chore: import upstream snapshot with attribution

lean/LeanCtxProofs/Handoff/StateMachine.lean

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+/-
+  LeanCTX Formal Verification — Agent Handoff State Machine
+
+  Formalizes the agent-to-agent handoff protocol as a state machine
+  with proven transition safety properties. Based on LeanMachines
+  methodology and VeriGuard offline verification pattern.
+
+  Mirrors: rust/src/core/a2a_transport.rs, handoff_ledger.rs
+  Reference: arXiv:2510.05156 (VeriGuard)
+-/
+import LeanCtxProofs.Basic
+
+namespace LeanCtxProofs.Handoff.StateMachine
+
+/-- Handoff lifecycle states. -/
+inductive HandoffState where
+  | idle
+  | preparing
+  | signed
+  | sent
+  | received
+  | accepted
+  | rejected
+  | completed
+  | failed
+  deriving DecidableEq, Repr
+
+/-- Events that drive state transitions. -/
+inductive HandoffEvent where
+  | prepare
+  | sign
+  | send
+  | receive
+  | accept
+  | reject
+  | complete
+  | fail
+  deriving DecidableEq, Repr
+
+/-- Transport content types. -/
+inductive ContentType where
+  | handoffBundle
+  | contextPackage
+  | a2aMessage
+  | a2aTask
+  deriving DecidableEq, Repr
+
+/-- Transport envelope validity requirements. -/
+structure EnvelopeInvariants where
+  hasValidSender : Bool
+  payloadNonEmpty : Bool
+  payloadWithinLimit : Bool
+  formatVersionValid : Bool
+  deriving DecidableEq, Repr
+
+/-- Check if an envelope satisfies all validity invariants. -/
+def envelopeValid (inv : EnvelopeInvariants) : Bool :=
+  inv.hasValidSender &&
+  inv.payloadNonEmpty &&
+  inv.payloadWithinLimit &&
+  inv.formatVersionValid
+
+/-- The state transition function. Returns none for invalid transitions. -/
+def transition (state : HandoffState) (event : HandoffEvent) : Option HandoffState :=
+  match state, event with
+  | .idle, .prepare => some .preparing
+  | .preparing, .sign => some .signed
+  | .preparing, .fail => some .failed
+  | .signed, .send => some .sent
+  | .signed, .fail => some .failed
+  | .sent, .receive => some .received
+  | .sent, .fail => some .failed
+  | .received, .accept => some .accepted
+  | .received, .reject => some .rejected
+  | .received, .fail => some .failed
+  | .accepted, .complete => some .completed
+  | .accepted, .fail => some .failed
+  | _, _ => none
+
+/-- Predicate for terminal states. -/
+def isTerminal (s : HandoffState) : Bool :=
+  match s with
+  | .completed => true
+  | .failed => true
+  | .rejected => true
+  | _ => false
+
+/-- Predicate for pre-send states. -/
+def isPreSend (s : HandoffState) : Bool :=
+  match s with
+  | .idle => true
+  | .preparing => true
+  | .signed => true
+  | _ => false
+
+-- ============================================================================
+-- Handoff State Machine Theorems
+-- ============================================================================
+
+/-- **Theorem 1: Terminal states have no valid outgoing transitions.** -/
+theorem terminal_is_sink (s : HandoffState) (e : HandoffEvent)
+    (h : isTerminal s = true) :
+    transition s e = none := by
+  cases s <;> cases e <;> simp [isTerminal] at h <;> simp [transition]
+
+/-- **Theorem 2: The idle state can only transition to preparing.** -/
+theorem idle_only_prepares (e : HandoffEvent)
+    (h : (transition .idle e).isSome = true) :
+    e = .prepare := by
+  cases e <;> simp [transition] at *
+
+/-- **Theorem 3: Sending requires a signed state (cannot skip signing).** -/
+theorem send_requires_signed (s : HandoffState)
+    (h : (transition s .send).isSome = true) :
+    s = .signed := by
+  cases s <;> simp [transition] at *
+
+/-- **Theorem 4: Accepting requires received state. -/
+theorem accept_requires_received (s : HandoffState)
+    (h : (transition s .accept).isSome = true) :
+    s = .received := by
+  cases s <;> simp [transition] at *
+
+/-- **Theorem 5: Completion requires acceptance. -/
+theorem complete_requires_accepted (s : HandoffState)
+    (h : (transition s .complete).isSome = true) :
+    s = .accepted := by
+  cases s <;> simp [transition] at *
+
+/-- **Theorem 6: The failure event is always valid except from idle and terminal states. -/
+theorem fail_from_active_states (s : HandoffState)
+    (h_active : !isTerminal s = true)
+    (h_not_idle : s ≠ .idle) :
+    (transition s .fail).isSome = true := by
+  cases s <;> simp [transition, isTerminal] at * <;> exact h_not_idle rfl
+
+/-- **Theorem 7: A valid transition sequence from idle to completed must pass
+    through all intermediate states.** -/
+theorem handoff_lifecycle_ordering :
+    transition .idle .prepare = some .preparing ∧
+    transition .preparing .sign = some .signed ∧
+    transition .signed .send = some .sent ∧
+    transition .sent .receive = some .received ∧
+    transition .received .accept = some .accepted ∧
+    transition .accepted .complete = some .completed := by
+  simp [transition]
+
+/-- **Theorem 8: Rejection is a terminal state.** -/
+theorem rejected_is_terminal : isTerminal .rejected = true := by rfl
+
+/-- **Theorem 9: A signed envelope that fails validation returns to failed.** -/
+theorem invalid_envelope_fails (_inv : EnvelopeInvariants)
+    (_h_invalid : envelopeValid _inv = false)
+    (s : HandoffState) (h_signed : s = .signed) :
+    transition s .fail = some .failed := by
+  rw [h_signed]; rfl
+
+/-- **Theorem 10: If envelope is valid and state is signed, send is possible.** -/
+theorem valid_envelope_enables_send (_inv : EnvelopeInvariants)
+    (_h_valid : envelopeValid _inv = true)
+    (s : HandoffState) (h_signed : s = .signed) :
+    (transition s .send).isSome = true := by
+  rw [h_signed]; simp [transition]
+
+end LeanCtxProofs.Handoff.StateMachine