phase15: implement Phase S root treatment for break control flow

🔧 **Phase S (Immediate Stabilization) Implementation**
- Create control flow utilities module (src/mir/utils/)
- Refactor loop_builder.rs duplicated code to utilities
- Fix PHI incoming predecessor capture per ChatGPT Pro analysis

📊 **AI Collaborative Analysis Complete**
- Task agent: Root cause identification
- Gemini: Strategic 3-phase approach
- codex: Advanced type inference solution (archived)
- ChatGPT Pro: Definitive staged treatment strategy

🗂️ **Documentation & Archive**
- Strategy document: docs/development/strategies/break-control-flow-strategy.md
- codex solutions: archive/codex-solutions/ (100+ lines changes)
- Update CLAUDE.md with 2025-09-23 progress

⚡ **Expected Impact**
- Resolve collect_prints null return issue
- Eliminate code duplication (4 locations unified)
- Foundation for Phase M (PHI unification) and Phase L (BuildOutcome)

🎯 Generated with [Claude Code](https://claude.ai/code)

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

src/mir/mod.rs

@@ -18,6 +18,7 @@ pub mod types; // core MIR enums (ConstValue, Ops, MirType)
 pub mod loop_api; // Minimal LoopBuilder facade (adapter-ready)
 pub mod loop_builder; // SSA loop construction with phi nodes
 pub mod optimizer;
+pub mod utils; // Phase 15 control flow utilities for root treatment
 pub mod optimizer_passes; // optimizer passes (normalize/diagnostics)
 pub mod optimizer_stats; // extracted stats struct
 pub mod passes;
@@ -44,6 +45,13 @@ pub use slot_registry::{BoxTypeId, MethodSlot};
 pub use value_id::{LocalId, ValueId, ValueIdGenerator};
 pub use verification::MirVerifier;
 pub use verification_types::VerificationError;
+// Phase 15 control flow utilities (段階的根治戦略)
+pub use utils::{
+    is_current_block_terminated,
+    capture_actual_predecessor_and_jump,
+    collect_phi_incoming_if_reachable,
+    execute_statement_with_termination_check,
+};
 
 /// MIR compilation result
 #[derive(Debug, Clone)]