{ "build_log_tail": "s)\n\u2714 [10417/10604] Built Critical2DKPZ.Analysis.Sobolev.Rellich.Scaling (2.4s)\n\u2714 [10418/10604] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSummandBound (3.0s)\n\u2714 [10419/10604] Built Critical2DKPZ.Analysis.Sobolev.WeightBounds (2.2s)\n\u2714 [10420/10604] Built Critical2DKPZ.Analysis.Sobolev.SmoothIntegral (3.7s)\n\u2714 [10421/10604] Built Critical2DKPZ.SHF.Moments.LongWordLimitCellBounds (3.0s)\n\u2714 [10422/10604] Built Critical2DKPZ.SHF.Symmetries.LatticeReversal (9.3s)\n\u2714 [10423/10604] Built Critical2DKPZ.Smoothing.UnitHorizonBounds (13s)\n\u2714 [10424/10609] Built Critical2DKPZ.Analysis.Sobolev.CompactJets (9.5s)\n\u2714 [10425/10609] Built Critical2DKPZ.Analysis.Sobolev.Rellich.HighFrequency (2.0s)\n\u2714 [10426/10609] Built Critical2DKPZ.Analysis.Sobolev.LocalizedEnergy (2.1s)\n\u2714 [10427/10609] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureLimit (3.3s)\n\u2714 [10428/10609] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureContinuity (3.8s)\n\u2714 [10429/10609] Built Critical2DKPZ.SHF.Moments.WordLimitTerminalFirstBlock (3.9s)\n\u2714 [10430/10609] Built Critical2DKPZ.Analysis.Sobolev.Rellich.RellichEstimate (4.2s)\n\u2714 [10431/10609] Built Critical2DKPZ.LocalSobolev.LatticeMoment (9.6s)\n\u2714 [10432/10609] Built Critical2DKPZ.Analysis.Sobolev.Rellich.Additivity (3.3s)\n\u2714 [10433/10609] Built Critical2DKPZ.Analysis.Sobolev.CompactTestIntegral (2.6s)\n\u2714 [10434/10609] Built Critical2DKPZ.Analysis.Sobolev.FiniteSeminorm (2.1s)\n\u2714 [10435/10609] Built Critical2DKPZ.OnePoint.BlockRatioComponentFactorization (4.4s)\n\u2714 [10436/10609] Built Critical2DKPZ.Analysis.Sobolev.WeightedFourierIntegrability (4.5s)\n\u2714 [10437/10610] Built Critical2DKPZ.LocalSobolev.ReversalLaw (4.1s)\n\u2714 [10438/10610] Built Critical2DKPZ.SHF.Moments.LongWordLimitCellApprox (4.9s)\n\u2714 [10439/10613] Built Critical2DKPZ.LocalSobolev.HeatStartCovariance (11s)\n\u2714 [10440/10614] Built Critical2DKPZ.Analysis.Sobolev.Rellich.SobolevYoungConvolution (1.0s)\n\u2714 [10441/10614] Built Critical2DKPZ.FutureProfiles.ProfileEstimateEnergy (6.8s)\n\u2714 [10442/10618] Built Critical2DKPZ.JointConvergence.ThmToyJointLimitEstimates (8.2s)\n\u2714 [10443/10618] Built Critical2DKPZ.Analysis.Sobolev.Rellich.RellichNet (2.7s)\n\u2714 [10444/10618] Built Critical2DKPZ.Analysis.Sobolev.Topology (2.2s)\n\u2714 [10445/10618] Built Critical2DKPZ.LocalSobolev.MeasurableFieldVersions (4.4s)\n\u2714 [10446/10618] Built Critical2DKPZ.SHF.Moments.WordLimitFirstBlock (3.6s)\n\u2714 [10447/10618] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureJoint (4.1s)\n\u2714 [10448/10619] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureWindows (4.3s)\n\u2714 [10449/10620] Built Critical2DKPZ.Definitions.LocNegSobolevTopMeasurableSpace (1.6s)\n\u2714 [10450/10620] Built Critical2DKPZ.Analysis.Sobolev.Rellich.RellichMollificationClosed (4.5s)\n\u2714 [10451/10620] Built Critical2DKPZ.SHF.Moments.SinglePairWordTimeFubini (4.5s)\n\u2714 [10452/10620] Built Critical2DKPZ.Analysis.Sobolev.Rellich.DualityAssembly (2.6s)\n\u2714 [10453/10620] Built Critical2DKPZ.Analysis.Sobolev.SmoothTestIntegral (4.2s)\n\u2714 [10454/10620] Built Critical2DKPZ.Analysis.Sobolev.Rellich.RellichJetNets (2.9s)\n\u2714 [10455/10620] Built Critical2DKPZ.Analysis.Sobolev.ClosedCarrier (1.9s)\n\u2714 [10456/10620] Built Critical2DKPZ.SHF.Moments.LongWordLimitCellLimit (3.8s)\n\u2714 [10457/10620] Built Critical2DKPZ.Analysis.Sobolev.LocalizerEnergy (2.2s)\n\u2714 [10458/10620] Built Critical2DKPZ.Smoothing.WidthClockPerturbation (8.9s)\n\u2714 [10459/10623] Built Critical2DKPZ.Definitions.LocNegSobolevTopBorelSpace (1.6s)\n\u2714 [10460/10624] Built Critical2DKPZ.OnePoint.BlockRatioPairFactorization (5.8s)\n\u2714 [10461/10624] Built Critical2DKPZ.Analysis.Sobolev.FiniteDimTightConvergence (2.6s)\n\u2714 [10462/10628] Built Critical2DKPZ.SHF.Moments.WordLimitFirstBlockAverage (3.9s)\n\u2714 [10463/10629] Built Critical2DKPZ.SHF.Moments.SinglePairWordRenewalWindowHorizon (4.4s)\n\u2714 [10464/10629] Built Critical2DKPZ.Analysis.Sobolev.Rellich.SobolevTestDuality (2.5s)\n\u2714 [10465/10631] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitFromCutoffEstimates (4.9s)\n\u2714 [10466/10633] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureConvergence (4.4s)\n\u2714 [10467/10633] Built Critical2DKPZ.Analysis.Sobolev.LocNegSobolevBorel (2.5s)\n\u2714 [10468/10635] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureAbsoluteMass (4.1s)\n\u2714 [10469/10635] Built Critical2DKPZ.JointConvergence.ThmToyJointLimitLattice (6.6s)\n\u2714 [10470/10637] Built Critical2DKPZ.Analysis.Sobolev.CountableEnergyTightness (1.6s)\n\u2714 [10471/10638] Built Critical2DKPZ.SHF.Moments.LongWordLimitTransfer (4.5s)\n\u2714 [10472/10638] Built Critical2DKPZ.Analysis.Sobolev.Rellich.RellichKernelFamilyBounds (2.4s)\n\u2714 [10473/10638] Built Critical2DKPZ.OnePoint.BlockRatioTiltedFactorization (3.0s)\n\u2714 [10474/10641] Built Critical2DKPZ.Provider.SecondMomentCriticalWindow (1.7s)\n\u2714 [10475/10645] Built Critical2DKPZ.SHF.Moments.WordLimitDominationBlock (4.2s)\n\u2714 [10476/10646] Built Critical2DKPZ.FutureProfiles.ProfileEstimateCorrections (10s)\n\u2714 [10477/10646] Built Critical2DKPZ.LocalSobolev.RegularizedPairingMeasurability (3.0s)\n\u2714 [10478/10649] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureSampling (3.7s)\n\u2714 [10479/10649] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureHorizon (3.9s)\n\u2714 [10480/10649] Built Critical2DKPZ.JointConvergence.ThmToyJointParts (3.4s)\n\u2714 [10481/10649] Built Critical2DKPZ.LocalSobolev.ModulatedSobolevMomentBounds (2.7s)\n\u2714 [10482/10649] Built Critical2DKPZ.Analysis.Sobolev.WeightedConvolution (10s)\n\u2714 [10483/10649] Built Critical2DKPZ.Analysis.Sobolev.FourierProduct (8.3s)\n\u2714 [10484/10652] Built Critical2DKPZ.JointConvergence.ThmToyJointLimitHighLp (11s)\n\u2714 [10485/10652] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureDensity (4.8s)\n\u2714 [10486/10652] Built Critical2DKPZ.Analysis.Sobolev.Rellich.RellichConvolutionJets (3.6s)\n\u2714 [10487/10652] Built Critical2DKPZ.LocalSobolev.LatticeProfileMass (4.6s)\n\u2714 [10488/10653] Built Critical2DKPZ.LocalSobolev.LatticeReversalMass (3.5s)\n\u2714 [10489/10656] Built Critical2DKPZ.SHF.Moments.WordPotentialInduction (3.6s)\n\u2714 [10490/10656] Built Critical2DKPZ.OnePoint.BlockRatioPairEstimate (9.1s)\n\u2714 [10491/10656] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureCutoff (3.3s)\n\u2714 [10492/10656] Built Critical2DKPZ.LocalSobolev.LatticeReversalInitialSlice (2.5s)\n\u2714 [10493/10656] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSampling (3.5s)\n\u2714 [10495/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitPhaseCells (3.8s)\n\u2714 [10496/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordInitialZero (3.5s)\n\u2714 [10497/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureGrid (3.9s)\n\u2714 [10498/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordContinuumBound (3.4s)\n\u2714 [10499/10662] Built Critical2DKPZ.Assembly.LatticeCentring (6.3s)\n\u2714 [10500/10662] Built Critical2DKPZ.LogNormality.LatticeInputs (23s)\n\u2714 [10501/10662] Built Critical2DKPZ.Analysis.Sobolev.Rellich.RellichConvolvedCompact (2.6s)\n\u2714 [10502/10662] Built Critical2DKPZ.LocalSobolev.RandomBoundaryTerminal (7.7s)\n\u2714 [10503/10662] Built Critical2DKPZ.LocalSobolev.LatticeReversalLawTransfer (2.8s)\n\u2714 [10504/10662] Built Critical2DKPZ.Analysis.Sobolev.WeightedConvolutionRepresentation (5.5s)\n\u2714 [10505/10662] Built Critical2DKPZ.OnePoint.BlockRatioOriginalLawEstimates (3.7s)\n\u2714 [10506/10662] Built Critical2DKPZ.FutureProfiles.SplitTranslationConsequences (5.2s)\n\u2714 [10507/10662] Built Critical2DKPZ.SHF.Moments.WordLimitDominationInduction (3.7s)\n\u2714 [10508/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitGeneralBlock (4.0s)\n\u2714 [10509/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureDensityMeasurable (4.7s)\n\u2714 [10510/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureSamplingHorizon (4.0s)\n\u2714 [10511/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitInterior (3.9s)\n\u2714 [10512/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSamplePotential (3.9s)\n\u2714 [10513/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitFinitePhaseCells (3.0s)\n\u2714 [10514/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureSupport (3.2s)\n\u2714 [10515/10662] Built Critical2DKPZ.JointConvergence.ThmToyJointLimit (6.9s)\n\u2714 [10516/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordInitialCutoff (3.7s)\n\u2714 [10517/10662] Built Critical2DKPZ.Analysis.Sobolev.Rellich.NegativeNormCompactness (2.9s)\n\u2714 [10518/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordFutureBoundHorizon (3.6s)\n\u2714 [10519/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordTestedEntrance (3.7s)\n\u2714 [10520/10662] Built Critical2DKPZ.Analysis.Sobolev.LocNegSobolevFourierReadout (2.6s)\n\u2714 [10521/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordEntranceL1 (5.2s)\n\u2714 [10522/10662] Built Critical2DKPZ.LocalSobolev.RandomBoundaryTerminalStep (4.1s)\n\u2714 [10523/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSampleTail (3.5s)\n\u2714 [10524/10662] Built Critical2DKPZ.SHF.Moments.WordLimitDominationMass (3.9s)\n\u2714 [10525/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitFusedCells (3.0s)\n\u2714 [10526/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordInitialFull (3.7s)\n\u2714 [10527/10662] Built Critical2DKPZ.Analysis.Sobolev.Rellich.FrozenDistributionBound (3.4s)\n\u2714 [10528/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordStepIntegral (3.6s)\n\u2714 [10529/10662] Built Critical2DKPZ.Smoothing.ShortClockVarianceRefined (6.7s)\n\u2714 [10530/10662] Built Critical2DKPZ.LocalSobolev.LatticeTestConvergence (5.7s)\n\u2714 [10531/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordInitialCutoffHorizon (4.3s)\n\u2714 [10532/10662] Built Critical2DKPZ.Analysis.Sobolev.Rellich.DistributionRepresentation (5.2s)\n\u2714 [10533/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordEntranceFormula (3.7s)\n\u2714 [10534/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitFusedSample (3.5s)\n\u2714 [10535/10662] Built Critical2DKPZ.OnePoint.BlockRatioTiltedPairEstimate (12s)\n\u2714 [10536/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordEntranceFullL1 (3.0s)\n\u2714 [10537/10662] Built Critical2DKPZ.LocalSobolev.LatticeReversalTerminalBoundary (4.0s)\n\u2714 [10538/10662] Built Critical2DKPZ.SHF.Moments.WordLimitDomination (3.2s)\n\u2714 [10539/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitFusedSites (3.3s)\n\u2714 [10540/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitShiftedPotential (4.1s)\n\u2714 [10541/10662] Built Critical2DKPZ.Analysis.Sobolev.LocNegSobolevEvaluation (2.4s)\n\u2714 [10542/10662] Built Critical2DKPZ.Analysis.Sobolev.LocNegSobolevPairing (1.0s)\n\u2714 [10543/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordInitialFullHorizon (3.4s)\n\u2714 [10544/10662] Built Critical2DKPZ.Analysis.Sobolev.Rellich.LocalCompactnessExtraction (3.0s)\n\u2714 [10545/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordEntranceWindows (3.5s)\n\u2714 [10546/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialPhaseShift (3.4s)\n\u2714 [10547/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSampleWindow (3.5s)\n\u2714 [10548/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordContinuumCutoffs (3.4s)\n\u2714 [10549/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitFusedSupport (2.0s)\n\u2714 [10550/10662] Built Critical2DKPZ.LocalSobolev.LimitDistribution (2.5s)\n\u2714 [10551/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitTimeBoundary (7.0s)\n\u2714 [10552/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordDiagramPathL1 (4.4s)\n\u2714 [10553/10662] Built Critical2DKPZ.LocalSobolev.LatticeReversalProfileIdentity (4.7s)\n\u2714 [10554/10662] Built Critical2DKPZ.OnePoint.BlockRatioTiltedLawEstimates (5.7s)\n\u2714 [10555/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordMovingRepresentation (2.0s)\n\u2714 [10556/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordEntranceWindowsHorizon (3.1s)\n\u2714 [10557/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialIntegrand (2.0s)\n\u2714 [10558/10662] Built Critical2DKPZ.Analysis.Sobolev.LocNegSobolevCompactness (1.7s)\n\u2714 [10559/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialShiftCells (3.4s)\n\u2714 [10560/10662] Built Critical2DKPZ.Smoothing.DiagonalClockPerturbation (8.6s)\n\u2714 [10561/10662] Built Critical2DKPZ.LogNormality.LatticeVariance (15s)\n\u2714 [10562/10662] Built Critical2DKPZ.SmallScales.HeatStartMoments (16s)\n\u2714 [10563/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordCutoffExhaustion (3.5s)\n\u2714 [10564/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordDiagramPathIntegral (3.4s)\n\u2714 [10565/10662] Built Critical2DKPZ.LocalSobolev.LatticeReversalTerminalRatio (3.2s)\n\u2714 [10566/10662] Built Critical2DKPZ.Provider.PropVD (3.2s)\n\u2714 [10567/10662] Built Critical2DKPZ.LocalSobolev.LatticeReversalExactClock (3.6s)\n\u2714 [10568/10662] Built Critical2DKPZ.Analysis.Sobolev.LocNegSobolevFourierCompactness (2.6s)\n\u2714 [10569/10662] Built Critical2DKPZ.FutureProfiles.AdaptiveLeftTail (18s)\n\u2714 [10570/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordEntranceBoundary (3.2s)\n\u2714 [10571/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialRepresentation (3.8s)\n\u2714 [10572/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordEntranceSpatialTail (3.0s)\n\u2714 [10573/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitUniformSpatialBound (4.2s)\n\u2714 [10574/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordFullCutoffLimit (4.6s)\n\u2714 [10575/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordContinuumApproximation (3.3s)\n\u2714 [10576/10662] Built Critical2DKPZ.LocalSobolev.NegSobolevLimit (6.7s)\n\u2714 [10577/10662] Built Critical2DKPZ.Analysis.Sobolev.LocNegSobolevEnergyConvergence (2.5s)\n\u2714 [10578/10662] Built Critical2DKPZ.CovarianceKernel.PointwiseMoments (4.4s)\n\u2714 [10579/10662] Built Critical2DKPZ.LocalSobolev.LatticeReversalPointwise (3.6s)\n\u2714 [10580/10662] Built Critical2DKPZ.Analysis.Sobolev.LocNegSobolevRellich (2.4s)\n\u2714 [10581/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordCutoffError (3.9s)\n\u2714 [10582/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialLattice (4.0s)\n\u2714 [10583/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitTimeWindow (3.8s)\n\u2714 [10584/10662] Built Critical2DKPZ.SHF.Moments.SinglePairEntranceLimitFromCutoffs (3.7s)\n\u2714 [10585/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialTranslated (4.3s)\n\u2714 [10586/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordTestedDiagramIdentity (6.6s)\n\u2714 [10587/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitGlobalGaussianBounds (4.4s)\n\u2714 [10588/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialBound (4.4s)\n\u2714 [10589/10662] Built Critical2DKPZ.CovarianceKernel.CovarianceLimit (3.9s)\n\u2714 [10590/10662] Built Critical2DKPZ.Analysis.Sobolev.LocNegSobolevTightness (2.0s)\n\u2714 [10591/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialCutoffGeometry (5.4s)\n\u2714 [10592/10662] Built Critical2DKPZ.LocalSobolev.LatticeReversalPointwiseL1 (3.9s)\n\u2714 [10593/10662] Built Critical2DKPZ.FutureProfiles.OriginComparison (7.3s)\n\u2714 [10594/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitLatticeFunctional (3.1s)\n\u2714 [10595/10662] Built Critical2DKPZ.FutureProfiles.ProfileEstimates (8.1s)\n\u2714 [10596/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordLimitFromEntranceIntegrals (3.3s)\n\u2714 [10597/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialNormalization (3.5s)\n\u2714 [10598/10662] Built Critical2DKPZ.LocalSobolev.TupleConvergence (2.5s)\n\u2714 [10599/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialPointwise (3.2s)\n\u2714 [10600/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitGlobalGaussianWeights (3.6s)\n\u2714 [10601/10662] Built Critical2DKPZ.LocalSobolev.LatticeReversalTestedExactError (3.6s)\n\u2714 [10602/10662] Built Critical2DKPZ.CovarianceKernel.CovarianceFubini (4.6s)\n\u2714 [10603/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitFunctionalBounds (3.1s)\n\u2714 [10604/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitTimeRepresentation (3.3s)\n\u2714 [10605/10662] Built Critical2DKPZ.Smoothing.UnitHorizonPerturbed (14s)\n\u2714 [10606/10662] Built Critical2DKPZ.LocalSobolev.FlatCovariance (5.2s)\n\u2714 [10607/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordContinuumCutoffApproximation (5.0s)\n\u2714 [10608/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialIntegral (2.9s)\n\u2714 [10609/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitSpatialError (3.1s)\n\u2714 [10610/10662] Built Critical2DKPZ.LogNormality.LatticeLogNormality (14s)\n\u2714 [10611/10662] Built Critical2DKPZ.FutureProfiles.WeightedOriginComparison (5.2s)\n\u2714 [10612/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitGlobalEntranceBound (3.1s)\n\u2714 [10613/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitGlobalRunBound (3.8s)\n\u2714 [10614/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitFunctionalAlgebra (3.0s)\n\u2714 [10615/10662] Built Critical2DKPZ.CovarianceKernel.RegularizedSpecification (4.3s)\n\u2714 [10616/10662] Built Critical2DKPZ.Smoothing.EnergyDilateUniform (4.5s)\n\u2714 [10617/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordDiscreteCutoffExhaustion (11s)\n\u2714 [10618/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitGlobalBlockBound (3.0s)\n\u2714 [10619/10662] Built Critical2DKPZ.LogNormality.SHFLogNormality (4.1s)\n\u2714 [10620/10662] Built Critical2DKPZ.Smoothing.LatticeSmoothingRescaling (5.3s)\n\u2714 [10621/10662] Built Critical2DKPZ.SHF.Moments.SinglePairWordLimit (2.7s)\n\u2714 [10622/10662] Built Critical2DKPZ.Provider.ShfLogNormality (2.9s)\n\u2714 [10623/10662] Built Critical2DKPZ.Assembly.Invariance (4.1s)\n\u2714 [10624/10662] Built Critical2DKPZ.NonGaussian.EndpointOne (4.3s)\n\u2714 [10625/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordFirstLetterLimit (6.9s)\n\u2714 [10626/10662] Built Critical2DKPZ.LocalSobolev.FlatNegSobolev (6.7s)\n\u2714 [10627/10662] Built Critical2DKPZ.Smoothing.EnergyDilateGreen (6.3s)\n\u2714 [10628/10662] Built Critical2DKPZ.SHF.Moments.TerminalWordLimitGlobalSpatialMajorant 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"name": "Quentin Berger" }, { "name": "Francesco Caravenna" }, { "name": "Jeremy Clark" }, { "name": "Alexander Dunlap" }, { "name": "Yu Gu" }, { "name": "Ziyang Liu" }, { "name": "Shuta Nakajima" }, { "name": "Rongfeng Sun" }, { "name": "Li-Cheng Tsai" }, { "name": "Zuodi Xie" }, { "name": "Nikos Zygouras" } ], "location": "arXiv:2610.31614", "note": "All main results: Theorem A, Theorem 1.2 with Remark 6.5, the comparison principle, Theorem 1.4(i)-(ii), Proposition 1.5, Theorem 1.6, Proposition 1.8, Proposition 3.8 and equation (1.16) with Lemma 4.3, and the key intermediate results (Theorems 3.1, 5.1, 8.1, Lemmas 3.6, 5.3, B.2, Propositions 4.1, 4.4-4.5). Numbering refers to arXiv version 1 (22 October 2026). Errata and deviations are listed in docs/ERRATA-AND-DEVIATIONS.md.", "relationship": "formalizes", "title": "The Critical 2D KPZ Process", "type": "paper" }, { "author_endorsement": "participated", "authors": [ { "name": "Scott Armstrong" } ], "location": "docs/four-results.pdf", "note": "Theorems A\u2013D: strict skewness, response to the initial condition, Brownian motion across scales and the finite-dimensional GFF tangent. All are proved at fixed parameters.", "relationship": "formalizes", "title": "Four results on the critical 2D KPZ process", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Antonio Auffinger" }, { "name": "Wei-Kuo Chen" } ], "location": "Communications in Mathematical Physics 335 (2015), 1429\u20131444, DOI 10.1007/s00220-014-2254-z; arXiv:1402.5132v3", "note": "AC15: Convex Gaussian specialization of Proposition 1, with all positive exponential moments, follows from FMP25 and NP16; no Parisi or stochastic-control theorem.", "relationship": "adapts", "title": "The Parisi formula has a unique minimizer", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Quentin Berger" }, { "name": "Francesco Caravenna" }, { "name": "Nicola Turchi" } ], "location": "preprint (2025; pinned revision 2026), arXiv:2508.02478v3", "note": "BCT25: No listed strong-disorder or uniform variance theorem is formalized; notation and methodological context only.", "relationship": "background", "title": "Strong Disorder for Stochastic Heat Flow and 2D Directed Polymers", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Sergey G. Bobkov" }, { "name": "Arnaud Marsiglietti" }, { "name": "James Melbourne" } ], "location": "Combinatorics, Probability and Computing 31 (2022), DOI 10.1017/S096354832100016X; arXiv:2007.11030v2", "note": "BMM22: Finite symmetric probability profiles, positive on their finite interval support and log-concave, satisfy the adapted central-atom bound with constant 487 in its stated moment normalization, including the half-integer-centered version; finite convolution closure is also proved.", "relationship": "adapts", "title": "Concentration functions and entropy bounds for discrete log-concave distributions", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Quentin Berger" }, { "name": "Nicola Turchi" }, { "name": "Nikos Zygouras" } ], "location": "preprint (2026), arXiv:2608.13359v1", "note": "BTZ26: No listed parameter-uniform fractional-moment or variance theorem is formalized.", "relationship": "background", "title": "Fractional moments of the Stochastic Heat Flow and 2D Directed Polymers", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Francesco Caravenna" }, { "name": "Francesca Cottini" }, { "name": "Maurizia Rossi" } ], "location": "Annals of Applied Probability 35 (2025), no. 4, 2604\u20132643; arXiv:2307.02453v3", "note": "CCR25: Fixed-horizon quasi-critical Gaussian planar linear CLT and fourth- and sixth-moment bounds for the planar Gaussian polymer with terminal test function 1, using the collision-word expansion; the algebraic bound with a finite configuration cutoff, at arbitrary particle order, remains conditional on its stated partition-moment and operator bounds.", "relationship": "adapts", "title": "Quasi-critical fluctuations for 2D directed polymers", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Cl\u00e9ment Cosco" }, { "name": "Anna Donadini" } ], "location": "Electronic Communications in Probability 30 (2025), paper 86, 1\u201311; arXiv:2402.14647v2", "note": "CD25: No listed subcritical central limit theorem or dyadic decoupling theorem is formalized; block-factorization precursor only.", "relationship": "background", "title": "On the central limit theorem for the log-partition function of 2D directed polymers", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Wei-Kuo Chen" } ], "location": "Annales de l\u2019Institut Henri Poincar\u00e9, Probabilit\u00e9s et Statistiques 62 (2026), no. 1, 195\u2013206; arXiv:2311.08351v2", "note": "Chen26: Normalized log-moment-generating-function convexity at all real orders, including the mean at zero, for finite convex functions of any finite-dimensional Gaussian with all positive exponential moments. No spin-glass applications.", "relationship": "adapts", "title": "A Gaussian Convexity for Logarithmic Moment Generating Functions with Applications in Spin Glasses", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Jeremy Clark" }, { "name": "Barkat Mian" } ], "location": "arXiv:2306.14849 (2023 preprint)", "note": "CM25: The local-time existence and occupation-approximation theorems are not formalized.", "relationship": "background", "title": "On planar Brownian motion singularly tilted through a point potential", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Jeremy Clark" }, { "name": "Barkat Mian" } ], "location": "Communications in Mathematical Physics 407 (2026), article 152; arXiv:2409.01510v1; DOI 10.1007/s00220-026-05677-3", "note": "CM26: Finite-slab annealing, limiting conditional bounds, approximate composition and dense-time flow are proved for the Gaussian period-two polymer, together with the Euler-shifted Gamma-integral dictionary. The supporting moment, sixth-moment, semigroup and comparison hypotheses are supplied for this model. The source\u2019s mollified-SHE conditional-mean proposition, continuum path-space construction and Volterra-derivative identity are not asserted verbatim.", "relationship": "adapts", "title": "Continuum polymer measures corresponding to the critical 2d stochastic heat flow", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Francesco Caravenna" }, { "name": "Rongfeng Sun" }, { "name": "Nikos Zygouras" } ], "location": "Annals of Applied Probability 27 (2017), no. 5, 3050\u20133112. DOI: 10.1214/17-AAP1276. arXiv: 1510.06287", "note": "CSZ17b: No listed universality, subcritical field-limit or multiscale-correlation theorem is formalized.", "relationship": "background", "title": "Universality in marginally relevant disordered systems", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Francesco Caravenna" }, { "name": "Rongfeng Sun" }, { "name": "Nikos Zygouras" } ], "location": "Electronic Journal of Probability 24 (2019), paper 101, 1\u201340. DOI: 10.1214/19-EJP353. arXiv: 1805.01465v4", "note": "CSZ19a: For the planar nearest-neighbor simple symmetric random walk, scalar and reachable-parity spatial renewal limits, leading scalar-density asymptotics and logarithmic bounds, and Gaussian free-polymer second moments; no general renewal-law or stochastic-subordinator theorem.", "relationship": "adapts", "title": "The Dickman subordinator, renewal theorems, and disordered systems", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Francesco Caravenna" }, { "name": "Rongfeng Sun" }, { "name": "Nikos Zygouras" } ], "location": "Communications in Mathematical Physics 372 (2019), 385\u2013440. DOI: 10.1007/s00220-019-03527-z. arXiv: 1808.03586v2", "note": "CSZ19b: Exact finite Gaussian planar polarized first-collision identity for probability profiles and its heat-profile specialization, with terminal disorder included; no printed critical-window third-moment limit.", "relationship": "adapts", "title": "On the moments of the (2+1)-dimensional directed polymer and stochastic heat equation in the critical window", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Francesco Caravenna" }, { "name": "Rongfeng Sun" }, { "name": "Nikos Zygouras" } ], "location": "Annals of Probability 48 (2020), no. 3, 1086\u20131127. DOI: 10.1214/19-AOP1383. arXiv: 1812.03911v3", "note": "CSZ20: No listed fixed-subcritical KPZ limit or source localization theorem is formalized.", "relationship": "background", "title": "The two-dimensional KPZ equation in the entire subcritical regime", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "F. Caravenna" }, { "name": "R. Sun" }, { "name": "N. Zygouras" } ], "location": "Inventiones Mathematicae 233 (2023), doi: [10.1007/s00222-023-01184-7](https://doi.org/10.1007/s00222-023-01184-7), arXiv:2109.03766v3", "note": "CSZ23: SHF existence, symmetries and covariance are proved for the Gaussian planar simple-walk model, together with squared-binomial exponential-moment and replica-Green bilinear estimates. The dense-limit and uniqueness hypotheses of the supporting existence lemma are supplied for this model. The source\u2019s general-disorder universality theorem is not formalized, and no identification with its construction is asserted.", "relationship": "adapts", "title": "The critical 2d stochastic heat flow", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Francesco Caravenna" }, { "name": "Rongfeng Sun" }, { "name": "Nikos Zygouras" } ], "location": "Probability Theory and Related Fields (to appear); arXiv:2504.06128v2 (2025)", "note": "CSZ25: Fourth- and sixth-moment bounds are proved for the Gaussian planar polymer with terminal test function 1, including geometric blocks. Almost-sure mutual singularity of the SHF terminal marginal with each deterministic finite measure is proved; the supporting variance-defect, symmetry, heat-start and dense-flow hypotheses are supplied for this model. The full source ball-density theorem is not formalized.", "relationship": "adapts", "title": "Singularity and regularity of the critical 2D stochastic heat flow", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "F. Caravenna" }, { "name": "R. Sun" }, { "name": "N. Zygouras" } ], "location": "lecture notes, arXiv:2412.10311v3 (25 May 2026)", "note": "CSZ26: Exact finite Gaussian-disorder chaos expansions for the period-two walk with the KPZ terminal-layer convention; no asymptotic transition or continuum construction theorem.", "relationship": "adapts", "title": "The critical 2d stochastic heat flow and related models", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Jeremy Clark" }, { "name": "Li-Cheng Tsai" } ], "location": "preprint (2025), arXiv:2507.16056v1", "note": "CT25: No conditional-GMC construction or coupling theorem is formalized.", "relationship": "background", "title": "Conditional GMC within the stochastic heat flow", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Hindy Drillick" }, { "name": "Jonathan Hou" }, { "name": "Shalin Parekh" } ], "location": "arXiv:2609.15832v1 (2026)", "note": "DHP26: Moving-time and fixed-time Gaussian polymer moment limits through order four are proved for products of compact endpoint-pair tests, with approximate composition and dense-time flow. The word-domination, non-pair-remainder, word-limit, sixth-moment, semigroup and comparison hypotheses of the supporting lemmas are supplied for this model. No general-disorder universality or arbitrary configuration-test claim is made.", "relationship": "adapts", "title": "A universality result for the critical 2d stochastic heat flow", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Maite Fern\u00e1ndez-Unzueta" }, { "name": "James Melbourne" }, { "name": "Gerardo Palafox-Castillo" } ], "location": "preprint (2025), arXiv:2510.06676v1", "note": "FMP25: Convex-branch log-moment-generating-function comparison on the finite moment domain, assuming `E[e^{rX}] < \u221e` for some `r > 0`, and adapted Ehrhard-law representation; no strictness/equality cases, concave branch or full extended-value theorem.", "relationship": "adapts", "title": "On convex functions of Gaussian variables", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Y. Gu" }, { "name": "J. Quastel" }, { "name": "L.-C. Tsai" } ], "location": "Probability and Mathematical Physics 2 (2021), doi: [10.2140/pmp.2021.2.179](https://doi.org/10.2140/pmp.2021.2.179), arXiv:1905.11310v2", "note": "GQT21: Two-particle semigroup law, positive form bounds for every particle number and bounds on real L\u00b2 bilinear forms through four particles, and adapted scalar/swapping estimates; no all-particle operator-semigroup or mollified-SHE convergence theorem.", "relationship": "adapts", "title": "Moments of the 2D SHE at criticality", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Yu Gu" }, { "name": "Li-Cheng Tsai" } ], "location": "preprint (2026), arXiv:2603.03246v1", "note": "GT26: Analytic collision-density estimates used by the note are proved. For each process satisfying the stated critical SHF definition, the proved result is the mean-centered, fixed-parameter, delayed heat-start log-log central limit theorem, obtained by a lattice argument; finite block expansions are proved. No moving-parameter/original-centering or conditional-GMC theorem.", "relationship": "adapts", "title": "Log Log Fluctuations of the Stochastic Heat Flow", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Paata Ivanisvili" } ], "location": "Studia Mathematica 246 (2019), DOI 10.4064/sm170730-22-1; arXiv:1605.04840", "note": "Ivan16: Convex-set, sum-one Ehrhard consequence via NP16, for arbitrary finite-dimensional Gaussian laws; no boundary-value or eligible-measure characterization theorem.", "relationship": "adapts", "title": "A boundary value problem and the Ehrhard inequality", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Ziyang Liu" }, { "name": "Zuodi Xie" } ], "location": "preprint (2026), arXiv:2609.12820v1", "note": "LX26: Adapted Ehrhard representation and weak closure, finite-domain convexity, normalized negative-moment comparisons and heat-profile log-SHF Ehrhard type are proved. The inverse-moment lower bound at p=\u22121 is proved for the Gaussian-model SHF; its supporting lemma retains explicit hypotheses, which are supplied in the non-Gaussianity proof. No all-negative-orders lower-bound claim is made.", "relationship": "adapts", "title": "Moments comparison inequalities for critical 2D stochastic heat flow, polymers and GMC", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Dimitris Lygkonis" }, { "name": "Nikos Zygouras" } ], "location": "Communications in Mathematical Physics 401 (2023); arXiv:2109.06115v2", "note": "LZ21: Adapted deterministic planar lattice-sum and absolutely summable pair-stratum bilinear estimates with explicit domain/constants; no subcritical moment limit or Erd\u0151s\u2013Taylor theorem.", "relationship": "adapts", "title": "Moments of the 2d directed polymer in the subcritical regime and a generalisation of the Erd\u0151s\u2013Taylor theorem", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Ziyang Liu" }, { "name": "Nikos Zygouras" } ], "location": "Communications in Mathematical Physics 407 (2026); arXiv:2410.14601v3", "note": "LZ26: the inverse-log Laplace-transform formula for the scalar collision density after the parameter change `\u03b8 = \u03d1 \u2212 \u03b3`, where `\u03b3` is Euler's constant, together with integrability, positivity, continuity and the leading small-time equivalent; no second correction term or all-order shrinking-ball theorem.", "relationship": "adapts", "title": "On the moments of the mass of shrinking balls under the Critical 2d Stochastic Heat Flow", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Joe Neeman" }, { "name": "Grigoris Paouris" } ], "location": "in Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics (2020), DOI 10.1007/978-3-030-46762-3_12; arXiv:1605.07233v1", "note": "NP16: The corrected sufficient direction of the Ornstein\u2013Uhlenbeck interpolation argument proves the finite-dimensional convex-set Ehrhard inequality, with explicit regularity restrictions; no full measurable Jensen equivalence or necessity theorem.", "relationship": "adapts", "title": "An interpolation proof of Ehrhard\u2019s inequality", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Alexander Shamov" } ], "location": "Journal of Functional Analysis 270 (2016), DOI 10.1016/j.jfa.2016.03.001; arXiv:1407.4418", "note": "Sha16: No listed abstract GMC existence/approximation, characterization, randomized-shift or Hilbert\u2013Schmidt moment theorem is formalized.", "relationship": "background", "title": "On Gaussian multiplicative chaos", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "S. Surendranath" }, { "name": "L.-C. Tsai" } ], "location": "Electronic Communications in Probability 30 (2025), doi: [10.1214/25-ECP685](https://doi.org/10.1214/25-ECP685), arXiv:2410.16550v2", "note": "ST25: Corrected limiting \u03b5=0 weighted kernel bounds on compact time intervals, collision-chain summability and the needed four-particle application; no regularized construction/convergence or printed universal chain constant.", "relationship": "adapts", "title": "Two-dimensional delta Bose gas in a weighted space", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Yair Shenfeld" }, { "name": "Ramon van Handel" } ], "location": "Advances in Mathematics 331 (2018), DOI 10.1016/j.aim.2018.04.013; arXiv:1709.00061", "note": "SVH18: Convex-set sum-one special case of Ehrhard\u2013Borell via NP16; no equality-case classification or full nonconvex weighted theorem.", "relationship": "adapts", "title": "The equality cases of the Ehrhard\u2013Borell inequality", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "L.-C. Tsai" } ], "location": "arXiv:2410.14657v3 (16 March 2026)", "note": "Tsai24: Uniqueness of finite-dimensional distributions on a dense set of times in a compact interval, under the Chapman\u2013Kolmogorov, independence and moment axioms through order four; four-particle weighted bound for 20, uniformly on (0,T]. The uniqueness application chooses p>6; no mollified-SHE construction/path continuity.", "relationship": "adapts", "title": "Stochastic heat flow by moments", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "Ramon van Handel" } ], "location": "Probability Theory and Related Fields 170 (2018), DOI 10.1007/s00440-017-0762-4; arXiv:1605.00285", "note": "VH17: Convex-set sum-one Ehrhard consequence via NP16; no stochastic-game representation or general reverse Brascamp\u2013Lieb theorem.", "relationship": "adapts", "title": "The Borell\u2013Ehrhard game", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "A. Ehrhard" } ], "location": "Math. Scand. 53 (1983), doi:10.7146/math.scand.a-12035", "note": "E83: Finite-threshold convex-set Ehrhard inequality for all finite-dimensional Gaussian laws, including singular covariance, via NP16. Attribution is based on FMP25 and NP16.", "relationship": "adapts", "title": "Sym\u00e9trisation dans l\u2019espace de Gauss", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "W. Hebisch" }, { "name": "L. Saloff-Coste" } ], "location": "Ann. Probab. 21 (1993), doi:10.1214/aop/1176989263", "note": "HS93: Planar simple-walk Gaussian upper bound and adapted same-parity squared-displacement estimate; no full polynomial-growth-group theorem.", "relationship": "adapts", "title": "Gaussian estimates for Markov chains and random walks on groups", "type": "paper" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "G. F. Lawler" }, { "name": "V. Limic" } ], "location": "Cambridge University Press (2010), doi:10.1017/CBO9780511750854", "note": "LL10: Planar nearest-neighbor, parity-correct additive local central limit theorem with C/n\u00b2 error and Gaussian upper bound; no general-walk relative moderate-deviation expansion.", "relationship": "adapts", "title": "Random Walk: A Modern Introduction", "type": "book" }, { "author_endorsement": "not-contacted", "authors": [ { "name": "M. Reed" }, { "name": "B. Simon" } ], "location": "Academic Press (1975)", "note": "RS75: Positive spectral-measure representation for real even planar locally-L\u00b2 kernels with explicit polynomial growth and nonnegative compact-test quadratic forms; no arbitrary-dimensional distributional equivalence.", "relationship": "adapts", "title": "Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness", "type": "book" } ], "related_formalizations": [], "repository_role": "substantive-development", "responsible_maintainers": [ { "name": "Scott Armstrong" } ], "result_origin": "source-based" }, "resource_usage": [ { "elapsed_seconds": 0.013, "max_rss_kib": 13328, "memory_source": "cgroup", "peak_tasks_observed": 1, "phase": "confinement-initial", "returncode": 0, "system_cpu_seconds": 0.014, "user_cpu_seconds": 0.018, "workspace_disk_peak_bytes": 0 }, { "cpu_max_applied": false, "cpu_usage_nanoseconds": 34750000, "deadline_fired": false, "exec_main_code": "1", "exec_main_status": "0", 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