Add limit inbound churn

Author: dapplion

specs/_features/limit_churn/beacon_chain.md

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+Limit churn -- The Beacon Chain
+
+## Table of contents
+
+<!-- TOC -->
+<!-- START doctoc generated TOC please keep comment here to allow auto update -->
+<!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->
+
+- [Introduction](#introduction)
+- [Configuration](#configuration)
+  - [Validator cycle](#validator-cycle)
+- [Helper functions](#helper-functions)
+  - [Beacon state accessors](#beacon-state-accessors)
+    - [New `get_validator_inbound_churn_limit`](#new-get_validator_inbound_churn_limit)
+- [Beacon chain state transition function](#beacon-chain-state-transition-function)
+  - [Epoch processing](#epoch-processing)
+    - [Registry updates](#registry-updates)
+
+<!-- END doctoc generated TOC please keep comment here to allow auto update -->
+<!-- /TOC -->
+
+## Introduction
+
+This is the beacon chain specification to limit the max inbound churn value, motivated to limit the validator active set growth rate.
+
+*Note:* This specification is built upon [Capella](../../capella/beacon_chain.md) and is under active development.
+
+## Configuration
+
+### Validator cycle
+
+| Name | Value |
+| - | - |
+| `MAX_PER_EPOCH_INBOUND_CHURN_LIMIT` | `uint64(12)` (= 12) |
+
+## Helper functions
+
+### Beacon state accessors
+
+#### New `get_validator_inbound_churn_limit`
+
+```python
+def get_validator_inbound_churn_limit(state: BeaconState) -> uint64:
+    """
+    Return the validator inbound churn limit for the current epoch.
+    """
+    active_validator_indices = get_active_validator_indices(state, get_current_epoch(state))
+    return min(
+      MAX_PER_EPOCH_INBOUND_CHURN_LIMIT,
+      max(
+        MIN_PER_EPOCH_CHURN_LIMIT,
+        uint64(len(active_validator_indices)) // CHURN_LIMIT_QUOTIENT
+      )
+    )
+```
+
+## Beacon chain state transition function
+
+### Epoch processing
+
+#### Registry updates
+
+```python
+def process_registry_updates(state: BeaconState) -> None:
+    # Process activation eligibility and ejections
+    for index, validator in enumerate(state.validators):
+        if is_eligible_for_activation_queue(validator):
+            validator.activation_eligibility_epoch = get_current_epoch(state) + 1
+
+        if (
+            is_active_validator(validator, get_current_epoch(state))
+            and validator.effective_balance <= EJECTION_BALANCE
+        ):
+            initiate_validator_exit(state, ValidatorIndex(index))
+
+    # Queue validators eligible for activation and not yet dequeued for activation
+    activation_queue = sorted([
+        index for index, validator in enumerate(state.validators)
+        if is_eligible_for_activation(state, validator)
+        # Order by the sequence of activation_eligibility_epoch setting and then index
+    ], key=lambda index: (state.validators[index].activation_eligibility_epoch, index))
+    # Dequeued validators for activation up to churn limit
+    # [Modified in limit churn]
+    for index in activation_queue[:get_validator_inbound_churn_limit(state)]:
+        validator = state.validators[index]
+        validator.activation_epoch = compute_activation_exit_epoch(get_current_epoch(state))
+```
+