## 3 Method
Almost the same can be said when comparing, following the same method, the original description of TRLs by [32] to the Acatech study. Appendix B shows the normalized vectors of word occurrences, and the resulting scalar product is 0.048 that corresponds to an arccosine of 87.27 degrees. Also, in this case, the two vectors are almost perpendicular, and thus, the two domains are almost orthogonal (i.e., independent). This demonstrates that not only is the TRM orthogonal to the digital domain, but also that the TRL measures aspects that differ from what Acatech does. To evaluate whether this low similarity could have occurred by chance, we conducted a non-parametric permutation test with 1000 iterations. In each iteration, the combined token pool from both documents was randomly shuffled and split into two new pseudo-documents preserving the original token counts of the TRM and Acatech texts. For each pair, we constructed term-frequency vectors using the same fixed vocabulary, applied normalization, and computed the cosine similarity. Across all 1000 permutations, none produced a similarity rate as low as the observed value of 0.048, resulting in an empirical \(p\)-value of 0.000. This strongly indicates that the similarity between the original texts is significantly lower than what would be expected by chance. Hence, the result statistically corroborates the interpretation that the TRM and Acatech documents are thematically independent, providing robust support for their conceptual orthogonality. Therefore, the two perspectives based on the 6 levels of Acatech study and on the 9 TRLs could help to properly map digitalization and innovation projects, taking into account the two distinct but interconnected perspectives. In real practice, we can imagine these two dimensions are not totally orthogonal since the higher the level of Industry 4.0, the higher the probability the company is well structured, with proper skilled resources, with a wide knowledge and experience base. Thus, we can imagine the implementation can be easier, the exploitation can be higher, and the transformation can be deeper where a more mature environment exists. Although digital transformation must be chosen today as a path by each and every company, the lower maturity levels (computerization and connectivity) are almost preconditions for every R&D activity in the 4.0 era. In fact, working with analogical processes and in a totally disconnected environment could prevent the real and full exploitation of any (even well-implemented) technology. Therefore, we should imagine that processes are controlled with PC/PLC and an IT infrastructure (even simple) is available. On the technology side, we affirmed that enabling technologies belong to commercially available off-the-shelf (COTS) products. Therefore, we can expect that their maturity is high. Unfortunately, specific requirements due to customized processes or specific environmental situations could reduce the level of applicability and adaptation, redesign, integration, and testing are necessary before introducing such technology into real operations. This way, we can introduce two thresholds for reducing the risk of R&D activities. On the Acatech maturity level, we propose a threshold at level 2 (connectivity), as it represents the foundational stage where systems and assets are at least digitally connected. This avoids the scenario of a highly innovative solution being deployed in a context with no digital infrastructure--a situation metaphorically described as 'technological oases surrounded by the desert'. In such low-maturity environments, even the most advanced solutions struggle due to a lack of integration, data availability, or operator readiness. Similarly, on the TRL scale, we suggest a minimum threshold at level 2 (the technology concept formulated), which implies that the technology is no longer a mere idea but has taken shape in a conceptual form and is likely to have been tested in principle.