The cedar stack's filesystem is not readonly.
However, you still mustn't store any data on it because the filesystem is ephemeral.
Any time your application restarts, whatever you had written to your application's filesystem disappears forever.
Any time you add a dyno, the two dynos each have their own ephemeral system; any data stored by one dyno to its ephemeral filesystem is not available to the other dyno or to any additional dynos you may add later.
Sqlite3 writes data to the local filesystem. You cannot use Sqlite3 with Heroku.
Heroku provides a default PostgreSQL installation, which Heroku manages. You can use that.
You can also use any third-party-managed cloud database system, such as Amazon RDS' or Xeround's MySQL, MongoHQ's or MongoLab's MongoDB, or Cloudant's CouchDB - all of which are available as Heroku addons.
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