Ganz gleich, ob der Saum stimmt, prüfen wir ihn.

It is a fixed expression meaning regardless of whether, whether or not, or no matter whether.

It helps to learn ganz gleich, ob ... as one chunk. Literally, ganz gleich is something like completely the same, but idiomatically it means it makes no difference.

So the sentence is saying that the answer to ob der Saum stimmt does not affect what happens next.

Because ob means whether.

German makes a clearer distinction than English:

• ob = whether
• wenn = when or if in a conditional/repeated sense
• falls = if, in case

Here the idea is not a condition like if the hem is correct, then we check it. The idea is whether the hem is correct or not, we check it. That is exactly the job of ob.

Because ob introduces a subordinate clause, and in German subordinate clauses the conjugated verb normally goes to the end.

Compare:

• Der Saum stimmt. = main clause
• ..., ob der Saum stimmt. = subordinate clause

So stimmt moves to the end because of the clause type.

This is because German main clauses follow the verb-second rule.

The whole opening part Ganz gleich, ob der Saum stimmt counts as the first element of the sentence. Once that first position is filled, the finite verb of the main clause must come next:

• first position: Ganz gleich, ob der Saum stimmt
• second position: prüfen
• then the subject: wir

That is why you get prüfen wir ihn.

If the main clause came first, you would have:

• Wir prüfen ihn, ganz gleich, ob der Saum stimmt.

Because ihn refers back to der Saum, and Saum is a masculine noun.

German pronouns have to match the noun’s grammatical gender and case:

• der Saum = masculine nominative
• den Saum = masculine accusative
• pronoun replacing it in the accusative = ihn

So prüfen wir ihn means we check it, where it refers to the masculine noun Saum.

Here stimmen means to be correct, to be right, or to be in order.

It is a very common German verb with several meanings depending on context. For example:

• Das stimmt. = That’s correct.
• Die Zahlen stimmen nicht. = The numbers are not right.
• Das Klavier stimmt nicht. = The piano is out of tune.

In this sentence, it means the hem is correct / as it should be.

Because German often leaves it out. Ob by itself already means whether and can imply whether or not.

So both are possible:

• Ganz gleich, ob der Saum stimmt, prüfen wir ihn.
• Ganz gleich, ob der Saum stimmt oder nicht, prüfen wir ihn.

The version with oder nicht is just more explicit or slightly more emphatic.

German uses commas very regularly to mark subordinate clauses.

In this sentence:

• the first comma introduces the ob-clause: Ganz gleich, ob ...
• the second comma closes that clause before the main clause begins: ..., prüfen wir ihn

So the commas show the structure clearly:

• Ganz gleich
• ob der Saum stimmt
• prüfen wir ihn

It is natural and correct, but it sounds a little more formal or polished than some everyday alternatives.

A very common spoken alternative is:

• Egal, ob der Saum stimmt, prüfen wir ihn.

So:

• ganz gleich, ob ... = a bit more formal or written
• egal, ob ... = more casual and conversational

Both are good German.