network: extend api test conventions

diff --git a/network/tests/api.rs b/network/tests/api.rs
index 280fd5e3..03cd7e74 100644
--- a/network/tests/api.rs
+++ b/network/tests/api.rs
@@ -1,10 +1,8 @@
 // SPDX-License-Identifier: CC0-1.0
 
-//! Test the API surface of `bitcoin-network-kind`.
+//! Test the API surface (not functionality) of `bitcoin-network-kind`.
 //!
-//! The point of these tests is to check the API surface as opposed to test the API functionality.
-//!
-//! See [Rust API Guidelines](https://rust-lang.github.io/api-guidelines/about.html).
+//! See [Rust API Guidelines](https://rust-lang.github.io/api-guidelines/about.html) and the [rust-bitcoin policies](../../docs/policy.md).
 
 #![allow(dead_code)]
 #![allow(unused_imports)]
@@ -12,6 +10,9 @@
 use core::fmt;
 use core::str::FromStr;
 
+#[cfg(feature = "arbitrary")]
+use arbitrary::Arbitrary;
+
 use bitcoin_network_kind::{Network, NetworkKind, ParseNetworkError, TestnetVersion};
 
 /// A struct that includes all public non-error enums.
@@ -41,7 +42,7 @@ impl Errors {
 
 /// C-SEND-SYNC: Tests that all public types implement `Send` + `Sync`.
 #[test]
-fn api_all_types_implement_send_sync() {
+fn c_send_sync() {
     fn is_send_sync<T: Send + Sync>() {}
 
     is_send_sync::<Enums>();
@@ -50,7 +51,7 @@ fn api_all_types_implement_send_sync() {
 
 /// C-DEBUG-NONEMPTY: Tests that all public types have non-empty Debug.
 #[test]
-fn api_all_types_have_non_empty_debug() {
+fn c_debug_nonempty() {
     let enums = Enums::new();
     let errors = Errors::new();
 
@@ -62,7 +63,7 @@ fn api_all_types_have_non_empty_debug() {
 
 /// C-GOOD-ERR: Tests that all public error types implement Display.
 #[test]
-fn api_all_error_types_implement_display() {
+fn c_good_err_display() {
     fn assert_display<T: fmt::Display>() {}
 
     assert_display::<ParseNetworkError>();
@@ -71,7 +72,7 @@ fn api_all_error_types_implement_display() {
 /// C-GOOD-ERR: Tests that all public error types implement [`std::error::Error`].
 #[test]
 #[cfg(feature = "std")]
-fn api_all_error_types_implement_error() {
+fn c_good_err_error() {
     fn assert_error<T: std::error::Error>() {}
 
     assert_error::<ParseNetworkError>();
@@ -79,7 +80,7 @@ fn api_all_error_types_implement_error() {
 
 /// C-CONV-TRAITS: Tests that conversion traits are implemented where expected.
 #[test]
-fn api_conversion_traits_implemented() {
+fn c_conv_traits() {
     fn assert_from<T: From<U>, U>() {}
     fn assert_fromstr<T: FromStr>() {}
     fn assert_asref_self<T: AsRef<T>>() {}
@@ -92,9 +93,18 @@ fn api_conversion_traits_implemented() {
 /// C-SERDE: Tests that serde traits are implemented where expected.
 #[test]
 #[cfg(feature = "serde")]
-fn api_serde_traits_implemented() {
+fn c_serde() {
     fn assert_serde<T: serde::Serialize + for<'de> serde::Deserialize<'de>>() {}
 
     assert_serde::<NetworkKind>();
     assert_serde::<Network>();
 }
+
+/// P-ARBITRARY: Tests that public types implement `Arbitrary`.
+#[test]
+#[cfg(feature = "arbitrary")]
+fn p_arbitrary() {
+    fn assert_arbitrary<T: for<'a> Arbitrary<'a>>() {}
+
+    assert_arbitrary::<NetworkKind>();
+}