feat: catchain overview

foundations/consensus/catchain-overview.mdx

@@ -10,6 +10,7 @@
 ## Problem
 
 No network can guarantee that
+
 - messages will be delivered,
 - messages will arrive in the order they were sent,
   - even if it's 2 messages between 2 nodes.
@@ -28,7 +29,7 @@
 
 ### Formal capabilities
 
 The protocol implements a [CRDT](https://en.wikipedia.org/wiki/Conflict-free_replicated_data_type) over the set of messages known to each node and achieves [eventual consistency](https://en.wikipedia.org/wiki/Eventual_consistency). As a synchronization mechanism, it uses the idea similar to [vector clock](https://en.wikipedia.org/wiki/Vector_clock) with modifications that preserve eventual consistency even when some nodes are Byzantine.
 
 <Aside type="note">
   The [ADNL](/foundations/network/adnl) protocol is responsible for message integrity, at-least-once delivery guarantees, and message authenticity.
@@ -39,7 +40,7 @@
 Catchain selects [five](https://github.com/ton-blockchain/ton/blob/34823b1ea378edbe3bc59f3bcc48126480a0b768/catchain/catchain-receiver.cpp#L36) neighbors at random and periodically refreshes the list each random interval between [60 and 120 seconds](https://github.com/ton-blockchain/ton/blob/34823b1ea378edbe3bc59f3bcc48126480a0b768/catchain/catchain-receiver.cpp#L988) in the current configuration. Note, that the neighbor relation is not symmetric: if B is a neighbor of A, it does not imply that A is also a neighbor of B.
 
 <Aside type="tip">
-  In the current implementation, [Mersenne Twister](https://en.wikipedia.org/wiki/Mersenne_Twister) is used to pick the random interval for refreshing the neighbor list. It is seeded with values from [std::random_device](https://en.cppreference.com/w/cpp/numeric/random/random_device.html), whose behavior is platform-dependent.
+  In the current implementation, [Mersenne Twister](https://en.wikipedia.org/wiki/Mersenne_Twister) is used to pick the random interval for refreshing the neighbor list. It is seeded with values from [std::random\_device](https://en.cppreference.com/w/cpp/numeric/random/random_device.html), whose behavior is platform-dependent.
 </Aside>
 
 ## Message identification
@@ -72,21 +73,20 @@
     C -- "(C; 2)<br/>prev: (C; 1)<br/>deps: (A; 1), (B; 1)" --> B
 ```
 
 These messages do not have an order by default. In asynchronous system they can be received in any order. Declaring message dependencies helps to establish a particial ordering on all messages in general and on each of node in particular. This is possible because in catchain "dependency" relation is antisymmetric, transitive and reflexive.
 
 ## Handling Byzantine nodes
 
 The key goal is not to allow Byzantine nodes break the particial order of the messages in the Cathcain. It theoretically can be broken by violating one of three key properties.
 
 ### Antisymmetry
 
 This property means, that $\forall A, B depends(A, B) -> !depends(B, A)$. Catchain preserves this property, as when `A` depends on `B`, `B` is included in the `body hash` field of `A`. Therefore `B` can't depend on `A` as it's `body hash` mush include `A`.
 
 ### Transitivity
 
 CHECK
-This property means, that $\forall A B C depends(A, B) && depends(B, C) -> depends(A, C)$. This property is preserved implicitly by honest nodes because if `A` depends on `B`, `A` will wait in queue for processing of `B`. Imagine a situation, when `
-
+This property means, that $\forall A B C depends(A, B) && depends(B, C) -> depends(A, C)$. This property is preserved implicitly by honest nodes because if `A` depends on `B`, `A` will wait in queue for processing of `B`. Imagine a situation, when \`
 
 ### Detecting forks (duplicate message IDs)
 
@@ -106,7 +106,7 @@
 <code>(A<sub>i</sub>, B<sub>j</sub>, C<sub>k</sub>, D<sub>m</sub> ...)</code>
 This vector tracks the last processed message for each validator. So, if A<sub>i</sub> is stored and A<sub>i+2</sub> arrives, the node must download A<sub>i+1</sub>.
 
-(Link to https://en.wikipedia.org/wiki/Vector_clock)
+(Link to [https://en.wikipedia.org/wiki/Vector\_clock](https://en.wikipedia.org/wiki/Vector_clock))
 
 ## Dependency retrieval process