fixup! Discover nat topology theory

Author: Emilia Hane

discv5/discv5-theory.md

@@ -363,25 +363,25 @@ as follows:
             Alice-->>Bob: hm(FINDNODE)
     ```
 
-Bob is behind a NAT. Bob is in Relay's kbuckets, they have a session together and Bob has
+Bob is behind NAT. Bob is in Relay's kbuckets, they have a session together and Bob has
 sent a packet to Relay in the last ~20 seconds hence Relay can get through Bob's NAT[^1].
 
 As part of recursive query for peers, Alice sends a [FINDNODE] request to Bob, who's ENR
-it received from Relay. By making an outgoing request to Bob, if Alice is behind a NAT,
+it received from Relay. By making an outgoing request to Bob, if Alice is behind NAT,
 Alice's NAT adds the filtering rule `(Alice's-LAN-ip, Alice's-LAN-port, Bob's-WAN-ip,
 Bob's-WAN-port, entry-lifetime)` to it's UDP session table[^2] [^3]. This means a hole now
 is punched for Bob in Alice's NAT for the duration of `entry-lifetime`. The request to Bob
-times out as Bob is behind a NAT.
+times out as Bob is behind NAT.
 
 Alice initiates an attempt to punch a hole in Bob's NAT via Relay. Alice resets the
-request time out on the timed out [FINDNODE] message and wraps the message's nonce in a
+request time-out on the timed out [FINDNODE] message and wraps the message's nonce in a
 [RELAYINIT] notification and sends it to Relay. The notification also contains its ENR and
 Bob's node id.
 
 Relay disassembles the [RELAYINIT] notification and uses the `target-id` to look up Bob's
 ENR in its kbuckets. With high probability, Relay will find Bob's ENR in its kbuckets as
 ~1 second ago, Relay assembled a [NODES] response for Alice containing Bob's ENR (see [UDP
-Communication] for recommended time out duration). Relay assembles a [RELAYMSG]
+Communication] for recommended time-out duration). Relay assembles a [RELAYMSG]
 notification with Alice's message nonce and ENR, then sends it to the address in Bob's
 ENR.
 
@@ -409,28 +409,37 @@ hence of its ability to relay.
 
 UDP session table entry lifetimes are configurable, though a common lower bound is 20
 seconds[^1]. Bob must periodically reset the session table entry for Alice in its NAT to
-keep the hole for Alice punched. If Alice too is behind a NAT, it must do the same for Bob.
-Implementations must ensure, when a node behind a NAT does not send a packet to a peer
+keep the hole for Alice punched. If Alice too is behind NAT, it must do the same for Bob.
+Implementations must ensure, when a node behind NAT does not send a packet to a peer
 within the entry lifetime then an empty packet is sent that is dropped by the peer.
 
 NAT hole punching unavoidably creates overhead for all nodes in the network but once a
 hole is punched, keeping it punched requires no interaction between peers. The incentive
-for nodes behind a NAT to keep holes for its peers punched is to avoid reestablishing a
+for nodes behind NAT to keep holes for its peers punched is to avoid reestablishing a
 session. If there is no hole for Alice in Bob's NAT when Alice carries out a
 [liveness check], Bob is considered offline and the session to Bob useless. If the node
-behind a NAT intends to frequently communicate with a peer, reestablishing the session is
+behind NAT intends to frequently communicate with a peer, reestablishing the session is
 more costly than managing the interval of sent packets to that peer.
 
-### Discovering if the local node is behind a NAT and must keep holes for peers punched
-
-A node may be assigned an externally reachable socket to advertise at start-up. If it is
-not, the [external socket used by the local node is discovered] at runtime and at start-up
-the node assumes it is behind at least one level of NAT and must activate the
-[mechanism for keeping holes punched][^1].
-Once an externally reachable IP address is known, implementations will try to bind to the
-address at some number of ports, randomly selected from a given range of probably unused
-ports. If binding succeeds for any port, the node is not behind a NAT and the
-[mechanism for keeping holes punched] is deactivated.
+### Discovering if the local node is behind NAT and must keep holes for peers punched
+
+A node may at start-up be assigned an externally reachable socket to advertise as well as a
+listen socket. If those sockets are not equivalent, the node is behind NAT and the
+[mechanism for keeping holes punched] is activated. Like so, a node assumes it is behind
+NAT if an externally reachable socket is omitted from the initial configuration and must
+activate the [mechanism for keeping holes punched]. The
+[external socket used by the local node is assessed] at runtime. Once a new externally
+reachable IP address is known, implementations will try to bind to the address at some
+number of randomly selected ports from a given range of probably unused ports. If binding
+succeeds with any port, the node is not behind NAT and the
+[mechanism for keeping holes punched] is
+deactivated. This solution assumes, in most scenarios where port-forwarding cannot be
+configured the local node host's address is private to the address realm of the device
+operating the NAT level furthest from the local node host[^1]. If the host and NAT device
+use the same IP address, binding will always succeed, so this method may give a false
+negative. However, this is not detrimental. A node behind NAT that deactivates the
+[mechanism for keeping holes punched] will more frequently have to re-establish sessions
+to its peers.
 
 [EIP-778]: ../enr.md
 [identity scheme]: ../enr.md#record-structure
@@ -448,7 +457,7 @@ ports. If binding succeeds for any port, the node is not behind a NAT and the
 [UDP communication]: ./discv5-wire.md#udp-communication
 [Sessions]: ./discv5-theory.md#sessions
 [liveness check]: ./discv5-theory.md#table-maintenance-in-practice
-[external socket used by the local node is discovered]: ./discv5-theory.md#maintaining-the-local-node-record
+[external socket used by the local node is assessed]: ./discv5-theory.md#maintaining-the-local-node-record
 [mechanism for keeping holes punched]: ./discv5-theory.md#job-of-keeping-the-hole-punched-falls-on-bob-and-bob's-incentive-to-do-so
 
 [^1]: https://pdos.csail.mit.edu/papers/p2pnat.pdf