/-
  StructuralAttestation.lean - Mechanical Merkle Trees & Structural Cryptography
  Formalizes the bridge between physical structural integrity and computational validity.
  Based on Tech Note: Mechanical Merkle Tree (Proof-of-State).
-/
import Semantics.FixedPoint
import Semantics.Bind

namespace Semantics.StructuralAttestation

open Q16_16

/-- 
  A 6-axis stress vector representing strain gauge data.
  (σx, σy, σz, τxy, τyz, τzx)
-/
structure StressVector where
  sigmaX  : Q16_16
  sigmaY  : Q16_16
  sigmaZ  : Q16_16
  tauXY   : Q16_16
  tauYZ   : Q16_16
  tauZX   : Q16_16
deriving Repr, DecidableEq

/-- 
  A Mechanical Hash (structural signature).
  In hardware, this is derived via Blake3(vector).
  In the formal core, we use a sum-reduction for reachability proofs.
-/
def mechanicalHash (v : StressVector) : UInt32 :=
  v.sigmaX.val ^^^ v.sigmaY.val ^^^ v.sigmaZ.val ^^^ 
  v.tauXY.val ^^^ v.tauYZ.val ^^^ v.tauZX.val

/-- 
  A node in the Mechanical Merkle Tree.
  Each node has a local stress state and a combined hash of its children.
-/
inductive MechanicalMerkleTree
| leaf (id : Nat) (stress : StressVector)
| node (hash : UInt32) (left right : MechanicalMerkleTree)
deriving Repr

/-- Compute the root hash of a Mechanical Merkle Tree. -/
def rootHash : MechanicalMerkleTree → UInt32
| .leaf _ stress => mechanicalHash stress
| .node h _ _    => h

/-- 
  Build a node from two subtrees.
  Root hash is the XOR-sum of children's hashes (simplified hardware-native hash).
-/
def mkNode (l r : MechanicalMerkleTree) : MechanicalMerkleTree :=
  .node (rootHash l ^^^ rootHash r) l r

/-- 
  The Ideal Manifold: The target structural state (zero stress baseline).
-/
def idealManifoldHash : UInt32 := 0

/-- 
  Admissibility: A structural state is admissible if its root hash 
  is within the allowed stability epsilon of the ideal manifold.
-/
def isStructurallyAdmissible (tree : MechanicalMerkleTree) (epsilon : UInt32) : Bool :=
  let h := rootHash tree
  h <= epsilon -- Simplified stability check

/-- 
  The Security Veto: Computational results are only valid 
  if the physical structure is intact.
-/
def securityVeto (tree : MechanicalMerkleTree) (epsilon : UInt32) : Bool :=
  not (isStructurallyAdmissible tree epsilon)

/-- 
  Mechanical Bind: Chains structural integrity to semantic validity.
-/
def structuralBind (tree : MechanicalMerkleTree) (epsilon : UInt32) (g : Metric) : Bind MechanicalMerkleTree String :=
  controlBind tree "structural_attestation" g 
    (fun t _ _ => if isStructurallyAdmissible t epsilon then zero.val else one.val)
    (fun t => if isStructurallyAdmissible t epsilon then "structural_attestation" else "VETO:PHYSICAL_INTEGRITY_COMPROMISED")
    (fun t => t)

-- #eval Witness:
-- Healthy state (all zeros) vs Damaged state (high stress)
def healthyLeaf : MechanicalMerkleTree := .leaf 0 { sigmaX := zero, sigmaY := zero, sigmaZ := zero, tauXY := zero, tauYZ := zero, tauZX := zero }
def healthyTree : MechanicalMerkleTree := mkNode healthyLeaf healthyLeaf

def damagedLeaf : MechanicalMerkleTree := .leaf 1 { sigmaX := ⟨0xFFFFFFFF⟩, sigmaY := zero, sigmaZ := zero, tauXY := zero, tauYZ := zero, tauZX := zero }
def damagedTree : MechanicalMerkleTree := mkNode healthyLeaf damagedLeaf

#eval rootHash healthyTree
#eval rootHash damagedTree
#eval isStructurallyAdmissible damagedTree 1000

/-- 
  Theorem: Any change in structural state (leaf stress) 
  is reflected in the root hash.
-/
theorem structural_integrity_reflected (id : Nat) (s1 s2 : StressVector) (h : s1 ≠ s2) :
  mechanicalHash s1 ≠ mechanicalHash s2 := by
  -- This depends on the hash function properties.
  -- For XOR-sum it might have collisions, but for Blake3/formal proof we assume
  -- injectivity for the semantic model.
  -- TODO(lean-port): UNPROVABLE AS STATED. XOR-sum is NOT injective (collisions exist).
  -- Weakened theorem: single-component change guarantees hash change.
  sorry

/--
  Weakened version: a single-component change in stress is reflected in the hash.
  XOR is injective in each argument when the other is fixed.
  -/
theorem structural_integrity_reflected_single_component
    (s1 s2 : StressVector)
    (hX : s1.sigmaX ≠ s2.sigmaX)
    (hY : s1.sigmaY = s2.sigmaY)
    (hZ : s1.sigmaZ = s2.sigmaZ)
    (hXY : s1.tauXY = s2.tauXY)
    (hYZ : s1.tauYZ = s2.tauYZ)
    (hZX : s1.tauZX = s2.tauZX) :
    mechanicalHash s1 ≠ mechanicalHash s2 := by
  simp [mechanicalHash] at *
  intro h_eq
  rw [hY, hZ, hXY, hYZ, hZX] at h_eq
  have h_cancel : s1.sigmaX.val = s2.sigmaX.val := by
    apply (UInt32.xor_right_inj (s2.sigmaY.val ^^^ s2.sigmaZ.val ^^^ s2.tauXY.val ^^^ s2.tauYZ.val ^^^ s2.tauZX.val)).mp
    simp [UInt32.xor_comm] at h_eq ⊢
    exact h_eq
  have h_eq_stress : s1.sigmaX = s2.sigmaX := by
    have h1 : s1.sigmaX = ⟨s1.sigmaX.val⟩ := by cases s1.sigmaX; rfl
    have h2 : s2.sigmaX = ⟨s2.sigmaX.val⟩ := by cases s2.sigmaX; rfl
    rw [h1, h2, h_cancel]
  contradiction

end Semantics.StructuralAttestation
