Learn Turkish: Radarda hiçbir tehlike belirtisinin olmadığını bildirdiler. - They reported that there was no sign of danger on the radar.

This is the core of how Turkish builds embedded clauses. The phrase 'there was no sign of danger' acts as the object of the main verb 'they reported'. In these noun clauses, the logical subject of the embedded action (tehlike belirtisi, sign of danger) takes the genitive case (-nin), linking it to the embedded verb, which takes a matching possessive suffix.

Could you break down the suffixes on olmadığını?

Certainly! It's built on ol- (to be/exist). First, -ma makes it negative. Then, -dık turns the verb into a noun clause (referring to a fact). Next, the possessive -ı matches the genitive subject (tehlike belirtisinin). Finally, the buffer -n- connects to the accusative -ı, marking the entire clause as the direct object of bildirdiler (they reported).

Why does belirtisinin have both -si and -nin attached to the root belirti?

The -si is there because tehlike belirtisi is a noun compound (literally 'danger its-sign'). When you need to make this whole compound the subject of your embedded clause, you must add the genitive suffix on top of it. So you get the root belirti + compound possessive -si + buffer -n- + genitive -in.

Does the use of hiçbir mean the verb must always be negative?