fix: us spelling

docs/docs/dev_docs/contracts/syntax/storage.md

@@ -89,7 +89,7 @@ To define that a variable is public, it is wrapped in the `PublicState` struct,
 
 #include_code public_state_struct /yarn-project/aztec-nr/aztec/src/state_vars/public_state.nr rust
 
-The `PublicState` struct is generic over the variable type `T` and its serialized size `T_SERIALISED_LEN`. 
+The `PublicState` struct is generic over the variable type `T` and its serialized size `T_SERIALIZED_LEN`. 
 :::info
 Currently, the length of the types must be specified when declaring the storage struct but the intention is that this will be inferred in the future.
 :::
@@ -98,15 +98,15 @@ The struct contains a `storage_slot` which, similar to Ethereum, is used to figu
 
 Beyond the struct, the `PublicState` also contains `serialization_methods`, which is a struct with methods that instruct the `PublicState` how to serialize and deserialize the variable.
 
-#include_code TypeSerialisationInterface /yarn-project/aztec-nr/aztec/src/types/type_serialisation.nr rust
+#include_code TypeSerializationInterface /yarn-project/aztec-nr/aztec/src/types/type_serialization.nr rust
 
 :::info
 The British haven't surrendered fully to US spelling, so serialization is currently inconsistent.
 :::
 
 The Aztec.nr library provides serialization methods for various common types. As an example, the Field serialization methods are defined as follows:
 
-#include_code field_serialization /yarn-project/aztec-nr/aztec/src/types/type_serialisation/field_serialisation.nr rust
+#include_code field_serialization /yarn-project/aztec-nr/aztec/src/types/type_serialization/field_serialization.nr rust
 
 
 :::info
@@ -260,15 +260,15 @@ As part of the initialization of the `Storage` struct, the `Singleton` is create
 
 #include_code start_vars_singleton /yarn-project/noir-contracts/src/contracts/docs_example_contract/src/main.nr rust
 
-### `initialise`
+### `initialize`
 
-As mention, the singleton is initialized to create the first note and value. Here is the source code for the initialise function:
+As mention, the singleton is initialized to create the first note and value. Here is the source code for the initialize function:
 
-#include_code initialise /yarn-project/aztec-nr/aztec/src/state_vars/singleton.nr rust
+#include_code initialize /yarn-project/aztec-nr/aztec/src/state_vars/singleton.nr rust
 
 When this function is called, a nullifier of the storage slot is created, preventing this Singleton from being initialized again.
 
-Unlike public states, which have a default initial value of `0` (or many zeros, in the case of a struct, array or map), a private state (of type `Singleton`, `ImmutableSingleton` or `Set`) does not have a default initial value. The `initialise` method (or `insert`, in the case of a `Set`) must be called.
+Unlike public states, which have a default initial value of `0` (or many zeros, in the case of a struct, array or map), a private state (of type `Singleton`, `ImmutableSingleton` or `Set`) does not have a default initial value. The `initialize` method (or `insert`, in the case of a `Set`) must be called.
 
 :::info
 Extend on what happens if you try to use non-initialized state.
@@ -310,13 +310,13 @@ As part of the initialization of the `Storage` struct, the `Singleton` is create
 
 #include_code storage_init /yarn-project/noir-contracts/src/contracts/schnorr_account_contract/src/main.nr rust
 
-### `initialise`
+### `initialize`
 
-#include_code initialise /yarn-project/aztec-nr/aztec/src/state_vars/immutable_singleton.nr rust
+#include_code initialize /yarn-project/aztec-nr/aztec/src/state_vars/immutable_singleton.nr rust
 
-Set the value of an ImmutableSingleton by calling the `initialise` method:
+Set the value of an ImmutableSingleton by calling the `initialize` method:
 
-#include_code initialise /yarn-project/noir-contracts/src/contracts/schnorr_account_contract/src/main.nr rust
+#include_code initialize /yarn-project/noir-contracts/src/contracts/schnorr_account_contract/src/main.nr rust
 
 Once initialized, an ImmutableSingleton's value remains unchangeable. This method can only be called once.
 
@@ -475,11 +475,11 @@ Several methods are available on `NoteGetterOptions` to construct the options in
 
 #### `fn new() -> NoteGetterOptions<Note, N, Field>`
 
-This function initialises a `NoteGetterOptions` that simply returns the maximum number of notes allowed in a call.
+This function initializes a `NoteGetterOptions` that simply returns the maximum number of notes allowed in a call.
 
 #### `fn with_filter(filter, filter_args) -> NoteGetterOptions<Note, N, FILTER_ARGS>`
 
-This function initialises a `NoteGetterOptions` with a [`filter`](#filter-fn-optionnote-max_read_requests_per_call-filter_args---optionnote-max_read_requests_per_call) and [`filter_args`](#filter_args-filter_args).
+This function initializes a `NoteGetterOptions` with a [`filter`](#filter-fn-optionnote-max_read_requests_per_call-filter_args---optionnote-max_read_requests_per_call) and [`filter_args`](#filter_args-filter_args).
 
 #### `.select`