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Note a more efficient computation of the auth difference.
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@ -45,15 +45,19 @@ whereas the conflicted state set may associate multiple events to the same key.
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The *auth chain* of an event *E* is the set containing all of *E*'s auth events,
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all of *their* auth events, and so on recursively, stretching back to the
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start of the room. Put differently, these are the events reachable by walking
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the graph induced by an event's `auth_events` links.
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the graph induced by an event's `auth_events` links. If *S* is a collection of
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events, the *full auth chain of S* is the union of the auth chains of every
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event *E* in *S*.
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**Auth difference.**
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The *auth difference* is calculated by first calculating the full auth
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chain for each state *S*<sub>*i*</sub>, that is the union of the auth
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chains for each event in *S*<sub>*i*</sub>, and then taking every event
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that doesn't appear in every auth chain. If *C*<sub>*i*</sub> is the
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full auth chain of *S*<sub>*i*</sub>, then the auth difference is
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∪ *C*<sub>*i*</sub> − ∩ *C*<sub>*i*</sub>.
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chain for each state *S*<sub>*i*</sub>, and then discarding the events
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belonging to each full auth chain. In symbols: if *C*(*S*) is the full auth
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chain of a collection of events *S*, the auth difference is
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∪<sub>*i*</sub> *C*(*S<sub>i*</sub>) - ∩<sub>*i*</sub> *C*(*S<sub>i</sub>*).
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This can be [computed more efficiently](https://github.com/matrix-org/matrix-spec/issues/1118) as
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*C*(*F*) - ∩<sub>*i*</sub> *C*(*S<sub>i* - *F*) ,
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where *F* is the full conflicted set.
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**Full conflicted set.**
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The *full conflicted set* is the union of the conflicted state set and
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