Add confirmation rule

docs/wiki/CL/confirmation-rule.md

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+# Fast Confirmation Rule
+
+## 1. Abstract
+A Confirmation Rule, within blockchain networks, refers to an algorithm implemented by network
+nodes that determines (either probabilistically or deterministically) the permanence of certain blocks on
+the blockchain. 
+
+## 2. Fast Confirmation Rule for Ethereum’s consensus protocol.
+### 2.1. Intro
+Regarding the Ethereum protocol, a confirmation rule is an algorithm run by nodes, enabling them to identify 
+a _confirmed chain_ by determining whether a certain block is confirmed. 
+When that is the case, the block is guaranteed to never be reorged under certain assumptions, 
+primarily about network synchrony and about the percentage of honest stake.
+
+In the context of LMD-GHOST, there is not yet a standardized rule for confirming blocks. The only Confirmation Rule 
+currently available for the Ethereum protocol is the FFG Finalization Rule.
+
+The Confirmation Rule is not a replacement for the FFG Finalization Rule, but it is rather complementary to it, since
+FFG ensures Finality in asynchronous conditions, and LMD-GHOST is a synchronous protocol.
+
+### 2.1 Use cases for the Fast Confirmation Rule
+Scenarios where there is a need for fast confirmation time, and relying on network synchrony is acceptable, 
+are possible, e.g. low-value cryptocurrency transactions. 
+Implementing the Fast Confirmation Rule in Ethereum, would provide a best-case confirmation time of only 
+one block, i.e., 12 seconds.
+
+### 2.2 Confirmation Rule for LMD-GHOST
+The Confirmation Rule for LMD-GHOST, would be treated as an independent protocol, and subsequently incorporate it 
+into FFG-Casper’s effects. This Confirmation Rule aims for fast block confirmations by adopting a heuristic that 
+balances speed against reduced safety guarantees, potentially confirming blocks immediately after their creation 
+under optimal conditions.
+
+### 2.3 Algorythm
+#### 2.3.1 High-level view
+In the research paper [^1], the Confirmation Rule is based on two safety indicators:
+* $Q_b^n$ : quantifies the support ratio for a specific block b relative to the total committee weight from the slot of b
+to slot n. This indicator **is** directly observable by users.
+
+and
+
+* $P_n^b$ : measures the honest proportion of support for block b; This indicator **is not** directly observable by users.
+
+With a suitable value of $P_n^b$, a user can reliably confirm block b. 
+
+Conversely, under certain adversarial conditions, reaching a specific threshold of $Q_n^b$, allows for the inference of 
+$P_n^b$, thereby enabling the confirmation of block b.
+
+#### 2.3.2 System model
+**Validators**
+-  $W$ a possibly infinite set of validators
+- $J$ the set of all honest validators (unknown composition), $J \subseteq W$
+- $A$ the set of all Byzantine validators, $A : = W \setminus J$
+- $signer(m)$ the signer of a given message $m$
+
+**Confirmation Rule Executors** 
+
+Validators and confirmation rule executors are different entities. 
+The latter are those executing the Confirmation Rule by having read-only access to the internal state of an honest
+validator of their choice.
+
+**Network Model**
+
+Honest validators have synchronised time
+ - $t$ is the time when (any) message is being sent
+ - $max(t, GST) + \triangle $ is the time (any) message is being received by
+
+    where
+   - $GST = Global Stabilization Time$ - known to all confirmation rule executors
+   - $\triangle$ is the maximum message latency after $GST$
+
+**Gossiping** 
+
+It's assumed that any honest validator immediately broadcasts any message that they receive.
+
+**View** 
+
+The view of a validator corresponds to the set of all the messages that the validator has received.
+- $V^{v,t}$ represents the set of all messages received by validator $v$ at time $t$.
+
+#### 2.3.3 Algorythm main properties - Safety
+
+#### 2.3.4 Algorythm main properties - Monotonicity
+
+### 2.4. Specification
+
+#### 2.5. Incorporating the rule in to FFG-Casper’s effects. 
+This means adding conditions that ensure that once a block is confirmed, the FFG-Casper protocol will 
+never remove (filter out) this block from the set of blocks to give as input to the LMD-GHOST protocol.
+
+Confirmation Rule PR [^2]
+
+# [Resources]
+[^1]: https://arxiv.org/pdf/2405.00549
+[^2]: https://github.com/ethereum/consensus-specs/pull/3339
+[^3]: https://arxiv.org/pdf/2003.03052