Accelerated approval and Orphan Drug Designation are two...

Accelerated approval and Orphan Drug Designation are two separate things. I agree with Rebekah and Pivalde.

Orphan designation is designed to encourage drug developers to develop therapies in these rare diseases where smaller patient pools means historically they were overlooked due to less reward after very risky drug development endeavour. So regulators encourage this development by giving the tax rebates, market exclusivity, reduced evaluation fees, etc. This has led to developers using strategy to develop a drug in its ODD disease area first, get it to market with these advantages, then expand to other larger indications.

Accelerated approval is similar but different, in that FDA considers some disease areas to have exceptionally high unmet need, i.e. lots of people suffering and no disease modifying therapies to help them. So when they agree that both; there is very high unmet need, and its likely a therapy with strong ph 2 data could ease this suffering, then they conditionally approve the therapy after ph 2 and give clear guidance on what clinical data they still want to see before full approval - generally a phase 3 run alongside the conditionally approved use. Recall how Biogen's Aducanumab received accelerated approval for early Alzheimer's in 2021, this was off ph 3 data, and they wanted more ph 3 data, but my point is AD is not an orphan designation as too many patients.
Check out the FDA list of accelerated approval, and there are cases of pretty small studies leading to accelerated approval. https://www.fda.gov/drugs/accelerated-approval-program/ongoing-non-malignant-hematological-neurological-and-other-disorder-indications-accelerated
One I quickly looked at Vyondys 53 for a variant of DMD had only around 25 patients in the study they used to accelerate its approval.
https://www.fda.gov/news-events/press-announcements/fda-grants-accelerated-approval-first-targeted-treatment-rare-duchenne-muscular-dystrophy-mutation#:~:text=The%20accelerated%20approval%20of%20Vyondys,patients%20treated%20with%20the%20drug.

This is all my understanding of the system, so dyor and feel free to correct me if I'm wrong. But its my view that with reasonably strong ATH434-201 data Alterity has a realistic chance of convincing FDA for accelerated approval before doing a ph 3, given there really isn't any disease modifying therapies for these thousands of patients.

Cheers