@ -47,20 +47,13 @@ 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.
If *S* is a collection of
events, the *full auth chain of S* is the union of the auth chains of every
event *E* in *S* .
**Auth difference.**
For each state *S<sub>i</sub>* , compute its full auth chain.
The *auth difference* is the set of events which belong to some, but not all,
of these full auth chains. In symbols: if *F* (*S*) is the full auth
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 > *).
This can be computed more efficiently as
*F* (*C*) - ∩< sub > *i*</ sub > *F* (*S*< sub > *i* - *C* </ sub > ) ,
where *C* is the conflicted state set.
The *auth difference* is calculated by first calculating the full auth
chain for each state *S* < sub > *i*</ sub > , that is the union of the auth
chains for each event in *S* < sub > *i*</ sub > , and then taking every event
that doesn't appear in every auth chain. If *C* < sub > *i*</ sub > is the
full auth chain of *S* < sub > *i*</ sub > , then the auth difference is
∪ *C*< sub > *i*< / sub > − ∩ *C*< sub > *i*< / sub > .
**Full conflicted set.**
The *full conflicted set* is the union of the conflicted state set and