feat(refinery): Integrate merge-slot gate for conflict resolution

Adds merge-slot integration to the Refinery's Engineer for serializing
conflict resolution. When a conflict is detected:
- Acquire the merge slot before creating a conflict resolution task
- If slot is held, defer task creation (MR stays in queue)
- Release slot after successful merge

This prevents cascading conflicts from multiple polecats racing to
resolve conflicts simultaneously.

Adds MergeSlot wrapper functions to beads package for slot operations.

(gt-4u49x)

🤖 Generated with Claude Code

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

internal/beads/beads.go

@@ -1436,3 +1436,130 @@ func (b *Beads) AddGateWaiter(gateID, waiter string) error {
 	}
 	return nil
 }
+
+// ===== Merge Slot Functions (serialized conflict resolution) =====
+
+// MergeSlotStatus represents the result of checking a merge slot.
+type MergeSlotStatus struct {
+	ID        string   `json:"id"`
+	Available bool     `json:"available"`
+	Holder    string   `json:"holder,omitempty"`
+	Waiters   []string `json:"waiters,omitempty"`
+	Error     string   `json:"error,omitempty"`
+}
+
+// MergeSlotCreate creates the merge slot bead for the current rig.
+// The slot is used for serialized conflict resolution in the merge queue.
+// Returns the slot ID if successful.
+func (b *Beads) MergeSlotCreate() (string, error) {
+	out, err := b.run("merge-slot", "create", "--json")
+	if err != nil {
+		return "", fmt.Errorf("creating merge slot: %w", err)
+	}
+
+	var result struct {
+		ID     string `json:"id"`
+		Status string `json:"status"`
+	}
+	if err := json.Unmarshal(out, &result); err != nil {
+		return "", fmt.Errorf("parsing merge-slot create output: %w", err)
+	}
+
+	return result.ID, nil
+}
+
+// MergeSlotCheck checks the availability of the merge slot.
+// Returns the current status including holder and waiters if held.
+func (b *Beads) MergeSlotCheck() (*MergeSlotStatus, error) {
+	out, err := b.run("merge-slot", "check", "--json")
+	if err != nil {
+		// Check if slot doesn't exist
+		if strings.Contains(err.Error(), "not found") {
+			return &MergeSlotStatus{Error: "not found"}, nil
+		}
+		return nil, fmt.Errorf("checking merge slot: %w", err)
+	}
+
+	var status MergeSlotStatus
+	if err := json.Unmarshal(out, &status); err != nil {
+		return nil, fmt.Errorf("parsing merge-slot check output: %w", err)
+	}
+
+	return &status, nil
+}
+
+// MergeSlotAcquire attempts to acquire the merge slot for exclusive access.
+// If holder is empty, defaults to BD_ACTOR environment variable.
+// If addWaiter is true and the slot is held, the requester is added to the waiters queue.
+// Returns the acquisition result.
+func (b *Beads) MergeSlotAcquire(holder string, addWaiter bool) (*MergeSlotStatus, error) {
+	args := []string{"merge-slot", "acquire", "--json"}
+	if holder != "" {
+		args = append(args, "--holder="+holder)
+	}
+	if addWaiter {
+		args = append(args, "--wait")
+	}
+
+	out, err := b.run(args...)
+	if err != nil {
+		// Parse the output even on error - it may contain useful info
+		var status MergeSlotStatus
+		if jsonErr := json.Unmarshal(out, &status); jsonErr == nil {
+			return &status, nil
+		}
+		return nil, fmt.Errorf("acquiring merge slot: %w", err)
+	}
+
+	var status MergeSlotStatus
+	if err := json.Unmarshal(out, &status); err != nil {
+		return nil, fmt.Errorf("parsing merge-slot acquire output: %w", err)
+	}
+
+	return &status, nil
+}
+
+// MergeSlotRelease releases the merge slot after conflict resolution completes.
+// If holder is provided, it verifies the slot is held by that holder before releasing.
+func (b *Beads) MergeSlotRelease(holder string) error {
+	args := []string{"merge-slot", "release", "--json"}
+	if holder != "" {
+		args = append(args, "--holder="+holder)
+	}
+
+	out, err := b.run(args...)
+	if err != nil {
+		return fmt.Errorf("releasing merge slot: %w", err)
+	}
+
+	var result struct {
+		Released bool   `json:"released"`
+		Error    string `json:"error,omitempty"`
+	}
+	if err := json.Unmarshal(out, &result); err != nil {
+		return fmt.Errorf("parsing merge-slot release output: %w", err)
+	}
+
+	if !result.Released && result.Error != "" {
+		return fmt.Errorf("slot release failed: %s", result.Error)
+	}
+
+	return nil
+}
+
+// MergeSlotEnsureExists creates the merge slot if it doesn't exist.
+// This is idempotent - safe to call multiple times.
+func (b *Beads) MergeSlotEnsureExists() (string, error) {
+	// Check if slot exists first
+	status, err := b.MergeSlotCheck()
+	if err != nil {
+		return "", err
+	}
+
+	if status.Error == "not found" {
+		// Create it
+		return b.MergeSlotCreate()
+	}
+
+	return status.ID, nil
+}