You will need to separate the notions of validity (“does this chain fulfill all validity guidelines”) and being lively (“amongst all legitimate chains, does it have probably the most work?”).
As an instance the 2 branches of the chain are A (created by Bitcoin miners) and B (created by BIP110 miners). A has ~10x extra work than B, however over time, after retargetting, may have a roughly equal variety of blocks.
To BIP110-enforcing nodes, solely B is legitimate, so their lively chain is important B. They don’t even “see” the A chain.
To Bitcoin nodes, each A and B are legitimate. Nonetheless, whatever the variety of blocks in every, or problem adjustment, the A chain has clearly extra proof-of-work than B (which is computed roughly as sum of the difficulties throughout all its blocks). Thus, Bitcoin nodes won’t ever think about B to be the lively chain, as a result of A has simply much more work. “being lively” is in follow what issues for customers, who will simply not see B.
Nonetheless, if the B chain by some means managed to get probably the most work at some later level (which inevitably means overtaking A in problem), Bitcoin nodes will swap over to it.
The issue adjustment rule (part of the validity guidelines) applies per department (as do all consensus guidelines): every department’s problem requirement is a operate simply of the blocks inside that very same department. The existence of one other department with one other problem is irrelevant for validity. In fact, the “decide most-work chain” nonetheless cares in regards to the distinction in problem between the branches (not directly, by way of the overall PoW they contribute to their respective branches).
Arduous forks are unrelated; these are adjustments to consensus guidelines which might be incompatible in each instructions. That’s not the case right here, the BIP110 chain is legitimate to Bitcoin nodes, simply inferior in proof-of-work so long as its problem is low.
