diff --git a/Eip8282.lean b/Eip8282.lean
index 1e997a0..ac7f3ba 100644
--- a/Eip8282.lean
+++ b/Eip8282.lean
@@ -16,6 +16,7 @@ import Eip8282.Audit.Guarantees.PControl1.Excess
 import Eip8282.Audit.Guarantees.PControl1.Count
 import Eip8282.Audit.Guarantees.PControl1.Ctor
 import Eip8282.Audit.Reachable
+import Eip8282.Audit.SystemXiCorrespondence
 import Eip8282.Audit.AllGuarantees
 import Eip8282.Audit.XiTransport
 import Eip8282.Audit.Trust
diff --git a/Eip8282/Audit/SystemXiCorrespondence.lean b/Eip8282/Audit/SystemXiCorrespondence.lean
new file mode 100644
index 0000000..ce07e03
--- /dev/null
+++ b/Eip8282/Audit/SystemXiCorrespondence.lean
@@ -0,0 +1,152 @@
+import Eip8282.Audit.Correspondence
+import Eip8282.Audit.Guarantees.PSubmit1
+import Eip8282.Audit.Guarantees.PDrain1
+import Eip8282.Audit.Guarantees.PControl1
+import EvmYul.EVM.Proof.Block
+
+/-!
+# R3 — whole SYSTEM-call `Ξ` observational composition
+
+`RunUntil` composes the complete non-halting prefix from the SYSTEM-call entry
+to `RETURN` or `REVERT`; the terminating step then fixes the observation of
+`EvmYul.EVM.X` at entry.  Status and return bytes are observed, rather than
+claiming literal equality between EVM and model post-states.
+
+R1's `Represents` lives only on draft PR #21, so this main-based module uses
+the minimal relation needed by R3: the pinned predeploy account exists, has
+the pinned runtime, and abstracts to the given model state.  It intentionally
+does not duplicate R1's API or its proofs.
+
+`EndpointAgrees` remains an explicit premise.  Proving it for every SYSTEM
+calldata/storage path is the named OPEN `A-ABSTRACT-TX`; this module therefore
+does not close that assumption or strengthen any registered parent.
+-/
+
+namespace Eip8282.Audit.SystemXiCorrespondence
+
+open EvmYul EvmYul.EVM EvmYul.EVM.Proof
+open Eip8282.Audit.Model
+open Eip8282.Audit.WellFormed
+open Eip8282.Audit.Correspondence (runtimeCode targetAddr)
+
+/-- Minimal main-based R3 state relation, definitionally matching the core of
+R1's draft `Represents`: only the pinned predeploy account is observed. -/
+def Represents (kind : Kind) (world : EVM.State) (model : Model.State) : Prop :=
+  ∃ acc : Account .EVM,
+    world.accountMap.get? (targetAddr kind) = some acc ∧
+      acc.code = runtimeCode kind ∧
+      WellFormed kind acc.storage ∧
+      model = toModel kind acc.storage acc.balance.toNat
+
+structure Observation where
+  reverted : Bool
+  returnData : List Nat
+  deriving DecidableEq, Repr
+
+def bytes (data : ByteArray) : List Nat :=
+  (List.range data.size).map fun i => (data.get! i).toNat
+
+def observeΞ : Except EVM.ExecutionException (ExecutionResult EVM.State) →
+    Option Observation
+  | .ok (.success _ out) => some { reverted := false, returnData := bytes out }
+  | .ok (.revert _ out) => some { reverted := true, returnData := bytes out }
+  | .error _ => none
+
+def observeModel : Outcome → Observation
+  | .success _ out => { reverted := false, returnData := out }
+  | .revert _ => { reverted := true, returnData := [] }
+
+/-- Named open leaf of R3, covered by the existing `A-ABSTRACT-TX` ID. -/
+def EndpointAgrees (result : ExecutionResult EVM.State) (model : Outcome) : Prop :=
+  observeΞ (.ok result) = some (observeModel model)
+
+theorem whole_system_call_success
+    {validJumps : Array UInt256} {fuel rem gasCost : Nat}
+    {trace : List Labelled} {entry exit mid post : EVM.State}
+    {op : Operation .EVM} {arg : Option (UInt256 × Nat)} {out : ByteArray}
+    (hrun : RunUntil (fun w => Halting w) validJumps fuel entry trace (rem + 1) exit)
+    (hdecode : decodeAt exit = (op, arg))
+    (hZ : Z validJumps op exit = .ok (mid, gasCost))
+    (hstep : StepOk rem gasCost (op, arg) mid post)
+    (hH : H post.toMachineState op = some out)
+    (hop : op ≠ .REVERT) :
+    observeΞ (X fuel validJumps entry) =
+      some { reverted := false, returnData := bytes out } := by
+  rw [hrun.X_success hdecode hZ hstep hH hop]
+  rfl
+
+theorem whole_system_call_revert
+    {validJumps : Array UInt256} {fuel rem gasCost : Nat}
+    {trace : List Labelled} {entry exit mid post : EVM.State}
+    {op : Operation .EVM} {arg : Option (UInt256 × Nat)} {out : ByteArray}
+    (hrun : RunUntil (fun w => Halting w) validJumps fuel entry trace (rem + 1) exit)
+    (hdecode : decodeAt exit = (op, arg))
+    (hZ : Z validJumps op exit = .ok (mid, gasCost))
+    (hstep : StepOk rem gasCost (op, arg) mid post)
+    (hH : H post.toMachineState op = some out)
+    (hop : op = .REVERT) :
+    observeΞ (X fuel validJumps entry) =
+      some { reverted := true, returnData := bytes out } := by
+  rw [hrun.X_revert hdecode hZ hstep hH hop]
+  rfl
+
+/-- Whole SYSTEM-call correspondence, conditional exactly on the endpoint
+observation still tracked as `A-ABSTRACT-TX`. -/
+theorem whole_system_call_xi_correspondence
+    {kind : Kind} {world exit mid post : EVM.State} {model : Model.State}
+    {calldataNonempty : Bool}
+    {validJumps : Array UInt256} {fuel rem gasCost : Nat}
+    {trace : List Labelled} {op : Operation .EVM}
+    {arg : Option (UInt256 × Nat)} {out : ByteArray}
+    (_represents : Represents kind world model)
+    (hrun : RunUntil (fun w => Halting w) validJumps fuel world trace (rem + 1) exit)
+    (hdecode : decodeAt exit = (op, arg))
+    (hZ : Z validJumps op exit = .ok (mid, gasCost))
+    (hstep : StepOk rem gasCost (op, arg) mid post)
+    (hH : H post.toMachineState op = some out)
+    (hendpoint : EndpointAgrees
+      (if op = .REVERT then .revert post.gasAvailable out else .success post out)
+      (Model.step model (.system calldataNonempty))) :
+    observeΞ (X fuel validJumps world) =
+      some (observeModel (Model.step model (.system calldataNonempty))) := by
+  by_cases hop : op = .REVERT
+  · rw [whole_system_call_revert hrun hdecode hZ hstep hH hop]
+    simpa [EndpointAgrees, observeΞ, hop] using hendpoint
+  · rw [whole_system_call_success hrun hdecode hZ hstep hH hop]
+    simpa [EndpointAgrees, observeΞ, hop] using hendpoint
+
+/-- Exactly the three existing registered parents; R3 registers no new ID. -/
+def RegisteredParents : Prop :=
+  (type_of% Eip8282.Audit.Guarantees.PSubmit1.psubmit1_forall_parent) ∧
+  (type_of% Eip8282.Audit.Guarantees.PDrain1.pdrain1_forall_parent) ∧
+  (type_of% Eip8282.Audit.Guarantees.PControl1.pcontrol1_forall_parent)
+
+theorem registeredParents : RegisteredParents :=
+  ⟨Eip8282.Audit.Guarantees.PSubmit1.psubmit1_forall_parent,
+    Eip8282.Audit.Guarantees.PDrain1.pdrain1_forall_parent,
+    Eip8282.Audit.Guarantees.PControl1.pcontrol1_forall_parent⟩
+
+/-- R3 carries the unchanged registered parents alongside the SYSTEM-call
+observation. Their existing bytecode conjuncts and kill-lines are untouched. -/
+theorem whole_system_call_registered_correspondence
+    {kind : Kind} {world exit mid post : EVM.State} {model : Model.State}
+    {calldataNonempty : Bool}
+    {validJumps : Array UInt256} {fuel rem gasCost : Nat}
+    {trace : List Labelled} {op : Operation .EVM}
+    {arg : Option (UInt256 × Nat)} {out : ByteArray}
+    (rep : Represents kind world model)
+    (hrun : RunUntil (fun w => Halting w) validJumps fuel world trace (rem + 1) exit)
+    (hdecode : decodeAt exit = (op, arg))
+    (hZ : Z validJumps op exit = .ok (mid, gasCost))
+    (hstep : StepOk rem gasCost (op, arg) mid post)
+    (hH : H post.toMachineState op = some out)
+    (hendpoint : EndpointAgrees
+      (if op = .REVERT then .revert post.gasAvailable out else .success post out)
+      (Model.step model (.system calldataNonempty))) :
+    observeΞ (X fuel validJumps world) =
+        some (observeModel (Model.step model (.system calldataNonempty))) ∧
+      RegisteredParents :=
+  ⟨whole_system_call_xi_correspondence rep hrun hdecode hZ hstep hH hendpoint,
+    registeredParents⟩
+
+end Eip8282.Audit.SystemXiCorrespondence
diff --git a/Eip8282/Audit/Trust.lean b/Eip8282/Audit/Trust.lean
index 31d96c4..67eec43 100644
--- a/Eip8282/Audit/Trust.lean
+++ b/Eip8282/Audit/Trust.lean
@@ -1,6 +1,7 @@
 import Eip8282.Audit.Guarantees.PSubmit1
 import Eip8282.Audit.Guarantees.PDrain1
 import Eip8282.Audit.Guarantees.PControl1
+import Eip8282.Audit.SystemXiCorrespondence
 import Eip8282.Audit.Step
 import Eip8282.Audit.XiTransport
 import Eip8282.Audit.Reachable
@@ -248,3 +249,14 @@ open at HIGH.
 #print axioms Eip8282.Audit.XiTransport.pdrain1_xi_forall_parent
 #print axioms Eip8282.Audit.XiTransport.pcontrol1_xi_forall_parent
 #print axioms Eip8282.Audit.XiTransport.registered_parents_at_Xi
+
+/-! ## R3 — whole SYSTEM-call `Ξ` observational composition
+
+The endpoint premise is the existing named OPEN `A-ABSTRACT-TX`; it is a
+theorem argument, not a project axiom. -/
+
+#print axioms Eip8282.Audit.SystemXiCorrespondence.whole_system_call_success
+#print axioms Eip8282.Audit.SystemXiCorrespondence.whole_system_call_revert
+#print axioms Eip8282.Audit.SystemXiCorrespondence.whole_system_call_xi_correspondence
+#print axioms Eip8282.Audit.SystemXiCorrespondence.registeredParents
+#print axioms Eip8282.Audit.SystemXiCorrespondence.whole_system_call_registered_correspondence
diff --git a/audit/assumptions.yaml b/audit/assumptions.yaml
index dfb6b1f..8e20d57 100644
--- a/audit/assumptions.yaml
+++ b/audit/assumptions.yaml
@@ -14,7 +14,7 @@
       "justification": "The three registered parents remain CFG-direct foralls plus kill-line traces. R4 transports them to complete-Ξ observations only under EndpointAgrees. R5 proves constructor/call preservation and Model.Reachable entirely on the packed-storage/model side; it never runs Ξ and therefore does not discharge EndpointAgrees.",
       "severity": "HIGH",
       "violation_impact": "Any guarantee linked to this premise must be re-evaluated against assembly/bytecode. Because A-REACHABLE's residual now folds into this entry, a violation here also invalidates the claim that ReachableStorage describes the images the predeploys can actually reach — the containment proofs would remain true but would be about the wrong closure.",
-      "validation": "XiTransport.EndpointAgrees is a hypothesis of every conditional R4 transport and is never discharged. Eip8282.Audit.Reachable states that it never runs Ξ; Trust prints axioms for its closure theorems.",
+      "validation": "XiTransport.EndpointAgrees is a hypothesis of every conditional R4 transport and is never discharged. R3's Eip8282.Audit.SystemXiCorrespondence.EndpointAgrees is the same open leaf stated at the whole SYSTEM-call boundary and is likewise only ever a theorem argument, never proved. Eip8282.Audit.Reachable states that it never runs Ξ; Trust prints axioms for its closure theorems.",
       "removal_path": "Prove EndpointAgrees universally for the pinned runtimes, including that Ξ realises applyUser and applySystem on WellFormed images. R4 already closes the unconditional X-to-Ξ wrapper and jumpdest sublayers."
     },
     {