feat: blob transactions

hub/columns/stack.tex

@@ -39,6 +39,7 @@
 		\item $\stackDecAddFlag$
 		\item $\stackDecBinFlag$
 		\item $\stackDecBtcFlag$
+		\item $\stackDecBlobHashFlag$
 		\item $\stackDecCallFlag$
 		\item $\stackDecConFlag$
 		\item $\stackDecCopyFlag$

hub/instruction_handling/stateless_constraints.tex

@@ -69,12 +69,6 @@
 			\item \If $\twoArgInst = 1$ \Then $\twoOneSP_{i}$,   see section~(\ref{hub: stack patterns: 2_1});
 			\item \If $\treArgInst = 1$ \Then $\threeOneSP_{i}$, see section~(\ref{hub: stack patterns: 3_1});
 		\end{enumerate}
-	\item[\underline{Zero high part for \wcpMod{}:}]\label{hub: instruction handling: stateless: wcp high part is zero}
-		\If $\stackDecWcpFlag_{i} = 1$ \Then we impose that
-		\begin{enumerate}
-			\item $\stackItemValHi{4}_{i} = 0$
-			\item $\stackItemValLo{4}_{i} \cdot (1 - \stackItemValLo{4}_{i}) = 0$ \quad (\trash)
-		\end{enumerate}
 	\item[\underline{Setting $\nonStackRows$:}] \If $\isStatelessInst_{i} = 1$ \Then we impose that
 		\[
 			\nonStackRows_{i} = \instIsExp_{i} + \cmc_{i}

hub/lookups/into_add_bin_mod_mul_shf_wcp.tex

@@ -43,5 +43,4 @@
 \end{description}
 \saNote{}
 The \wcpMod{} doesn't have a ``$\resHi$'' column.
-For that module we omit $\stackItemValHi{4}$ from the source and ``$\resHi$'' from the target.
-Recall from section~(\ref{hub: instruction handling: stateless: wcp high part is zero}) that for \wcpMod{}-instructions we impose the vanishing of the ``result's'' high part.
+For that module we change ``$\resHi$'' from the target to 0 to ensure the high paty of the result is 0. 

hub/lookups/into_instruction_decoder.tex

@@ -21,6 +21,7 @@
 				\item $\stackDecAddFlag$
 				\item $\stackDecBinFlag$
 				\item $\stackDecBtcFlag$
+				\item $\stackDecBlobHashFlag$
 				\item $\stackDecCallFlag$
 				\item $\stackDecConFlag$
 				\item $\stackDecCopyFlag$
@@ -66,6 +67,7 @@
 				\item $\addFlag$
 				\item $\binFlag$
 				\item $\btcFlag$
+				\item $\blobHashFlag$
 				\item $\callFlag$
 				\item $\conFlag$
 				\item $\copyFlag$

pkg/flags_stamps_selectors.sty

@@ -1725,3 +1725,5 @@
 \newcommand{\iBlsRefTableSelect}{\imported{\blsRefTableSelect}}
 \newcommand{\stackDecBlsRefTableFlag}{\stackInstructionDecodedColumn{\blsRefTableFlag}}
 
+\newcommand{\blobHashFlag}{\col{BLOB\_HASH\_FLAG}}
+\newcommand{\stackDecBlobHashFlag}{\stackInstructionDecodedColumn{\blobHashFlag}}

pkg/rlp_patterns.sty

@@ -254,6 +254,22 @@
         \end{array} \right]
     }
 
+%%  BLOB HASH
+%%%%%%%%%%%
+
+\newcommand{\rlpProcessBlobHashName} {\rlpDataProcessingCompoundConstraints{BLOBHASH}}
+\newcommand{\rlpProcessBlobHash} [1] {
+    \setkeys[RLP]{var}{#1}
+    \rlpProcessBytesThirtyTwoName _{\cmdRLP@var@anchorRow}
+        \left[ \begin{array}{ll}
+            \utt{Rel. row offset:} & \cmdRLP@var@relOffset \\
+            \utt{Data hi part:}    & \cmdRLP@var@dataHi \\
+            \utt{Data lo part:}    & \cmdRLP@var@dataLo \\
+        \end{array} \right]
+    }
+
+%% DATA PRICING 
+
 \newcommand{\rlpUtilsInstCallDataPricingName}    {\rlpUtilsInstructionCall{DATA\_PRICING}}
 \newcommand{\rlpUtilsInstCallDataPricing}    [1] {
     \setkeys[RLP]{var}{#1}
@@ -276,6 +292,8 @@
         \end{array} \right]
     }
 
+%% ADDRESS
+
 \newcommand{\rlpProcessAddressName}    {\rlpDataProcessingCompoundConstraints{ADDRESS}}
 \newcommand{\rlpProcessAddress}    [1] {
     \setkeys[RLP]{var}{#1}

pkg/rlp_tx.sty

@@ -42,6 +42,8 @@
 \newcommand{\phaseValueValue}                         {\rlpTxnPhase{value}}
 \newcommand{\phaseDataValue}                          {\rlpTxnPhase{data}}
 \newcommand{\phaseAccessListValue}                    {\rlpTxnPhase{access\_list}}
+\newcommand{\phaseMaxFeePerBlobGasValue}              {\rlpTxnPhase{max\_fee\_per\_blob\_gas}}
+\newcommand{\phaseBlobVersionedHashesValue}           {\rlpTxnPhase{blob\_versioned\_hashes}}
 \newcommand{\phaseBetaValue}                          {\rlpTxnPhase{beta}}
 \newcommand{\phaseYValue}                             {\rlpTxnPhase{y}}
 \newcommand{\phaseRValue}                             {\rlpTxnPhase{r}}
@@ -60,6 +62,8 @@
 \newcommand{\phaseValue}                              {\col{IS\_VALUE}}
 \newcommand{\phaseData}                               {\col{IS\_DATA}}
 \newcommand{\phaseAccessList}                         {\col{IS\_ACCESS\_LIST}}
+\newcommand{\phaseMaxFeePerBlobGas}                   {\col{IS\_MAX\_FEE\_PER\_BLOB\_GAS}}
+\newcommand{\phaseBlobVersionedHashes}                {\col{IS\_BLOB\_VERSIONED\_HASHES}}
 \newcommand{\phaseBeta}                               {\col{IS\_BETA}}
 \newcommand{\phaseY}                                  {\col{IS\_Y}}
 \newcommand{\phaseR}                                  {\col{IS\_R}}

pkg/rlp_txn_v2.sty

@@ -20,6 +20,7 @@
 \newcommand{\numberOfNonZero}           {NUMBER\_OF\_NONZERO\_BYTES}
 \newcommand{\nbWarmedAddress}           {NUMBER\_OF\_PREWARMED\_ADDRESSES}
 \newcommand{\nbWarmedStorageKey}        {NUMBER\_OF\_PREWARMED\_STORAGE\_KEYS}
+\newcommand{\maxFeePerBlobGas}			{MAX\_FEE\_PER\_BLOB\_GAS}
 
 \newcommand{\rlpTxnTransactionColumn} [1] {\col{txn}\separator\col{{#1}}}
 
@@ -28,6 +29,7 @@
 \newcommand{\rlpTxnTransactionColumnTypeZeroTx}           {\rlpTxnTransactionColumn{\typeZeroTx}}
 \newcommand{\rlpTxnTransactionColumnTypeOneTx}            {\rlpTxnTransactionColumn{\typeOneTx}}
 \newcommand{\rlpTxnTransactionColumnTypeTwoTx}            {\rlpTxnTransactionColumn{\typeTwoTx}}
+\newcommand{\rlpTxnTransactionColumnTypeThreeTx}          {\rlpTxnTransactionColumn{\typeThreeTx}}
 \newcommand{\rlpTxnTransactionColumnChainId}              {\rlpTxnTransactionColumn{\chainId}}
 \newcommand{\rlpTxnTransactionColumnGasPrice}             {\rlpTxnTransactionColumn{\gasPrice}}
 \newcommand{\rlpTxnTransactionColumnMaxPriorityFeePerGas} {\rlpTxnTransactionColumn{\maxPriorityFeePerGas}}
@@ -41,7 +43,10 @@
 \newcommand{\rlpTxnTransactionColumnNumberOfNonZero}      {\rlpTxnTransactionColumn{\numberOfNonZero}}
 \newcommand{\rlpTxnTransactionColumnNbWarmedAddress}      {\rlpTxnTransactionColumn{\nbWarmedAddress}}
 \newcommand{\rlpTxnTransactionColumnNbWarmedStorageKey}   {\rlpTxnTransactionColumn{\nbWarmedStorageKey}}
+\newcommand{\rlpTxnTransactionColumnMaxFeePerBlobGas}     {\rlpTxnTransactionColumn{\maxFeePerBlobGas}}
 \newcommand{\rlpTxnTransactionColumnRequiresEvmExecution} {\rlpTxnTransactionColumn{REQUIRES\_EVM\_EXECUTION}}
+\newcommand{\rlpTxnCommonColumnNumberOfBlobs}             {\rlpTxnTransactionColumn{NUMBER\_OF\_BLOBS}}
+
 
 \newcommand{\rlpTxnCommonColumnReplayProtection}          {\col{REPLAY\_PROTECTION}}
 \newcommand{\rlpTxnCommonColumnYparity}                   {\col{Y\_PARITY}}

pkg/txn_data.sty

@@ -44,6 +44,7 @@
 \newcommand{\finalRefundCounterName     } {\col{REFUND\_COUNTER\_FINAL}}
 \newcommand{\effectiveRefundName        } {\col{REFUND\_EFFECTIVE}}
 \newcommand{\cumulativeConsumedGasName  } {\col{GAS\_CUMULATIVE}}
+\newcommand{\cumulativeConsumedBlobGasName  } {\col{BLOB\_GAS\_CUMULATIVE}}
 \newcommand{\beaconRootName             } {\col{BEACON\_ROOT}}
 \newcommand{\relBlockNumberName         } {\col{REL\_BLOCK\_NUMBER}}
 \newcommand{\absBlockNumberName         } {\col{ABS\_BLOCK\_NUMBER}}
@@ -104,6 +105,9 @@
 \newcommand{\cumulativeConsumedGas}   {\cumulativeConsumedGasName                      }
 \newcommand{\txCumulativeConsumedGas} {\transactionSignifier\cumulativeConsumedGasName }
 
+\newcommand{\cumulativeConsumedBlobGas}   {\cumulativeConsumedBlobGasName                      }
+\newcommand{\txCumulativeConsumedBlobGas} {\transactionSignifier\cumulativeConsumedBlobGasName }
+
 \newcommand{\maxCtTypeZero} {\redm{9}}
 \newcommand{\maxCtTypeOne}  {\redm{10}}
 \newcommand{\maxCtTypeTwo}  {\redm{10}}

rlp_txn/_local.tex

@@ -16,11 +16,13 @@
 \def\locValidPhaseTransitionTypeZero  {\locValidPhaseTransition\loc{\_type\_0}}
 \def\locValidPhaseTransitionTypeOne   {\locValidPhaseTransition\loc{\_type\_1}}
 \def\locValidPhaseTransitionTypeTwo   {\locValidPhaseTransition\loc{\_type\_2}}
+\def\locValidPhaseTransitionTypeThree {\locValidPhaseTransition\loc{\_type\_3}}
 
-\def\locWillRemainInSamePhase         {\loc{will\_remain\_in\_same\_phase}}
-\def\locWillRemainInSamePhaseTypeZero {\locWillRemainInSamePhase\loc{\_type\_0}}
-\def\locWillRemainInSamePhaseTypeOne  {\locWillRemainInSamePhase\loc{\_type\_1}}
-\def\locWillRemainInSamePhaseTypeTwo  {\locWillRemainInSamePhase\loc{\_type\_2}}
+\def\locWillRemainInSamePhase            {\loc{will\_remain\_in\_same\_phase}}
+\def\locWillRemainInSamePhaseTypeZero    {\locWillRemainInSamePhase\loc{\_type\_0}}
+\def\locWillRemainInSamePhaseTypeOne     {\locWillRemainInSamePhase\loc{\_type\_1}}
+\def\locWillRemainInSamePhaseTypeTwo     {\locWillRemainInSamePhase\loc{\_type\_2}}
+\def\locWillRemainInSamePhaseTypeThree   {\locWillRemainInSamePhase\loc{\_type\_3}}
 
 \def\locPhaseWillNotChangeAndPhaseIsntRlpPrefix  {\loc{phase\_wont\_change\_and\_isnt\_global\_RLP\_prefix}}
 \def\locLimbUnconditionallyPartakesInLt          {\loc{limb\_unconditionally\_partakes\_in\_LT}}
@@ -30,6 +32,7 @@
 \def\locRlpComponentsTypeZero           {\locRlpComponents\loc{\_type\_0}}
 \def\locRlpComponentsTypeOne            {\locRlpComponents\loc{\_type\_1}}
 \def\locRlpComponentsTypeTwo            {\locRlpComponents\loc{\_type\_2}}
+\def\locRlpComponentsTypeThree          {\locRlpComponents\loc{\_type\_3}}
 
 \def\locAccessListLengthCountdown        {\loc{AL\_RLP\_length\_countdown}}
 \def\locAccessListItemCountdown          {\loc{access\_list\_item\_countdown}}
@@ -50,6 +53,9 @@
 \def\locAccessListIsNonempty       {\loc{access\_list\_is\_nonempty}}
 \def\locAccessListIsEmpty          {\loc{access\_list\_is\_empty}}
 
+\def\locBlobHashLengthCountdown        {\loc{BH\_RLP\_length\_countdown}}
+\def\locBlobHashIndex				   {\loc{BH\_INDEX}}
+
 \def\locAddressPrefixPlusAddressHiPart {\loc{prefix\_and\_address\_hi\_part}}
 \def\locIsDeploymentTransaction        {\loc{is\_deployment\_transaction}}
 \def\locIsMessageCallTransaction       {\loc{is\_message\_call\_transaction}}

rlp_txn/columns/shared.tex

@@ -40,7 +40,7 @@
 	\item \typeZeroTx{}
 	\item \typeOneTx{}
 	\item \typeTwoTx{}
-	    % \item \typeThreeTx{}
+	\item \typeThreeTx{}
 	    % \item \typeFourTx{}
     \end{enumerate}
 \end{multicols}
@@ -60,6 +60,8 @@
 	\item \phaseBeta{}
 	\item \phaseMaxPriorityFeePerGas{}
 	\item \phaseMaxFeePerGas{}
+	\item \phaseMaxFeePerBlobGas{}
+	\item \phaseBlobVersionedHashes{}
 	\item \phaseY{}
 	\item \phaseR{}
 	\item \phaseS{}
@@ -99,6 +101,11 @@
 	\rlpTxnSharedColumnIsDep{}:
 	transaction-constant binary column;
 	turns on precisely for deployment transactions;
+	\item 
+	\markAsJustifiedHere{}
+	\rlpTxnCommonColumnNumberOfBlobs{}:
+	transaction-constant column;
+	contains the number of blobs of the BLOB-transaction (else 0);
 \end{enumerate}
 The following are \textbf{counter-constant}, \textbf{binary} columns used in particular in the \rlp{}-ization of \textbf{access lists},
 see section~(\ref{rlp txn: phase constraints: access list: approach}).

rlp_txn/columns/transaction.tex

@@ -25,6 +25,9 @@
     \item
 	\markAsJustifiedHere{}
 	\rlpTxnTransactionColumnGasLimit{}:
+	\item
+	\markAsJustifiedHere{}
+	\rlpTxnTransactionColumnMaxFeePerBlobGas
     \item
 	\markAsJustifiedHere{}
 	\rlpTxnTransactionColumnToHi{}:

rlp_txn/generalities/_inputs.tex

@@ -15,4 +15,5 @@ \subsection{Finalization constraints}
 \subsection{Constraints for miscellaneous transaction columns}                    \label{rlp txn: generalities: miscellaneous txn columns}             \input{generalities/miscellaneous_transaction_columns}
 \subsection{\rlpTxnComputationColumnCounterConstantAuxiliaryData{k} constraints}  \label{rlp txn: generalities: TMP k column generalities}             \input{generalities/aux_k}
 \subsection{\rlpTxnSharedColumnRequiresEvmExecution{} constraints}                \label{rlp txn: generalities: requires evm execution column}         \input{generalities/requires_evm_execution}
+\subsection{\rlpTxnCommonColumnNumberOfBlobs{} constraints}     	              \label{rlp txn: generalities: number blob hashes}			           \input{generalities/number_blob_hashes}
 

rlp_txn/generalities/binarities.tex

@@ -4,6 +4,7 @@
 	\item \typeZeroTx{}
 	\item \typeOneTx{}
 	\item \typeTwoTx{}
+	\item \typeThreeTx{}
 	\item \phaseRlpPrefix{}
 	\item \phaseChainId{}
 	\item \phaseNonce{}
@@ -15,6 +16,8 @@
 	\item \phaseValue{}
 	\item \phaseData{}
 	\item \phaseAccessList{}
+	\item \phaseMaxFeePerBlobGas{}
+	\item \phaseBlobVersionedHashes{}
 	\item \phaseBeta{}
 	\item \phaseY{}
 	\item \phaseR{}

rlp_txn/generalities/lt_lx_lc_bits.tex

@@ -25,6 +25,8 @@
             + & \phaseValue                _{i} \\
             + & \phaseData                 _{i} \\
             + & \phaseAccessList           _{i} \\
+            + & \phaseMaxFeePerBlobGas     _{i} \\
+            + & \phaseBlobVersionedHashes  _{i} \\
             % + & \phaseBeta                 _{i} \\
             % + & \phaseY                    _{i} \\
             % + & \phaseR                    _{i} \\

rlp_txn/generalities/number_blob_hashes.tex

@@ -0,0 +1,7 @@
+We impose the following
+\begin{enumerate}
+    \item
+	\rlpTxnCommonColumnNumberOfBlobs{} \textbf{transaction-constant}
+	\item $\typeThreeTx_{i} = 0$ \Then $\rlpTxnCommonColumnNumberOfBlobs_{i} = 0$
+\end{enumerate}
+

rlp_txn/generalities/perspectives.tex

@@ -20,6 +20,8 @@
 	    + & (1 - \phaseValue                _{i}) & \!\!\!\cdot\!\!\! & \phaseValue                _{i + 1} \\
 	    + & (1 - \phaseData                 _{i}) & \!\!\!\cdot\!\!\! & \phaseData                 _{i + 1} \\
 	    + & (1 - \phaseAccessList           _{i}) & \!\!\!\cdot\!\!\! & \phaseAccessList           _{i + 1} \\
+	    + & (1 - \phaseMaxFeePerBlobGas     _{i}) & \!\!\!\cdot\!\!\! & \phaseMaxFeePerBlobGas     _{i + 1} \\
+	    + & (1 - \phaseBlobVersionedHashes  _{i}) & \!\!\!\cdot\!\!\! & \phaseBlobVersionedHashes  _{i + 1} \\
 	    + & (1 - \phaseBeta                 _{i}) & \!\!\!\cdot\!\!\! & \phaseBeta                 _{i + 1} \\
 	    + & (1 - \phaseY                    _{i}) & \!\!\!\cdot\!\!\! & \phaseY                    _{i + 1} \\
 	    + & (1 - \phaseR                    _{i}) & \!\!\!\cdot\!\!\! & \phaseR                    _{i + 1} \\

rlp_txn/generalities/phase_end.tex

@@ -15,6 +15,8 @@
             + & \phaseValue                _{i} & \!\!\!\cdot\!\!\! & (1 - \phaseValue                _{i + 1}) \\
             + & \phaseData                 _{i} & \!\!\!\cdot\!\!\! & (1 - \phaseData                 _{i + 1}) \\
             + & \phaseAccessList           _{i} & \!\!\!\cdot\!\!\! & (1 - \phaseAccessList           _{i + 1}) \\
+            + & \phaseMaxFeePerBlobGas     _{i} & \!\!\!\cdot\!\!\! & (1 - \phaseMaxFeePerBlobGas     _{i + 1}) \\
+            + & \phaseBlobVersionedHashes  _{i} & \!\!\!\cdot\!\!\! & (1 - \phaseBlobVersionedHashes  _{i + 1}) \\
             + & \phaseBeta                 _{i} & \!\!\!\cdot\!\!\! & (1 - \phaseBeta                 _{i + 1}) \\
             + & \phaseY                    _{i} & \!\!\!\cdot\!\!\! & (1 - \phaseY                    _{i + 1}) \\
             + & \phaseR                    _{i} & \!\!\!\cdot\!\!\! & (1 - \phaseR                    _{i + 1}) \\

rlp_txn/generalities/phase_flag_sum.tex

@@ -13,6 +13,8 @@
         + & \phaseValue                _{i} \\
         + & \phaseData                 _{i} \\
         + & \phaseAccessList           _{i} \\
+        + & \phaseMaxFeePerBlobGas     _{i} \\
+        + & \phaseBlobVersionedHashes  _{i} \\
         + & \phaseBeta                 _{i} \\
         + & \phaseY                    _{i} \\
         + & \phaseR                    _{i} \\

rlp_txn/generalities/transaction_decoding.tex

@@ -6,7 +6,7 @@
 			+ & \typeZeroTx _{i} \\
 			+ & \typeOneTx  _{i} \\
 			+ & \typeTwoTx  _{i} \\
-			% + & \typeThreeTx _{i} \\
+			+ & \typeThreeTx _{i} \\
 			% + & \typeFourTx  _{i} \\
 		\end{array} \right]
 		\vspace{2mm} \\
@@ -15,7 +15,7 @@
 			+ & 0 & \!\!\!\cdot\!\!\! & \typeZeroTx  _{i} \\
 			+ & 1 & \!\!\!\cdot\!\!\! & \typeOneTx   _{i} \\
 			+ & 2 & \!\!\!\cdot\!\!\! & \typeTwoTx   _{i} \\
-			% + & 3 & \!\!\!\cdot\!\!\! & \typeThreeTx _{i} \\
+			+ & 3 & \!\!\!\cdot\!\!\! & \typeThreeTx _{i} \\
 			% + & 4 & \!\!\!\cdot\!\!\! & \typeFourTx  _{i} \\
 		\end{array} \right]
 	\end{array} \right.
@@ -31,12 +31,6 @@
 		we impose that $\locTransactionTypeSum _{i} = \locPhaseFlagSum _{i}$
 	\item
 		\If $\isTxn _{i} = 1$ \Then $\rlpTxnTransactionColumnTxType _{i} = \locWeightedTransactionTypeSum _{i}$
-		% \begin{enumerate}
-		% 	\item $\ct       _{i}   = 0$ (\sanityCheck)
-		% 	\item $\maxCt    _{i}   = 0$ (\sanityCheck)
-		% 	\item $\phaseEnd _{i}   = 0$ (\sanityCheck)
-		% 	\item $\lc       _{i}   = 0$ (\sanityCheck)
-		% \end{enumerate}
 \end{enumerate}
 \saNote{} \label{rlp txn: generalities: transaction decoding: flag exclusivity}
 The above implicitly imposes flag exclusivity on the ``transaction type flags.''

rlp_txn/generalities/transaction_type_phase_transitions.tex

@@ -108,6 +108,50 @@
         \\
     \end{array} \right.
 \]
+and
+\[
+    \hspace*{-2cm}
+    \left\{ \begin{array}{lcl}
+        \locValidPhaseTransitionTypeThree _{i} & \define &
+        \left[ \begin{array}{clcl}
+            + & \phaseRlpPrefix            _{i} & \cdot & \phaseChainId              _{i + 1} \\
+            + & \phaseChainId              _{i} & \cdot & \phaseNonce                _{i + 1} \\
+            + & \phaseNonce                _{i} & \cdot & \phaseMaxPriorityFeePerGas _{i + 1} \\
+            + & \phaseMaxPriorityFeePerGas _{i} & \cdot & \phaseMaxFeePerGas         _{i + 1} \\
+            + & \phaseMaxFeePerGas         _{i} & \cdot & \phaseGasLimit             _{i + 1} \\
+            + & \phaseGasLimit             _{i} & \cdot & \phaseTo                   _{i + 1} \\
+            + & \phaseTo                   _{i} & \cdot & \phaseValue                _{i + 1} \\
+            + & \phaseValue                _{i} & \cdot & \phaseData                 _{i + 1} \\
+            + & \phaseData                 _{i} & \cdot & \phaseAccessList           _{i + 1} \\
+            + & \phaseAccessList           _{i} & \cdot & \phaseMaxFeePerBlobGas     _{i + 1} \\
+            + & \phaseMaxFeePerBlobGas     _{i} & \cdot & \phaseBlobVersionedHashes  _{i + 1} \\
+            + & \phaseBlobVersionedHashes  _{i} & \cdot & \phaseY                    _{i + 1} \\            
+            + & \phaseY                    _{i} & \cdot & \phaseR                    _{i + 1} \\
+            + & \phaseR                    _{i} & \cdot & \phaseS                    _{i + 1} \\
+            + & \phaseS                    _{i} & \cdot & \phaseRlpPrefix            _{i + 1} \\
+        \end{array} \right]
+        \vspace{2mm} \\
+        \locWillRemainInSamePhaseTypeThree _{i} & \define &
+        \left[ \begin{array}{clcl}
+            + & \phaseRlpPrefix            _{i} & \cdot & \phaseRlpPrefix            _{i + 1} \\
+            + & \phaseChainId              _{i} & \cdot & \phaseChainId              _{i + 1} \\
+            + & \phaseNonce                _{i} & \cdot & \phaseNonce                _{i + 1} \\
+            + & \phaseMaxPriorityFeePerGas _{i} & \cdot & \phaseMaxPriorityFeePerGas _{i + 1} \\
+            + & \phaseMaxFeePerGas         _{i} & \cdot & \phaseMaxFeePerGas         _{i + 1} \\
+            + & \phaseGasLimit             _{i} & \cdot & \phaseGasLimit             _{i + 1} \\
+            + & \phaseTo                   _{i} & \cdot & \phaseTo                   _{i + 1} \\
+            + & \phaseValue                _{i} & \cdot & \phaseValue                _{i + 1} \\
+            + & \phaseData                 _{i} & \cdot & \phaseData                 _{i + 1} \\
+            + & \phaseAccessList           _{i} & \cdot & \phaseAccessList           _{i + 1} \\
+            + & \phaseMaxFeePerBlobGas     _{i} & \cdot & \phaseMaxFeePerBlobGas     _{i + 1} \\
+            + & \phaseBlobVersionedHashes  _{i} & \cdot & \phaseBlobVersionedHashes  _{i + 1} \\
+            + & \phaseY                    _{i} & \cdot & \phaseY                    _{i + 1} \\
+            + & \phaseR                    _{i} & \cdot & \phaseR                    _{i + 1} \\
+            + & \phaseS                    _{i} & \cdot & \phaseS                    _{i + 1} \\
+        \end{array} \right]
+        \\
+    \end{array} \right.
+\]
 and we impose that
 \begin{enumerate}
     \item
@@ -131,4 +175,11 @@
 	    + & \locWillRemainInSamePhaseTypeTwo _{i} \\
 	\end{array} \right]
 	= 1 $
+     \item
+    \If $\typeThreeTx  _{i} = 1$ \Then
+    $ \left[ \begin{array}{clcl}
+        + & \locValidPhaseTransitionTypeThree  _{i} \\
+        + & \locWillRemainInSamePhaseTypeThree _{i} \\
+    \end{array} \right]
+    = 1 $
 \end{enumerate}