diff --git a/prover/backend/execution/prove.go b/prover/backend/execution/prove.go
index 335a9d515..89192ef52 100644
--- a/prover/backend/execution/prove.go
+++ b/prover/backend/execution/prove.go
@@ -143,8 +143,11 @@ func mustProveAndPass(
 
 		if setupCfgChecksum != traces.Checksum() {
 			// This check is failing on prod but works locally.
-			// 	utils.Panic("traces checksum in the setup manifest does not match the one in the config")
-			logrus.Warnf("the setup checksum does not match the provided trace limits: provided=%++v", traces)
+			// @alex: since this is a setup-related constraint, it would likely be
+			// more interesting to directly include that information in the setup
+			// instead of the config. That way we are guaranteed to not pass the
+			// wrong value at runtime.
+			utils.Panic("traces checksum in the setup manifest does not match the one in the config")
 		}
 
 		// TODO: implements the collection of the functional inputs from the prover response
diff --git a/prover/circuits/execution/builder.go b/prover/circuits/execution/builder.go
index 7a7b28d8f..122a77c7b 100644
--- a/prover/circuits/execution/builder.go
+++ b/prover/circuits/execution/builder.go
@@ -5,7 +5,6 @@ import (
 	"github.com/consensys/gnark/constraint"
 	"github.com/consensys/gnark/frontend"
 	"github.com/consensys/gnark/frontend/cs/scs"
-	"github.com/consensys/gnark/profile"
 	"github.com/consensys/linea-monorepo/prover/zkevm"
 )
 
@@ -25,9 +24,6 @@ func (b *builder) Compile() (constraint.ConstraintSystem, error) {
 func makeCS(z *zkevm.ZkEvm) constraint.ConstraintSystem {
 	circuit := Allocate(z)
 
-	pro := profile.Start(profile.WithPath("./profiling-execution.pprof"))
-	defer pro.Stop()
-
 	scs, err := frontend.Compile(fr.Modulus(), scs.NewBuilder, &circuit, frontend.WithCapacity(1<<24))
 	if err != nil {
 		panic(err)
diff --git a/prover/circuits/execution/circuit.go b/prover/circuits/execution/circuit.go
index 48d449d1e..36f772c3d 100644
--- a/prover/circuits/execution/circuit.go
+++ b/prover/circuits/execution/circuit.go
@@ -1,9 +1,10 @@
 package execution
 
 import (
+	"math/big"
+
 	"github.com/consensys/linea-monorepo/prover/config"
 	public_input "github.com/consensys/linea-monorepo/prover/public-input"
-	"math/big"
 
 	"github.com/consensys/gnark-crypto/ecc"
 	"github.com/consensys/gnark/backend/plonk"
@@ -63,17 +64,23 @@ func assign(
 	proof wizard.Proof,
 	funcInputs public_input.Execution,
 ) CircuitExecution {
-	wizardVerifier := wizard.GetWizardVerifierCircuitAssignment(comp, proof)
 
-	return CircuitExecution{
-		WizardVerifier: *wizardVerifier,
-		FuncInputs: FunctionalPublicInputSnark{
-			FunctionalPublicInputQSnark: FunctionalPublicInputQSnark{
-				L2MessageHashes: L2MessageHashes{Values: make([][32]frontend.Variable, limits.BlockL2L1Logs)}, // TODO use a maximum from config
+	var (
+		wizardVerifier = wizard.GetWizardVerifierCircuitAssignment(comp, proof)
+		res            = CircuitExecution{
+			WizardVerifier: *wizardVerifier,
+			FuncInputs: FunctionalPublicInputSnark{
+				FunctionalPublicInputQSnark: FunctionalPublicInputQSnark{
+					L2MessageHashes: L2MessageHashes{Values: make([][32]frontend.Variable, limits.BlockL2L1Logs)}, // TODO use a maximum from config
+				},
 			},
-		},
-		PublicInput: new(big.Int).SetBytes(funcInputs.Sum(nil)),
-	}
+			PublicInput: new(big.Int).SetBytes(funcInputs.Sum(nil)),
+		}
+	)
+
+	res.FuncInputs.Assign(&funcInputs)
+
+	return res
 }
 
 // Define of the wizard circuit
diff --git a/prover/circuits/internal/utils.go b/prover/circuits/internal/utils.go
index 7870b0ecf..ea22a3927 100644
--- a/prover/circuits/internal/utils.go
+++ b/prover/circuits/internal/utils.go
@@ -30,6 +30,16 @@ func AssertEqualIf(api frontend.API, cond, a, b frontend.Variable) {
 	api.AssertIsEqual(api.Mul(cond, a), api.Mul(cond, b))
 }
 
+// AssertIsLessIf asserts cond ≠ 0 ⇒ (a < b)
+func AssertIsLessIf(api frontend.API, cond, a, b frontend.Variable) {
+	var (
+		condIsNonZero = api.Sub(1, api.IsZero(cond))
+		a_            = api.Mul(condIsNonZero, api.Add(a, 1))
+		b_            = api.Mul(condIsNonZero, b)
+	)
+	api.AssertIsLessOrEqual(a_, b_)
+}
+
 func SliceToTable(api frontend.API, slice []frontend.Variable) *logderivlookup.Table {
 	table := logderivlookup.New(api)
 	for i := range slice {
diff --git a/prover/circuits/pi-interconnection/assign.go b/prover/circuits/pi-interconnection/assign.go
index 616884bb9..a817c4736 100644
--- a/prover/circuits/pi-interconnection/assign.go
+++ b/prover/circuits/pi-interconnection/assign.go
@@ -287,7 +287,7 @@ func (c *Compiled) Assign(r Request) (a Circuit, err error) {
 			// @alex: Not sure this check is a duplicate because we already check
 			// that the state root hash is well-propagated and this should be
 			// enough that the rolling hash update events are emitted in sequence.
-			if executionFPI.FirstRollingHashUpdateNumber != lastRollingHashNumber+1 {
+			if executionFPI.FirstRollingHashUpdateNumber <= lastRollingHashNumber {
 				err = fmt.Errorf("execution #%d fails CHECK_RHASH_CONSEC:\n\tinitial rolling hash message number %d is not right after the last finalized one %d", i, executionFPI.FirstRollingHashUpdateNumber, lastRollingHashNumber)
 				return
 			}
diff --git a/prover/circuits/pi-interconnection/circuit.go b/prover/circuits/pi-interconnection/circuit.go
index 045d23efd..eb6e2953d 100644
--- a/prover/circuits/pi-interconnection/circuit.go
+++ b/prover/circuits/pi-interconnection/circuit.go
@@ -186,7 +186,7 @@ func (c *Circuit) Define(api frontend.API) error {
 		rollingHashUpdated := api.Mul(inRange, api.Sub(1, finalRhMsgNumZero))
 
 		// CHECK_RHASH_CONSEC
-		internal.AssertEqualIf(api, rollingHashUpdated, pi.FirstRollingHashUpdateNumber, api.Add(finalRollingHashMsgNum, 1))
+		internal.AssertIsLessIf(api, rollingHashUpdated, finalRollingHashMsgNum, pi.FirstRollingHashUpdateNumber)
 		finalRollingHashMsgNum = api.Select(rollingHashUpdated, pi.LastRollingHashUpdateNumber, finalRollingHashMsgNum)
 		copy(finalRollingHash[:], internal.SelectMany(api, rollingHashUpdated, pi.FinalRollingHashUpdate[:], finalRollingHash[:]))
 
diff --git a/prover/protocol/compiler/vortex/compiler.go b/prover/protocol/compiler/vortex/compiler.go
index e5ab15b72..26c3c7868 100644
--- a/prover/protocol/compiler/vortex/compiler.go
+++ b/prover/protocol/compiler/vortex/compiler.go
@@ -566,7 +566,6 @@ func (ctx *Ctx) processStatusPrecomputed() {
 
 			_, ok := ctx.PolynomialsTouchedByTheQuery[name]
 			if !ok {
-				logrus.Warnf("got an unconstrained column: %v -> marking as ignored", name)
 				comp.Columns.MarkAsIgnored(name)
 				continue
 			}
diff --git a/prover/zkevm/arithmetization/zkevm.bin b/prover/zkevm/arithmetization/zkevm.bin
index 2d470f894..852448483 100644
--- a/prover/zkevm/arithmetization/zkevm.bin
+++ b/prover/zkevm/arithmetization/zkevm.bin
@@ -1 +1 @@
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\ No newline at end of file
diff --git a/prover/zkevm/prover/publicInput/logs/extracted_data.go b/prover/zkevm/prover/publicInput/logs/extracted_data.go
index 8a0de54fe..d8ce26731 100644
--- a/prover/zkevm/prover/publicInput/logs/extracted_data.go
+++ b/prover/zkevm/prover/publicInput/logs/extracted_data.go
@@ -46,8 +46,8 @@ func DefineExtractedData(comp *wizard.CompiledIOP, logCols LogColumns, sel Selec
 	}
 	// the LogColumns we extract data from, and which we will use to check for consistency
 	logsTable := []ifaces.Column{
-		logCols.OutgoingHi,
-		logCols.OutgoingLo,
+		logCols.DataHi,
+		logCols.DataLo,
 	}
 
 	comp.InsertGlobal(
@@ -97,8 +97,8 @@ func DefineExtractedData(comp *wizard.CompiledIOP, logCols LogColumns, sel Selec
 
 // CheckBridgeAddress checks if a row does indeed contain the data corresponding to a the bridge address
 func CheckBridgeAddress(run *wizard.ProverRuntime, lCols LogColumns, sel Selectors, pos int) bool {
-	outHi := lCols.OutgoingHi.GetColAssignmentAt(run, pos)
-	outLo := lCols.OutgoingLo.GetColAssignmentAt(run, pos)
+	outHi := lCols.DataHi.GetColAssignmentAt(run, pos)
+	outLo := lCols.DataLo.GetColAssignmentAt(run, pos)
 	bridgeAddrHi := sel.L2BridgeAddressColHI.GetColAssignmentAt(run, 0)
 	bridgeAddrLo := sel.L2BridgeAddressColLo.GetColAssignmentAt(run, 0)
 	if outHi.Equal(&bridgeAddrHi) && outLo.Equal(&bridgeAddrLo) {
@@ -113,8 +113,8 @@ func CheckFirstTopic(run *wizard.ProverRuntime, lCols LogColumns, pos int, logTy
 	firstTopicBytes := GetFirstTopic(logType) // fixed expected value for the topic on the first topic row
 	firstTopicHi.SetBytes(firstTopicBytes[:16])
 	firstTopicLo.SetBytes(firstTopicBytes[16:])
-	outHi := lCols.OutgoingHi.GetColAssignmentAt(run, pos)
-	outLo := lCols.OutgoingLo.GetColAssignmentAt(run, pos)
+	outHi := lCols.DataHi.GetColAssignmentAt(run, pos)
+	outLo := lCols.DataLo.GetColAssignmentAt(run, pos)
 	if firstTopicHi.Equal(&outHi) && firstTopicLo.Equal(&outLo) {
 		return true
 	}
@@ -155,8 +155,8 @@ func AssignExtractedData(run *wizard.ProverRuntime, lCols LogColumns, sel Select
 	for i := 0; i < lCols.Ct.Size(); i++ {
 		// the following conditional checks if row i contains a message that should be picked
 		if IsPositionTargetMessage(run, lCols, sel, i, logType) {
-			hi := lCols.OutgoingHi.GetColAssignmentAt(run, i)
-			lo := lCols.OutgoingLo.GetColAssignmentAt(run, i)
+			hi := lCols.DataHi.GetColAssignmentAt(run, i)
+			lo := lCols.DataLo.GetColAssignmentAt(run, i)
 			// pick the messages and add them to the msgHi/Lo ExtractedData columns
 			Hi[counter].Set(&hi)
 			Lo[counter].Set(&lo)
diff --git a/prover/zkevm/prover/publicInput/logs/mock_logs.go b/prover/zkevm/prover/publicInput/logs/mock_logs.go
index f76ee1c18..941a20161 100644
--- a/prover/zkevm/prover/publicInput/logs/mock_logs.go
+++ b/prover/zkevm/prover/publicInput/logs/mock_logs.go
@@ -39,7 +39,7 @@ type LogColumns struct {
 	AbsLogNum                              ifaces.Column
 	AbsLogNumMax                           ifaces.Column // total number of logs in the conflated batch
 	Ct                                     ifaces.Column // counter column used inside a column segment used for one specific log
-	OutgoingHi, OutgoingLo                 ifaces.Column // the Hi and Lo parts of outgoing data
+	DataHi, DataLo                         ifaces.Column // the Hi and Lo parts of outgoing data
 	TxEmitsLogs                            ifaces.Column
 }
 
@@ -131,8 +131,8 @@ func NewLogColumns(comp *wizard.CompiledIOP, size int, name string) LogColumns {
 		AbsLogNum:    createCol("ABS_LOG_NUM"),
 		AbsLogNumMax: createCol("ABS_LOG_NUM_MAX"),
 		Ct:           createCol("CT"),
-		OutgoingHi:   createCol("OUTGOING_HI"),
-		OutgoingLo:   createCol("OUTGOING_LO"),
+		DataHi:       createCol("OUTGOING_HI"),
+		DataLo:       createCol("OUTGOING_LO"),
 		TxEmitsLogs:  createCol("TX_EMITS_LOGS"),
 	}
 
@@ -160,8 +160,8 @@ func NewLogColumnsAssignmentBuilder(lc *LogColumns) LogColumnsAssignmentBuilder
 		AbsLogNum:    common.NewVectorBuilder(lc.AbsLogNum),
 		AbsLogNumMax: common.NewVectorBuilder(lc.AbsLogNumMax),
 		Ct:           common.NewVectorBuilder(lc.Ct),
-		OutgoingHi:   common.NewVectorBuilder(lc.OutgoingHi),
-		OutgoingLo:   common.NewVectorBuilder(lc.OutgoingLo),
+		OutgoingHi:   common.NewVectorBuilder(lc.DataHi),
+		OutgoingLo:   common.NewVectorBuilder(lc.DataLo),
 		TxEmitsLogs:  common.NewVectorBuilder(lc.TxEmitsLogs),
 	}
 
diff --git a/prover/zkevm/prover/publicInput/logs/selectors.go b/prover/zkevm/prover/publicInput/logs/selectors.go
index 430ced2c8..33a71a33e 100644
--- a/prover/zkevm/prover/publicInput/logs/selectors.go
+++ b/prover/zkevm/prover/publicInput/logs/selectors.go
@@ -195,12 +195,12 @@ func NewSelectorColumns(comp *wizard.CompiledIOP, lc LogColumns) Selectors {
 	// selectors that light up when OutgoingHi/OutgoingLo contain the expected first topic data
 	SelectFirstTopicL2L1Hi, ComputeSelectFirstTopicL2L1Hi := dedicated.IsZero(
 		comp,
-		sym.Sub(lc.OutgoingHi, firstTopicL2L1Hi),
+		sym.Sub(lc.DataHi, firstTopicL2L1Hi),
 	)
 
 	SelectFirstTopicL2L1Lo, ComputeSelectFirstTopicL2L1Lo := dedicated.IsZero(
 		comp,
-		sym.Sub(lc.OutgoingLo, firstTopicL2L1Lo),
+		sym.Sub(lc.DataLo, firstTopicL2L1Lo),
 	)
 
 	// compute the expected data in the first topic of a rolling hash log
@@ -212,12 +212,12 @@ func NewSelectorColumns(comp *wizard.CompiledIOP, lc LogColumns) Selectors {
 	// selectors that light up when OutgoingHi/OutgoingLo contain the expected first topic data
 	SelectFirstTopicRollingHi, ComputeSelectFirstTopicRollingHi := dedicated.IsZero(
 		comp,
-		sym.Sub(lc.OutgoingHi, firstTopicRollingHi),
+		sym.Sub(lc.DataHi, firstTopicRollingHi),
 	)
 
 	SelectFirstTopicRollingLo, ComputeSelectFirstTopicRollingLo := dedicated.IsZero(
 		comp,
-		sym.Sub(lc.OutgoingLo, firstTopicRollingLo),
+		sym.Sub(lc.DataLo, firstTopicRollingLo),
 	)
 
 	bridgeAddrColHi := comp.InsertProof(0, ifaces.ColIDf("LOGS_FETCHER_BRIDGE_ADDRESS_HI"), 1)
@@ -229,12 +229,12 @@ func NewSelectorColumns(comp *wizard.CompiledIOP, lc LogColumns) Selectors {
 	// selectors that light up when OutgoingHi/OutgoingLo contain the Hi/Lo parts of the l2BridgeAddress
 	SelectorL2BridgeAddressHi, ComputeSelectorL2BridgeAddressHi := dedicated.IsZero(
 		comp,
-		sym.Sub(lc.OutgoingHi, accessBridgeHi),
+		sym.Sub(lc.DataHi, accessBridgeHi),
 	)
 
 	SelectorL2BridgeAddressLo, ComputeSelectorL2BridgeAddressLo := dedicated.IsZero(
 		comp,
-		sym.Sub(lc.OutgoingLo, accessBridgeLo),
+		sym.Sub(lc.DataLo, accessBridgeLo),
 	)
 
 	// generate the final selector object
diff --git a/prover/zkevm/prover/publicInput/public_input.go b/prover/zkevm/prover/publicInput/public_input.go
index 6cd1fcf41..7ab94cd5d 100644
--- a/prover/zkevm/prover/publicInput/public_input.go
+++ b/prover/zkevm/prover/publicInput/public_input.go
@@ -109,8 +109,8 @@ func NewPublicInputZkEVM(comp *wizard.CompiledIOP, settings *Settings, ss *state
 				AbsLogNum:    getCol("loginfo.ABS_LOG_NUM"),
 				AbsLogNumMax: getCol("loginfo.ABS_LOG_NUM_MAX"),
 				Ct:           getCol("loginfo.CT"),
-				OutgoingHi:   getCol("loginfo.ADDR_HI"),
-				OutgoingLo:   getCol("loginfo.ADDR_LO"),
+				DataHi:       getCol("loginfo.DATA_HI"),
+				DataLo:       getCol("loginfo.DATA_LO"),
 				TxEmitsLogs:  getCol("loginfo.TXN_EMITS_LOGS"),
 			},
 			StateSummary: ss,