No file is created in the assigned multiprocess directory

I've been trying to use multiprocessing mode but I'm struggling to make it work properly.
Even though I set the multiprocess directory, no metric writes any files. I've checked for permissions for writing in the directory and they exist.
I'm currently trying to work with a Gauge in the livesum mode. The metric is incrementing properly within the application but no updates are made available to Prometheus. Is anything else other than setting the directory and a multiprocess mode for the Gauge needed that I might be missing?
I'm using Prometheus inside a Docker container with the port forwarding.

まず、設定されたマルチプロセスディレクトリを使って、報告された Gauge を livesum モードで再現し、その後、issue に記載されたマルチプロセス設定と Docker から Prometheus への接続を調べます。完了条件は、メトリクスファイルも Prometheus の更新も現れない理由を特定し、再現可能な修正または不足している設定を文書化することです。