feat: seed Homebrew formula + auto-update workflow

Mirror of installer/homebrew/fai.rb in fai/platform. Source
of truth is the platform repo; this is a passive distribution
mirror.

Auto-update workflow at .forgejo/workflows/update.yml runs
every 4 hours, diffs the latest platform release against
Formula/fai.rb, and rewrites version + sha256 when a new
version ships. Manual trigger via workflow_dispatch.

Users install with:
  brew tap fai/tap https://git.flemming.ai/fai/homebrew-tap
  brew install fai

End-state matches Phase 1 of
docs/releases/go-live-checklist.md.

Formula/fai.rb

@@ -0,0 +1,78 @@
+# Homebrew formula skeleton for the F∆I Platform CLI.
+#
+# Lives in this repo as the canonical source — the actual
+# distribution is a checkout of `fai/homebrew-tap` (a separate
+# Forgejo repo, seeded by
+# `scripts/bootstrap-distribution-repos.sh`) that carries a copy
+# of this file at `Formula/fai.rb`. The tap repo's
+# `.forgejo/workflows/update.yml` (sourced from
+# `installer/homebrew/forgejo-workflow-update.yml` in this repo)
+# auto-bumps the version + sha256 entries against each new
+# platform release on a 4-hourly cron.
+#
+# To install a release from the tap:
+#
+#   brew tap fai/tap https://git.flemming.ai/fai/homebrew-tap
+#   brew install fai
+#
+# To install from this checkout for testing:
+#
+#   brew install --build-from-source ./installer/homebrew/fai.rb
+#
+# This file is a *skeleton*. The :url / :sha256 placeholders are
+# populated by the release pipeline once macOS builds land on the
+# Forgejo Release page. The class name (`Fai`) is what Homebrew
+# uses to address the formula; lowercase `fai` is the binary on
+# disk after install.
+
+class Fai < Formula
+  desc "Deterministic workflow engine for AI-assisted data " \
+       "processing in regulated environments"
+  homepage "https://flemming.ai"
+  version "0.12.1"
+  license "Apache-2.0"
+
+  # Platform-specific binary URLs + sha256 are filled in per
+  # release. cargo-zigbuild-built linux artefacts come from the
+  # same release; the formula consumes them on Apple Silicon and
+  # Intel macs via stanza selectors.
+  if Hardware::CPU.arm?
+    url "https://git.flemming.ai/fai/platform/releases/download/" \
+        "v#{version}/fai-macos-aarch64"
+    sha256 "REPLACE_WITH_AARCH64_SHA256_FROM_MANIFEST"
+  else
+    url "https://git.flemming.ai/fai/platform/releases/download/" \
+        "v#{version}/fai-macos-x86_64"
+    sha256 "REPLACE_WITH_X86_64_SHA256_FROM_MANIFEST"
+  end
+
+  # Plain binary — no source build needed. We rely on the upstream
+  # CI to have produced + signed it. Notarization is a separate
+  # follow-up.
+  def install
+    bin.install Dir["*"].first => "fai"
+  end
+
+  # `brew test fai` runs this — keeps the formula honest. We don't
+  # start the daemon; we only verify the binary is callable.
+  test do
+    assert_match version.to_s, shell_output("#{bin}/fai --version")
+  end
+
+  def caveats
+    <<~EOS
+      The F∆I daemon is not started automatically. After install:
+
+        fai bootstrap            # writes ~/.fai/ layout + PATH marker
+        fai daemon start         # starts the local hub
+        fai install debug.echo   # smoke-test the install path
+
+      For Studio, install separately from
+      https://flemming.ai/get.
+
+      Note: this binary is not yet notarized. macOS Gatekeeper will
+      ask for confirmation on first launch. The notarization step
+      is tracked as the remaining half of system-gap S-16.
+    EOS
+  end
+end