$$ \newcommand \Genesis {\mathrm{Genesis}} \newcommand \GenesisID {\Genesis\mathrm{ID}} \newcommand \pk {\mathrm{pk}} \newcommand \spk {\mathrm{spk}} \newcommand \Tx {\mathrm{Tx}} \newcommand \TxType {\mathrm{TxType}} \newcommand \TxTail {\Tx\mathrm{Tail}} \newcommand \Hash {\mathrm{Hash}} \newcommand \FirstValidRound {r_\mathrm{fv}} \newcommand \LastValidRound {r_\mathrm{lv}} \newcommand \sppk {\mathrm{sppk}} \newcommand \nonpart {\mathrm{nonpart}} \newcommand \MaxTxTail {\mathrm{TxTail}_{\max}} \newcommand \abs[1] {\lvert #1 \rvert} \newcommand \floor[1] {\left \lfloor #1 \right \rfloor } $$

$$ \newcommand \MaxTxnNoteBytes {T_{m,\max}} \newcommand \Stake {\mathrm{Stake}} \newcommand \Fee {\mathrm{fee}} \newcommand \MinTxnFee {T_{\Fee,\min}} \newcommand \PayoutsGoOnlineFee {B_{p,\Fee}} \newcommand \Eligibility {\mathrm{A_e}} \newcommand \Units {\mathrm{Units}} \newcommand \MinBalance {b_{\min}} $$

Validity and State Changes

The new Ledger’s state that results from applying a valid block is the account state that results from applying each transaction in that block, in sequence.

For a block to be valid, each transaction in its transaction sequence MUST be valid at the block’s round $ r $ and for the block’s genesis identifier $ \GenesisID_B $.

For a transaction

$$ \Tx = (\GenesisID, \TxType, \FirstValidRound, \LastValidRound, I, I^\prime, I_0, f, a, x, N, \pk, \sppk, \nonpart, \ldots) $$

(where $ \ldots $ represents fields specific to transaction types besides payand keyreg) to be valid at the intermediate state $ \rho $ in round $ r $ for the genesis identifier $ \GenesisID_B $, the following conditions MUST all hold:

It MUST represent a transition between two valid account states.
Either $ \GenesisID = \GenesisID_B $ or $ \GenesisID $ is the empty string.
$ \TxType $ is either pay, keyreg, acfg, axfer, afrz, appl, stpf, or hb.
There are no extra fields that do not correspond to $ \TxType $.
$ 0 \leq \LastValidRound - \FirstValidRound \leq \MaxTxTail $.
$ \FirstValidRound \leq r \leq \LastValidRound $.
$ \abs{N} \leq \MaxTxnNoteBytes $.
$ I \neq I_\mathrm{pool} $, $ I \neq I_f $, and $ I \neq 0 $.
$ \Stake(r+1, I) \geq f \geq \MinTxnFee $.
The transaction is properly authorized as described in the Authorization and Signatures section.
$ \Hash(\Tx) \notin \TxTail_r $.
If $ x \neq 0 $, there exists no $ \Tx^\prime \in \TxTail $ with sender $ I^\prime $, lease value $ x^\prime $, and last valid round $ \LastValidRound^\prime $ such that $ I^\prime = I $, $ x^\prime = x $, and $ \LastValidRound^\prime \geq r $.
If $ \TxType $ is pay,
- $ I \neq I_k $ or both $ I^\prime \neq I_\mathrm{pool} $ and $ I_0 \neq 0 $.
- $ \Stake(r+1, I) - f > a $ if $ I^\prime \neq I $ and $ I^\prime \neq 0 $.
- If $ I_0 \neq 0 $, then $ I_0 \neq I $.
- If $ I_0 \neq 0 $, $ I $ cannot hold any assets.
If $ \TxType $ is keyreg,
- $ p_{\rho, I} \ne 2 $ (i.e., nonparticipatory accounts may not issue keyreg transactions)
- If $ \nonpart $ is True then $ \spk = 0 $, $ \pk = 0 $ and $ \sppk = 0 $

Given that a transaction is valid, it produces the following updated account state for intermediate state $ \rho+1 $:

For $ I $:
- If $ I_0 \neq 0 $ then $ a_{\rho+1, I} = a^\prime_{\rho+1, I} = a^\ast_{\rho+1, I} = p_{\rho+1, I} = \pk_{\rho+1, I} = 0 $;
- otherwise,
  - $ a_{\rho+1, I} = \Stake(\rho+1, I) - a - f $ if $ I^\prime \neq I $ and $ a_{\rho+1, I} = \Stake(\rho+1, I) - f $ otherwise.
  - $ a^\prime_{\rho+1, I} = T_{r+1} $.
  - $ a^\ast_{\rho+1, I} = a^\ast_{\rho, I} + (T_{r+1} - a^\prime_{\rho, I}) \floor{\frac{a_{\rho, I}}{A}} $.
  - If $ \TxType $ is pay, then $ \pk_{\rho+1, I} = \pk_{\rho, I} $ and $ p_{\rho+1, I} = p_{\rho, I} $
  - Otherwise (i.e., if $ \TxType $ is keyreg),
    - $ \pk_{\rho+1, I} = \pk $
    - $ p_{\rho+1, I} = 0 $ if $ \pk = 0 $ and $ \nonpart = \texttt{False} $
    - $ p_{\rho+1, I} = 2 $ if $ \pk = 0 $ and $ \nonpart = \texttt{True} $
    - $ p_{\rho+1, I} = 1 $ if $ \pk \ne 0 $
    - If $ f > \PayoutsGoOnlineFee $, then $ \Eligibility{\rho+1, I} = \texttt{True} $
For $ I^\prime $ if $ I \neq I^\prime $ and either $ I^\prime \neq 0 $ or $ a \neq 0 $:
- $ a_{\rho+1, I^\prime} = \Stake(\rho+1, I^\prime) + a $.
- $ a^\prime_{\rho+1, I^\prime} = T_{r+1} $.
- $ a^\ast_{\rho+1, I^\prime} = a^\ast_{\rho, I^\prime} + (T_{r+1} - a^\prime_{\rho, I^\prime}) \floor{\frac{a_{\rho, I^\prime}}{A}} $.
For $ I_0 $ if $ I_0 \neq 0 $:
- $ a_{\rho+1, I_0} = \Stake(\rho+1, I_0) + \Stake(\rho+1, I) - a - f $.
- $ a^\prime_{\rho+1, I_0} = T_{r+1} $.
- $ a^\ast_{\rho+1, I_0} = a^\ast_{\rho, I_0} + (T_{r+1} - a^\prime_{\rho, I_0}) \floor{\frac{a_{\rho, I_0}}{A}} $.
For all other $ I^\ast \neq I $, the account state is identical to that in view $ \rho $.

For transaction types other than pay and keyreg, account state is updated based on the reference logic described in the Transaction section.

Additionally, for all types of transactions, if the rekey to address of the transaction is nonzero and does not match the transaction sender address, then the transaction sender account’s spending key is set to the rekey to address. If the rekey to address of the transaction does match the transaction sender address, then the transaction sender account’s spending key is set to zero.

The rest of this section describes the legacy Distribution Rewards system. If the $ R_r $ rewards rate parameter is $ 0 $, all computations keep values constant and no legacy reward distribution is carried out.

The final intermediate account $ \rho_k $ state changes the balance of the incentive pool as follows:

$$ a_{\rho_k, I_\mathrm{pool}} = a_{\rho_{k-1}, I_\mathrm{pool}} - R_r(\Units(r)) $$

An account state in the intermediate state $ \rho+1 $ and at round $ r $ is valid if all following conditions hold:

For all addresses $ I \notin \{I_\mathrm{pool}, I_f\} $, either $ \Stake(\rho+1, I) = 0 $ or $ \Stake(\rho+1, I) \geq \MinBalance \times (1 + N_A) $, where $ N_A $ is the number of assets held by that account.
$ \sum_I \Stake(\rho+1, I) = \sum_I \Stake(\rho, I) $.

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Validity and State Changes