Add Dog infrastructure package for Deacon helper workers (gt-0x5og.2)

Dogs are reusable workers managed by the Deacon for cross-rig infrastructure
tasks. Unlike polecats (single-rig, ephemeral), dogs have worktrees into
multiple rigs and persist between tasks.

Key components:
- internal/dog/types.go: Dog struct, State enum, DogState JSON schema
- internal/dog/manager.go: Manager with Add/Remove/List/Get/Refresh operations
- internal/dog/manager_test.go: Unit tests

Features:
- Multi-rig worktrees: Each dog gets a worktree per configured rig
- State tracking: .dog.json with idle/working state, last-active, work assignment
- Worktree refresh: Recreate stale worktrees with fresh branches
- Branch cleanup: Remove orphaned dog branches across all rigs

Directory structure: ~/gt/deacon/dogs/<name>/
  - <rig>/ (worktree into each rig: gastown/, beads/, etc.)
  - .dog.json (state file)

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/dog/types.go

@@ -0,0 +1,40 @@
+// Package dog manages Dogs - Deacon's helper workers for infrastructure tasks.
+// Dogs are reusable workers with multi-rig worktrees, managed by the Deacon.
+// Unlike polecats (single-rig, ephemeral), dogs handle cross-rig infrastructure work.
+package dog
+
+import (
+	"time"
+)
+
+// State represents a dog's operational state.
+type State string
+
+const (
+	// StateIdle means the dog is available for work.
+	StateIdle State = "idle"
+	// StateWorking means the dog is executing a task.
+	StateWorking State = "working"
+)
+
+// Dog represents a Deacon helper worker.
+type Dog struct {
+	Name       string            // Dog name (e.g., "alpha")
+	State      State             // Current state
+	Path       string            // Path to kennel dir (~/gt/deacon/dogs/<name>)
+	Worktrees  map[string]string // Rig name -> worktree path
+	LastActive time.Time         // Last activity timestamp
+	Work       string            // Current work assignment (bead ID or molecule)
+	CreatedAt  time.Time         // When dog was added to kennel
+}
+
+// DogState is the persistent state stored in .dog.json.
+type DogState struct {
+	Name       string            `json:"name"`
+	State      State             `json:"state"`
+	LastActive time.Time         `json:"last_active"`
+	Work       string            `json:"work,omitempty"`       // Current work assignment
+	Worktrees  map[string]string `json:"worktrees,omitempty"`  // Rig -> path (for verification)
+	CreatedAt  time.Time         `json:"created_at"`
+	UpdatedAt  time.Time         `json:"updated_at"`
+}