feat(lean4): add formal verification specs for ensemble models

Lean 4 formalization of the decision tree + MLP ensemble architecture.
Axiomatizes Float properties (sigmoid bounds, ReLU nonnegativity) since
Lean's Float ops are extern-backed. Proves MLP output is bounded in (0,1)
and ensemble output is always a valid decision. No mathlib dependency.

Signed-off-by: Sienna Meridian Satterwhite <sienna@sunbeam.pt>

lean4/Sunbeam/Model/Sigmoid.lean

@@ -0,0 +1,29 @@
+import Sunbeam.Model.Basic
+
+namespace Sunbeam
+
+/-- The sigmoid function σ(x) = 1 / (1 + exp(-x)). -/
+def sigmoid (x : Float) : Float :=
+  1.0 / (1.0 + Float.exp (-x))
+
+/-! ## Trust boundary: sigmoid axioms
+
+These axioms capture IEEE-754 properties of sigmoid that hold for all finite
+float inputs. They cannot be proved inside Lean because `Float` operations are
+`@[extern]` (opaque to the kernel). The axioms form a documented trust boundary:
+we trust the C runtime's `exp` implementation.
+
+When TorchLean ships its verified Float32 kernel, these axioms can be replaced
+with proofs against that kernel.
+-/
+
+/-- Sigmoid output is always positive: exp(-x) ≥ 0 ⟹ 1+exp(-x) ≥ 1 ⟹ 1/(1+exp(-x)) > 0. -/
+axiom sigmoid_pos (x : Float) : sigmoid x > 0
+
+/-- Sigmoid output is always less than 1: 1+exp(-x) > 1 ⟹ 1/(1+exp(-x)) < 1. -/
+axiom sigmoid_lt_one (x : Float) : sigmoid x < 1
+
+/-- Sigmoid is monotonically increasing (derivative = σ(1-σ) > 0). -/
+axiom sigmoid_monotone {x y : Float} (h : x ≤ y) : sigmoid x ≤ sigmoid y
+
+end Sunbeam