Production-Ready Phoenix Deployment

Problem/Feature Description

A fintech startup has built a Phoenix web application called PayCore that handles payment processing and user account management. The team has been developing it locally against a development database and is now ready to go live. Their DevOps engineer has flagged several blockers: the application currently has no health monitoring endpoint (making load-balancer integration impossible), secrets are embedded directly in version-controlled config files (a compliance violation), and their deployment runbook still uses mix commands that require the full Elixir toolchain installed in production.

The engineering lead has asked you to prepare the production deployment configuration from scratch. The app's module name is PayCore and its Ecto repo is PayCore.Repo. You should produce all the necessary configuration and source files to make the application production-ready and deployable as an OTP release. The app already has a basic router and application supervisor — you are wiring up the production layer on top of that.

The team also needs a DEPLOYMENT.md guide so operations staff can follow the correct sequence when pushing new versions or running database migrations without downtime.

Output Specification

Produce the following files:

• config/runtime.exs — runtime configuration that reads secrets from environment variables. The app needs DATABASE_URL, SECRET_KEY_BASE, PHX_HOST, and PORT configured.
• lib/pay_core/release.ex — a Release module with functions for running and rolling back Ecto migrations suitable for use in a deployed OTP release (without the Mix tool available).
• lib/pay_core_web/controllers/health_controller.ex — a controller that exposes a health check endpoint verifying the database is reachable. Return JSON responses.
• lib/pay_core/application.ex — the Application module with a proper supervision tree and telemetry wiring.
• Dockerfile — a container image definition using a build and a runtime stage.
• DEPLOYMENT.md — a deployment guide explaining environment variable requirements, how to run migrations in production, and the correct startup sequence.

Do not add routes to router.ex — just produce the controller and note the route configuration needed in DEPLOYMENT.md.