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Co-authored-by: Richard van der Hoff <1389908+richvdh@users.noreply.github.com>
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content/rooms/fragments/v2-state-res.md
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@ -45,7 +45,9 @@ whereas the conflicted state set may associate multiple events to the same key.
The *auth chain* of an event *E* is the set containing all of *E*'s auth events, 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 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 start of the room. Put differently, these are the events reachable by walking
the graph induced by an event's `auth_events` links. If *S* is a collection of the graph induced by an event's `auth_events` links.
If *S* is a collection of
events, the *full auth chain of S* is the union of the auth chains of every events, the *full auth chain of S* is the union of the auth chains of every
event *E* in *S*. event *E* in *S*.
@ -55,7 +57,8 @@ chain for each state *S*<sub>*i*</sub>, and then discarding the events
belonging to each full auth chain. In symbols: if *F*(*S*) is the full auth belonging to each full auth chain. In symbols: if *F*(*S*) is the full auth
chain of a collection of events *S*, the auth difference is chain of a collection of events *S*, the auth difference is
∪<sub>*i*</sub> *F*(*S<sub>i*</sub>) - ∩<sub>*i*</sub> *F*(*S<sub>i</sub>*). ∪<sub>*i*</sub> *F*(*S<sub>i*</sub>) - ∩<sub>*i*</sub> *F*(*S<sub>i</sub>*).
This can be [computed more efficiently](https://github.com/matrix-org/matrix-spec/issues/1118) as
This can be computed more efficiently as
*F*(*C*) - ∩<sub>*i*</sub> *F*(*S<sub>i* - *C*) , *F*(*C*) - ∩<sub>*i*</sub> *F*(*S<sub>i* - *C*) ,
where *C* is the conflicted state set. where *C* is the conflicted state set.