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>

apps/selfhost/vm/boxes/mini_vm_core.nyash

@@ -541,13 +541,19 @@ static box MiniVm {
     local k_print = "\"kind\":\"Print\""
     loop (true) {
       guard = guard + 1
-      if guard > 200 { if trace == 1 { print("[collect][guard_break] guard="+guard) } break }
+      if guard > 200 {
+        if trace == 1 { print("[collect][guard_break] guard="+guard) }
+        if trace == 1 { print("[collect][loop_exit] guard="+guard+" out.size="+out.size()) }
+        if trace == 1 { print("[collect][return] out.size="+out.size()) }
+        return out
+      }
       local p = index_of_from(json, k_print, pos)
       if trace == 1 { print("[collect][loop] pos="+pos+" p="+p+" guard="+guard) }
-      if p < 0 { 
-        if trace == 1 { print("[collect][p_break] p="+p) } 
-        if trace == 1 { print("[collect][pre_break] about to break, out.size="+out.size()) }
-        break 
+      if p < 0 {
+        if trace == 1 { print("[collect][p_break] p="+p) }
+        if trace == 1 { print("[collect][loop_exit] guard="+guard+" out.size="+out.size()) }
+        if trace == 1 { print("[collect][return] out.size="+out.size()) }
+        return out
       }
       // bound current Print slice to [this, next)
       local obj_start = p
@@ -761,13 +767,8 @@ static box MiniVm {
       pos = obj_end + 1
       if pos <= p { pos = p + k_print.length() }
     }
-    if trace == 1 { print("[collect][loop_exit] starting cleanup") }
-    if trace == 1 { print("[collect][guard_val] "+guard) }
-    if trace == 1 { print("[collect][out_ref_check] checking out reference") }
-    if trace == 1 { print("[collect][calling_size] about to call out.size()") }
-    local outsize = out.size()
-    if trace == 1 { print("[collect][size_result] size="+outsize) }
-    if trace == 1 { print("[collect][return] returning out with size="+outsize) }
+    if trace == 1 { print("[collect][loop_exit] guard="+guard+" out.size="+out.size()) }
+    if trace == 1 { print("[collect][return] out.size="+out.size()) }
     return out
   }
 }