Hmmmm! Perhaps, choice of nodes & economic incentives mixed with different sidechain implementations (SIP) can indeed have ripple effects on the entire network including the mainchain (Bitcoin).

Hypothesis: Gini Coefficient & Mining Centralization.

The Gini coefficient is a mathematical measure of inequality in a distribution. In the context of mining, we can use it to quantify the distribution of mining power among participants. A Gini coefficient of 0 represents perfect equality (everyone has the same amount of mining power), while a Gini coefficient of 1 represents maximum inequality (one participant has all the mining power).

Now, let's consider a scenario where a #sidechain introduces a highly profitable mining method that requires expensive hardware, creating an economic incentive for miners to switch. This can indeed lead to centralization if only a few entities can afford the expensive nodes, resulting in an increase in the Gini coefficient for mining power distribution.

But, mathematically I don’t think this would happen early on the process if sidechain developers & researchers aim to strike a balance between innovation & preserving the fundamental principles of decentralization that underpin Bitcoin's security & robustness (Decentralized sidechain governance, different PoW algorithms for different sidechains, dynamic rewards & incentives for mainchain miners). But the idea of PoS should be avoid..