8=======>

2022-09-11 · +7d

gru_s4 · in-sample — the model trained on this date · 191 tokens predicted

These numbers are in-sample. The model was trained on this date, so predicted-vs-actual agreement here is not evidence of skill.
+1d+7d+30dasset cohort only
rank IC
+0.2037
191 of 191 tokens assessed
long-short decile
+10.36%
realised beta-adjusted alpha
direction hit
75.9%
in alpha space · 97.4% on raw price
BTC over horizon
-11.06%
the unhedgeable market factor

Predicted vs actual (191 rows, sorted by pred)

tokennamechainanchor pxpred px ▾pred Δactual pxactual Δalpha errhitβ90dvol 30dtarget
ALEPHAleph CloudEthereum0.1270.12672-0.22%0.1131-10.94%0.1131✓0.0183k2022-09-18
TRBTellor TributesEthereum16.5816.5024-0.47%14.09-15.02%0.0660✓0.791.5M2022-09-18
AAVEAaveEthereum91.6390.8234-0.88%73.06-20.27%0.0379✓1.535.6M2022-09-18
ASMAssemble AIEthereum0.02130.021111-0.89%0.01968-7.61%0.0001✓0.60206k2022-09-18
NCTPolySwarmEthereum0.012930.012802-0.99%0.01153-10.83%0.0274✓0.66233k2022-09-18
BELBella ProtocolEthereum0.6760.668913-1.05%0.552-18.34%0.0579✓1.153.5M2022-09-18
INDEXThe IndexRobinhood1.91.8799-1.06%2.25+18.42%0.2357✗0.4861k2022-09-18
TRXTRONTron0.064190.063414-1.21%0.060789-5.30%0.0152✗0.49123k2022-09-18
ETHEthereumEthereum1,766.951,745.16-1.23%1,334.72-24.46%0.1074✓1.37575.8M2022-09-18
TWTTrust WalletBinance Smart Chain1.02751.0147-1.24%0.9352-8.98%0.0146✓0.572.6M2022-09-18
GTGateEthereum4.33014.2757-1.26%4.1187-4.88%0.0485✗0.73690k2022-09-18
TRACOriginTrailEthereum0.21410.211399-1.26%0.1831-14.48%0.0161✓1.09138k2022-09-18
LCXLCXEthereum0.05080.050102-1.37%0.0491-3.35%0.0903✗0.94234k2022-09-18
BFCBifrostEthereum0.075460.074418-1.38%0.06225-17.51%0.0597✓1.0124k2022-09-18
LTCLitecoinLitecoin62.1861.2845-1.44%52.65-15.33%0.0296✓1.0413.5M2022-09-18
FORTFortaEthereum0.23120.227854-1.45%0.1846-20.16%0.1206✓0.7766k2022-09-18
KCSKuCoinnative9.7559.6094-1.49%8.956-8.19%0.0308✗0.861.2M2022-09-18
NEXONEXOEthereum0.9740.959379-1.50%0.879-9.75%0.0532✗1.201.5M2022-09-18
YGGYield Guild GamesEthereum0.5150.507251-1.50%0.384-25.44%0.1343✓1.234,2692022-09-18
STORJStorjEthereum0.555060.546697-1.51%0.4662-16.01%0.0021✓1.3439k2022-09-18
LEOLEO TokenEthereum5.06274.9859-1.52%4.6704-7.75%0.0581✓0.06117k2022-09-18
BTTBitTorrentEthereum9.10e-78.96e-7-1.52%8.00e-7-12.09%0.0257✓0.7515k2022-09-18
TLMAlien WorldsEthereum0.02550.025109-1.53%0.02202-13.65%0.0011✓1.132,9142022-09-18
AVTAventusEthereum1.421.3982-1.54%1.42+0.00%0.0011✓-0.14124k2022-09-18
ACHAlchemy PayEthereum0.0131930.012986-1.57%0.011882-9.94%0.0102✓0.85920k2022-09-18
GODSGods UnchainedEthereum0.331390.325989-1.63%0.43553+31.43%0.3720✗0.70326k2022-09-18
BNTBancor NetworkEthereum0.5120.503647-1.63%0.4415-13.77%0.0064✓1.18384k2022-09-18
OGOG Fan TokenSolana6.1396.0365-1.67%5.554-9.53%0.0059✓0.663.1M2022-09-18
ARPAARPAEthereum0.03930.038643-1.67%0.0332-15.52%0.0322✓1.0288k2022-09-18
WBTCWrapped BitcoinEthereum21,663.6021,290.01-1.72%19,440.70-10.26%0.0166✓0.9213k2022-09-18
BCHSVBitcoin Cash SV54.45453.5134-1.73%48.437-11.05%0.0019✓0.87275k2022-09-18
BTTCBTTC9.10e-78.94e-7-1.79%7.90e-7-13.19%0.0360✓0.741.7M2022-09-18
SWFTCSWFTCOINEthereum0.0015580.00153-1.80%0.001548-0.64%0.1017✗0.77353k2022-09-18
CERECere NetworkEthereum0.0063090.006195-1.81%0.0063-0.14%0.0619✗0.3830k2022-09-18
IOTAIOTAIOTA0.29230.286951-1.83%0.2517-13.89%0.0121✓1.022.6M2022-09-18
ATMAtletico Madrid Fan TokenSolana4.644.5548-1.84%4.22-9.05%0.0039✓0.621.4M2022-09-18
ELAElastosEthereum1.6551.6245-1.84%1.531-7.49%0.0282✗0.7536k2022-09-18
ORBSOrbsEthereum0.03960.038865-1.86%0.03461-12.60%0.0351✓0.692,1832022-09-18
AIOZAIOZ NetworkEthereum0.06110.059962-1.86%0.0557-8.84%0.0267✗0.8682k2022-09-18
SUNSun TokenTron0.0065370.006414-1.87%0.005544-15.18%0.0671✓0.672,0442022-09-18
COTICOTIEthereum0.09970.097819-1.89%0.0912-8.53%0.0480✗1.01336k2022-09-18
BTCBitcoinBitcoin21,831.7221,417.50-1.90%19,417.64-11.06%0.0192✗1.00473.4M2022-09-18
LPTLivepeerEthereum11.2311.0164-1.90%8.65-22.97%0.0822✓1.36298k2022-09-18
ASRAS Roma Fan TokenSolana4.3544.271-1.91%3.731-14.31%0.0916✓0.372.2M2022-09-18
ZECZcashZcash64.2763.0398-1.91%53.33-17.02%0.0291✓1.181.2M2022-09-18
DKAdKargoEthereum0.046640.045744-1.92%0.04034-13.51%0.0502✓0.6414k2022-09-18
CHRChromiaEthereum0.1830.179439-1.95%0.1496-18.25%0.0449✓1.171,7442022-09-18
SHIBShiba InuEthereum0.000012990.000012736-1.96%0.00001061-18.32%0.0633✓1.021.0M2022-09-18
DIADIAEthereum0.405260.397243-1.98%0.37245-8.10%0.0544✗1.0132k2022-09-18
MOVRMoonriverBase12.886612.6311-1.98%11.3049-12.27%0.0089✓1.0222k2022-09-18
DOGEDogecoinDogecoin0.0637030.062438-1.99%0.0573-10.05%0.0325✗1.011.3M2022-09-18
DODODODOEthereum0.13330.130638-2.00%0.1208-9.38%0.0607✗1.191.4M2022-09-18
NANOnanopayBase0.9277880.909215-2.00%0.785842-15.30%0.0438✓0.8749k2022-09-18
ZRX0x ProtocolEthereum0.3137870.307487-2.01%0.266614-15.03%0.0271✓0.99471k2022-09-18
HIGHHighstreetEthereum1.5171.4864-2.02%1.336-11.93%0.0249✗1.1271k2022-09-18
RARESuperRareEthereum0.21060.206355-2.02%0.1768-16.05%0.0194✓1.15108k2022-09-18
SOLSolanaSolana35.0134.2977-2.03%31.1-11.17%0.0436✗1.2154.5M2022-09-18
STEEMSteemnative0.2350.230208-2.04%0.2197-6.51%0.0551✗0.87503k2022-09-18
AVAXAvalancheAvalanche20.6920.2655-2.05%16.72-19.19%0.0316✓1.3718.0M2022-09-18
SANDThe SandboxEthereum0.97480.954787-2.05%0.8289-14.97%0.0075✓1.27899k2022-09-18
POWRPowerledgerEthereum0.23030.22555-2.06%0.1954-15.15%0.0386✓0.8957k2022-09-18
FETArtificial Superintelligence AllianceEthereum0.09410.092155-2.07%0.0811-13.82%0.0118✓0.9914k2022-09-18
NAKANakamoto GamesPolygon0.06450.063132-2.12%0.0619-4.03%0.1012✗1.0379k2022-09-18
OGNOrigin TokenEthereum0.177890.174113-2.12%0.14138-20.52%0.0834✓1.07268k2022-09-18
BCHBitcoin CashBitcoin Cash130.35127.5761-2.13%111.83-14.21%0.0072✓1.194.4M2022-09-18
SUPERSuperVerseEthereum0.143820.140759-2.13%0.12379-13.93%0.0136✓1.21151k2022-09-18
OXTOrchid ProtocolEthereum0.11560.113135-2.13%0.0991-14.27%0.0297✓0.88169k2022-09-18
JUVJuventus Fan TokenSolana5.435.3142-2.13%5.19-4.42%0.0538✗0.662.0M2022-09-18
ZENHorizenBase16.4716.1184-2.13%13.34-19.00%0.0424✓1.2584k2022-09-18
XVSVenusEthereum5.14.9906-2.15%4.63-9.22%0.0263✗0.86859k2022-09-18
HIVEHivenative0.57920.566688-2.16%0.512-11.60%0.0286✓0.62826k2022-09-18
PROPropyEthereum0.720.704431-2.16%0.69-4.17%0.0065✓0.2346k2022-09-18
CBETHCoinbase Wrapped Staked ETHEthereum1,656.911,620.51-2.20%1,293.99-21.90%0.1078✓1.003.4M2022-09-18
UMAUMAEthereum2.7822.7201-2.23%2.396-13.87%0.0348✓0.79586k2022-09-18
LSKLiskEthereum1.08631.0621-2.23%0.954978-12.09%0.0161✓0.7734k2022-09-18
PHAPHALAEthereum0.10270.100411-2.23%0.0931-9.35%0.0144✓0.772,6892022-09-18
XCNOnyxcoinEthereum0.074140.072486-2.23%0.06377-13.99%0.1122✓0.14378k2022-09-18
ACMAC Milan Fan TokenSolana4.4054.3065-2.24%3.699-16.03%0.0888✓0.542.3M2022-09-18
WOOWOOEthereum0.1680.164241-2.24%0.1415-15.77%0.0062✓1.321,0012022-09-18
ENJEnjin CoinEthereum0.5430.530791-2.25%0.468-13.81%0.0175✓1.2274k2022-09-18
VSYSV.SYSTEMSnative0.0016360.001599-2.25%0.001429-12.65%0.0327✓0.686,5532022-09-18
KSMKusamaHydration51.950.7237-2.27%39.58-23.74%0.1290✓1.02395k2022-09-18
XLMStellarStellar0.1143870.111792-2.27%0.1072-6.28%0.0618✗0.896.4M2022-09-18
DASHDashDash48.3547.2498-2.28%40.12-17.02%0.0372✓1.08321k2022-09-18
XMRMoneroMonero159.22155.5562-2.30%140.49-11.76%0.0132✓0.981.3M2022-09-18
BARFC Barcelona Fan TokenSolana6.576.4186-2.30%5.56-15.37%0.0800✓0.542.1M2022-09-18
SCSiacoinnative0.004190.004093-2.31%0.00356-15.04%0.0288✓0.95103k2022-09-18
ADACardanoCardano0.51010.49825-2.32%0.4478-12.21%0.0114✓1.0138.3M2022-09-18
DUSKDUSKEthereum0.13780.134592-2.33%0.1145-16.91%0.0305✓1.122.9M2022-09-18
C98Coin98Ethereum0.44450.434131-2.33%0.3859-13.18%0.0194✓1.1781k2022-09-18
XYMSymbolnative0.0423220.041334-2.33%0.039181-7.42%0.0084✓0.5323k2022-09-18
XTZTezosTezos1.68551.6458-2.36%1.4386-14.65%0.0099✓1.06241k2022-09-18
ENSEthereum Name ServiceEthereum15.715.3286-2.37%12.84-18.22%0.0583✓1.011.8M2022-09-18
XEMNEMnative0.0467850.045678-2.37%0.039656-15.24%0.0366✓0.8928k2022-09-18
MANADecentralandEthereum0.803760.78474-2.37%0.70221-12.63%0.0222✓1.14584k2022-09-18
CRVCurve DAOEthereum1.1831.1549-2.38%0.935-20.96%0.0285✓1.564.4M2022-09-18
AGLDAdventure GoldEthereum0.42550.415353-2.38%0.3151-25.95%0.1465✓1.11202k2022-09-18
1INCH1INCHEthereum0.6490.633463-2.39%0.572-11.86%0.0185✓1.03178k2022-09-18
ASTRAstarEthereum0.03720.036306-2.40%0.0363-2.42%0.1023✗0.877,8252022-09-18
UOSUltraEthereum0.456780.445789-2.41%0.38485-15.75%0.0291✓1.01379k2022-09-18
MTLMetal DAOMetal L21.2511.2209-2.41%1.065-14.87%0.0271✓0.931.1M2022-09-18
NEARNEAR ProtocolNEAR4.8964.7772-2.43%3.918-19.98%0.0811✓1.001.4M2022-09-18
COMPCompoundEthereum55.2553.9035-2.44%47.61-13.83%0.0268✗1.298,9662022-09-18
QNTQuantEthereum108.82106.1388-2.46%104.08-4.36%0.0921✗0.953.5M2022-09-18
SPELLSpellEthereum0.0013670.001334-2.47%0.001075-21.36%0.1167✓0.842.2M2022-09-18
BOBABoba NetworkEthereum0.33280.324539-2.48%0.299-10.16%0.0408✗1.0575k2022-09-18
ANKRAnkr NetworkEthereum0.037810.036868-2.49%0.03069-18.83%0.0580✓1.0745k2022-09-18
BATBasic AttentionEthereum0.351690.34288-2.51%0.30461-13.39%0.0080✓1.0834k2022-09-18
SUSHISushiEthereum1.30291.2701-2.52%1.0284-21.07%0.0763✓1.151.1M2022-09-18
GMTGMTEthereum0.73510.716487-2.53%0.6036-17.89%0.0084✓1.53226k2022-09-18
ALGOAlgorandAlgorand0.32640.318113-2.54%0.293-10.23%0.0334✗0.995.9M2022-09-18
CVCCivicEthereum0.15180.147923-2.55%0.129-15.02%0.0193✓1.00110k2022-09-18
CITYManchester City Fan TokenSolana6.736.5579-2.56%6.01-10.70%0.0284✓0.502.1M2022-09-18
RADRadworksEthereum2.632.5625-2.56%2.09-20.53%0.1310✓0.62262k2022-09-18
JASMYJasmyCoinEthereum0.009440.009198-2.56%0.00752-20.34%0.0884✓0.963.2M2022-09-18
CWEBCoinwebEthereum0.0239730.023357-2.57%0.026132+9.01%0.1208✗0.07455k2022-09-18
ICPInternet ComputerEthereum7.1736.9885-2.57%5.851-18.43%0.0593✓1.014.3M2022-09-18
KNCKyber Network CrystalEthereum2.00771.9549-2.63%1.4393-28.31%0.2064✓0.851.4M2022-09-18
DEXEDeXeEthereum3.2783.1917-2.63%2.925-10.77%0.0433✓0.38720k2022-09-18
ALICEMy Neighbor AliceEthereum2.2022.1439-2.64%1.808-17.89%0.0202✓1.2832k2022-09-18
ADXheyAuraEthereum0.174140.169498-2.67%0.16044-7.87%0.0369✗0.783512022-09-18
ATOMCosmos HubCosmos15.69915.2802-2.67%14.707-6.32%0.1137✗1.3018.7M2022-09-18
FTTFTXEthereum27.8927.1443-2.67%23.45-15.92%0.0269✓1.026.8M2022-09-18
DNTdistrict0xEthereum0.04970.048354-2.71%0.0427-14.08%0.0247✓0.85138k2022-09-18
RUNETHORChainTHORChain1.991.9359-2.72%1.646-17.29%0.0393✗1.7260k2022-09-18
ORCAOrcaSolana0.88850.864317-2.72%0.8499-4.34%0.1670✗1.5794k2022-09-18
PORPortugal National Team Fan TokenSolana4.8474.714-2.74%4.9458+2.04%0.2277✗1.53129k2022-09-18
OMGOMG NetworkEthereum1.92411.8711-2.75%1.6754-12.93%0.0207✓1.1223k2022-09-18
SKLSKALEEthereum0.05010.048692-2.81%0.037-26.15%0.1380✓1.17536k2022-09-18
SNXSynthetixEthereum2.9632.8775-2.89%2.44-17.65%0.0186✓1.572.9M2022-09-18
BICOBiconomyEthereum0.51570.500783-2.89%0.4395-14.78%0.0304✓0.85418k2022-09-18
XECeCashnative0.000045620.00004428-2.94%0.00003918-14.12%0.0188✓0.882.5M2022-09-18
RIFRootstock Infrastructure FrameworkEthereum0.06620.064242-2.96%0.0565-14.65%0.0154✓1.23555k2022-09-18
MEDMediblocOsmosis0.0218870.021232-2.99%0.020014-8.56%0.0136✓0.6212k2022-09-18
APEApeCoinEthereum5.6825.5102-3.02%5.086-10.49%0.0851✗1.416.4M2022-09-18
IDEXIDEXEthereum0.073070.070847-3.04%0.06413-12.23%0.0144✓0.977022022-09-18
API3Api3Ethereum1.8381.7818-3.06%1.433-22.03%0.0977✓1.02627k2022-09-18
QTUMQtumQtum3.30663.2053-3.06%2.8489-13.84%0.0046✓1.0419k2022-09-18
UNIUniswapEthereum6.4916.2921-3.06%5.466-15.79%0.0232✓1.406.9M2022-09-18
CHZChilizEthereum0.20830.201918-3.06%0.2313+11.04%0.2531✗1.003.2M2022-09-18
XPRXPR NetworkEthereum0.0029040.002814-3.10%0.002574-11.36%0.0161✓0.901.2M2022-09-18
CBKCobakEthereum0.85180.824763-3.17%0.78032-8.39%0.0372✗0.7913k2022-09-18
POKTPocket NetworkEthereum0.12540.121411-3.18%0.1002-20.10%0.1193✓0.62191k2022-09-18
TKOTokocryptoBinance Smart Chain0.2850.275928-3.18%0.254-10.88%0.0088✓0.78563k2022-09-18
LRCLoopringEthereum0.36190.350238-3.22%0.3025-16.41%0.0081✓1.1872k2022-09-18
PORTOFC PortoBinance Smart Chain7.14686.9163-3.23%5.6084-21.53%0.1974✓0.109.1M2022-09-18
IMXImmutableEthereum0.86630.837931-3.27%0.7498-13.45%0.0271✓1.18946k2022-09-18
PSGParis Saint-Germain Fan TokenSolana8.988.6814-3.33%7.93-11.69%0.0202✓0.602.4M2022-09-18
AMPAmpEthereum0.006610.00639-3.33%0.00503-23.90%0.1642✓0.64911k2022-09-18
XYOXYO NetworkEthereum0.008440.008156-3.37%0.00744-11.85%0.0464✗1.18406k2022-09-18
CELRCeler NetworkEthereum0.018280.017662-3.38%0.015-17.94%0.0462✓1.008742022-09-18
EWTEnergy Web TokenEthereum4.5014.3479-3.40%3.847-14.53%0.0115✓0.95286k2022-09-18
PONDMarlinEthereum0.0113140.010928-3.41%0.011219-0.84%0.1434✗1.006302022-09-18
ETCEthereum Classicnative38.5637.2116-3.50%29.61-23.21%0.0428✓1.5910.6M2022-09-18
ALPINEAlpine F1 Team Fan TokenBinance Smart Chain4.67894.515-3.50%3.63-22.42%0.1473✓0.618.1M2022-09-18
LINKChainlinkEthereum8.037.7479-3.51%7.523-6.31%0.1029✗1.1317.5M2022-09-18
NMRNumeraireEthereum18.9318.2548-3.57%15.52-18.01%0.0983✓0.55384k2022-09-18
AUCTIONBounceEthereum7.637.3574-3.57%6.16-19.27%0.0483✓1.10230k2022-09-18
CTKShentuOsmosis1.0240.987162-3.60%0.864-15.62%0.0857✓0.412.7M2022-09-18
CTSICartesiEthereum0.15450.148935-3.60%0.1381-10.61%0.0436✗1.02336k2022-09-18
FISStafiEthereum0.35010.337486-3.60%0.3429-2.06%0.1391✗1.057782022-09-18
RLCiExec RLCEthereum1.31451.2669-3.62%1.2237-6.91%0.0909✗1.071.0M2022-09-18
DOTPolkadotPolkadot7.7027.4222-3.63%6.443-16.35%0.0046✓1.1710.0M2022-09-18
AXSAxie InfinityEthereum14.5614.0269-3.66%12.03-17.38%0.0140✓1.19925k2022-09-18
STXStacksnative0.39030.375888-3.69%0.3266-16.32%0.0142✓1.08324k2022-09-18
GRTThe GraphEthereum0.11670.112377-3.70%0.1-14.31%0.0283✓1.242.5M2022-09-18
PEOPLEConstitutionDAOEthereum0.023320.022456-3.71%0.01917-17.80%0.0337✓1.069.7M2022-09-18
GITCOINGITCOIN2.30572.2176-3.82%1.7772-22.92%0.0881✓1.1413k2022-09-18
BORABORAKlay Token0.291460.280269-3.84%0.25124-13.80%0.0043✓0.9015k2022-09-18
BANDBandEthereum1.3691.3164-3.84%1.165-14.90%0.0267✓1.27343k2022-09-18
MASKMask NetworkEthereum1.461.4038-3.85%1.17-19.86%0.0568✓1.0779k2022-09-18
GALAGALAEthereum0.0520.049978-3.89%0.042-19.23%0.0369✓1.17190k2022-09-18
ROSEOasisBinance Smart Chain0.065210.062559-4.07%0.05724-12.22%0.0578✗1.251.3M2022-09-18
MINAMina Protocolnative0.6860.657504-4.15%0.592-13.70%0.0213✓1.08111k2022-09-18
GLMRMoonbeamBase0.5950.570136-4.18%0.473-20.50%0.0511✓1.1664k2022-09-18
FIDABonfidaSolana0.5130.491228-4.24%0.426-16.96%0.0179✓1.067,7812022-09-18
CELLCellframeEthereum0.29290.280405-4.27%0.2612-10.82%0.0556✗1.0883k2022-09-18
METISMetisEthereum31.9830.5602-4.44%23.19-27.49%0.0763✓1.70168k2022-09-18
BRISEBitgertEthereum7.30e-76.97e-7-4.45%5.65e-7-22.56%0.1090✓0.862.3M2022-09-18
FLOWFlownative2.1162.0204-4.52%1.653-21.88%0.0336✓1.43967k2022-09-18
XVGVergenative0.003810.003638-4.52%0.00322-15.49%0.0034✓1.01481k2022-09-18
YFIyearn.financeEthereum10,194.939,718.41-4.67%8,342.07-18.17%0.0160✓1.444.2M2022-09-18
GLMGolemEthereum0.33080.31508-4.75%0.2724-17.65%0.0562✓0.7684k2022-09-18
SANTOSSantos FC Fan TokenBinance Smart Chain12.59411.9926-4.78%12.26-2.65%0.0660✗0.3816.0M2022-09-18
LAZIOLazio Fan TokenBinance Smart Chain7.60947.2427-4.82%6.0254-20.82%0.1545✓0.2511.9M2022-09-18
DYDXdYdXCosmos1.6481.5676-4.88%1.197-27.37%0.1243✓1.2443k2022-09-18
GTCGitcoinEthereum2.332.2146-4.95%1.79-23.18%0.0617✓1.29227k2022-09-18
OPTIMOptimism1.4021.3239-5.57%0.929-33.74%0.1519✓1.732.7M2022-09-18
FILFilecoinFilecoin6.4176.0276-6.07%5.265-17.95%0.0223✓0.966.2M2022-09-18
LUNATerraTerra 20.000431380.000401711-6.88%0.00027312-36.69%0.3423✓0.372.1M2022-09-18
AERGOAergo [OLD]Ethereum0.26110.239673-8.21%0.1267-51.47%0.5433✓0.8024k2022-09-18
Δ columns are percentage price moves; alpha err and the hit column are in beta-adjusted log-return space, which is what the model actually predicts. “pending” means the horizon has not matured yet. Rows are capped for readability — add &limit=2000 to widen.