522 | 0.214 | 0.797 | 0.888 |
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