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solo-chains/docs/bridge/etbereum-to-solo-chain.md

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+# Ethereum State Verification Diagram
+
+## Altair Sync protocol
+
+### Preliminaries
+- Ethereum epochs consis of 32 slots, where each slot is 12s
+- Ethereum distributes all validators in attestation 32 attestation committees (one per slot)
+- At the beginning of each epoch, each validator is assigned a slot
+- Ethereum pseudo-randomly selects, among all validators, a block producer for a slot n
+- The block produced for slot n needs to be attested by the attestation committee for slot n
+
+
+### The need for a sync protocol
+- For a light client, determining the canonical chain can become expensive (as we need to verify a bunch of attestions)
+- In order to verify a block header, you need the information of the previous header
+
+### The Altair sync protocol
+- A sync committe made up of 512 pseudo-randomly chosen validators is selected every 256 epochs (approx, 27hours)
+- Each block header includes the aggregated signature of the validators in the sync committee,
+- Each header lists the current and the next sync committee
+- Sync committee members are rewarded with 0.1ETH for their service, and they are charged that amount if they dont sign
+- 2/3rds quorum needs to be reached
+- For now sync committee members are not slashed if the vote for a malicious header (although subject to change after EIP-7657)
+
+### Verification PseudoCode
+
+```python
+def validate_light_client_update(snapshot: LightClientSnapshot,
+                                 update: LightClientUpdate,
+                                 genesis_validators_root: Root) -> None:
+    # Verify update slot is larger than snapshot slot
+    assert update.header.slot > snapshot.header.slot
+
+    # Verify update does not skip a sync committee period
+    snapshot_period = compute_epoch_at_slot(snapshot.header.slot) // EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+    update_period = compute_epoch_at_slot(update.header.slot) // EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+    assert update_period in (snapshot_period, snapshot_period + 1)
+
+    # Verify update header root is the finalized root of the finality header, if specified
+    if update.finality_header == BeaconBlockHeader():
+        signed_header = update.header
+        assert update.finality_branch == [Bytes32() for _ in range(floorlog2(FINALIZED_ROOT_INDEX))]
+    else:
+        signed_header = update.finality_header
+        assert is_valid_merkle_branch(
+            leaf=hash_tree_root(update.header),
+            branch=update.finality_branch,
+            depth=floorlog2(FINALIZED_ROOT_INDEX),
+            index=get_subtree_index(FINALIZED_ROOT_INDEX),
+            root=update.finality_header.state_root,
+        )
+
+    # Verify update next sync committee if the update period incremented
+    if update_period == snapshot_period:
+        sync_committee = snapshot.current_sync_committee
+        assert update.next_sync_committee_branch == [Bytes32() for _ in range(floorlog2(NEXT_SYNC_COMMITTEE_INDEX))]
+    else:
+        sync_committee = snapshot.next_sync_committee
+        assert is_valid_merkle_branch(
+            leaf=hash_tree_root(update.next_sync_committee),
+            branch=update.next_sync_committee_branch,
+            depth=floorlog2(NEXT_SYNC_COMMITTEE_INDEX),
+            index=get_subtree_index(NEXT_SYNC_COMMITTEE_INDEX),
+            root=update.header.state_root,
+        )
+
+    # Verify sync committee has sufficient participants
+    assert sum(update.sync_committee_bits) >= MIN_SYNC_COMMITTEE_PARTICIPANTS
+
+    # Verify sync committee aggregate signature
+    participant_pubkeys = [pubkey for (bit, pubkey) in zip(update.sync_committee_bits, sync_committee.pubkeys) if bit]
+    domain = compute_domain(DOMAIN_SYNC_COMMITTEE, update.fork_version, genesis_validators_root)
+    signing_root = compute_signing_root(signed_header, domain)
+    assert bls.FastAggregateVerify(participant_pubkeys, signing_root, update.sync_committee_signature)
+```
+
+### Overall Diagram
+
+<p align="center">
+  <img src="images/beacon_chain_altair.drawio.png" width="1000">
+</p>