diff --git a/changelog.d/14677.doc b/changelog.d/14677.doc
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+Describe the ideas and the internal machinery behind faster joins.
diff --git a/docs/SUMMARY.md b/docs/SUMMARY.md
index 8d68719958..ade77d4926 100644
--- a/docs/SUMMARY.md
+++ b/docs/SUMMARY.md
@@ -97,6 +97,7 @@
     - [Log Contexts](log_contexts.md)
     - [Replication](replication.md)
     - [TCP Replication](tcp_replication.md)
+    - [Faster remote joins](development/synapse_architecture/faster_joins.md)
   - [Internal Documentation](development/internal_documentation/README.md)
     - [Single Sign-On]()
       - [SAML](development/saml.md)
diff --git a/docs/development/synapse_architecture/faster_joins.md b/docs/development/synapse_architecture/faster_joins.md
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+# How do faster joins work?
+
+This is a work-in-progress set of notes with two goals:
+- act as a reference, explaining how Synapse implements faster joins; and
+- record the rationale behind our choices.
+
+See also [MSC3902](https://github.com/matrix-org/matrix-spec-proposals/pull/3902).
+
+The key idea is described by [MSC706](https://github.com/matrix-org/matrix-spec-proposals/pull/3902). This allows servers to
+request a lightweight response to the federation `/send_join` endpoint.
+This is called a **faster join**, also known as a **partial join**. In these
+notes we'll usually use the word "partial" as it matches the database schema.
+
+## Overview: processing events in a partially-joined room
+
+The response to a partial join consists of
+- the requested join event `J`,
+- a list of the servers in the room (according to the state before `J`),
+- a subset of the state of the room before `J`,
+- the full auth chain of that state subset.
+
+Synapse marks the room as partially joined by adding a row to the database table
+`partial_state_rooms`. It also marks the join event `J` as "partially stated",
+meaning that we have neither received nor computed the full state before/after
+`J`. This is done by adding a row to `partial_state_events`.
+
+<details><summary>DB schema</summary>
+
+```
+matrix=> \d partial_state_events
+Table "matrix.partial_state_events"
+  Column  │ Type │ Collation │ Nullable │ Default
+══════════╪══════╪═══════════╪══════════╪═════════
+ room_id  │ text │           │ not null │
+ event_id │ text │           │ not null │
+ 
+matrix=> \d partial_state_rooms
+                Table "matrix.partial_state_rooms"
+         Column         │  Type  │ Collation │ Nullable │ Default 
+════════════════════════╪════════╪═══════════╪══════════╪═════════
+ room_id                │ text   │           │ not null │ 
+ device_lists_stream_id │ bigint │           │ not null │ 0
+ join_event_id          │ text   │           │          │ 
+ joined_via             │ text   │           │          │ 
+
+matrix=> \d partial_state_rooms_servers
+     Table "matrix.partial_state_rooms_servers"
+   Column    │ Type │ Collation │ Nullable │ Default 
+═════════════╪══════╪═══════════╪══════════╪═════════
+ room_id     │ text │           │ not null │ 
+ server_name │ text │           │ not null │ 
+```
+
+Indices, foreign-keys and check constraints are omitted for brevity.
+</details>
+
+While partially joined to a room, Synapse receives events `E` from remote
+homeservers as normal, and can create events at the request of its local users.
+However, we run into trouble when we enforce the [checks on an event].
+
+> 1. Is a valid event, otherwise it is dropped. For an event to be valid, it
+     must contain a room_id, and it must comply with the event format of that
+>    room version.
+> 2. Passes signature checks, otherwise it is dropped.
+> 3. Passes hash checks, otherwise it is redacted before being processed further.
+> 4. Passes authorization rules based on the event’s auth events, otherwise it
+>    is rejected.
+> 5. **Passes authorization rules based on the state before the event, otherwise
+>    it is rejected.**
+> 6. **Passes authorization rules based on the current state of the room,
+>    otherwise it is “soft failed”.**
+
+[checks on an event]: https://spec.matrix.org/v1.5/server-server-api/#checks-performed-on-receipt-of-a-pdu
+
+We can enforce checks 1--4 without any problems.
+But we cannot enforce checks 5 or 6 with complete certainty, since Synapse does
+not know the full state before `E`, nor that of the room.
+
+### Partial state
+
+Instead, we make a best-effort approximation.
+While the room is considered partially joined, Synapse tracks the "partial
+state" before events.
+This works in a similar way as regular state:
+
+- The partial state before `J` is that given to us by the partial join response.
+- The partial state before an event `E` is the resolution of the partial states
+  after each of `E`'s `prev_event`s.
+- If `E` is rejected or a message event, the partial state after `E` is the
+  partial state before `E`.
+- Otherwise, the partial state after `E` is the partial state before `E`, plus
+  `E` itself.
+
+More concisely, partial state propagates just like full state; the only
+difference is that we "seed" it with an incomplete initial state.
+Synapse records that we have only calculated partial state for this event with
+a row in `partial_state_events`.
+
+While the room remains partially stated, check 5 on incoming events to that
+room becomes:
+
+> 5. Passes authorization rules based on **the resolution between the partial
+>    state before `E` and `E`'s auth events.** If the event fails to pass
+>    authorization rules, it is rejected.
+
+Additionally, check 6 is deleted: no soft-failures are enforced.
+
+While partially joined, the current partial state of the room is defined as the
+resolution across the partial states after all forward extremities in the room.
+
+_Remark._ Events with partial state are _not_ considered
+[outliers](../room-dag-concepts.md#outliers).
+
+### Approximation error
+
+Using partial state means the auth checks can fail in a few different ways[^2].
+
+[^2]: Is this exhaustive?
+
+- We may erroneously accept an incoming event in check 5 based on partial state
+  when it would have been rejected based on full state, or vice versa.
+- This means that an event could erroneously be added to the current partial
+  state of the room when it would not be present in the full state of the room,
+  or vice versa.
+- Additionally, we may have skipped soft-failing an event that would have been
+  soft-failed based on full state.
+
+(Note that the discrepancies described in the last two bullets are user-visible.)
+
+This means that we have to be very careful when we want to lookup pieces of room
+state in a partially-joined room. Our approximation of the state may be
+incorrect or missing. But we can make some educated guesses. If
+
+- our partial state is likely to be correct, or
+- the consequences of our partial state being incorrect are minor,
+
+then we proceed as normal, and let the resync process fix up any mistakes (see
+below).
+
+When is our partial state likely to be correct?
+
+- It's more accurate the closer we are to the partial join event. (So we should
+  ideally complete the resync as soon as possible.)
+- Non-member events: we will have received them as part of the partial join
+  response, if they were part of the room state at that point. We may
+  incorrectly accept or reject updates to that state (at first because we lack
+  remote membership information; later because of compounding errors), so these
+  can become incorrect over time.
+- Local members' memberships: we are the only ones who can create join and
+  knock events for our users. We can't be completely confident in the
+  correctness of bans, invites and kicks from other homeservers, but the resync
+  process should correct any mistakes.
+- Remote members' memberships: we did not receive these in the /send_join
+  response, so we have essentially no idea if these are correct or not.
+
+In short, we deem it acceptable to trust the partial state for non-membership
+and local membership events. For remote membership events, we wait for the
+resync to complete, at which point we have the full state of the room and can
+proceed as normal.
+
+### Fixing the approximation with a resync
+
+The partial-state approximation is only a temporary affair. In the background,
+synapse beings a "resync" process. This is a continuous loop, starting at the
+partial join event and proceeding downwards through the event graph. For each 
+`E` seen in the room since partial join, Synapse will fetch 
+
+- the event ids in the state of the room before `E`, via 
+  [`/state_ids`](https://spec.matrix.org/v1.5/server-server-api/#get_matrixfederationv1state_idsroomid);
+- the event ids in the full auth chain of `E`, included in the `/state_ids` 
+  response; and
+- any events from the previous two bullets that Synapse hasn't persisted, via
+  [`/state](https://spec.matrix.org/v1.5/server-server-api/#get_matrixfederationv1stateroomid).
+
+This means Synapse has (or can compute) the full state before `E`, which allows
+Synapse to properly authorise or reject `E`. At this point ,the event
+is considered to have "full state" rather than "partial state". We record this
+by removing `E` from the `partial_state_events` table.
+
+\[**TODO:** Does Synapse persist a new state group for the full state
+before `E`, or do we alter the (partial-)state group in-place? Are state groups
+ever marked as partially-stated? \]
+
+This scheme means it is possible for us to have accepted and sent an event to 
+clients, only to reject it during the resync. From a client's perspective, the 
+effect is similar to a retroactive 
+state change due to state resolution---i.e. a "state reset".[^3]
+
+[^3]: Clients should refresh caches to detect such a change. Rumour has it that 
+sliding sync will fix this.
+
+When all events since the join `J` have been fully-stated, the room resync
+process is complete. We record this by removing the room from
+`partial_state_rooms`.
+
+## Faster joins on workers
+
+For the time being, the resync process happens on the master worker.
+A new replication stream `un_partial_stated_room` is added. Whenever a resync
+completes and a partial-state room becomes fully stated, a new message is sent
+into that stream containing the room ID.
+
+## Notes on specific cases
+
+> **NB.** The notes below are rough. Some of them are hidden under `<details>`
+disclosures because they have yet to be implemented in mainline Synapse.
+
+### Creating events during a partial join
+
+When sending out messages during a partial join, we assume our partial state is 
+accurate and proceed as normal. For this to have any hope of succeeding at all,
+our partial state must contain an entry for each of the (type, state key) pairs
+[specified by the auth rules](https://spec.matrix.org/v1.3/rooms/v10/#authorization-rules):
+
+- `m.room.create`
+- `m.room.join_rules`
+- `m.room.power_levels`
+- `m.room.third_party_invite`
+- `m.room.member`
+
+The first four of these should be present in the state before `J` that is given
+to us in the partial join response; only membership events are omitted. In order
+for us to consider the user joined, we must have their membership event. That
+means the only possible omission is the target's membership in an invite, kick
+or ban.
+
+The worst possibility is that we locally invite someone who is banned according to
+the full state, because we lack their ban in our current partial state. The rest 
+of the federation---at least, those who are fully joined---should correctly 
+enforce the [membership transition constraints](
+    https://spec.matrix.org/v1.3/client-server-api/#room-membership
+). So any the erroneous invite should be ignored by fully-joined
+homeservers and resolved by the resync for partially-joined homeservers.
+
+
+
+In more generality, there are two problems we're worrying about here:
+
+- We might create an event that is valid under our partial state, only to later
+  find out that is actually invalid according to the full state.
+- Or: we might refuse to create an event that is invalid under our partial
+  state, even though it would be perfectly valid under the full state.
+
+However we expect such problems to be unlikely in practise, because
+
+- We trust that the room has sensible power levels, e.g. that bad actors with
+  high power levels are demoted before their ban.
+- We trust that the resident server provides us up-to-date power levels, join
+  rules, etc.
+- State changes in rooms are relatively infrequent, and the resync period is
+  relatively quick.
+
+#### Sending out the event over federation
+
+**TODO:** needs prose fleshing out.
+
+Normally: send out in a fed txn to all HSes in the room.
+We only know that some HSes were in the room at some point. Wat do.
+Send it out to the list of servers from the first join.
+**TODO** what do we do here if we have full state?
+If the prev event was created by us, we can risk sending it to the wrong HS. (Motivation: privacy concern of the content. Not such a big deal for a public room or an encrypted room. But non-encrypted invite-only...)
+But don't want to send out sensitive data in other HS's events in this way.
+
+Suppose we discover after resync that we shouldn't have sent out one our events (not a prev_event) to a target HS. Not much we can do.
+What about if we didn't send them an event but shouldn't've?
+E.g. what if someone joined from a new HS shortly after you did? We wouldn't talk to them.
+Could imagine sending out the "Missed" events after the resync but... painful to work out what they shuld have seen if they joined/left.
+Instead, just send them the latest event (if they're still in the room after resync) and let them backfill.(?)
+- Don't do this currently.
+- If anyone who has received our messages sends a message to a HS we missed, they can backfill our messages
+- Gap: rooms which are infrequently used and take a long time to resync.
+
+### Joining after a partial join
+
+**NB.** Not yet implemented.
+
+<details>
+
+**TODO:** needs prose fleshing out. Liase with Matthieu. Explain why /send_join
+(Rich was surprised we didn't just create it locally. Answer: to try and avoid
+a join which then gets rejected after resync.)
+
+We don't know for sure that any join we create would be accepted.
+E.g. the joined user might have been banned; the join rules might have changed in a way that we didn't realise... some way in which the partial state was mistaken.
+Instead, do another partial make-join/send-join handshake to confirm that the join works.
+- Probably going to get a bunch of duplicate state events and auth events.... but the point of partial joins is that these should be small. Many are already persisted = good.
+- What if the second send_join response includes a different list of reisdent HSes? Could ignore it.
+  - Could even have a special flag that says "just make me a join", i.e. don't bother giving me state or servers in room. Deffo want the auth chain tho.
+- SQ: wrt device lists it's a lot safer to ignore it!!!!!
+- What if the state at the second join is inconsistent with what we have? Ignore it?
+
+</details>
+
+### Leaving (and kicks and bans) after a partial join
+
+**NB.** Not yet implemented.
+
+<details>
+
+When you're fully joined to a room, to have `U` leave a room their homeserver
+needs to
+
+- create a new leave event for `U` which will be accepted by other homeservers,
+  and
+- send that event `U` out to the homeservers in the federation.
+
+When is a leave event accepted? See
+[v10 auth rules](https://spec.matrix.org/v1.5/rooms/v10/#authorization-rules):
+
+> 4. If type is m.room.member: [...]
+     >
+     >    5. If membership is leave:
+             >
+             >       1. If the sender matches state_key, allow if and only if that user’s current membership state is invite, join, or knock.
+>       2. [...]
+
+I think this means that (well-formed!) self-leaves are governed entirely by
+4.5.1. This means that if we correctly calculate state which says that `U` is
+invited, joined or knocked and include it in the leave's auth events, our event
+is accepted by checks 4 and 5 on incoming events.
+
+> 4. Passes authorization rules based on the event’s auth events, otherwise
+     >    it is rejected.
+> 5. Passes authorization rules based on the state before the event, otherwise
+     >    it is rejected.
+
+The only way to fail check 6 is if the receiving server's current state of the
+room says that `U` is banned, has left, or has no membership event. But this is
+fine: the receiving server already thinks that `U` isn't in the room.
+
+> 6. Passes authorization rules based on the current state of the room,
+     >    otherwise it is “soft failed”.
+
+For the second point (publishing the leave event), the best thing we can do is
+to is publish to all HSes we know to be currently in the room. If they miss that
+event, they might send us traffic in the room that we don't care about. This is
+a problem with leaving after a "full" join; we don't seek to fix this with
+partial joins.
+
+(With that said: there's nothing machine-readable in the /send response. I don't
+think we can deduce "destination has left the room" from a failure to /send an
+event into that room?)
+
+#### Can we still do this during a partial join?
+
+We can create leave events and can choose what gets included in our auth events,
+so we can be sure that we pass check 4 on incoming events. For check 5, we might
+have an incorrect view of the state before an event.
+The only way we might erroneously think a leave is valid is if
+
+- the partial state before the leave has `U` joined, invited or knocked, but
+- the full state before the leave has `U` banned, left or not present,
+
+in which case the leave doesn't make anything worse: other HSes already consider
+us as not in the room, and will continue to do so after seeing the leave.
+
+The remaining obstacle is then: can we safely broadcast the leave event? We may
+miss servers or incorrectly think that a server is in the room. Or the
+destination server may be offline and miss the transaction containing our leave
+event.This should self-heal when they see an event whose `prev_events` descends
+from our leave.
+
+Another option we considered was to use federation `/send_leave` to ask a
+fully-joined server to send out the event on our behalf. But that introduces
+complexity without much benefit. Besides, as Rich put it,
+
+> sending out leaves is pretty best-effort currently
+
+so this is probably good enough as-is.
+
+#### Cleanup after the last leave
+
+**TODO**: what cleanup is necessary? Is it all just nice-to-have to save unused
+work?
+</details>