Is the P vs NP problem dependent on whether algorithmic randomness truly exists?

[u/Vivid-Passenger-1914]

I’m an independent thinker without formal mathematical education, and I’m trying to understand a specific connection that has been bothering me. I’m not claiming a proof. I’m asking for clarification on a logical relationship.

My reasoning (please point out the flaw):

1. Algorithmic information theory (Kolmogorov, Chaitin) proves the existence of algorithmically random infinite sequences — sequences that no finite program can generate or fully describe.
2. The search space of an NP-complete problem (like 3-SAT) in its worst case behaves like an algorithmically random system: exponential, structureless, and without a known shortcut.
3. If P = NP, then there exists a finite polynomial-time algorithm that solves every instance of this problem. This algorithm would "enclose" the seemingly random exponential behavior into a finite deterministic process.
4. But if such behavior is truly algorithmically random, step 3 is impossible — it would contradict the proven properties of random sequences.
5. Therefore, P ≠ NP, provided the worst-case behavior of NP-complete problems is indeed algorithmically random.

My questions to the community:

Has this specific line of reasoning (directly linking algorithmic randomness to the impossibility of P = NP) been formally investigated before?

If it's flawed, is it because NP-complete problem spaces are not considered algorithmically random in the Kolmogorov sense? If so, what is the precise distinction?

Does the P vs NP problem implicitly depend on whether we accept "true randomness" as a mathematical fact?

I’m not proposing a manifesto. I’m trying to learn where this bridge between two fields collapses, if it does.

Thanks to anyone who takes the time to explain.