notebooks/altair_incentives.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "emotional-assistant",
   "metadata": {},
   "source": [
    "## How to use\n",
    "\n",
    "In this noteboook we test the rewards given out by the protocol to different types of validators. Our `fast` config reduces the size of most constants to avoid allocating more memory than necessary (we'll only test with a few validators). We also reduce the number of slots per epoch to speed things up. All these changes are without loss of generality.\n",
    "\n",
    "You may test various spec versions by renaming either of the `specs_*.py` files in the `beaconrunner` folder to `specs.py`. Current version tested is v1.1.0-alpha.7."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "structured-shannon",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os, sys\n",
    "sys.path.insert(1, os.path.realpath(os.path.pardir))\n",
    "sys.path.insert(1, os.path.realpath(os.path.pardir) + \"/beaconrunner\")\n",
    "import beaconrunner as br\n",
    "\n",
    "import types\n",
    "from eth2spec.utils.ssz.ssz_impl import hash_tree_root\n",
    "\n",
    "from cadCAD_tools.profiling.visualizations import visualize_substep_impact\n",
    "\n",
    "import pandas as pd\n",
    "import plotly.express as px\n",
    "import plotly.io as pio\n",
    "pd.options.plotting.backend = \"plotly\"\n",
    "pio.renderers.default = \"plotly_mimetype+notebook_connected\"\n",
    "import plotly.graph_objects as go"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "saving-kelly",
   "metadata": {},
   "source": [
    "Below are metrics extracted from the state of the simulation. We don't really care about most of them except for `get_current_validator_state`, but they are left here for future use/reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "enhanced-staff",
   "metadata": {},
   "outputs": [],
   "source": [
    "def extract_state(s):\n",
    "    validators = s[\"network\"].validators\n",
    "    validator = validators[1]\n",
    "    head = br.specs.get_head(validator.store)\n",
    "    current_state = validator.store.block_states[head].copy()\n",
    "    return current_state\n",
    "\n",
    "def current_slot(params, step, sL, s, _input):\n",
    "    return (\"current_slot\", s[\"network\"].validators[0].data.slot)\n",
    "\n",
    "def total_balance_asap(params, step, sL, s, _input):\n",
    "    validators = s[\"network\"].validators\n",
    "    current_state = extract_state(s)\n",
    "    current_epoch = br.specs.get_current_epoch(current_state)\n",
    "    asap_indices = [i for i, v in enumerate(validators) if v.validator_behaviour == \"asap\"]\n",
    "    asap_balances = [b for i, b in enumerate(current_state.balances) if i in asap_indices]\n",
    "    return (\"total_balance_asap\", sum(asap_balances))\n",
    "\n",
    "def get_base_reward(params, step, sL, s, _input):\n",
    "    current_state = extract_state(s)\n",
    "    base_reward = br.specs.get_base_reward(current_state, 0)\n",
    "    return (\"base_reward\", base_reward)\n",
    "\n",
    "def get_block_proposer(params, step, sL, s, _input):\n",
    "    current_state = extract_state(s)\n",
    "    block_proposer = [v.validator_index for v in s[\"network\"].validators if v.data.current_proposer_duties[s[\"current_slot\"] % br.specs.SLOTS_PER_EPOCH]][0]\n",
    "    return (\"block_proposer\", block_proposer)\n",
    "\n",
    "def get_block_proposer_balance(params, step, sL, s, _input):\n",
    "    current_state = extract_state(s)\n",
    "    block_proposer_balance = current_state.balances[s[\"block_proposer\"]]\n",
    "    return (\"block_proposer_balance\", block_proposer_balance)\n",
    "\n",
    "def get_sync_committee(params, step, sL, s, _input):\n",
    "    current_state = extract_state(s)\n",
    "    current_epoch = br.specs.get_current_epoch(current_state)\n",
    "    sync_committee = current_state.current_sync_committee.pubkeys\n",
    "    val_pubkeys = [v.pubkey for v in current_state.validators]\n",
    "    sync_committee_indices = [val_pubkeys.index(pubkey) for pubkey in sync_comittee]\n",
    "    return (\"sync_committee\", sync_committee_indices)\n",
    "\n",
    "def get_head(params, step, sL, s, _input):\n",
    "    validators = s[\"network\"].validators\n",
    "    validator = validators[0]\n",
    "    head = br.specs.get_head(validator.store).hex()[0:6]\n",
    "    return (\"head\", head)\n",
    "\n",
    "def get_current_validator_state(params, step, sL, s, _input):\n",
    "    current_state = extract_state(s)\n",
    "    current_validator_state = []\n",
    "    for v in s[\"network\"].validators:\n",
    "        current_validator_state += [{\n",
    "            \"slot\": v.data.slot,\n",
    "            \"validator_index\": v.validator_index,\n",
    "            \"balance\": current_state.balances[v.validator_index],\n",
    "            \"block_proposer\": 1 if s[\"block_proposer\"] == v.validator_index else 0,\n",
    "            \"attester\": 1 if v.data.current_attest_slot == v.data.slot else 0,\n",
    "            \"sync_committee\": len(v.data.current_sync_committee),\n",
    "        }]\n",
    "    return (\"current_validator_state\", current_validator_state)\n",
    "\n",
    "observers = {\n",
    "    \"current_slot\": current_slot,\n",
    "    \"total_balance_asap\": total_balance_asap,\n",
    "    \"base_reward\": get_base_reward,\n",
    "    \"block_proposer\": get_block_proposer,\n",
    "    \"block_proposer_balance\": get_block_proposer_balance,\n",
    "#     \"sync_committee\": get_sync_committee,\n",
    "    \"head\": get_head,\n",
    "    \"current_validator_state\": get_current_validator_state,\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "current-piano",
   "metadata": {},
   "source": [
    "Run the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "silent-abortion",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:root:Starting simulation 0 / run 0 / subset 0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "will simulate 4 epochs ( 16 slots ) at frequency 1 moves/second\n",
      "total 192 simulation steps\n",
      "19 proposing block for slot 1\n",
      "6 proposing block for slot 2\n",
      "7 proposing block for slot 3\n",
      "14 proposing block for slot 4\n",
      "9 proposing block for slot 5\n",
      "10 proposing block for slot 6\n",
      "0 proposing block for slot 7\n",
      "10 proposing block for slot 8\n",
      "13 proposing block for slot 9\n",
      "timestep 100 of run 1\n",
      "18 proposing block for slot 10\n",
      "3 proposing block for slot 11\n",
      "0 proposing block for slot 12\n",
      "2 proposing block for slot 13\n",
      "3 proposing block for slot 14\n",
      "12 proposing block for slot 15\n",
      "11 proposing block for slot 16\n"
     ]
    }
   ],
   "source": [
    "from random import sample\n",
    "from beaconrunner.validators.ASAPValidator import ASAPValidator\n",
    "\n",
    "num_validators = 20\n",
    "\n",
    "# Initiate validators\n",
    "validators = []\n",
    "for i in range(num_validators):\n",
    "    new_validator = ASAPValidator(i)\n",
    "    validators.append(new_validator)\n",
    "\n",
    "# Create a genesis state\n",
    "(genesis_state, genesis_block) = br.simulator.get_genesis_state_block(validators)\n",
    "\n",
    "# Validators load the state\n",
    "[v.load_state(genesis_state.copy(), genesis_block.copy()) for v in validators]\n",
    "\n",
    "# We skip the genesis block\n",
    "br.simulator.skip_genesis_block(validators)\n",
    "\n",
    "# Create the network\n",
    "set_a = br.network.NetworkSet(validators=list(range(num_validators)))\n",
    "network_sets = list([set_a])\n",
    "network = br.network.Network(validators = validators, sets = network_sets)\n",
    "\n",
    "# Set simulation parameters\n",
    "parameters = br.simulator.SimulationParameters({\n",
    "    \"num_epochs\": 4,\n",
    "    \"run_index\": 1,\n",
    "    \"frequency\": 1,\n",
    "    \"network_update_rate\": 1.0,\n",
    "})\n",
    "\n",
    "df = br.simulator.simulate(network, parameters, observers) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "liable-aurora",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "df = df.drop(columns=['network'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "communist-charleston",
   "metadata": {},
   "source": [
    "We collect the validator state data in a separate dataframe, of schema `(slot, validator_index, balance, block_proposer, attester, sync_committee)`. We ignore the first few epochs (rewards aren't given out, or imperfectly) and make sure the key `(slot, validator_index)` is unique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3111b718-767b-43e1-b0c8-3a040944bc9f",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>current_slot</th>\n",
       "      <th>total_balance_asap</th>\n",
       "      <th>base_reward</th>\n",
       "      <th>block_proposer</th>\n",
       "      <th>block_proposer_balance</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>640000000000</td>\n",
       "      <td>2560000</td>\n",
       "      <td>19</td>\n",
       "      <td>32000000000</td>\n",
       "      <td>168f82</td>\n",
       "      <td>[{'slot': 1, 'validator_index': 0, 'balance': ...</td>\n",
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       "      <td>0</td>\n",
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       "      <td>Initial State</td>\n",
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       "    <tr>\n",
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       "      <td>1</td>\n",
       "      <td>640000000000</td>\n",
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       "      <td>19</td>\n",
       "      <td>32000000000</td>\n",
       "      <td>168f82</td>\n",
       "      <td>[{'slot': 1, 'validator_index': 0, 'balance': ...</td>\n",
       "      <td>1.626053e+09</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Initial measure runtime</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>640000000000</td>\n",
       "      <td>2560000</td>\n",
       "      <td>19</td>\n",
       "      <td>32000000000</td>\n",
       "      <td>168f82</td>\n",
       "      <td>[{'slot': 1, 'validator_index': 0, 'balance': ...</td>\n",
       "      <td>1.626053e+09</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>Attestations</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>640000000000</td>\n",
       "      <td>2560000</td>\n",
       "      <td>19</td>\n",
       "      <td>32000000000</td>\n",
       "      <td>168f82</td>\n",
       "      <td>[{'slot': 1, 'validator_index': 0, 'balance': ...</td>\n",
       "      <td>1.626053e+09</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>Measure runtime 0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>640000000000</td>\n",
       "      <td>2560000</td>\n",
       "      <td>19</td>\n",
       "      <td>32000000000</td>\n",
       "      <td>168f82</td>\n",
       "      <td>[{'slot': 1, 'validator_index': 0, 'balance': ...</td>\n",
       "      <td>1.626053e+09</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>Sync committee</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1724</th>\n",
       "      <td>16</td>\n",
       "      <td>640132299955</td>\n",
       "      <td>2560000</td>\n",
       "      <td>11</td>\n",
       "      <td>32004319997</td>\n",
       "      <td>0aea1b</td>\n",
       "      <td>[{'slot': 16, 'validator_index': 0, 'balance':...</td>\n",
       "      <td>1.626053e+09</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>192</td>\n",
       "      <td>Measure runtime 1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1725</th>\n",
       "      <td>16</td>\n",
       "      <td>640132299955</td>\n",
       "      <td>2560000</td>\n",
       "      <td>11</td>\n",
       "      <td>32004319997</td>\n",
       "      <td>0aea1b</td>\n",
       "      <td>[{'slot': 16, 'validator_index': 0, 'balance':...</td>\n",
       "      <td>1.626053e+09</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>192</td>\n",
       "      <td>Block proposals</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1726</th>\n",
       "      <td>16</td>\n",
       "      <td>640132299955</td>\n",
       "      <td>2560000</td>\n",
       "      <td>11</td>\n",
       "      <td>32004319997</td>\n",
       "      <td>0aea1b</td>\n",
       "      <td>[{'slot': 16, 'validator_index': 0, 'balance':...</td>\n",
       "      <td>1.626053e+09</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>192</td>\n",
       "      <td>Measure runtime 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1727</th>\n",
       "      <td>17</td>\n",
       "      <td>640132299955</td>\n",
       "      <td>2560000</td>\n",
       "      <td>11</td>\n",
       "      <td>32004319997</td>\n",
       "      <td>0aea1b</td>\n",
       "      <td>[{'slot': 17, 'validator_index': 0, 'balance':...</td>\n",
       "      <td>1.626053e+09</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>192</td>\n",
       "      <td>Simulation tick</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1728</th>\n",
       "      <td>17</td>\n",
       "      <td>640132299955</td>\n",
       "      <td>2560000</td>\n",
       "      <td>11</td>\n",
       "      <td>32004319997</td>\n",
       "      <td>0aea1b</td>\n",
       "      <td>[{'slot': 17, 'validator_index': 0, 'balance':...</td>\n",
       "      <td>1.626053e+09</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "      <td>192</td>\n",
       "      <td>Measure runtime 3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1729 rows × 14 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      current_slot  total_balance_asap  base_reward  block_proposer  \\\n",
       "0                1        640000000000      2560000              19   \n",
       "1                1        640000000000      2560000              19   \n",
       "2                1        640000000000      2560000              19   \n",
       "3                1        640000000000      2560000              19   \n",
       "4                1        640000000000      2560000              19   \n",
       "...            ...                 ...          ...             ...   \n",
       "1724            16        640132299955      2560000              11   \n",
       "1725            16        640132299955      2560000              11   \n",
       "1726            16        640132299955      2560000              11   \n",
       "1727            17        640132299955      2560000              11   \n",
       "1728            17        640132299955      2560000              11   \n",
       "\n",
       "      block_proposer_balance    head  \\\n",
       "0                32000000000  168f82   \n",
       "1                32000000000  168f82   \n",
       "2                32000000000  168f82   \n",
       "3                32000000000  168f82   \n",
       "4                32000000000  168f82   \n",
       "...                      ...     ...   \n",
       "1724             32004319997  0aea1b   \n",
       "1725             32004319997  0aea1b   \n",
       "1726             32004319997  0aea1b   \n",
       "1727             32004319997  0aea1b   \n",
       "1728             32004319997  0aea1b   \n",
       "\n",
       "                                current_validator_state      run_time  \\\n",
       "0     [{'slot': 1, 'validator_index': 0, 'balance': ...  0.000000e+00   \n",
       "1     [{'slot': 1, 'validator_index': 0, 'balance': ...  1.626053e+09   \n",
       "2     [{'slot': 1, 'validator_index': 0, 'balance': ...  1.626053e+09   \n",
       "3     [{'slot': 1, 'validator_index': 0, 'balance': ...  1.626053e+09   \n",
       "4     [{'slot': 1, 'validator_index': 0, 'balance': ...  1.626053e+09   \n",
       "...                                                 ...           ...   \n",
       "1724  [{'slot': 16, 'validator_index': 0, 'balance':...  1.626053e+09   \n",
       "1725  [{'slot': 16, 'validator_index': 0, 'balance':...  1.626053e+09   \n",
       "1726  [{'slot': 16, 'validator_index': 0, 'balance':...  1.626053e+09   \n",
       "1727  [{'slot': 17, 'validator_index': 0, 'balance':...  1.626053e+09   \n",
       "1728  [{'slot': 17, 'validator_index': 0, 'balance':...  1.626053e+09   \n",
       "\n",
       "      simulation  subset  run  substep  timestep            substep_label  \n",
       "0              0       0    1        0         0            Initial State  \n",
       "1              0       0    1        1         1  Initial measure runtime  \n",
       "2              0       0    1        2         1             Attestations  \n",
       "3              0       0    1        3         1        Measure runtime 0  \n",
       "4              0       0    1        4         1           Sync committee  \n",
       "...          ...     ...  ...      ...       ...                      ...  \n",
       "1724           0       0    1        5       192        Measure runtime 1  \n",
       "1725           0       0    1        6       192          Block proposals  \n",
       "1726           0       0    1        7       192        Measure runtime 2  \n",
       "1727           0       0    1        8       192          Simulation tick  \n",
       "1728           0       0    1        9       192        Measure runtime 3  \n",
       "\n",
       "[1729 rows x 14 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize_substep_impact(df, relative=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "patient-lottery",
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools\n",
    "import pandas as pd\n",
    "pd.set_option('display.max_rows', 100)\n",
    "validator_df = pd.DataFrame(\n",
    "    itertools.chain(*df[((df.substep == 0) | (df.substep == max(df.substep))) & (df.timestep % 12 == 1) & (df.current_slot > 11)][\"current_validator_state\"].iloc[:])\n",
    ")\n",
    "validator_df[\"previous_balance\"] = validator_df.groupby([\"validator_index\"])[[\"balance\"]].shift()\n",
    "validator_df[\"balance_diff\"] = validator_df[\"balance\"] - validator_df[\"previous_balance\"]\n",
    "validator_df = validator_df[validator_df.slot > 12]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "unsigned-arctic",
   "metadata": {},
   "source": [
    "## Obtaining rewards per duty\n",
    "\n",
    "We isolate validators who occupied a unique role over a slot to obtain the rewards for block proposers and sync committee members. When rewards are given out during the epoch transition, the minimum received by any validator is received by a validator who neither proposed a block for the whole epoch and was never part of the sync committee, giving us the attester reward received by one validator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "brilliant-static",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "block proposer reward = 1599997.0\n"
     ]
    }
   ],
   "source": [
    "block_proposer_reward = validator_df[(validator_df.block_proposer == 1) & (validator_df.sync_committee == 0)].iloc[0][\"balance_diff\"]\n",
    "print(f\"block proposer reward = {block_proposer_reward}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "prompt-portrait",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "attester reward = 2160000.0\n"
     ]
    }
   ],
   "source": [
    "attester_reward = min(validator_df[validator_df.slot % br.specs.SLOTS_PER_EPOCH == 0][\"balance_diff\"])\n",
    "print(f\"attester reward = {attester_reward}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "breathing-butter",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sync committee reward = 100000.0\n"
     ]
    }
   ],
   "source": [
    "sync_committee_reward = validator_df[(validator_df.block_proposer == 0) & (validator_df.sync_committee == 1)].iloc[0][\"balance_diff\"]\n",
    "print(f\"sync committee reward = {sync_committee_reward}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "polished-arabic",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "base reward = 2560000\n"
     ]
    }
   ],
   "source": [
    "base_reward = df.iloc[0][\"base_reward\"]\n",
    "print(f\"base reward = {base_reward}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "engaging-observation",
   "metadata": {},
   "source": [
    "Make our checks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "available-description",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "expected total per epoch = 51200000 vs. realised total = 51199988.0\n",
      "percent of attester rewards = 0.84375, expected 0.84375\n",
      "percent of sync committee rewards = 0.03125, expected 0.03125\n",
      "percent of block proposer rewards = 0.124999765625, expected 0.125\n"
     ]
    }
   ],
   "source": [
    "total_per_epoch = num_validators * base_reward\n",
    "total_for_proposers = int(br.specs.SLOTS_PER_EPOCH) * block_proposer_reward\n",
    "expected_proposers = float(br.specs.PROPOSER_WEIGHT) / br.specs.WEIGHT_DENOMINATOR\n",
    "\n",
    "total_for_attesters = num_validators * attester_reward\n",
    "expected_attesters = float(br.specs.TIMELY_SOURCE_WEIGHT + br.specs.TIMELY_TARGET_WEIGHT + br.specs.TIMELY_HEAD_WEIGHT) / br.specs.WEIGHT_DENOMINATOR\n",
    "\n",
    "total_for_sync_committee = int(br.specs.SLOTS_PER_EPOCH) * int(br.specs.SYNC_COMMITTEE_SIZE) * sync_committee_reward\n",
    "expected_sync = float(br.specs.SYNC_REWARD_WEIGHT) / br.specs.WEIGHT_DENOMINATOR\n",
    "\n",
    "print(f\"expected total per epoch = {total_per_epoch} vs. realised total = {total_for_proposers + total_for_attesters + total_for_sync_committee}\")\n",
    "print(f\"percent of attester rewards = {total_for_attesters / total_per_epoch}, expected {expected_attesters}\")\n",
    "print(f\"percent of sync committee rewards = {total_for_sync_committee / total_per_epoch}, expected {expected_sync}\")\n",
    "print(f\"percent of block proposer rewards = {total_for_proposers / total_per_epoch}, expected {expected_proposers}\")"
   ]
  },
  {
   "cell_type": "raw",
   "id": "driven-allocation",
   "metadata": {},
   "source": [
    "Simulating validator rewards in Altair"
   ]
  },
  {
   "cell_type": "raw",
   "id": "touched-messenger",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "raw",
   "id": "caring-publisher",
   "metadata": {},
   "source": [
    "// References + footnotes\n",
    "\n",
    "// Authors\n",
    "let authorData = [\"barnabe\"];"
   ]
  },
  {
   "cell_type": "raw",
   "id": "persistent-proof",
   "metadata": {},
   "source": []
  }
 ],
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  "desc": "Checking incentive soundness in Altair",
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