diff --git a/docs/protocols/alpha.rst b/docs/protocols/alpha.rst
index a3ac166308d42747d314754fc03b005f0987328a..1ca7866abd68facdf966676e734a259737cc68a2 100644
--- a/docs/protocols/alpha.rst
+++ b/docs/protocols/alpha.rst
@@ -91,6 +91,17 @@ Breaking Changes
   baker's spendable balance to their frozen deposits. Bakers need to use the
   ``stake`` pseudo-operation to increase their frozen deposits. (MR :gl:`!8087`)
 
+- The Exponential Moving Average of the Liquidity Baking Toggle Vote
+  is now represented on 64 bits (instead of 32 bits in previous
+  versions of the protocol). This affects the binary and JSON
+  encodings of block receipts, the
+  ``liquidity_baking_toggle_ema_threshold`` parameter, and the
+  ``liquidity_baking_escape_ema`` field of the context. Note that in
+  JSON, 32-bit integers are represented as JSON numbers but 64-bit
+  integers are represented as JSON strings. (MR :gl:`!8987`)
+
+- The context field ``liquidity_baking_escape_ema`` is renamed
+  ``liquidity_baking_toggle_ema``. (MR :gl:`!8987`)
 
 RPC Changes
 -----------
diff --git a/src/proto_alpha/lib_parameters/default_parameters.ml b/src/proto_alpha/lib_parameters/default_parameters.ml
index 084af2915bbee3d5579e5180a191e6e5d221a112..e356a0ea0fa2b6cd4efd0c3ee6c308fd3ed0e9f7 100644
--- a/src/proto_alpha/lib_parameters/default_parameters.ml
+++ b/src/proto_alpha/lib_parameters/default_parameters.ml
@@ -163,7 +163,7 @@ let constants_mainnet =
     min_proposal_quorum = 5_00l;
     (* 1/2 window size of 2000 blocks with precision of 1_000_000
        for integer computation *)
-    liquidity_baking_toggle_ema_threshold = 1_000_000_000l;
+    liquidity_baking_toggle_ema_threshold = 1_000_000_000L;
     (* The rationale behind the value of this constant is that an
        operation should be considered alive for about one hour:
 
diff --git a/src/proto_alpha/lib_protocol/alpha_context.mli b/src/proto_alpha/lib_protocol/alpha_context.mli
index ed61572120d77f66abae2511c41823f271f03bd2..4bfabb1194e9d88cb2b0b89fa34bd0352e17b325 100644
--- a/src/proto_alpha/lib_protocol/alpha_context.mli
+++ b/src/proto_alpha/lib_protocol/alpha_context.mli
@@ -875,7 +875,7 @@ module Constants : sig
       quorum_min : int32;
       quorum_max : int32;
       min_proposal_quorum : int32;
-      liquidity_baking_toggle_ema_threshold : int32;
+      liquidity_baking_toggle_ema_threshold : int64;
       max_operations_time_to_live : int;
       minimal_block_delay : Period.t;
       delay_increment_per_round : Period.t;
@@ -952,7 +952,7 @@ module Constants : sig
 
   val min_proposal_quorum : context -> int32
 
-  val liquidity_baking_toggle_ema_threshold : context -> int32
+  val liquidity_baking_toggle_ema_threshold : context -> int64
 
   val minimal_block_delay : context -> Period.t
 
@@ -4692,7 +4692,7 @@ module Toggle_EMA : sig
 
   val zero : t
 
-  val to_int32 : t -> Int32.t
+  val to_int64 : t -> Int64.t
 
   val encoding : t Data_encoding.t
 end
diff --git a/src/proto_alpha/lib_protocol/constants_parametric_repr.ml b/src/proto_alpha/lib_protocol/constants_parametric_repr.ml
index 9ae4402ed0708807d8a81d200a68066e656bddd8..0f8434b425268fa325bdfe8899dd8c791c3ff186 100644
--- a/src/proto_alpha/lib_protocol/constants_parametric_repr.ml
+++ b/src/proto_alpha/lib_protocol/constants_parametric_repr.ml
@@ -158,7 +158,7 @@ type t = {
   quorum_min : int32;
   quorum_max : int32;
   min_proposal_quorum : int32;
-  liquidity_baking_toggle_ema_threshold : int32;
+  liquidity_baking_toggle_ema_threshold : int64;
   max_operations_time_to_live : int;
   minimal_block_delay : Period_repr.t;
   delay_increment_per_round : Period_repr.t;
@@ -545,7 +545,7 @@ let encoding =
              (obj8
                 (req "quorum_max" int32)
                 (req "min_proposal_quorum" int32)
-                (req "liquidity_baking_toggle_ema_threshold" int32)
+                (req "liquidity_baking_toggle_ema_threshold" int64)
                 (req "max_operations_time_to_live" int16)
                 (req "minimal_block_delay" Period_repr.encoding)
                 (req "delay_increment_per_round" Period_repr.encoding)
diff --git a/src/proto_alpha/lib_protocol/constants_parametric_repr.mli b/src/proto_alpha/lib_protocol/constants_parametric_repr.mli
index f90cd43a6988800d2addcaee705b2253b36b920d..f9c9c40b7e08822abb645190720b7dcc4adc113c 100644
--- a/src/proto_alpha/lib_protocol/constants_parametric_repr.mli
+++ b/src/proto_alpha/lib_protocol/constants_parametric_repr.mli
@@ -183,7 +183,7 @@ type t = {
   (* in centile of a percentage *)
   quorum_max : int32;
   min_proposal_quorum : int32;
-  liquidity_baking_toggle_ema_threshold : int32;
+  liquidity_baking_toggle_ema_threshold : int64;
   max_operations_time_to_live : int;
   minimal_block_delay : Period_repr.t;
   delay_increment_per_round : Period_repr.t;
diff --git a/src/proto_alpha/lib_protocol/constants_storage.mli b/src/proto_alpha/lib_protocol/constants_storage.mli
index 43093986d2402ddc608d8fbceb7e7aa705c4ee63..d4820eed64d8a48d97bad839589cd5e42bd005da 100644
--- a/src/proto_alpha/lib_protocol/constants_storage.mli
+++ b/src/proto_alpha/lib_protocol/constants_storage.mli
@@ -66,7 +66,7 @@ val quorum_max : Raw_context.t -> int32
 
 val min_proposal_quorum : Raw_context.t -> int32
 
-val liquidity_baking_toggle_ema_threshold : Raw_context.t -> int32
+val liquidity_baking_toggle_ema_threshold : Raw_context.t -> int64
 
 val parametric : Raw_context.t -> Constants_parametric_repr.t
 
diff --git a/src/proto_alpha/lib_protocol/init_storage.ml b/src/proto_alpha/lib_protocol/init_storage.ml
index 6ece1c93ed0be58a54de80087dc96a1a4a9828d5..f9ce84c704c8fc73946c867ab133409d68d0719f 100644
--- a/src/proto_alpha/lib_protocol/init_storage.ml
+++ b/src/proto_alpha/lib_protocol/init_storage.ml
@@ -151,6 +151,44 @@ let initialize_total_supply_for_o ctxt =
     ctxt
     (Tez_repr.of_mutez_exn 940_000_000_000_000L)
 
+(** Migration of the context field storing the Liquidity Baking
+    EMA. The key of the field is renamed from
+    "liquidity_baking_escape_ema" to "liquidity_baking_toggle_ema" and
+    it is now stored on an int64 instead of an int32. *)
+let migrate_liquidity_baking_ema ctxt =
+  let legacy_key = ["liquidity_baking_escape_ema"] in
+  let get_and_remove_legacy_field ctxt =
+    Raw_context.get ctxt legacy_key >>=? fun ema_bytes ->
+    Raw_context.remove_existing ctxt legacy_key >>=? fun ctxt ->
+    return (ctxt, ema_bytes)
+  in
+  (get_and_remove_legacy_field ctxt >|= function
+   | Ok (ctxt, ema_bytes) -> (
+       match
+         Data_encoding.Binary.of_bytes_opt Data_encoding.int32 ema_bytes
+       with
+       | Some ema_i32 -> (ctxt, ema_i32)
+       | None ->
+           Logging.log
+             Logging.Error
+             "Migration of Liquidity Baking EMA: decoding error, the field %S \
+              was expected to be an int32 but it is %a. Defaulting to 0."
+             (String.concat "/" legacy_key)
+             Hex.pp
+             (Hex.of_bytes ema_bytes) ;
+           (ctxt, 0l))
+   | Error trace ->
+       Logging.log
+         Logging.Error
+         "%a@.Migration of Liquidity Baking EMA: the key %S was not found in \
+          context so defaulting to 0."
+         pp_trace
+         trace
+         (String.concat "/" legacy_key) ;
+       (ctxt, 0l))
+  >>= fun (ctxt, ema_i32) ->
+  Storage.Liquidity_baking.Toggle_ema.init ctxt (Int64.of_int32 ema_i32)
+
 let prepare_first_block _chain_id ctxt ~typecheck_smart_contract
     ~typecheck_smart_rollup ~level ~timestamp ~predecessor =
   Raw_context.prepare_first_block ~level ~timestamp ctxt
@@ -232,7 +270,8 @@ let prepare_first_block _chain_id ctxt ~typecheck_smart_contract
       migrate_stake_distribution_for_o ctxt >>=? fun ctxt ->
       initialize_total_supply_for_o ctxt >>= fun ctxt ->
       Remove_zero_amount_ticket_migration_for_o.remove_zero_ticket_entries ctxt
-      >>= fun ctxt -> return (ctxt, []))
+      >>= fun ctxt ->
+      migrate_liquidity_baking_ema ctxt >>=? fun ctxt -> return (ctxt, []))
   >>=? fun (ctxt, balance_updates) ->
   List.fold_left_es patch_script ctxt Legacy_script_patches.addresses_to_patch
   >>=? fun ctxt ->
diff --git a/src/proto_alpha/lib_protocol/liquidity_baking_migration.ml b/src/proto_alpha/lib_protocol/liquidity_baking_migration.ml
index 59a8eb2c654908aa7ef58e382f4b65080f1fb10c..bdce19c0b1c9a79727cf666e80c6261a1c6a8bb0 100644
--- a/src/proto_alpha/lib_protocol/liquidity_baking_migration.ml
+++ b/src/proto_alpha/lib_protocol/liquidity_baking_migration.ml
@@ -198,7 +198,7 @@ let init ctxt ~typecheck =
   (* We use a custom origination nonce because it is unset when stitching from 009 *)
   let nonce = Operation_hash.hash_string ["Drip, drip, drip."] in
   let ctxt = Raw_context.init_origination_nonce ctxt nonce in
-  Storage.Liquidity_baking.Toggle_ema.init ctxt 0l >>=? fun ctxt ->
+  Storage.Liquidity_baking.Toggle_ema.init ctxt 0L >>=? fun ctxt ->
   let current_level =
     Raw_level_repr.to_int32 (Level_storage.current ctxt).level
   in
diff --git a/src/proto_alpha/lib_protocol/liquidity_baking_storage.ml b/src/proto_alpha/lib_protocol/liquidity_baking_storage.ml
index 7dd169ceb5c7188002ffa020a74305d3a02b70b5..2c416fd82f8b4728a988dd9145fc817bbe896f88 100644
--- a/src/proto_alpha/lib_protocol/liquidity_baking_storage.ml
+++ b/src/proto_alpha/lib_protocol/liquidity_baking_storage.ml
@@ -30,7 +30,7 @@ let get_cpmm_address = Storage.Liquidity_baking.Cpmm_address.get
 
 let get_toggle_ema ctxt =
   Storage.Liquidity_baking.Toggle_ema.get ctxt >>=? fun ema ->
-  Toggle_EMA.of_int32 ema
+  Toggle_EMA.of_int64 ema
 
 let on_cpmm_exists ctxt f =
   get_cpmm_address ctxt >>=? fun cpmm_contract ->
@@ -44,7 +44,7 @@ let on_cpmm_exists ctxt f =
 let update_toggle_ema ctxt ~toggle_vote =
   get_toggle_ema ctxt >>=? fun old_ema ->
   let new_ema = compute_new_ema ~toggle_vote old_ema in
-  Storage.Liquidity_baking.Toggle_ema.update ctxt (Toggle_EMA.to_int32 new_ema)
+  Storage.Liquidity_baking.Toggle_ema.update ctxt (Toggle_EMA.to_int64 new_ema)
   >|=? fun ctxt -> (ctxt, new_ema)
 
 let check_ema_below_threshold ctxt ema =
diff --git a/src/proto_alpha/lib_protocol/raw_context.ml b/src/proto_alpha/lib_protocol/raw_context.ml
index 8833613bf244d1da21b4fb047eef267abf502e6e..fcec1fb08537c40bbe67918d75832eb565da3e51 100644
--- a/src/proto_alpha/lib_protocol/raw_context.ml
+++ b/src/proto_alpha/lib_protocol/raw_context.ml
@@ -1052,7 +1052,7 @@ let prepare_first_block ~level ~timestamp ctxt =
             quorum_max = c.quorum_max;
             min_proposal_quorum = c.min_proposal_quorum;
             liquidity_baking_toggle_ema_threshold =
-              c.liquidity_baking_toggle_ema_threshold;
+              Int64.of_int32 c.liquidity_baking_toggle_ema_threshold;
             minimal_block_delay = c.minimal_block_delay;
             delay_increment_per_round = c.delay_increment_per_round;
             consensus_committee_size = c.consensus_committee_size;
diff --git a/src/proto_alpha/lib_protocol/storage.ml b/src/proto_alpha/lib_protocol/storage.ml
index 9e8e5acdbd831d5e27e54e19bf5000dcd9d459a6..0e927688dba14e53dd91d719e6414802b1159a16 100644
--- a/src/proto_alpha/lib_protocol/storage.ml
+++ b/src/proto_alpha/lib_protocol/storage.ml
@@ -1599,10 +1599,9 @@ module Liquidity_baking = struct
   module Toggle_ema =
     Make_single_data_storage (Registered) (Raw_context)
       (struct
-        (* The old "escape" name is kept here to avoid migrating this. *)
-        let name = ["liquidity_baking_escape_ema"]
+        let name = ["liquidity_baking_toggle_ema"]
       end)
-      (Encoding.Int32)
+      (Encoding.Int64)
 
   module Cpmm_address =
     Make_single_data_storage (Registered) (Raw_context)
diff --git a/src/proto_alpha/lib_protocol/storage.mli b/src/proto_alpha/lib_protocol/storage.mli
index 79e21499d427b545ed216e60ce0d3609f5b0ab33..d050121895fde2a59206d139a1845cb212cf000a 100644
--- a/src/proto_alpha/lib_protocol/storage.mli
+++ b/src/proto_alpha/lib_protocol/storage.mli
@@ -693,7 +693,7 @@ module Liquidity_baking : sig
     The liquidity baking subsidy is not sent to the CPMM if this EMA is above
     the threshold set in constants. **)
   module Toggle_ema :
-    Single_data_storage with type t := Raw_context.t and type value = Int32.t
+    Single_data_storage with type t := Raw_context.t and type value = Int64.t
 
   (** Constant product market maker contract that receives liquidity baking subsidy. **)
   module Cpmm_address :
diff --git a/src/proto_alpha/lib_protocol/test/helpers/assert.ml b/src/proto_alpha/lib_protocol/test/helpers/assert.ml
index 4e491c3b294741829e0c40583ddcc4c50954858c..d2da6c5c26b7803aca1814b0306dde2badec69bd 100644
--- a/src/proto_alpha/lib_protocol/test/helpers/assert.ml
+++ b/src/proto_alpha/lib_protocol/test/helpers/assert.ml
@@ -136,6 +136,9 @@ let not_equal_int64 ~loc (a : int64) (b : int64) =
 let leq_int64 ~loc (a : int64) (b : int64) =
   leq ~loc Compare.Int64.compare "Int64 comparison" Int64.pp a b
 
+let lt_int64 ~loc (a : int64) (b : int64) =
+  lt ~loc Compare.Int64.compare "Int64 comparison" Int64.pp a b
+
 let equal_z ~loc (a : Z.t) (b : Z.t) =
   equal ~loc Compare.Z.( = ) "Z are not equal" Z.pp_print a b
 
diff --git a/src/proto_alpha/lib_protocol/test/integration/test_liquidity_baking.ml b/src/proto_alpha/lib_protocol/test/integration/test_liquidity_baking.ml
index 9a63b0b546d329fe7b2374cb93acbdefeb028258..1c51c7e0c3257d19fb6adb3142226df8adef274b 100644
--- a/src/proto_alpha/lib_protocol/test/integration/test_liquidity_baking.ml
+++ b/src/proto_alpha/lib_protocol/test/integration/test_liquidity_baking.ml
@@ -257,7 +257,7 @@ let liquidity_baking_toggle_ema n_vote_on n_vote_off level bake_after
   >>=? fun (_blk, toggle_ema) ->
   Assert.leq_int
     ~loc:__LOC__
-    (toggle_ema |> Alpha_context.Toggle_EMA.to_int32 |> Int32.to_int)
+    (toggle_ema |> Alpha_context.Toggle_EMA.to_int64 |> Int64.to_int)
     expected_toggle_ema
   >>=? fun () -> return_unit
 
diff --git a/src/proto_alpha/lib_protocol/test/unit/test_liquidity_baking_repr.ml b/src/proto_alpha/lib_protocol/test/unit/test_liquidity_baking_repr.ml
index 11bd5db88e18de3f6c2b9800d78bfbd97c0264de..e3eee00daa1a2bb2fd724c789f72f00920ad9620 100644
--- a/src/proto_alpha/lib_protocol/test/unit/test_liquidity_baking_repr.ml
+++ b/src/proto_alpha/lib_protocol/test/unit/test_liquidity_baking_repr.ml
@@ -33,12 +33,12 @@
 
 open Protocol
 
-let ema_of_int32 ema = Toggle_EMA.of_int32 ema >|= Environment.wrap_tzresult
+let ema_of_int64 ema = Toggle_EMA.of_int64 ema >|= Environment.wrap_tzresult
 
-let ema_to_int32 = Toggle_EMA.to_int32
+let ema_to_int64 = Toggle_EMA.to_int64
 
 let compute_new_ema ~toggle_vote ema =
-  Toggle_votes_repr.compute_new_ema ~toggle_vote ema |> ema_to_int32
+  Toggle_votes_repr.compute_new_ema ~toggle_vote ema |> ema_to_int64
 
 (* Folds compute_new_ema on a list of votes *)
 let compute_new_ema_n toggle_votes initial_ema =
@@ -46,55 +46,55 @@ let compute_new_ema_n toggle_votes initial_ema =
     (fun ema toggle_vote -> Toggle_votes_repr.compute_new_ema ~toggle_vote ema)
     initial_ema
     toggle_votes
-  |> ema_to_int32
+  |> ema_to_int64
 
 let ema_range =
   [
-    0l;
-    1l;
-    10l;
-    100l;
-    1000l;
-    10_000l;
-    100_000l;
-    1_000_000l;
-    10_000_000l;
-    100_000_000l;
-    200_000_000l;
-    300_000_000l;
-    400_000_000l;
-    500_000_000l;
-    600_000_000l;
-    760_000_000l;
-    800_000_000l;
-    900_000_000l;
-    1_000_000_000l;
-    1_100_000_000l;
-    1_200_000_000l;
-    1_300_000_000l;
-    1_400_000_000l;
-    1_500_000_000l;
-    1_600_000_000l;
-    1_700_000_000l;
-    1_800_000_000l;
-    1_900_000_000l;
-    1_990_000_000l;
-    1_999_000_000l;
-    1_999_900_000l;
-    1_999_990_000l;
-    1_999_999_000l;
-    1_999_999_900l;
-    1_999_999_990l;
-    1_999_999_999l;
-    2_000_000_000l;
+    0L;
+    1L;
+    10L;
+    100L;
+    1000L;
+    10_000L;
+    100_000L;
+    1_000_000L;
+    10_000_000L;
+    100_000_000L;
+    200_000_000L;
+    300_000_000L;
+    400_000_000L;
+    500_000_000L;
+    600_000_000L;
+    760_000_000L;
+    800_000_000L;
+    900_000_000L;
+    1_000_000_000L;
+    1_100_000_000L;
+    1_200_000_000L;
+    1_300_000_000L;
+    1_400_000_000L;
+    1_500_000_000L;
+    1_600_000_000L;
+    1_700_000_000L;
+    1_800_000_000L;
+    1_900_000_000L;
+    1_990_000_000L;
+    1_999_000_000L;
+    1_999_900_000L;
+    1_999_990_000L;
+    1_999_999_000L;
+    1_999_999_900L;
+    1_999_999_990L;
+    1_999_999_999L;
+    2_000_000_000L;
   ]
 
 (* Test that new_ema = old_ema when voting Pass. *)
 let test_ema_pass () =
   List.iter_es
     (fun old_ema ->
-      ema_of_int32 old_ema >>=? fun ema ->
-      Assert.equal_int32
+      ema_of_int64 old_ema >>=? fun ema ->
+      Assert.equal_int64
         ~loc:__LOC__
         (compute_new_ema ~toggle_vote:Toggle_vote_pass ema)
         old_ema)
@@ -104,10 +104,10 @@ let test_ema_pass () =
 let test_ema_in_bound_off () =
   List.iter_es
     (fun old_ema ->
-      ema_of_int32 old_ema >>=? fun ema ->
+      ema_of_int64 old_ema >>=? fun ema ->
       let new_ema = compute_new_ema ~toggle_vote:Toggle_vote_off ema in
-      Assert.leq_int32 ~loc:__LOC__ 0l new_ema >>=? fun () ->
-      Assert.leq_int32 ~loc:__LOC__ new_ema 2_000_000_000l)
+      Assert.leq_int64 ~loc:__LOC__ 0L new_ema >>=? fun () ->
+      Assert.leq_int64 ~loc:__LOC__ new_ema 2_000_000_000L)
     ema_range
 
 (* Test that new_ema > old_ema when voting Off, except if old_ema is
@@ -115,32 +115,32 @@ let test_ema_in_bound_off () =
 let test_ema_increases_off () =
   List.iter_es
     (fun old_ema ->
-      ema_of_int32 old_ema >>=? fun ema ->
-      Assert.lt_int32
+      ema_of_int64 old_ema >>=? fun ema ->
+      Assert.lt_int64
         ~loc:__LOC__
         old_ema
         (compute_new_ema ~toggle_vote:Toggle_vote_off ema))
-    (List.filter (fun ema -> Compare.Int32.(ema < 1_999_999_000l)) ema_range)
+    (List.filter (fun ema -> Compare.Int64.(ema < 1_999_999_000L)) ema_range)
 
 (* Test that the increase in EMA caused by an Off vote is bounded by 1,000,000 *)
 let test_ema_increases_off_bound () =
   List.iter_es
     (fun old_ema ->
-      ema_of_int32 old_ema >>=? fun ema ->
-      Assert.leq_int32
+      ema_of_int64 old_ema >>=? fun ema ->
+      Assert.leq_int64
         ~loc:__LOC__
-        (Int32.sub (compute_new_ema ~toggle_vote:Toggle_vote_off ema) old_ema)
-        1_000_000l)
+        (Int64.sub (compute_new_ema ~toggle_vote:Toggle_vote_off ema) old_ema)
+        1_000_000L)
     ema_range
 
 (* Test that new_ema is still between 0 and 2,000,000,000 after an Off vote. *)
 let test_ema_in_bound_on () =
   List.iter_es
     (fun old_ema ->
-      ema_of_int32 old_ema >>=? fun ema ->
+      ema_of_int64 old_ema >>=? fun ema ->
       let new_ema = compute_new_ema ~toggle_vote:Toggle_vote_on ema in
-      Assert.leq_int32 ~loc:__LOC__ 0l new_ema >>=? fun () ->
-      Assert.leq_int32 ~loc:__LOC__ new_ema 2_000_000_000l)
+      Assert.leq_int64 ~loc:__LOC__ 0L new_ema >>=? fun () ->
+      Assert.leq_int64 ~loc:__LOC__ new_ema 2_000_000_000L)
     ema_range
 
 (* Test that new_ema < old_ema when voting On, except if old_ema is
@@ -148,38 +148,38 @@ let test_ema_in_bound_on () =
 let test_ema_decreases_on () =
   List.iter_es
     (fun old_ema ->
-      ema_of_int32 old_ema >>=? fun ema ->
-      Assert.lt_int32
+      ema_of_int64 old_ema >>=? fun ema ->
+      Assert.lt_int64
         ~loc:__LOC__
         (compute_new_ema ~toggle_vote:Toggle_vote_on ema)
         old_ema)
-    (List.filter (fun ema -> Compare.Int32.(ema > 1000l)) ema_range)
+    (List.filter (fun ema -> Compare.Int64.(ema > 1000L)) ema_range)
 
 (* Test that the decrease in EMA caused by an On vote is bounded by 1,000,000 *)
 let test_ema_decreases_on_bound () =
   List.iter_es
     (fun old_ema ->
-      ema_of_int32 old_ema >>=? fun ema ->
-      Assert.leq_int32
+      ema_of_int64 old_ema >>=? fun ema ->
+      Assert.leq_int64
         ~loc:__LOC__
-        (Int32.sub (compute_new_ema ~toggle_vote:Toggle_vote_on ema) old_ema)
-        1_000_000l)
+        (Int64.sub (compute_new_ema ~toggle_vote:Toggle_vote_on ema) old_ema)
+        1_000_000L)
     ema_range
 
 (* Test that 1385 Off votes are needed to reach the threshold from 0. *)
 let test_ema_many_off () =
   let open Toggle_votes_repr in
-  ema_of_int32 0l >>=? fun initial_ema ->
-  Assert.leq_int32
+  ema_of_int64 0L >>=? fun initial_ema ->
+  Assert.leq_int64
     ~loc:__LOC__
     (compute_new_ema_n
        (Stdlib.List.init 1385 (fun _ -> Toggle_vote_off))
        initial_ema)
-    1_000_000_000l
+    1_000_000_000L
   >>=? fun () ->
-  Assert.leq_int32
+  Assert.leq_int64
     ~loc:__LOC__
-    1_000_000_000l
+    1_000_000_000L
     (compute_new_ema_n
        (Stdlib.List.init 1386 (fun _ -> Toggle_vote_off))
        initial_ema)
@@ -187,20 +187,20 @@ let test_ema_many_off () =
 (* Test that 1385 On votes are needed to reach the threshold from the max value of the EMA (2,000,000,000). *)
 let test_ema_many_on () =
   let open Toggle_votes_repr in
-  ema_of_int32 2_000_000_000l >>=? fun initial_ema ->
-  Assert.leq_int32
+  ema_of_int64 2_000_000_000L >>=? fun initial_ema ->
+  Assert.leq_int64
     ~loc:__LOC__
-    1_000_000_000l
+    1_000_000_000L
     (compute_new_ema_n
        (Stdlib.List.init 1385 (fun _ -> Toggle_vote_on))
        initial_ema)
   >>=? fun () ->
-  Assert.leq_int32
+  Assert.leq_int64
     ~loc:__LOC__
     (compute_new_ema_n
        (Stdlib.List.init 1386 (fun _ -> Toggle_vote_on))
        initial_ema)
-    1_000_000_000l
+    1_000_000_000L
 
 (* Test that the EMA update function is symmetric:
    from two dual values of the EMA (that is, two values x and y such that
@@ -210,17 +210,17 @@ let test_ema_many_on () =
 let test_ema_symmetry () =
   List.iter_es
     (fun ema ->
-      let opposite_ema = Int32.(sub 2_000_000_000l ema) in
-      ema_of_int32 ema >>=? fun ema ->
-      ema_of_int32 opposite_ema >>=? fun opposite_ema ->
+      let opposite_ema = Int64.(sub 2_000_000_000L ema) in
+      ema_of_int64 ema >>=? fun ema ->
+      ema_of_int64 opposite_ema >>=? fun opposite_ema ->
       let new_ema = compute_new_ema ~toggle_vote:Toggle_vote_on ema in
       let new_opposite_ema =
         compute_new_ema ~toggle_vote:Toggle_vote_off opposite_ema
       in
-      Assert.equal_int32
+      Assert.equal_int64
         ~loc:__LOC__
-        Int32.(add new_ema new_opposite_ema)
-        2_000_000_000l)
+        Int64.(add new_ema new_opposite_ema)
+        2_000_000_000L)
     ema_range
 
 let tests =
diff --git a/src/proto_alpha/lib_protocol/toggle_EMA.ml b/src/proto_alpha/lib_protocol/toggle_EMA.ml
index ab3fb3c5d0cfade3c8d3383080a719ad220e3180..86ff588368eda6fed6f61fad72418a7b379e85b7 100644
--- a/src/proto_alpha/lib_protocol/toggle_EMA.ml
+++ b/src/proto_alpha/lib_protocol/toggle_EMA.ml
@@ -24,29 +24,29 @@
 (*                                                                           *)
 (*****************************************************************************)
 
-(** Exponential moving average of toggle votes. Represented as an int32 between
+(** Exponential moving average of toggle votes. Represented as an int64 between
     0 and 2,000,000,000. It is an exponential moving average of the "off" votes
     over a window of the most recent 2000 blocks that did not vote "pass". *)
 
-(* The exponential moving average is represented as an Int32 between 0l and 2_000_000_000l *)
-type t = Int32.t (* Invariant 0 <= ema <= 2_000_000_000l *)
+(* The exponential moving average is represented as an Int64 between 0L and 2_000_000_000L *)
+type t = Int64.t (* Invariant 0 <= ema <= 2_000_000_000L *)
 
 (* This error is not registered because we don't expect it to be
    raised. *)
-type error += Toggle_ema_out_of_bound of Int32.t
+type error += Toggle_ema_out_of_bound of Int64.t
 
-let check_bounds x = Compare.Int32.(0l <= x && x <= 2_000_000_000l)
+let check_bounds x = Compare.Int64.(0L <= x && x <= 2_000_000_000L)
 
-let of_int32 (x : Int32.t) : t tzresult Lwt.t =
+let of_int64 (x : Int64.t) : t tzresult Lwt.t =
   if check_bounds x then return x else tzfail @@ Toggle_ema_out_of_bound x
 
-let zero : t = Int32.zero
+let zero : t = Int64.zero
 
 (* The conv_with_guard combinator of Data_encoding expects a (_, string) result. *)
-let of_int32_for_encoding x =
+let of_int64_for_encoding x =
   if check_bounds x then Ok x else Error "out of bounds"
 
-let to_int32 (ema : t) : Int32.t = ema
+let to_int64 (ema : t) : Int64.t = ema
 
 (* We perform the computations in Z to avoid overflows. *)
 
@@ -67,14 +67,14 @@ let recenter f ema = Z.(add z_1_000_000_000 (f (sub ema z_1_000_000_000)))
 let z_500_000 = Z.of_int 500_000
 
 let update_ema_off (ema : t) : t =
-  let ema = Z.of_int32 ema in
-  recenter (fun ema -> Z.add (attenuate ema) z_500_000) ema |> Z.to_int32
+  let ema = Z.of_int64 ema in
+  recenter (fun ema -> Z.add (attenuate ema) z_500_000) ema |> Z.to_int64
 
 let update_ema_on (ema : t) : t =
-  let ema = Z.of_int32 ema in
-  recenter (fun ema -> Z.sub (attenuate ema) z_500_000) ema |> Z.to_int32
+  let ema = Z.of_int64 ema in
+  recenter (fun ema -> Z.sub (attenuate ema) z_500_000) ema |> Z.to_int64
 
-let ( < ) : t -> Int32.t -> bool = Compare.Int32.( < )
+let ( < ) : t -> Int64.t -> bool = Compare.Int64.( < )
 
 let encoding : t Data_encoding.t =
-  Data_encoding.(conv_with_guard to_int32 of_int32_for_encoding int32)
+  Data_encoding.(conv_with_guard to_int64 of_int64_for_encoding int64)
diff --git a/src/proto_alpha/lib_protocol/toggle_EMA.mli b/src/proto_alpha/lib_protocol/toggle_EMA.mli
index 0a68ba0f302a886929c8d4e2f87c69183ce0911f..bc1a56679c2c7a81ee6cc495cbf55f76b25b92c8 100644
--- a/src/proto_alpha/lib_protocol/toggle_EMA.mli
+++ b/src/proto_alpha/lib_protocol/toggle_EMA.mli
@@ -24,21 +24,21 @@
 (*                                                                           *)
 (*****************************************************************************)
 
-(** Exponential moving average of toggle votes. Represented as an int32 between
+(** Exponential moving average of toggle votes. Represented as an int64 between
     0 and 2,000,000,000. It is an exponential moving average of the "off" votes
     over a window of the most recent 2000 blocks that did not vote "pass". *)
 
 type t
 
-val of_int32 : Int32.t -> t tzresult Lwt.t
+val of_int64 : Int64.t -> t tzresult Lwt.t
 
 val zero : t
 
-val to_int32 : t -> Int32.t
+val to_int64 : t -> Int64.t
 
 val encoding : t Data_encoding.t
 
-val ( < ) : t -> Int32.t -> bool
+val ( < ) : t -> Int64.t -> bool
 
 val update_ema_off : t -> t
 
diff --git a/tezt/tests/expected/RPC_test.ml/Alpha- (mode client) RPC regression tests- misc_protocol.out b/tezt/tests/expected/RPC_test.ml/Alpha- (mode client) RPC regression tests- misc_protocol.out
index ea3a7a036434cee8db0ed28646b9f0a7c9b4e0e4..2c1d8cb3775476e2d5c727cbd5df219828f7f9a0 100644
--- a/tezt/tests/expected/RPC_test.ml/Alpha- (mode client) RPC regression tests- misc_protocol.out	
+++ b/tezt/tests/expected/RPC_test.ml/Alpha- (mode client) RPC regression tests- misc_protocol.out	
@@ -24,7 +24,7 @@
       "seed_nonce_revelation_tip_weight": 1, "vdf_revelation_tip_weight": 1 },
   "cost_per_byte": "250", "hard_storage_limit_per_operation": "60000",
   "quorum_min": 2000, "quorum_max": 7000, "min_proposal_quorum": 500,
-  "liquidity_baking_toggle_ema_threshold": 1000000000,
+  "liquidity_baking_toggle_ema_threshold": "1000000000",
   "max_operations_time_to_live": 240, "minimal_block_delay": "1",
   "delay_increment_per_round": "1", "consensus_committee_size": 256,
   "consensus_threshold": 0,
diff --git a/tezt/tests/expected/RPC_test.ml/Alpha- (mode light) RPC regression tests- misc_protocol.out b/tezt/tests/expected/RPC_test.ml/Alpha- (mode light) RPC regression tests- misc_protocol.out
index 5c1aa74201e4e80eee0efba4bdec523b69108897..be1e5ca68614e718a75b9c205bf24fed55605b09 100644
--- a/tezt/tests/expected/RPC_test.ml/Alpha- (mode light) RPC regression tests- misc_protocol.out	
+++ b/tezt/tests/expected/RPC_test.ml/Alpha- (mode light) RPC regression tests- misc_protocol.out	
@@ -24,7 +24,7 @@
       "seed_nonce_revelation_tip_weight": 1, "vdf_revelation_tip_weight": 1 },
   "cost_per_byte": "250", "hard_storage_limit_per_operation": "60000",
   "quorum_min": 2000, "quorum_max": 7000, "min_proposal_quorum": 500,
-  "liquidity_baking_toggle_ema_threshold": 1000000000,
+  "liquidity_baking_toggle_ema_threshold": "1000000000",
   "max_operations_time_to_live": 240, "minimal_block_delay": "1",
   "delay_increment_per_round": "1", "consensus_committee_size": 256,
   "consensus_threshold": 0,
diff --git a/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy) RPC regression tests- misc_protocol.out b/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy) RPC regression tests- misc_protocol.out
index 9570e77408b3fb77208ca5399729257044b8d647..7c0173123e03ce2fb85be143366d85594be3abde 100644
--- a/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy) RPC regression tests- misc_protocol.out	
+++ b/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy) RPC regression tests- misc_protocol.out	
@@ -24,7 +24,7 @@
       "seed_nonce_revelation_tip_weight": 1, "vdf_revelation_tip_weight": 1 },
   "cost_per_byte": "250", "hard_storage_limit_per_operation": "60000",
   "quorum_min": 2000, "quorum_max": 7000, "min_proposal_quorum": 500,
-  "liquidity_baking_toggle_ema_threshold": 1000000000,
+  "liquidity_baking_toggle_ema_threshold": "1000000000",
   "max_operations_time_to_live": 240, "minimal_block_delay": "1",
   "delay_increment_per_round": "1", "consensus_committee_size": 256,
   "consensus_threshold": 0,
diff --git a/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy_server_data_dir) RPC regression tests- misc_protocol.out b/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy_server_data_dir) RPC regression tests- misc_protocol.out
index 288bf411f6594fcf667168dfa23c3c61db4419ea..bd5f1b32aa8904ad00e62c0ed8bf0cf1980693d7 100644
--- a/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy_server_data_dir) RPC regression tests- misc_protocol.out	
+++ b/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy_server_data_dir) RPC regression tests- misc_protocol.out	
@@ -24,7 +24,7 @@
       "seed_nonce_revelation_tip_weight": 1, "vdf_revelation_tip_weight": 1 },
   "cost_per_byte": "250", "hard_storage_limit_per_operation": "60000",
   "quorum_min": 2000, "quorum_max": 7000, "min_proposal_quorum": 500,
-  "liquidity_baking_toggle_ema_threshold": 1000000000,
+  "liquidity_baking_toggle_ema_threshold": "1000000000",
   "max_operations_time_to_live": 240, "minimal_block_delay": "1",
   "delay_increment_per_round": "1", "consensus_committee_size": 256,
   "consensus_threshold": 0,
diff --git a/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy_server_rpc) RPC regression tests- misc_protocol.out b/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy_server_rpc) RPC regression tests- misc_protocol.out
index 288bf411f6594fcf667168dfa23c3c61db4419ea..bd5f1b32aa8904ad00e62c0ed8bf0cf1980693d7 100644
--- a/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy_server_rpc) RPC regression tests- misc_protocol.out	
+++ b/tezt/tests/expected/RPC_test.ml/Alpha- (mode proxy_server_rpc) RPC regression tests- misc_protocol.out	
@@ -24,7 +24,7 @@
       "seed_nonce_revelation_tip_weight": 1, "vdf_revelation_tip_weight": 1 },
   "cost_per_byte": "250", "hard_storage_limit_per_operation": "60000",
   "quorum_min": 2000, "quorum_max": 7000, "min_proposal_quorum": 500,
-  "liquidity_baking_toggle_ema_threshold": 1000000000,
+  "liquidity_baking_toggle_ema_threshold": "1000000000",
   "max_operations_time_to_live": 240, "minimal_block_delay": "1",
   "delay_increment_per_round": "1", "consensus_committee_size": 256,
   "consensus_threshold": 0,