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The 09-localhost ClientState maintains a single field used to track the latest sequence of the state machine i.e. the height of the blockchain. 
type ClientState struct {
  / the latest height of the blockchain
  LatestHeight clienttypes.Height
}
The 09-localhost ClientState is instantiated in the InitGenesis handler of the 02-client submodule in core IBC. It calls CreateLocalhostClient, declaring a new ClientState and initializing it with its own client prefixed store. 
func (k Keeper)

CreateLocalhostClient(ctx sdk.Context)

error {
    var clientState localhost.ClientState
  return clientState.Initialize(ctx, k.cdc, k.ClientStore(ctx, exported.LocalhostClientID), nil)
}
It is possible to disable the localhost client by removing the 09-localhost entry from the allowed_clients list through governance.

​
Client updates

The latest height is updated periodically through the ABCI BeginBlock interface of the 02-client submodule in core IBC. See BeginBlocker in abci.go. 
func BeginBlocker(ctx sdk.Context, k keeper.Keeper) {
  / ...
    if clientState, found := k.GetClientState(ctx, exported.Localhost); found {
    if k.GetClientStatus(ctx, clientState, exported.Localhost) == exported.Active {
    k.UpdateLocalhostClient(ctx, clientState)
}
 
}
}
The above calls into the 09-localhost UpdateState method of the ClientState . It retrieves the current block height from the application context and sets the LatestHeight of the 09-localhost client. 
func (cs ClientState)

UpdateState(ctx sdk.Context, cdc codec.BinaryCodec, clientStore sdk.KVStore, clientMsg exported.ClientMessage) []exported.Height {
    height := clienttypes.GetSelfHeight(ctx)

cs.LatestHeight = height

  clientStore.Set(host.ClientStateKey(), clienttypes.MustMarshalClientState(cdc, &cs))

return []exported.Height{
    height
}
}
Note that the 09-localhost ClientState is not updated through the 02-client interface leveraged by conventional IBC light clients.