# QC Fix DAG — L10: h00/h01 Helper Factoring

**Date:** 2026-05-13  
**Examiner:** subagent-task  
**Verdict:** PASS

## Input
- `0-Core-Formalism/lean/Semantics/Semantics/Physics/UniversalBridge.lean`

## Transformation
- Created `hermiteSharedTerms` private helper factoring shared Q16.16 arithmetic
- Refactored `h00` and `h01` to use helper

## Output
- `0-Core-Formalism/lean/Semantics/Semantics/Physics/UniversalBridge.lean` (modified)

## Verification
- **Command:** `lake build`
- **Result:** PASS
- **Jobs:** 3530

## Diff
```diff
diff --git a/0-Core-Formalism/lean/Semantics/Semantics/Physics/UniversalBridge.lean b/0-Core-Formalism/lean/Semantics/Semantics/Physics/UniversalBridge.lean
index c652b1bb..9913a2b7 100644
--- a/0-Core-Formalism/lean/Semantics/Semantics/Physics/UniversalBridge.lean
+++ b/0-Core-Formalism/lean/Semantics/Semantics/Physics/UniversalBridge.lean
@@ -33,6 +33,13 @@ private def q16_add (a b : Int) : Int := a + b
 
 private def q16_sub (a b : Int) : Int := a - b
 
+private def hermiteSharedTerms (t : Int) : Int × Int × Int × Int :=
+  let t2 := q16Mul t t
+  let t3 := q16Mul t2 t
+  let term3 := q16Mul (3 * scale) t2
+  let term2 := q16Mul (2 * scale) t3
+  (t2, t3, term3, term2)
+
 -- ============================================================================
 -- Normalized variable t = (Re − 2300) / 1700, as Q16.16
 -- ============================================================================
@@ -48,18 +55,12 @@ def normalizedT (re : Int) : Option Int :=
 
 /-- Basis function h00(t) = (1 − t)²(1 + 2t) = 1 − 3t² + 2t³ -/
 def h00 (t : Int) : Int :=
-  let t2 := q16Mul t t
-  let t3 := q16Mul t2 t
-  let term3 := q16Mul (3 * scale) t2
-  let term2 := q16Mul (2 * scale) t3
+  let (_, _, term3, term2) := hermiteSharedTerms t
   q16_sub (q16_add scale term2) term3
 
 /-- Basis function h01(t) = t²(3 − 2t) = 3t² − 2t³ -/
 def h01 (t : Int) : Int :=
-  let t2 := q16Mul t t
-  let t3 := q16Mul t2 t
-  let term3 := q16Mul (3 * scale) t2
-  let term2 := q16Mul (2 * scale) t3
+  let (_, _, term3, term2) := hermiteSharedTerms t
   q16_sub term3 term2
 
 /-- Basis function h10(t) = (1 − t)²·t -/
```