Android applications are cryptographically signed by the developer of the application when they are packaged. When you install an application, the signing certificate is pinned by the operating system and trusted on first use (TOFU). This prevents an app with the same app ID (domain.company.application) having a different certificate be installed. This has a few benefits:
- You ensure updates are only able to be delivered by the same entity, providing the signing certificates isn't compromised.
- An app can't be tampered with since it will require being re-signed.
- You can use the hash of the certificates as a form of app / developer verification.
Outside of signing, apps are also protected by downgrade protections to prevent downgrade attacks.
A limitation with TOFU is that it doesn't verify it an app is legitimate, only that it is different from the original install. App stores provide far more verification on an application being listed and are more likely to assure you getting a legitimate app than getting a random APK file off the internet.
AppVerifier is an app by one of our app developers that lets you check the signing certificate hashes of an app. You can compare the signing hash with one the developer publishes with your own install to validate you have an authentic package. #GrapheneOS will eventually add this as a UI feature (e.g. in the install dialog) in the later future to not necessitate having an additional app.

This information is heavily used to verify apps in an Alpha build app store called Accrescent which we'd like other app store apps to follow the model of. I will explain further about the workings of it later.
Other app stores like F-Droid and recently Google Play compile the apps and/or sign them. The former only allowing own signings certificates if there is reproducible builds (a minimal amount). This is problematic, as it adds an additional trusted party. Apps should be exclusively signed by developers as a compromise of a shared signing certificate means a pwn of every app using that certificate. It also makes updates impossible should the apps be exited from the app store or if you want to get from another source. It is even more telling as F-Droid builds apps on extremely old infrastructure that missed features from processors added in the late 2000s - early 2010s.