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<!-- TOC -->
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- [Ethereum 2.0 Phase 0 -- The Beacon Chain](#ethereum-20-phase-0----the-beacon-chain)
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- [Table of contents](#table-of-contents)
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- [Introduction](#introduction)
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- [Notation](#notation)
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- [Terminology](#terminology)
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- [Constants](#constants)
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- [Misc](#misc)
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- [Deposit contract](#deposit-contract)
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- [Gwei values](#gwei-values)
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- [Initial values](#initial-values)
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- [Time parameters](#time-parameters)
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- [State list lengths](#state-list-lengths)
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- [Reward and penalty quotients](#reward-and-penalty-quotients)
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- [Status flags](#status-flags)
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- [Max operations per block](#max-operations-per-block)
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- [Signature domains](#signature-domains)
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- [Data structures](#data-structures)
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- [Beacon chain operations](#beacon-chain-operations)
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- [Proposer slashings](#proposer-slashings)
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- [`ProposerSlashing`](#proposerslashing)
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- [Attester slashings](#attester-slashings)
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- [`AttesterSlashing`](#attesterslashing)
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- [`SlashableAttestation`](#slashableattestation)
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- [Attestations](#attestations)
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- [`Attestation`](#attestation)
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- [`AttestationData`](#attestationdata)
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- [`AttestationDataAndCustodyBit`](#attestationdataandcustodybit)
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- [Deposits](#deposits)
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- [`Deposit`](#deposit)
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- [`DepositData`](#depositdata)
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- [`DepositInput`](#depositinput)
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- [Exits](#exits)
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- [`Exit`](#exit)
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- [Beacon chain blocks](#beacon-chain-blocks)
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- [`BeaconBlock`](#beaconblock)
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- [`BeaconBlockBody`](#beaconblockbody)
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- [`ProposalSignedData`](#proposalsigneddata)
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- [Beacon chain state](#beacon-chain-state)
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- [`BeaconState`](#beaconstate)
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- [`Validator`](#validator)
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- [`Crosslink`](#crosslink)
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- [`PendingAttestation`](#pendingattestation)
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- [`Fork`](#fork)
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- [`Eth1Data`](#eth1data)
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- [`Eth1DataVote`](#eth1datavote)
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- [Custom Types](#custom-types)
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- [Helper functions](#helper-functions)
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- [`hash`](#hash)
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- [`hash_tree_root`](#hashtreeroot)
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- [`slot_to_epoch`](#slottoepoch)
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- [`get_previous_epoch`](#getpreviousepoch)
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- [`get_current_epoch`](#getcurrentepoch)
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- [`get_epoch_start_slot`](#getepochstartslot)
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- [`is_active_validator`](#isactivevalidator)
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- [`get_active_validator_indices`](#getactivevalidatorindices)
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- [`shuffle`](#shuffle)
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- [`split`](#split)
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- [`get_epoch_committee_count`](#getepochcommitteecount)
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- [`get_shuffling`](#getshuffling)
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- [`get_previous_epoch_committee_count`](#getpreviousepochcommitteecount)
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- [`get_current_epoch_committee_count`](#getcurrentepochcommitteecount)
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- [`get_next_epoch_committee_count`](#getnextepochcommitteecount)
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- [`get_crosslink_committees_at_slot`](#getcrosslinkcommitteesatslot)
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- [`get_block_root`](#getblockroot)
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- [`get_randao_mix`](#getrandaomix)
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- [`get_active_index_root`](#getactiveindexroot)
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- [`generate_seed`](#generateseed)
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- [`get_beacon_proposer_index`](#getbeaconproposerindex)
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- [`merkle_root`](#merkleroot)
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- [`get_attestation_participants`](#getattestationparticipants)
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- [`is_power_of_two`](#ispoweroftwo)
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- [`int_to_bytes1`, `int_to_bytes2`, ...](#inttobytes1-inttobytes2)
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- [`get_effective_balance`](#geteffectivebalance)
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- [`get_total_balance`](#gettotalbalance)
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- [`get_fork_version`](#getforkversion)
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- [`get_domain`](#getdomain)
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- [`get_bitfield_bit`](#getbitfieldbit)
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- [`verify_bitfield`](#verifybitfield)
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- [`verify_slashable_attestation`](#verifyslashableattestation)
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- [`is_double_vote`](#isdoublevote)
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- [`is_surround_vote`](#issurroundvote)
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- [`integer_squareroot`](#integersquareroot)
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- [`get_entry_exit_effect_epoch`](#getentryexiteffectepoch)
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- [`bls_verify`](#blsverify)
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- [`bls_verify_multiple`](#blsverifymultiple)
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- [`bls_aggregate_pubkeys`](#blsaggregatepubkeys)
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- [`validate_proof_of_possession`](#validateproofofpossession)
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- [`process_deposit`](#processdeposit)
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- [Routines for updating validator status](#routines-for-updating-validator-status)
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- [`activate_validator`](#activatevalidator)
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- [`initiate_validator_exit`](#initiatevalidatorexit)
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- [`exit_validator`](#exitvalidator)
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- [`penalize_validator`](#penalizevalidator)
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- [`prepare_validator_for_withdrawal`](#preparevalidatorforwithdrawal)
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- [Ethereum 1.0 deposit contract](#ethereum-10-deposit-contract)
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- [Deposit arguments](#deposit-arguments)
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- [Withdrawal credentials](#withdrawal-credentials)
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- [`Deposit` logs](#deposit-logs)
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- [`ChainStart` log](#chainstart-log)
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- [Vyper code](#vyper-code)
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- [On startup](#on-startup)
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- [Beacon chain processing](#beacon-chain-processing)
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- [Beacon chain fork choice rule](#beacon-chain-fork-choice-rule)
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- [Beacon chain state transition function](#beacon-chain-state-transition-function)
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- [Per-slot processing](#per-slot-processing)
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- [Slot](#slot)
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- [Block roots](#block-roots)
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- [Per-block processing](#per-block-processing)
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- [Slot](#slot-1)
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- [Proposer signature](#proposer-signature)
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- [RANDAO](#randao)
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- [Eth1 data](#eth1-data)
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- [Operations](#operations)
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- [Proposer slashings](#proposer-slashings-1)
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- [Attester slashings](#attester-slashings-1)
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- [Attestations](#attestations-1)
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- [Deposits](#deposits-1)
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- [Exits](#exits-1)
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- [Per-epoch processing](#per-epoch-processing)
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- [Helpers](#helpers)
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- [Eth1 data](#eth1-data-1)
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- [Justification](#justification)
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- [Crosslinks](#crosslinks)
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- [Rewards and penalties](#rewards-and-penalties)
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- [Justification and finalization](#justification-and-finalization)
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- [Attestation inclusion](#attestation-inclusion)
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- [Crosslinks](#crosslinks-1)
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- [Ejections](#ejections)
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- [Validator registry and shuffling seed data](#validator-registry-and-shuffling-seed-data)
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- [Final updates](#final-updates)
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- [State root verification](#state-root-verification)
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- [Table of contents](#table-of-contents)
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- [Introduction](#introduction)
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- [Notation](#notation)
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- [Terminology](#terminology)
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- [Constants](#constants)
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- [Misc](#misc)
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- [Deposit contract](#deposit-contract)
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- [Gwei values](#gwei-values)
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- [Initial values](#initial-values)
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- [Time parameters](#time-parameters)
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- [State list lengths](#state-list-lengths)
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- [Reward and penalty quotients](#reward-and-penalty-quotients)
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- [Status flags](#status-flags)
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- [Max operations per block](#max-operations-per-block)
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- [Signature domains](#signature-domains)
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- [Data structures](#data-structures)
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- [Beacon chain operations](#beacon-chain-operations)
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- [Proposer slashings](#proposer-slashings)
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- [`ProposerSlashing`](#proposerslashing)
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- [Attester slashings](#attester-slashings)
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- [`AttesterSlashing`](#attesterslashing)
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- [`SlashableAttestation`](#slashableattestation)
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- [Attestations](#attestations)
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- [`Attestation`](#attestation)
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- [`AttestationData`](#attestationdata)
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- [`AttestationDataAndCustodyBit`](#attestationdataandcustodybit)
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- [Deposits](#deposits)
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- [`Deposit`](#deposit)
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- [`DepositData`](#depositdata)
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- [`DepositInput`](#depositinput)
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- [Exits](#exits)
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- [`Exit`](#exit)
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- [Beacon chain blocks](#beacon-chain-blocks)
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- [`BeaconBlock`](#beaconblock)
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- [`BeaconBlockBody`](#beaconblockbody)
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- [`ProposalSignedData`](#proposalsigneddata)
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- [Beacon chain state](#beacon-chain-state)
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- [`BeaconState`](#beaconstate)
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- [`Validator`](#validator)
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- [`Crosslink`](#crosslink)
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- [`PendingAttestation`](#pendingattestation)
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- [`Fork`](#fork)
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- [`Eth1Data`](#eth1data)
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- [`Eth1DataVote`](#eth1datavote)
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- [Custom Types](#custom-types)
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- [Helper functions](#helper-functions)
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- [`hash`](#hash)
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- [`hash_tree_root`](#hash_tree_root)
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- [`slot_to_epoch`](#slot_to_epoch)
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- [`get_previous_epoch`](#get_previous_epoch)
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- [`get_current_epoch`](#get_current_epoch)
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- [`get_epoch_start_slot`](#get_epoch_start_slot)
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- [`is_active_validator`](#is_active_validator)
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- [`get_active_validator_indices`](#get_active_validator_indices)
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- [`shuffle`](#shuffle)
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- [`split`](#split)
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- [`get_epoch_committee_count`](#get_epoch_committee_count)
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- [`get_shuffling`](#get_shuffling)
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- [`get_previous_epoch_committee_count`](#get_previous_epoch_committee_count)
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- [`get_current_epoch_committee_count`](#get_current_epoch_committee_count)
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- [`get_next_epoch_committee_count`](#get_next_epoch_committee_count)
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- [`get_crosslink_committees_at_slot`](#get_crosslink_committees_at_slot)
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- [`get_block_root`](#get_block_root)
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- [`get_randao_mix`](#get_randao_mix)
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- [`get_active_index_root`](#get_active_index_root)
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- [`generate_seed`](#generate_seed)
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- [`get_beacon_proposer_index`](#get_beacon_proposer_index)
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- [`merkle_root`](#merkle_root)
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- [`get_attestation_participants`](#get_attestation_participants)
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- [`is_power_of_two`](#is_power_of_two)
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- [`int_to_bytes1`, `int_to_bytes2`, ...](#int_to_bytes1-int_to_bytes2-)
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- [`get_effective_balance`](#get_effective_balance)
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- [`get_total_balance`](#get_total_balance)
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- [`get_fork_version`](#get_fork_version)
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- [`get_domain`](#get_domain)
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- [`get_bitfield_bit`](#get_bitfield_bit)
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- [`verify_bitfield`](#verify_bitfield)
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- [`verify_slashable_attestation`](#verify_slashable_attestation)
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- [`is_double_vote`](#is_double_vote)
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- [`is_surround_vote`](#is_surround_vote)
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- [`integer_squareroot`](#integer_squareroot)
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- [`get_entry_exit_effect_epoch`](#get_entry_exit_effect_epoch)
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- [`bls_verify`](#bls_verify)
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- [`bls_verify_multiple`](#bls_verify_multiple)
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- [`bls_aggregate_pubkeys`](#bls_aggregate_pubkeys)
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- [`validate_proof_of_possession`](#validate_proof_of_possession)
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- [`process_deposit`](#process_deposit)
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- [Routines for updating validator status](#routines-for-updating-validator-status)
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- [`activate_validator`](#activate_validator)
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- [`initiate_validator_exit`](#initiate_validator_exit)
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- [`exit_validator`](#exit_validator)
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- [`penalize_validator`](#penalize_validator)
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- [`prepare_validator_for_withdrawal`](#prepare_validator_for_withdrawal)
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- [Ethereum 1.0 deposit contract](#ethereum-10-deposit-contract)
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- [Deposit arguments](#deposit-arguments)
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- [Withdrawal credentials](#withdrawal-credentials)
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- [`Deposit` logs](#deposit-logs)
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- [`ChainStart` log](#chainstart-log)
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- [Vyper code](#vyper-code)
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- [On startup](#on-startup)
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- [Beacon chain processing](#beacon-chain-processing)
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- [Beacon chain fork choice rule](#beacon-chain-fork-choice-rule)
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- [Beacon chain state transition function](#beacon-chain-state-transition-function)
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- [Per-slot processing](#per-slot-processing)
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- [Slot](#slot)
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- [Block roots](#block-roots)
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- [Per-block processing](#per-block-processing)
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- [Slot](#slot-1)
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- [Proposer signature](#proposer-signature)
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- [RANDAO](#randao)
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- [Eth1 data](#eth1-data)
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- [Operations](#operations)
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- [Proposer slashings](#proposer-slashings-1)
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- [Attester slashings](#attester-slashings-1)
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- [Attestations](#attestations-1)
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- [Deposits](#deposits-1)
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- [Exits](#exits-1)
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- [Per-epoch processing](#per-epoch-processing)
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- [Helpers](#helpers)
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- [Eth1 data](#eth1-data-1)
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- [Justification](#justification)
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- [Crosslinks](#crosslinks)
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- [Rewards and penalties](#rewards-and-penalties)
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- [Justification and finalization](#justification-and-finalization)
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- [Attestation inclusion](#attestation-inclusion)
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- [Crosslinks](#crosslinks-1)
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- [Ejections](#ejections)
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- [Validator registry and shuffling seed data](#validator-registry-and-shuffling-seed-data)
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- [Final updates](#final-updates)
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- [State root verification](#state-root-verification)
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- [References](#references)
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- [Normative](#normative)
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- [Informative](#informative)
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- [Normative](#normative)
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- [Informative](#informative)
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- [Copyright](#copyright)
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<!-- /TOC -->
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