# FAMM-Sidon-Baker Analogue — Lean Formalization Sketch

**File:** `Semantics.FAMMBaker.SidonVCN.lean`

```lean
-- Sidon projection and collision structure
def sidonProjection (addr : Fin 8) : Nat := addr.val

structure SidonCollision where
  i j k l : Fin 8
  hneq : {i, j} ≠ {k, l}

-- Collapse functional (linear form in logs)
def collapseFunctional (collisions : List SidonCollision) : Q16_16 :=
  collisions.foldl (· + ·) 0  -- weighted sum

-- Scar energy measure
def scarEnergy (state : BraidState) : Q16_16 :=
  state.ene.scars.foldl (· + ·.pressure.toQ16_16) 0

-- Main theorem skeleton
theorem fammySidonBakerRigidity 
  (state : BraidState) 
  (hcoll : collapseFunctional (findCollisions state) = 0) :
  scarEnergy state > 0 := by
  -- Either collapse is structurally impossible (rigidity)
  -- Or it produces scar energy
  sorry
```

**Next steps:**
1. Add to `lakefile.toml` under `lean_libs`  
2. Create `SilverSight/0-Core-Formalism/lean/Semantics/FAMMBaker/`  
3. Wire into RRC alignment pipeline
