diff --git a/casper4/fixed_address_creator.py b/casper4/fixed_address_creator.py
index ee282d1..65a362c 100644
--- a/casper4/fixed_address_creator.py
+++ b/casper4/fixed_address_creator.py
@@ -16,3 +16,18 @@ print('Send %d wei to %s' % (t.startgas * t.gasprice,
 
 print('Contract address: 0x'+utils.encode_hex(utils.mk_contract_address(t.sender, 0)))
 print('Code: 0x'+utils.encode_hex(rlp.encode(t)))
+
+sighash = serpent.compile('sqrt.se.py')
+
+# Create transaction
+t = transactions.Transaction(0, 30 * 10**9, 2999999, '', 0, sighash)
+t.startgas = t.intrinsic_gas_used + 50000 + 200 * len(sighash)
+t.v = 27
+t.r = 45
+t.s = 79
+print("Sqrt")
+print('Send %d wei to %s' % (t.startgas * t.gasprice,
+                             '0x'+utils.encode_hex(t.sender)))
+
+print('Contract address: 0x'+utils.encode_hex(utils.mk_contract_address(t.sender, 0)))
+print('Code: 0x'+utils.encode_hex(rlp.encode(t)))
diff --git a/casper4/simple_casper.v.py b/casper4/simple_casper.v.py
index d483114..3b5dcc1 100644
--- a/casper4/simple_casper.v.py
+++ b/casper4/simple_casper.v.py
@@ -28,6 +28,9 @@ second_next_dynasty_wei_delta: wei_value
 # Total deposits during this dynasty
 total_deposits: public(wei_value[num])
 
+# Mapping of dynasty to start epoch of that dynasty
+dynasty_start_epoch: public(num[num])
+
 # Information for use in processing cryptoeconomic commitments
 consensus_messages: public({
     # How many prepares are there for this hash (hash of message hash + view source) from the current dynasty
@@ -43,18 +46,17 @@ consensus_messages: public({
     # And from the previous dynasty
     prev_dyn_commits: wei_value[bytes32],
     # Was the block committed?
-    committed: bool
+    committed: bool,
+    # Value used to calculate the per-epoch fee that validators should be charged
+    deposit_scale_factor: decimal
 }[num]) # index: epoch
 
 # ancestry[x][y] = k > 0: x is a kth generation ancestor of y
-ancestry: num[bytes32][bytes32]
+ancestry: public(num[bytes32][bytes32])
 
 # Number of validators
 nextValidatorIndex: public(num)
 
-# Constant that guides the size of validator rewards
-interest_rate: decimal(1 / sec)
-
 # Time between blocks
 block_time: timedelta
 
@@ -79,11 +81,22 @@ total_destroyed: wei_value
 # Sighash calculator library address
 sighasher: address
 
-def __init__():
+
+# Reward for preparing or committing, as fraction of deposit size
+reward_factor: public(decimal)
+
+# Desired total ether given out assuming 1M ETH deposited
+reward_at_1m_eth: decimal
+
+# Have I already been initialized?
+initialized: bool
+
+def initiate():
+    assert not self.initialized
+    self.initialized = True
     # Set Casper parameters
-    self.interest_rate = 0.000000001
     self.block_time = 14
-    self.epoch_length = 256
+    self.epoch_length = 100
     # Only ~11.5 days, for testing purposes
     self.withdrawal_delay = 1000000
     # Only ~1 day, for testing purposes
@@ -92,7 +105,7 @@ def __init__():
     self.owner = 0x1db3439a222c519ab44bb1144fc28167b4fa6ee6
     # Add an initial validator
     self.validators[0] = {
-        deposit: as_wei_value(3, finney),
+        deposit: as_wei_value(3, ether),
         dynasty_start: 0,
         dynasty_end: 1000000000000000000000000000000,
         withdrawal_epoch: 1000000000000000000000000000000,
@@ -109,18 +122,40 @@ def __init__():
     # Set an initial root of the epoch hash chain
     self.consensus_messages[0].ancestry_hash_justified[0x0000000000000000000000000000000000000000000000000000000000000000] = True
     # Set initial total deposit counter
-    self.total_deposits[0] = as_wei_value(3, finney)
+    self.total_deposits[0] = as_wei_value(3, ether)
+    # Set deposit scale factor
+    self.consensus_messages[0].deposit_scale_factor = 1000000000000000000.0
+    # Total ETH given out assuming 1m ETH deposits
+    self.reward_at_1m_eth = 12.5
 
 # Called at the start of any epoch
 def initialize_epoch(epoch: num):
+    # Check that the epoch actually has started
     computed_current_epoch = block.number / self.epoch_length
     assert epoch <= computed_current_epoch and epoch == self.current_epoch + 1
+    # Set the epoch number
     self.current_epoch = epoch
+    # Increment the dynasty
     if self.consensus_messages[epoch - 1].committed:
         self.dynasty += 1
         self.total_deposits[self.dynasty] = self.total_deposits[self.dynasty - 1] + self.next_dynasty_wei_delta
         self.next_dynasty_wei_delta = self.second_next_dynasty_wei_delta
         self.second_next_dynasty_wei_delta = 0
+        self.dynasty_start_epoch[self.dynasty] = epoch
+    # Compute square root factor
+    ether_deposited_as_number = self.total_deposits[self.dynasty] / as_wei_value(1, ether)
+    sqrt = ether_deposited_as_number / 2.0
+    for i in range(20):
+        sqrt = (sqrt + (ether_deposited_as_number / sqrt)) / 2
+    # Reward factor is the reward given for preparing or committing as a
+    # fraction of that validator's deposit size
+    base_coeff = 1.0 / sqrt * (self.reward_at_1m_eth / 1000)
+    # Rules:
+    # * You are penalized 2x per epoch
+    # * If you prepare, you get 1.5x, and if you commit you get another 1.5x
+    # Hence, assuming 100% performance, your reward per epoch is x
+    self.reward_factor = 1.5 * base_coeff
+    self.consensus_messages[epoch].deposit_scale_factor = self.consensus_messages[epoch - 1].deposit_scale_factor * (1 - 2 * base_coeff)
 
 # Send a deposit to join the validator set
 def deposit(validation_addr: address, withdrawal_addr: address):
@@ -162,6 +197,14 @@ def flick_status(validator_index: num, logout_msg: bytes <= 1024):
     if login_flag:
         # Check that we are logged out
         assert self.validators[validator_index].dynasty_end < self.dynasty
+        # Apply the per-epoch deposit penalty
+        prev_login_epoch = self.dynasty_start_epoch[self.validators[validator_index].dynasty_start]
+        prev_logout_epoch = self.dynasty_start_epoch[self.validators[validator_index].dynasty_end + 1]
+        self.validators[validator_index].deposit = \
+            floor(self.validators[validator_index].deposit *
+                    (self.consensus_messages[prev_logout_epoch].deposit_scale_factor /
+                     self.consensus_messages[prev_login_epoch].deposit_scale_factor))
+        # Log back in
         self.validators[validator_index].dynasty_start = self.dynasty + 2
         self.validators[validator_index].dynasty_end = 1000000000000000000000000000000
         self.second_next_dynasty_wei_delta += self.validators[validator_index].deposit
@@ -179,6 +222,13 @@ def flick_status(validator_index: num, logout_msg: bytes <= 1024):
 def withdraw(validator_index: num):
     # Check that we can withdraw
     assert self.current_epoch >= self.validators[validator_index].withdrawal_epoch
+    # Apply the per-epoch deposit penalty
+    prev_login_epoch = self.dynasty_start_epoch[self.validators[validator_index].dynasty_start]
+    prev_logout_epoch = self.dynasty_start_epoch[self.validators[validator_index].dynasty_end + 1]
+    self.validators[validator_index].deposit = \
+        floor(self.validators[validator_index].deposit *
+                (self.consensus_messages[prev_logout_epoch].deposit_scale_factor /
+                 self.consensus_messages[prev_login_epoch].deposit_scale_factor))
     # Withdraw
     send(self.validators[validator_index].withdrawal_addr, self.validators[validator_index].deposit)
     self.validators[validator_index] = {
@@ -215,6 +265,8 @@ def prepare(validator_index: num, prepare_msg: bytes <= 1024):
     # Check that we are in the right epoch
     assert self.current_epoch == block.number / self.epoch_length
     assert self.current_epoch == epoch
+    # Check that we are at least (epoch length / 4) blocks into the epoch
+    # assert block.number % self.epoch_length >= self.epoch_length / 4
     # Check that this validator was active in either the previous dynasty or the current one
     ds = self.validators[validator_index].dynasty_start
     de = self.validators[validator_index].dynasty_end
@@ -227,8 +279,8 @@ def prepare(validator_index: num, prepare_msg: bytes <= 1024):
     # Check that we have not yet prepared for this epoch
     #assert self.validators[validator_index].max_prepared == epoch - 1
     # Pay the reward if the blockhash is correct
-    if True: #~blockhash(epoch * self.epoch_length) == hash:
-        reward = floor(self.validators[validator_index].deposit * self.interest_rate * self.block_time / 2)
+    if True:  #if blockhash(epoch * self.epoch_length) == hash:
+        reward = floor(self.validators[validator_index].deposit * self.reward_factor)
         self.validators[validator_index].deposit += reward
         self.total_deposits[self.dynasty] += reward
     # Can't prepare for this epoch again
@@ -266,6 +318,8 @@ def commit(validator_index: num, commit_msg: bytes <= 1024):
     # Check that we are in the right epoch
     assert self.current_epoch == block.number / self.epoch_length
     assert self.current_epoch == epoch
+    # Check that we are at least (epoch length / 2) blocks into the epoch
+    # assert block.number % self.epoch_length >= self.epoch_length / 2
     # Check that the commit is justified
     assert self.consensus_messages[epoch].hash_justified[hash]
     # Check that this validator was active in either the previous dynasty or the current one
@@ -278,8 +332,8 @@ def commit(validator_index: num, commit_msg: bytes <= 1024):
     # Check that we have not yet committed for this epoch
     #assert self.validators[validator_index].max_committed == epoch - 1
     # Pay the reward if the blockhash is correct
-    if True: #~blockhash(epoch * self.epoch_length) == hash:
-        reward = floor(self.validators[validator_index].deposit * self.interest_rate * self.block_time / 2)
+    if True:  #if blockhash(epoch * self.epoch_length) == hash:
+        reward = floor(self.validators[validator_index].deposit * self.reward_factor)
         self.validators[validator_index].deposit += reward
         self.total_deposits[self.dynasty] += reward
     # Can't commit for this epoch again
@@ -415,12 +469,17 @@ def commit_non_justification_slash(validator_index: num, commit_msg: bytes <= 10
     }
 
 # Fill in the table for which hash is what-degree ancestor of which other hash
-def derive_ancestry(top: bytes32, middle: bytes32, bottom: bytes32):
-    assert self.ancestry[middle][top]
-    assert self.ancestry[bottom][middle]
-    self.ancestry[bottom][top] = self.ancestry[bottom][middle] + self.ancestry[middle][top]
+def derive_parenthood(older: bytes32, hash: bytes32, newer: bytes32):
+    assert sha3(concat(hash, older)) == newer
+    self.ancestry[older][newer] = 1
 
-def prepare_non_justification_slash(validator_index: num, prepare_msg: bytes <= 1024):
+# Fill in the table for which hash is what-degree ancestor of which other hash
+def derive_ancestry(oldest: bytes32, middle: bytes32, recent: bytes32):
+    assert self.ancestry[middle][recent]
+    assert self.ancestry[oldest][middle]
+    self.ancestry[oldest][recent] = self.ancestry[oldest][middle] + self.ancestry[middle][recent]
+
+def prepare_non_justification_slash(validator_index: num, prepare_msg: bytes <= 1024) -> num:
     # Get hash for signature, and implicitly assert that it is an RLP list
     # consisting solely of RLP elements
     sighash = extract32(raw_call(self.sighasher, prepare_msg, gas=200000, outsize=32), 0)
@@ -440,8 +499,14 @@ def prepare_non_justification_slash(validator_index: num, prepare_msg: bytes <=
     # Check that the view change is old enough
     assert self.current_epoch == block.number / self.epoch_length
     assert (self.current_epoch - epoch) * self.block_time * self.epoch_length > self.insufficiency_slash_delay
-    # Check that the source ancestry hash not had enough prepares
-    assert not self.consensus_messages[source_epoch].ancestry_hash_justified[source_ancestry_hash]
+    # Check that the source ancestry hash not had enough prepares, OR that there is not the
+    # correct ancestry link between the current ancestry hash and source ancestry hash
+    c1 = self.consensus_messages[source_epoch].ancestry_hash_justified[source_ancestry_hash]
+    if epoch - 1 > source_epoch:
+        c2 = self.ancestry[source_ancestry_hash][ancestry_hash] == epoch - 1 - source_epoch
+    else:
+        c2 = source_ancestry_hash == ancestry_hash
+    assert not (c1 and c2)
     # Delete the offending validator, and give a 4% "finder's fee"
     validator_deposit = self.validators[validator_index].deposit
     send(msg.sender, validator_deposit / 25)
diff --git a/casper4/simple_casper_tester.py b/casper4/simple_casper_tester.py
index 1a725c9..99cf08b 100644
--- a/casper4/simple_casper_tester.py
+++ b/casper4/simple_casper_tester.py
@@ -9,7 +9,7 @@ s = t.state()
 t.languages['viper'] = compiler.Compiler()
 t.gas_limit = 9999999
 
-EPOCH_LENGTH = 256
+EPOCH_LENGTH = 100
 
 # Install RLP decoder library
 s.state.set_balance('0xfe2ec957647679d210034b65e9c7db2452910b0c', 9350880000000000)
@@ -56,23 +56,27 @@ def mk_status_flicker(epoch, login, key):
 # Begin the test
 
 print("Starting tests")
+casper.initiate()
 # Initialize the first epoch
-s.state.block_number = EPOCH_LENGTH
+s.state.block_number = EPOCH_LENGTH 
 casper.initialize_epoch(1)
 assert casper.get_nextValidatorIndex() == 1
 start = s.snapshot()
 print("Epoch initialized")
+print("Reward factor: %.8f" % (casper.get_reward_factor() * 2 / 3))
 # Send a prepare message
 casper.prepare(0, mk_prepare(1, '\x35' * 32, '\x00' * 32, 0, '\x00' * 32, t.k0))
 epoch_1_anchash = utils.sha3(b'\x35' * 32 + b'\x00' * 32)
 assert casper.get_consensus_messages__hash_justified(1, b'\x35' * 32)
 assert casper.get_consensus_messages__ancestry_hash_justified(1, epoch_1_anchash)
+print('Gas consumed for a prepare', s.state.receipts[-1].gas_used - s.state.receipts[-2].gas_used)
 print("Prepare message processed")
 # Send a commit message
 casper.commit(0, mk_commit(1, '\x35' * 32, t.k0))
 # Check that we committed
 assert casper.get_consensus_messages__committed(1)
 print("Commit message processed")
+print('Gas consumed for a commit', s.state.receipts[-1].gas_used - s.state.receipts[-2].gas_used)
 # Initialize the second epoch 
 s.state.block_number += EPOCH_LENGTH
 casper.initialize_epoch(2)
@@ -130,11 +134,12 @@ p5 = mk_prepare(5, '\x78' * 32, epoch_4_anchash, 3, epoch_3_anchash, t.k0)
 casper.prepare(0, p5)
 # Test the COMMIT_REQ slashing condition
 kommit = mk_commit(5, b'\x80' * 32, t.k0)
-s.state.block_number += EPOCH_LENGTH * 30
+epoch_inc = 1 + int(86400 / 14 / EPOCH_LENGTH)
+s.state.block_number += EPOCH_LENGTH * epoch_inc
 print("Speeding up time to test remaining two slashing conditions")
-for i in range(6, 36):
+for i in range(6, 6 + epoch_inc):
     casper.initialize_epoch(i)
-print("Epochs up to 36 initialized")
+print("Epochs up to %d initialized" % (6 + epoch_inc))
 snapshot = s.snapshot()
 casper.commit_non_justification_slash(0, kommit)
 s.revert(snapshot)
@@ -146,7 +151,11 @@ except:
 assert not success
 print("COMMIT_REQ slashing condition works")
 # Test the PREPARE_REQ slashing condition
-casper.derive_ancestry(epoch_3_anchash, epoch_2_anchash, epoch_1_anchash)
+casper.derive_parenthood(epoch_3_anchash, b'\x67' * 32, epoch_4_anchash)
+assert casper.get_ancestry(epoch_3_anchash, epoch_4_anchash) == 1
+assert casper.get_ancestry(epoch_4_anchash, epoch_5_anchash) == 1
+casper.derive_ancestry(epoch_3_anchash, epoch_4_anchash, epoch_5_anchash)
+assert casper.get_ancestry(epoch_3_anchash, epoch_5_anchash) == 2
 snapshot = s.snapshot()
 casper.prepare_non_justification_slash(0, p4)
 s.revert(snapshot)
@@ -166,7 +175,7 @@ assert casper.get_current_epoch() == 1
 assert casper.get_consensus_messages__ancestry_hash_justified(0, b'\x00' * 32)
 print("Epoch 1 initialized")
 for k in (t.k1, t.k2, t.k3, t.k4, t.k5, t.k6):
-    casper.deposit(utils.privtoaddr(k), utils.privtoaddr(k), value=3 * 10**15)
+    casper.deposit(utils.privtoaddr(k), utils.privtoaddr(k), value=3 * 10**18)
 print("Processed 6 deposits")
 casper.prepare(0, mk_prepare(1, b'\x10' * 32, b'\x00' * 32, 0, b'\x00' * 32, t.k0))
 casper.commit(0, mk_commit(1, b'\x10' * 32, t.k0))
@@ -186,9 +195,9 @@ s.state.block_number += EPOCH_LENGTH
 casper.initialize_epoch(3)
 print("Epoch 3 initialized")
 assert casper.get_dynasty() == 2
-assert 3 * 10**15 <= casper.get_total_deposits(0) < 4 * 10**15
-assert 3 * 10**15 <= casper.get_total_deposits(1) < 4 * 10**15
-assert 21 * 10**15 <= casper.get_total_deposits(2) < 22 * 10**15
+assert 3 * 10**18 <= casper.get_total_deposits(0) < 4 * 10**18
+assert 3 * 10**18 <= casper.get_total_deposits(1) < 4 * 10**18
+assert 21 * 10**18 <= casper.get_total_deposits(2) < 22 * 10**18
 print("Confirmed new total_deposits")
 try:
     # Try to log out, but sign with the wrong key
@@ -245,8 +254,8 @@ s.state.block_number += EPOCH_LENGTH
 casper.initialize_epoch(5)
 print("Epoch 5 initialized")
 assert casper.get_dynasty() == 4
-assert 21 * 10**15 <= casper.get_total_deposits(3) <= 22 * 10**15
-assert 12 * 10**15 <= casper.get_total_deposits(4) <= 13 * 10**15
+assert 21 * 10**18 <= casper.get_total_deposits(3) <= 22 * 10**18
+assert 12 * 10**18 <= casper.get_total_deposits(4) <= 13 * 10**18
 epoch_5_anchash = utils.sha3(b'\x50' * 32 + epoch_4_anchash)
 # Do three prepares
 for i, k in enumerate([t.k0, t.k1, t.k2]):
@@ -270,8 +279,13 @@ casper.initialize_epoch(6)
 assert casper.get_dynasty() == 5
 print("Epoch 6 initialized")
 # Log back in
+old_deposit_start = casper.get_dynasty_start_epoch(casper.get_validators__dynasty_start(4))
+old_deposit_end = casper.get_dynasty_start_epoch(casper.get_validators__dynasty_end(4) + 1)
+old_deposit = casper.get_validators__deposit(4)
 casper.flick_status(4, mk_status_flicker(6, 1, t.k4))
+new_deposit = casper.get_validators__deposit(4)
 print("One validator logging back in")
+print("Penalty from %d epochs: %.4f" % (old_deposit_end - old_deposit_start, 1 - new_deposit / old_deposit))
 assert casper.get_validators__dynasty_start(4) == 7
 # Here three prepares and three commits should be sufficient!
 epoch_6_anchash = utils.sha3(b'\x60' * 32 + epoch_5_anchash)
@@ -299,8 +313,8 @@ s.state.block_number += EPOCH_LENGTH
 casper.initialize_epoch(8)
 assert casper.get_dynasty() == 7
 print("Epoch 8 initialized")
-assert 12 * 10**15 <= casper.get_total_deposits(6) <= 13 * 10**15
-assert 15 * 10**15 <= casper.get_total_deposits(7) <= 16 * 10**15
+assert 12 * 10**18 <= casper.get_total_deposits(6) <= 13 * 10**18
+assert 15 * 10**18 <= casper.get_total_deposits(7) <= 16 * 10**18
 epoch_8_anchash = utils.sha3(b'\x80' * 32 + epoch_7_anchash)
 # Do three prepares
 for i, k in enumerate([t.k0, t.k1, t.k2]):
diff --git a/casper4/sqrt.se.py b/casper4/sqrt.se.py
new file mode 100644
index 0000000..fe4775a
--- /dev/null
+++ b/casper4/sqrt.se.py
@@ -0,0 +1,12 @@
+with inp = ~calldataload(0):
+    foo = inp
+    exp = 0
+    while foo >= 256:
+        foo = ~div(foo, 256)
+        exp += 1
+    with x = ~div(inp, 16 ** exp):
+        while 1:
+            y = ~div(x + ~div(inp, x) + 1, 2)
+            if x == y:
+                return x
+            x = y