added verifier check in sticker, fixed the edge case in product (#204)

* added the verifier check for local opening
* fixed the edge case for product

---------

Co-authored-by: AlexandreBelling <alexandrebelling8@gmail.com>

prover/protocol/compiler/splitter/sticker/sticker.go

@@ -1,8 +1,10 @@
 package sticker
 
 import (
+	"fmt"
 	"strings"
 
+	"github.com/consensys/gnark/frontend"
 	"github.com/consensys/linea-monorepo/prover/maths/common/smartvectors"
 	"github.com/consensys/linea-monorepo/prover/maths/common/vector"
 	"github.com/consensys/linea-monorepo/prover/maths/field"
@@ -434,6 +436,22 @@ func (ctx *stickContext) compileFixedEvaluation() {
 			y := run.QueriesParams.MustGet(q.ID).(query.LocalOpeningParams).Y
 			run.AssignLocalPoint(newQ.ID, y)
 		})
+
+		// The verifier ensures that the old and new queries have the same assignement
+		ctx.comp.InsertVerifier(round, func(run *wizard.VerifierRuntime) error {
+			oldParams := run.GetLocalPointEvalParams(q.ID)
+			newParams := run.GetLocalPointEvalParams(queryName(q.ID))
+
+			if oldParams != newParams {
+				return fmt.Errorf("sticker verifier failed for local opening %v - %v", q.ID, queryName(q.ID))
+			}
+
+			return nil
+		}, func(api frontend.API, run *wizard.WizardVerifierCircuit) {
+			oldParams := run.GetLocalPointEvalParams(q.ID)
+			newParams := run.GetLocalPointEvalParams(queryName(q.ID))
+			api.AssertIsEqual(oldParams.Y, newParams.Y)
+		})
 	}
 
 }

prover/symbolic/product.go

@@ -60,7 +60,7 @@ func NewProduct(items []*Expression, exponents []int) *Expression {
 	}
 
 	for i := range items {
-		if items[i].ESHash.IsZero() {
+		if items[i].ESHash.IsZero() && exponents[i] != 0 {
 			return NewConstant(0)
 		}
 	}