fix: small fixes

Author: jaybuidl

contracts/src/arbitration/KlerosCore.sol

@@ -1263,6 +1263,7 @@ contract KlerosCore is IArbitratorV2, Initializable, UUPSProxiable {
                 _dispute.courtID,
                 _court.parent,
                 _court.jurorsForCourtJump,
+                disputeKitID,
                 _round.nbVotes
             );
 
@@ -1271,6 +1272,7 @@ contract KlerosCore is IArbitratorV2, Initializable, UUPSProxiable {
             // Fall back to `DisputeKitClassic` which is always supported.
             newDisputeKitID = DISPUTE_KIT_CLASSIC;
             disputeKitJump = (newDisputeKitID != disputeKitID);
+            newRoundNbVotes = (newRoundNbVotes * 2) + 1; // Reset nbVotes to the default logic.
         }
     }
 

contracts/src/arbitration/dispute-kits/DisputeKitClassicBase.sol

@@ -633,6 +633,7 @@ abstract contract DisputeKitClassicBase is IDisputeKit, Initializable, UUPSProxi
         uint96 _currentCourtID,
         uint96 _parentCourtID,
         uint256 _currentCourtJurorsForJump,
+        uint256 _currentDisputeKitID,
         uint256 _currentRoundNbVotes
     )
         public
@@ -665,7 +666,10 @@ abstract contract DisputeKitClassicBase is IDisputeKit, Initializable, UUPSProxi
             newCourtID = courtJump ? _parentCourtID : _currentCourtID;
         }
         if (newDisputeKitID == 0) {
-            newDisputeKitID = DISPUTE_KIT_CLASSIC;
+            newDisputeKitID = _currentDisputeKitID;
+        }
+        if (!disputeKitJump) {
+            disputeKitJump = (newDisputeKitID != _currentDisputeKitID);
         }
     }
 

contracts/src/arbitration/interfaces/IDisputeKit.sol

@@ -130,6 +130,7 @@ interface IDisputeKit {
     /// @param _currentCourtID The ID of the current court.
     /// @param _parentCourtID The ID of the parent court.
     /// @param _currentCourtJurorsForJump The court jump threshold defined by the current court.
+    /// @param _currentDisputeKitID The ID of the current dispute kit.
     /// @param _currentRoundNbVotes The number of votes in the current round.
     /// @return newCourtID Court ID after jump.
     /// @return newDisputeKitID Dispute kit ID after jump.
@@ -141,6 +142,7 @@ interface IDisputeKit {
         uint96 _currentCourtID,
         uint96 _parentCourtID,
         uint256 _currentCourtJurorsForJump,
+        uint256 _currentDisputeKitID,
         uint256 _currentRoundNbVotes
     )
         external