diff --git a/changelogs/server_server/newsfragments/1042.clarification b/changelogs/server_server/newsfragments/1042.clarification
new file mode 100644
index 000000000..2f3fad6ff
--- /dev/null
+++ b/changelogs/server_server/newsfragments/1042.clarification
@@ -0,0 +1 @@
+Clarify the meaning of "unconflicted state map" and "auth chain" in state res v2.
diff --git a/content/rooms/fragments/v2-state-res.md b/content/rooms/fragments/v2-state-res.md
index b238e1d82..3e901f235 100644
--- a/content/rooms/fragments/v2-state-res.md
+++ b/content/rooms/fragments/v2-state-res.md
@@ -31,11 +31,22 @@ the `membership` is `leave` or `ban` and the `sender` does not match the
might remove someone's ability to do something in the room.
**Unconflicted state map and conflicted state set.**
-The *unconflicted state map* is the state where the value of each key
-exists and is the same in each state *S**i*. The *conflicted
-state set* is the set of all other state events. Note that the
-unconflicted state map only has one event per `(event_type, state_key)`,
-whereas the conflicted state set may have multiple events.
+The keys of the state maps *Si* are 2-tuples of strings of the form
+*K* = `(event_type, state_key)`. The values *V* are state events.
+The key-value pairs (*K*, *V*) across all state maps *Si* can be
+divided into two collections.
+If a given key *K* is present in every *Si* with the same value *V*
+in each state map, then the pair (*K*, *V*) belongs to the *unconflicted state map*.
+Otherwise (*K*, *V*) belongs to the *conflicted state set*.
+
+Note that the unconflicted state map only has one event for each key *K*,
+whereas the conflicted state set may associate multiple events to the same key.
+
+**Auth chain.**
+The *auth chain* of an event *E* is the set containing all of *E*'s auth events,
+all of *their* auth events, and so on recursively, stretching back to the
+start of the room. Put differently, these are the events reachable by walking
+the graph induced by an event's `auth_events` links.
**Auth difference.**
The *auth difference* is calculated by first calculating the full auth
@@ -112,9 +123,9 @@ the auth event is not rejected.
The *resolution* of a set of states is obtained as follows:
-1. Take all *power events* and any events in their auth chains,
- recursively, that appear in the *full conflicted set* and order them
- by the *reverse topological power ordering*.
+1. Select all *power events* that appear in the *full conflicted set*. Compute
+ the union of their auth chains, including the power events themselves.
+ Sort the union using the *reverse topological power ordering*.
2. Apply the *iterative auth checks algorithm*, starting from the
*unconflicted state map*, to the list of events from the previous
step to get a partially resolved state.