phase-20.45: PRIMARY no-fallback reps + MIR v0 shape fixes

- Fix MIR v0 shape in lowers: functions[] + name="main" + blocks.id
  * lower_return_int_box.hako
  * lower_return_binop_box.hako
- runner_min: adopt LowerReturnBinOpBox before ReturnInt
- Add PRIMARY no-fallback canaries (all PASS):
  * return-binop / array-size / load-store / return-logical (OR)
- Fix phase2043 runner_min canary alias (Runner -> BuilderRunnerMinBox)
- Update docs: phase-20.45 README (PRIMARY reps), CURRENT_TASK progress

Ancillary: keep builder/provider/canary files in sync; no unrelated behavior changes.

lang/src/mir/builder/internal/pattern_util_box.hako

@@ -5,6 +5,27 @@ using selfhost.shared.common.string_helpers as StringHelpers
 
 static box PatternUtilBox {
   map_cmp(sym) { if sym=="<" {return "Lt"} if sym==">" {return "Gt"} if sym=="<=" {return "Le"} if sym==">=" {return "Ge"} if sym=="==" {return "Eq"} if sym=="!=" {return "Ne"} return null }
+  // Normalize (op, swapped, limit) → (cmp, limit') where cmp in {Lt, Le, Gt, Ge}
+  // swapped=0: i ? L, swapped=1: L ? i
+  normalize_cmp_limit(op, swapped, limit_str) {
+    local op1 = "" + op
+    local ls = "" + limit_str
+    if swapped == 0 {
+      if op1 == "<" { return "Lt:" + ls }
+      if op1 == "<=" { return "Lt:" + StringHelpers.int_to_str(JsonFragBox._str_to_int(ls) + 1) }
+      if op1 == ">" { return "Gt:" + ls }
+      if op1 == ">=" { return "Ge:" + ls }
+      if op1 == "!=" { return "Lt:" + ls } // count(init=0,step=1) 前提の近似
+      return null
+    } else {
+      if op1 == ">" { return "Lt:" + ls }
+      if op1 == ">=" { return "Lt:" + StringHelpers.int_to_str(JsonFragBox._str_to_int(ls) + 1) }
+      if op1 == "<" { return "Gt:" + ls }
+      if op1 == "<=" { return "Ge:" + ls }
+      if op1 == "!=" { return "Lt:" + ls } // 安全近似（入替側）
+      return null
+    }
+  }
   // Normalize limit for canonical (i < limit) form.
   // When swapped==0, expects op in {'<','<='}; when swapped==1 (Int on lhs, Var on rhs), expects op in {'>','>='}.
   // Returns adjusted limit string or null if unsupported.
@@ -38,4 +59,47 @@ static box PatternUtilBox {
     local kv=s.indexOf("\"value\":",kb); if kv<0 { return null }
     return JsonFragBox.read_bool_after(s, kv+8)
   }
+
+  // Find the last Local(Int) before a given position (name-agnostic).
+  // Returns string digits or null when not found.
+  find_any_local_int_before(s, before_pos) {
+    local pos = 0; local last_k = -1; local n = ("" + s).length()
+    loop(true) {
+      local k = JsonFragBox.index_of_from(s, "\"type\":\"Local\"", pos)
+      if k < 0 || k >= before_pos { break }
+      last_k = k
+      pos = k + 1
+    }
+    if last_k < 0 { return null }
+    // Limit search to the next Local or before_pos
+    local next = JsonFragBox.index_of_from(s, "\"type\":\"Local\"", last_k + 1)
+    if next < 0 || next > before_pos { next = before_pos }
+    // Constrain to Local.expr → Int
+    local ti = ("" + s).indexOf("\"expr\":{\"type\":\"Int\"", last_k)
+    if ti < 0 || ti >= next { return null }
+    local kv = ("" + s).indexOf("\"value\":", ti)
+    if kv < 0 || kv >= next { return null }
+    return JsonFragBox.read_int_after(s, kv + 8)
+  }
+
+  // Find the last Local(String) before a given position (name-agnostic).
+  // Returns raw string (unquoted) or null when not found.
+  find_any_local_string_before(s, before_pos) {
+    local pos = 0; local last_k = -1
+    loop(true) {
+      local k = JsonFragBox.index_of_from(s, "\"type\":\"Local\"", pos)
+      if k < 0 || k >= before_pos { break }
+      last_k = k
+      pos = k + 1
+    }
+    if last_k < 0 { return null }
+    local next = JsonFragBox.index_of_from(s, "\"type\":\"Local\"", last_k + 1)
+    if next < 0 || next > before_pos { next = before_pos }
+    // Constrain to Local.expr → String
+    local ts = ("" + s).indexOf("\"expr\":{\"type\":\"String\"", last_k)
+    if ts < 0 || ts >= next { return null }
+    local kv = ("" + s).indexOf("\"value\":", ts)
+    if kv < 0 || kv >= next { return null }
+    return JsonFragBox.read_string_after(s, kv + 8)
+  }
 }