Stats

Premises1 fetchedAug7-Sep5completed15min venuebars: BTC2880/2880,ETH2823/2880,SOL2859/2880; zero duplicates,missing57ETH21SOL; exclude gap-crossingreturns. https://runway.adityaperswal.workers.dev/data/crypto-bars . NumPyseed2026090608,20000paths perasset,16hours64polls; sample16 independentblocks eachoffourcontiguous15minlogreturns. Blockcandidates2876/2667/2810. Prioranalysis405roundedADRstops3.663/4.840/6.386%,targets1.5ADR. Firstpollclosecrossingonly; nointrabarcontinuousfills. Stopfirst.795/1.360/1.030%;targetfirst1.165/2.940/.560%;neither98.040/95.700/98.410%. Conditionalstopovershootmedian.124/.188/1.218percentagepoints;95th.612/1.187/3.348pp;hitN159/272/206. These are MonteCarlo outputs NOT calibrated liveprobabilities, strategywinrates or validatedlosslimits. Short30dayrallysample,missingness potentiallynonrandom,stationaryresampling/destroyedlongdependence,andunverified15minbaraggregation/outlierprovenance limit soundness. No fees/depth/delay afterpoll; no newoutofsamplebacktest. Strongcounterargument mostpathsavoidthresholds; answered rareunobservedjumps/depthcanstilldominate1%risk. Validinferenceonly: continuousrangestop assumptiondoesnotboundpollingloss. Do notsize using thisconditionalbootstrap or widen targets. Existingdaily/hourlystrategyrejectionsremain. Script/results archived; sourceclosestvenueproxy notglobalmarket.

Numpy seed9060600. Joint portfolio daily return blocks retain contemporaneous six-sector dependence;20,000 paths×20sessions,5-session circular blocks,training andholdout distributions separately. Deploy fractions0/.25/.5/1 of278.67fund into theoretical fractional equal-sleeve strategy; remainder850.99account cash. Model does not enforce whole-share granularity, venue fills or fixed weights after historical drift. Fullfund baseline holdout-path profitfrequency51.51%,medianP&L+.2704USD,5th−10.5123,95th+11.8105;23.875%frequency ofaccount drawdown>1%,95thdrawdown1.5327%. Ten/twenty-session block sensitivities profit51.65/53.97%,median+.2704/+.6030USD. These are conditional resampling frequencies,NOT prospectively estimated supply-trade win probabilities or a monthly funding forecast. Trend/trendlowvol fullfund5dayblock profitfrequencies37.10/34.95%,negative medianP&L−1.4186/−.8456USD. Exit-odds bootstrap draws whole entry-week groups10,000times: baseline598closed trades target40.9699%,stop53.5117%,time5.5184%;target95%[35.2013,46.6561],stop[47.6561,59.3962]. Daily trigger idealization and unseen tails remain. Plug-in quarterKelly capital formula .25*(p/averageLoss−(1−p)/averageWin), using baselinep.439799,w.0243920,l.0185731, gives17.8203%equity; four-week meanCI spanszero and mixed control cohort has no incident edge,so allowable size0. Never turn a conditional Monte Carlo frequency into p. Two fund liquidations cannot supply a loss estimate either. All24deployment scenarios and6block sensitivities recorded. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; fund trade source query_trades fund=supply IDs3,6.

Premise1 netbaseholdoutpayoffs analyses398-400. NumPyseed2026090606,20000circular2trade-blockbootstrapmeans: BTC95%range[-2.881,1.818]%,ETH[-1.355,2.364]%,SOL[-3.736,.484]%; allcross0. TinyN7/10/9 means these empiricalrangesare not calibratedpopulationconfidence. Hypothetical20trades at10%total-equitynotional,starting850.99 equity/235.86fundcash,cappedcash and25%position: medianendequity837.91/857.29/823.28; lossfreq84.66/29.055/98.815%. Doesnotapply1%stopriskgate,andisnotdeploymentor20trades/monthforecast. Premise2 samplefive24hourlogreturnblocks from2026history,5904validblocks each,20000x120hourpaths; lastcloseADRstop3.663/4.840/6.386%,target5.495/7.261/9.579%. Firsthourlyclosecrossing stop/target/timeoutBTC41.835/21.35/36.815%,ETH42.785/21.98/35.235%,SOL34.465/16.845/48.69%; meanmodelednet-.860/-.960/-.901%. Unconditionalhistoricalblocks preserveintradaydependence,not entryconditioning,multidayregimes,crossassetjointtails,intrahourtouchesor15minvenuepolling. Hence exitodds are scenarios,not the rule's winprobability. StrongcounterargumentETH20trademedianpositive: selectionsurvivorship,negative35tradetraining anddoublingcostsnegativeholdout rebut. Kellycorrection360: quarter(p-q/(W/L)) is riskfraction; dividebydecimalL fornotional. ETHplug-inrisk2.786% implies105.34%notional beforecaps,not2.786%notional. Unknownrobustedge setsactualzero before212.7475position/235.86fund/8.509riskcaps. Allsimulationfiguresrecorded6149-6151,codearchive363-385. Source https://runway.adityaperswal.workers.dev/data/crypto-bars .

Premises: 1. The later SPY unconditional sample has 1,420 completed nights, win probability 37.1127%, average win 0.3810%, average loss 0.4890%, and mean payoff -0.1661% after 10bp per side. Its quarter-Kelly allocation is zero. 2. A five-trade block bootstrap (10,000 samples) gives a mean-payoff interval wholly below zero; the small positive 2bp-cost variants have intervals crossing zero. 3. A separate 100,000-path bootstrap of 25 trades, hypothetically reinvesting 25% of account equity per trade, produces median SPY P&L -$8.51, 5th/95th percentiles -$19.54/+$1.02, and 6.961% profitable paths. None reached +$349.01 in this empirical simulation; that is not a mathematical impossibility claim. Conditional-rule 25 trades can span more than a month. Initial equity $850.99, allocation $212.7475; actual allocation remains zero. 4. Parametric Gaussian and variance-matched Student-t(5) simulations use 100,000 ordinary 17.5-hour nights with 70 synthetic quarter-hours, raw later log-return mean/variance and current lagged ATR barriers. SPY stop-first probabilities are 23.426%/22.746%, target-first 9.727%/9.379%, timeout 66.847%/67.875%; both costed means are about -0.1752%. These are model assumptions, not measured venue exit odds: volatility is homogeneous, increments independent, weekends and real jumps uncalibrated. Daily endpoints alone show 2.2535% beyond -1 ATR and 0.4930% beyond +1.5 ATR, only lower bounds on barrier touching. Neither model validates actual 15-minute stops, extended-hours liquidity or profit-taking. Bootstrap seeds 90606/90607; barrier seed 90608. Sources: https://runway.adityaperswal.workers.dev/data/stock-bars; simulations.json, barriers.json and scripts.

Numpy seed60606. Resample50000 whole10-session OHLCwindows from13training events, separately50000from6holdout events; normalize each entryopen to1. Fixed currentSep4 barriers -ATR14/close=-9.93029% and+2ADR20/close=+16.25249%; these contemporary barriers are diagnostic,not an out-of-sample historical rule. Openinggaps execute first atopen; otherwise samebarbothhit usesstopfirst; timeexitT-1close. Fee5bp/slip10bp eachside. Trainingmean+3.318961%,win61.48%,target7.866%,stop0%,time92.134%;holdoutmean-5.847043%,win16.676%,target16.676%,stop83.324%,time0%,meanexit5.1824sessions,p05-10.200095%. Only6independent holdoutwindows;50000draws donot increase evidence. Modeledriskbreach>8.5099USD at49.14notional=0%,becauseempiricalsampleanddailybarfillassumptions omit unseenjumps/15minexecution; NOT a safetybound. No measuredprobability of surpriseannouncement. Separate12-trade iid compounding simulation50000paths resamples6baselineholdoutreturns with rebalancedfundfractions0/.25/.5/1: medianending49.14/34.69212/23.70674/9.94125USD,p05=49.14/27.60792/14.86756/3.66715;lossprob0/98.78/99.042/99.354%. Twelvequarters is a multiyear scenario,not thismonth forecast. Invariant assumeddistribution,no taxes/recurringoverhead; fees already intrade returns. QuarterKelly0 fromobservededge overrides all hypotheticalallocations. Source https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=HAIN,SPY,XLP&timeframe=1Day&feed=iex&adjustment=all .

Premises:1 mark exits at bids after fees;2 target must fit measured range and reward/risk;3 Monte Carlo precision is conditional model precision, not empirical edge. First choose largest baseline net among145affordablecontracts with>=4sessions (allbaseline netnegative): Sep18K62call bid.01ask.02. Two-session1.5ATR14 rise=.987857 gives modeledbid target .02 after rounding down; equals entry beforefees, so no admissible base-hit trade. stop0 is only zero-bid diagnostic, not a recommended venue exit. Blend100kpath mean-$1.462946, win10.301%,avgwin$.165684,avgloss$1.649978;HARmean-$1.225398;low-$1.661492 at$.20assumedfee. Secondary counterexample chosen after results: largest HAR net among same>=4session set, Sep18K60.5call bid.04ask.07. S58.10,K60.5,n9sessions,r.04,q.0138,midcalibratedmarkIV.145572289,halfspread.015. Two-session1.5ATR move gives rawbid.119338,target roundeddown.11;stop.03. Target profit beforefee$4 againstpremium$7, already below1.5RR; with$.20cost 3.80/7.20=.52778, also below1.5 usingplanned$4stoploss. No trade. NumPyseed2026090606,100000paths,52steps; dt=1/(252*26),dlogS=-.5sigma²dt+sigma sqrt(dt)Z, common draws acrossscenarios. Aftereachstep bid=max(BSM at decreasingT, fixedmarkIV minusinitialhalfspread,0). First stop/target hit exits at observed modeledbid; rest end2sessions. Blend physicalvol12.30249%: win11.486%,avgwin$4.39266,avgloss$4.47374,mean-$3.45535,stop86.398%,target10.609%,time2.993%. HAR15.99295%: win15.786%,avgwin4.84070,avgloss4.61075,mean-3.11874,stop83.762%,target15.578%. Low9.84199%mean-3.73230. Fee$1.30 instead$.20 reduces eachmean$1.10; all12scenarios qKelly=max(0,(p-(1-p)/(W/L))/4)=0. Fullpremium7+1.30=8.30 affordable, but allocation0. Zero observedfullpremiumloss in some simulated cases does not bound realgaploss. Limitations: staticIV/spread, no overnight/holidayjumps, Americanexercise, queuing or real liquidity; targetovershoot fills optimistic. Actual option backtestN0. No removal/widening of exits to rescuemean. Source https://runway.adityaperswal.workers.dev/data/option-chain/XLF?feed=indicative and adjustedstock-bars; all12scenariofigures recorded.

Premises:(1)contractsharesarevolumedisclosures,notrealizedpriceindexes;(2)assumeequalbaselineunitprices90%contract/10%spot,baseheliumrevenue100,cost65,allcostsvariable;(3)uniformindependentcontractrepricing[-5,+10]%,spot[0,+100]%,volumeretention[.8,1.1],costinflation[0,40]%areassumptionsNOTestimatedlikelihoods. Python192gridcombinationsand100000numpyseed20260906draws. Atunchangedcontractsandvolume,spotdoubling=>revenue110;costinflation0/10/20/40%=>profit45/38.5/32/19versusbase35. 15.3846%unitcostinflationerasesprofitincrease. Assumed8%APDgroupheliumrevenueshare=>only.8%groupsalesupliftbeforecosts,mixandvolume;8%isnotdisclosedexactshare. Drawprofit-change5/50/95quantiles-61.17/-21.31/+22.20%;22.199%drawsexceedbaseprofitand6.924%drawshaveprofitupbutmargin%down. Thesearemodelgeometry,NOT22.199%winchanceorforecast. Fixedcosts,workingcapital,capex,correlationsandrepricingclausescouldworsen/improveoutcomes;cannotassignKellyfromassumeduniforms. Valid inference: need deliveredprice-costspreadandvolume,notspotpriceonly. Sourcecontractanchor https://investors.airproducts.com/static-files/1c55c69d-3196-4a46-b646-fd85adeec0f2 ;originalmodelnote295,obs5437–5438. No equity-price simulation justified without empirical payoff distribution.

Premises: 1.TXNM Sep4price58,offer61.25 gives3.25USD/5.60345% gross spread. Sensitivity uses break40/45/50/55,180/270/365days,hurdle0/4/6% and either no dividends or assumedcontinued.4225quarterly prorated. These are assumptions, not estimated probabilities or standalone valuations. At break50,270days and4%annual alternative return, requiredsuccess probability87.1697% withoutdividends or76.1309% with1.25014USD assumeddividends. Costed win7.59741%/loss11.89916% in dividendcase; no empiricalp means actualsize0. Acquisitioncashsettlement hasno modeledsellfee; faileddealmarketexitcosted15bpeachway. 2.Numpy100000Bernoulli paths per36p/break/horizon scenarios,seed90605,check analyticalmeans; assumed60/75/90%success produceswidelydifferentKelly. Unknownp cannotbecomethemarket-impliedthresholdbyassertion. 3.Wrapper19quarterlypayoffs,circular3-cohort blocks,10000paths,seed90604:MRGR mean-.32820%,95%CI[-.50152,-.17937];MNA-.26958%,CI[-.59914,.05320]. QuarterKellyclipped0both. Hypothetical25%fundallocation for4quarters (notproposed) MRGR5/50/95percentileterminal-.61930/-.31185/-.03280%;MNA-.88974/-.21603/.32215%. These stationarysmall-sampleblockscannotboundunseencrashes. 4.Own3operatorliquidations p33.33%,W7.93994%,L5.26143%,mean-.86097%,Kelly0; notnaturalstrategyoutcomes. NeverpoolthesePEADtradeswithmergerdeals. Sources https://runway.adityaperswal.workers.dev/data/stock-bars ; query_trades fundquant ; https://www.txnmenergy.com/investors/acquisition.aspx ; https://www.prnewswire.com/news-releases/txnm-energy-board-declares-quarterly-common-stock-dividend-302699014.html .

100000numpy paths,seed60604,10sessions; sample two5-day blocks from latest252dailySRRKclose returns including tails. Diagnostic exits at first sampled close crossing +2ADR(+6.8113%) or -1ATR(-3.6738%), otherwiseday10; fees5/slip10bp eachside. This approximates neither continuous fills nor15minutevenue execution. Inject independent-30%adversejump atuniformday with assumedwindowprobability0/1/5/10%; it matters onlybeforemodeledexit. NoeventhazardestimatedfromN1, noapprovaljumpmodel, existinghistoricaltailscanoverlapinjectedstress. Means1.4974/1.3593/.7600/.0374%,win47.536/47.288/46.265/45.027%;5thpercentiles-7.4857/-7.5778/-9.5225/-14.2296%. At10%assumedhazard,4.603%paths lose>$8.5099whenhypotheticallydeployingfull49.14. Evenzero-addedhazardhasovershoot becausechecksareatdailyclose. These are conditional stress outputs, notforecastwinprobabilitiesorapprovedsizing. A30%jumpalone on49.14loses14.742USD>account1%8.5099; atmost28.3663USDwouldmeetthatparticularjump-onlybudget,notaguaranteeagainstworsejumps. Full-losscap8.5099alsofailswhole-shareaffordability. Empiricalmomentumedge303negative;quarterKelly0overridespositivebootstrappedpathmean. Source https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=SRRK&timeframe=1Day&feed=iex&adjustment=all . Facts end atbarreturns; allhazard/jumpparametersareexplicitassumptions.

Premises: evaluateplannedbidexits,notonlyterminalfairvalue; usephysicalpathsindependentofthemarkIV; allscenarioresultsconditionaluntilvalidatedagainstactualoptionhistory. FixedNFLXSep11K72put S78.25,Fridaybid.02ask.03,4remainingtradingsessions; midcalibratedsessionIV32.94478%,rate4%,q0. Initialterminal2-sessionGBM withfixedIV/halfspread.005 andfees.20percontract givesblendphysicalvol38.03027%win16.93%,avgwin18.2765,avgloss2.9420,mean+.6503; trainingwinsorvol35.93251%mean-.04315,lowvol30.15233%mean-1.54882. Positiveunboundedtailmeanisnotbase-hitvalidation. Explicitexitdiagnostic: 1.5ATR14decline=3.4575underlyingpoints over2sessions givesBSMbid.091519,roundtargetdown.09; stop.01belowinitialbid.02. Targetnetprofit5.80versusfullpremium+assumedfees3.20=1.8125RR. Notanorder. NumPyseed2026090605,100000paths,52equal15minute-likegridsteps over2/252years; commonnormaldrawsforallvolscenarios, dlogS=-.5sigma²dt+sigma√dtZ. RemainingTdecreases4/252to2/252; modeledbid=max(BSM-.005,0). Firstbid<=.01stopor>=.09target exitsatmodeledobservedbid, othersatend. Blendwin16.382%,avgwin7.399572,avgloss2.460156,mean-.844935; stop83.514%,target16.252%,time.234%. Winsorwin15.161%,mean-.972319; lowwin11.074%,mean-1.383048. qKelly=max(0,(p-(1-p)/(avgwin/avgloss))/4)=0allscenarios. This matchesneitherhistoricaloptionliquiditynoractualclosurevariance: continuousvariancegridcompressesovernight,IV/spreadfixed,noovernightjump/stochasticIV/latency/Americanpathmodel. Favorableovershootfillsassumed,notpromised. Stopsdonotboundfullpremiumrisk; onecontract3+feesaffordablebutedgezero. Source https://runway.adityaperswal.workers.dev/data/option-chain/NFLX?feed=indicative ; https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=NFLX&timeframe=1Day&adjustment=all&feed=iex . Reject, donotremoveexitstoaccommodateoptimisticmean.

Premises1 Fixedcontrol306-308 hourlypayoffs BTCN3p1/3,W21.3586%,L10.2452%; ETHN3p1/3,W32.5817%,L18.3817%; SOLN4p.25,W7.9297%,L14.4321%. 2 Plug-inquarterKelly BTC.33874%equity, ETH/SOL0. BTCnaive notional$2.88 is below$10cryptominimum; uncertainty gate independentlyzero. 3 NumPyseed20260906 20kIIDbootstrapmeans95%ranges BTC[-14.1482,21.3586]%,ETH[-28.8701,32.5817]%,SOL[-25.2149,4.4192]%; these tiny-sampleempiricalintervalsarenotcalibratedconfidence. Conditional20trade10%equityexposurescenariosfrom850.99endmedians852.80/825.07/711.47; lossfrequencies48.685/62.845/99.885%. BTCempiricalmedianpositivecannotcancelnegativefullallocationcompoundreturnorwideuncertainty. IIDassumptionomitsregime/serialdependence; forcedterminalwinnernotnaturalexit;20tradesnotmonthlyforecast. 4 No calibratedpositiveedge => actualsize0before212.7475positioncap235.86fundcap8.509plannedrisk. Conclusion preservecash; neverroundKellyup tovenueminimum. Source https://runway.adityaperswal.workers.dev/data/crypto-bars ; recorded306-308.

Premises:1 buyatask/sellatbid;2 highphysicalvolatilitydoesnotguaranteeIVrepricing;3 simulatedmeansarenotvalidatedwin/lossedge. HypotheticalSep4snapshots: SNAPOct2K4.5put S5.48,bid.01ask.03,ATR14.316429,19sessions; MARASep18K8.5put S11.30,bid.01ask.02,ATR14.979286,9sessions. CalibrateBSMtosession-clockmidpoint withr4%,q0, impliedvol48.93596%SNAP/78.62248%MARA; do notcarryfeedIVacrossclockswithoutrecalibration. NumPyseed2026090602,100000terminalGBMdraws percontract/scenario; zeroexpectedstockreturn,5sessions, physicalvol0.8min(RV21,RV63,EWMA) orfixedvarianceblendforecast; markIVunchangedorhalfwaytoforecast. Terminalbid=max(BSM-halfobservedspread,0); fees0.20/100sharecontract. SNAPforecast/noIVrecovery win21.095%,avgwin6.03493,avgloss2.73711,mean-0.88665dollars; lowvolmean-1.80669; halfIVrecoveryforecastmean+0.32171. MARAforecast/noIVrecovery win17.303%,avgwin13.29695,avgloss2.05319,mean+0.60284; lowvolmean-1.15111. Thus optimisticMARAmeanisdrivenbyrarelargeoutcomes, notbasehits orobservededge. QuarterKelly formula max(0,(p-(1-p)/(avgwin/avgloss))/4) givesconditional1.1334%MARAforecast,0%lowvol; executablevalidatedallocation0inallcases. SNAPoneATRdeclineover5sessions producesbid.02038 below.03entry; twoATRbid.07167. Bothinitialbids.01 leave nopositivepenny stopbelowentrybid; a.01stopalreadytouchesatentry. InitialpathcheckwithbelowentryoneATRtargetwasdiscardedasnotvalidprofit-takingstrategy; terminalscenario explicitlymodelsnostop/targetfills. 15minuteexitgap/stochasticIV/jumps/dynamicspreads/Americanexercise omitted; simulationcannotcertifyreal15minuteexecution. All8scenarioinputs/resultsrecorded. Sources https://runway.adityaperswal.workers.dev/data/option-chain/SNAP?feed=indicative and /MARA?feed=indicative, underlyingbars2023–Sep4 2026. Rejectbothforentry; no inventedexitproposal.

Premises: 1. Completed later SPLV monthly cohorts44, win29.5455%, average win1.32691%, average loss1.10213%, mean-.38446% after assumed10bp one-way cost. Quarter-Kelly max(0,.25*(p-(1-p)/(W/L)))=0. 2. Circular3month blocks resampled from these44 observed monthly payoffs,10000 paths,seed90603,horizon6months. A hypothetical12.5% of fund cash per monthly trade (not recommended) yields terminal5th/median/95th percentiles -.82239/-.25872/+.34792%; loss probability77.67%; 95th monthly-marked drawdown.82239%. 3. No simulated path earns349.01 on245.69 fund cash; actual size remains0. Simulation assumes stationary payoffs, monthly marks and no unseen jumps, and does not calibrate real 15minute stops or intraday drawdown. An alternative selected EEMV point estimate has positive naive quarterKelly0.6355% but confidence includes losses and50bp stress loses29.04%, so it does not qualify. Three own liquidated trades separately give p33.33%, W7.93994%, L5.26143%, mean-.860974%, clipped quarterKelly0; those are operator exits, not natural strategy outcomes. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; query_trades fund=quant ; saved trades.json/simulation.json.

Premises1 Test255 hourly21netreturns:p10/21=.47619,W3.60267%,L4.05042%,mean-.40609%; quarterKelly=max(0,(p-(1-p)/(W/L))/4)=0. 2 NumPyseed20260906,20000paths each20trades,circular3returnblocks preserveadjacenttrades; hypothetical10/25%equity exposure compoundedfrom850.99. Ending5/median/95percentiles10%=$830.05/$843.50/$859.39,lossfrequency78.345%;25%=$799.12/$831.89/$871.69,loss78.95%. SampledDD>10%zero atbothsizes is NOT riskbound: smallsampleexcludesunseentails/gaps/regimes. Theseareconditionalempiricalscenarios,notcalibratedfutureprobabilities,not20tradesbymonthend. 3 CurrentADR99.9264/ETH2479.918=4.03%,1.5ADRtarget6.04% illustrationonly. Fees/slip/gapcosts reduceactualRR; actualposition0before212.7475cap/235.86fund/8.509plannedlosslimits. Conclusion noexposure; reducingallocationcannotmakeexpectancypositive. Strongcounterexamplepositive5%taildoesnotimproveaveragenetedge. Source https://runway.adityaperswal.workers.dev/data/crypto-bars ; test255.

NumPyseed90602,10000 IID paths each10trades, reinvest10%currentcapital pertrade, sampling each diagnostic's3–7 naturalreturns. NOT a calendar-time/venue-stop simulation. Example Maersk terminal5/50/95[-2.259,2.423,7.410]%,loss20.38%,DD95 3.637%;COHU[-1.410,10.877,27.477]%,loss7.65%,DD955.466%. AXTselectedextreme produces median+11430.9% and95th+1180856.7%, an implausible investment forecast driven by resamplingonehugewinner; no independenttailmodel. Plug-inquarterKelly fractions0.475–1.754 acrossnames, but authorized0 for all: every meanCI spanszero and executionmodel incomplete. Positions capped212.7475USD,nominalrisk8.5099USD,fund278.67USD; caps cannot createedge. Resampled longtrendwin sizes cannot justify1–2ADR swingtargets. Results and every measuredfigure recorded3251–3258; scripts/trades archived. Sources https://runway.adityaperswal.workers.dev/data/stock-bars ; https://query1.finance.yahoo.com/v8/finance/chart/ .

NumPyseed2026090602 after20000eventbootstrap;10000drawsfrom165contiguousfive-session2026OHLCblocks,normalizedbypriorcloseandscaledto2.57. Fixedstop2.50142857,target2.67285714;open-gapchecksfirst,ambiguousintradayboth-touchstopfirst. Firsttouchstop49.19%,target42.52%,neither8.29%;terminal5/50/95percentiles-6.967213/0/7.476636%. Theseareresampledunconditionaltapepaths,notearningsconditionalwinodds,notnetstrategyreturns,notvenue15minfills. Blocksdependandcan'tgeneratenewextremes. Premises:twoboundariesreachable;eventholdoutuncertain;currentpreannouncementregimenotvalidated. Conclusionillustrativelevelsareplausiblerangesbut0size. NoMonteCarlooutputoverrides244/245uncertainty. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; completeblocksreconstructiblefromarchivedbars/code.

Premises1 Hourlyholdout212 has11naturalnettrade returns, mean-1.88186%,p27.27%,W3.41768%,L3.86918%. QuarterKelly max(0,(p-(1-p)/(W/L))/4)=0. 2 Numpyseed20260906,20000scenario paths of20trades, circularblocks2 sampledfrom11returns preserve neighboringpair order. Hypothetical10%/25%equityallocations compound eachsamplednetreturn from850.99equity. No annualization or20tradesbydeadlineclaim. At10% endingp5/median/p95=$798.22/$819.35/$841.94;98.845% paths lose. At25% $724.59/$773.64/$828.14;98.905% lose,48.58%maxdrawdown>10%. These conditionalempiricalscenario frequencies are NOT calibratedfuture probabilities: smallselectedsample,no unseenfat-tails, changingregimes, gaps, dynamicspreads orcashfundcapmodel.25%scenario maybreakplanned1%lossconstraint and isnotproposal. Mean20trade-scenario2.5/97.5percentiles[-3.43274,-.26580]% are a distribution ofscenario means, NOT a confidenceinterval ofthe11tradepopulationmean. Separateactual11tradebootstrap in212 spanszero. 3 Negativeplug-inKelly=>authorizednotional0 beforeposition212.75,fund235.86,plannedloss8.509dollar caps. Conclusion holdcash; reducingstake canreduce modeleddrawdown butdoesnotcreatepositiveedge. Source https://runway.adityaperswal.workers.dev/data/crypto-bars ; recordedtest212; local ltc_trades.json/simulation.json.

NumPy seed20260906 after two20000-sample payoff bootstraps;10000 draws from166 contiguous five-session 2026 blocks. Scale each OHLC/previous-close sequence to83.57, freeze stop81.422143,target86.791786. Opening gaps checked before intraday low/high, ambiguous both-touch stops first. Terminal5/50/95 percentiles -8.533444/-.724514/+7.272082%; stop-first60.45%,target-first30.84%,neither8.71%;95th percentile close-path drawdown8.988345%. Full code/input archive this run; source https://runway.adityaperswal.workers.dev/data/stock-bars . These are unconditional resampled path frequencies, not earnings-conditional win probabilities or executable15minute fills. Overlapping blocks are dependent; one historical regime, no new extreme gap beyond population. Prices/levels diagnostic only. Premises: current volatility permits both range boundaries in five sessions; historical paths cannot identify an event premium; fixed costed holdout is inconclusive/negative under stress. Conclusion size0, not a bearish forecast. Counterexample: a future unique catalyst could beat this distribution; requires fresh independent evidence rather than a wider target.

Premises: (1) option exits occur at bids and discrete15minute checks; (2) mark volatility cannot be presumed to converge to forecast; (3) simulation cannot supply empiricaledge without validated inputs. Diagnostic hypothetical QQQ260908C00731000 fromSep4quote: S719.10,K731,ask0.03,bid0.02,feedIV8.99%,expirySep8. Not an availableFridayentry andnot aTuesdaystandingorder. InvertBSM midpoint0.025 usingT1/252,r4%,q0 to session-clockIV11.6548779%; this calibration prevents an artificial initialprice jump from changing clocks. Seed20260906;100000 paths per6scenarios;26equal steps/session. UnderlyingGBM zeroexpectedreturn, sigma10.5292%(0.8RV21) or16.3489%(forecast). MarkIV stayscalibrated, moveshalfway, or fully toassumedphysicalvolatstart. Reprice remainingtime eachstep; sellbid=max(BSM-0.005,0); target0.08capped, stop0.01actualbid, liquidationatfinalstep. $0.20roundtripfees; wholecontract100. Atforecastvol withNOIVrecovery: win22.457%,avgwin$4.80,avgloss$2.7700,mean-$1.0700; quarterKelly0. Lowerphysicalvol noIVrecovery: win11.017%,mean-$1.8197. Halfconvergence forecastcase mean+$2.2189/win65.675%; fullconvergence mean+$4.4906/win95.867%. These optimistic returns are assumedinstantrepricing, not evidence itoccurs. Stoploss overshootsnominal$2riskbecausecheckingdiscrete; fullpremium$3plusfeesmustcount. Expiresynthetic paths are liquidatedatclose; exercise/autoliquidation couldhappenearlier inreality, so forbidden asactualexitplan. Ignoresweekendjumps, bid-sizevariation, stochasticvol, hedgefeedback andmodifiedfeeduncertainty. Outputsall6scenarios savedobservation. SensitivitydominatesMonteCarlosamplingerror; confidenceaboutmodelparameters notestablished. ActualadmissiblequarterKellyallocation0, evenwhereassumedscenarioformula positive. Source https://runway.adityaperswal.workers.dev/data/option-chain/QQQ?feed=indicative . Reject candidate andderive no realstop/targetproposalfromsyntheticodds.

Premises:1 SPYrange laterhistory includes44calendar months,19trades andnegativeestimatedexpectancy.2 Resample44monthlyreturns including zero inactive months in circular3-monthblocks,10000paths seed906; 6monthhorizon andhypothetical12.5%fundallocation eachentry, remainingcashreturn0.3 Terminalfundreturn5th/median/95thpercentiles -0.59601/-0.070053/+0.560251%;58.54% paths lose,95thpercentilemonthly-markedDD0.59601%. No simulated path earns349.01dollars on245.69fundcash. Conclusion actualallocation0 becausequarterKellynegative;12.5%isastressscenario,not recommendation. Distribution assumesstationarity and cannotrepresent unseenjumps,15minuteexitdelays,intradayDD,executioncostchangesorcorrelatedfunddrawdowns. Zero simulated targetsuccess doesnotmean trueprobabilityzero. Fundinggaprequires142.052% offundcash and41.012% ofaccountcapitalin26days, whileexperimentspans6months: wronghorizonandordersofmagnitudetoexpectthisruletofundrunway. Counterargument positive unseenflowstatecouldmatter; mustcollectandvalidateitprospectivelyinstead ofleverageorrelaxingstops. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; artifacts/stats.py frozen906.

Using fixed diagnostic's5net natural payoffs, NumPyseed906 produces10000IID paths each5trades, reinvest10%changingcapital pertrade. Terminal5/50/95percentiles[-2.2383,11.7462,28.4979]%,lossfrequency8.11%,95%trade-stepDD3.1173%. Conditional empirical illustration only: no calendar holding window, barrier-touch model, clustered regimes or unknown tail;5selectedtrades give unreliable odds. QuarterKelly plugin .25*(p/avgloss-(1-p)/avgwin)=1.56943capitalfraction fromp.4,avgwin.661459,avgloss.055673. This absurdly large estimate demonstrates estimationrisk, not permission. Authorized fraction0 because confidence spanszero,trainingclosed0,currentcrossfalse andexitmodel incomplete. $212.7475positioncap and$8.5099nominalriskbudget do not establish edge. GEV941.95 allows0whole shares undercap; fractional exits only regularsession under venue. Illustrative10%fundallocation27.867 would also requirefractionalshare. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; archive2958–2997, audit.py. No order.

Premises:historicaldailyportfoliooutcomesareavailablebutnosignalconditionedfuturedistribution; actualrangeholdoutp45.173%,W1.671877%,L1.522449% yieldsnegativebinaryexpectancyandclippedquarterKelly0. NumPyseed2026090504,10000paths,circular5sessionblocksofnetdailyportfolio returns,19sessions,pathreturns multipliedby.1(illustrative10%fundexposure),remainingcash0yield. Range terminalp5/median/p95-.43042/-.03387/+.39688%,lossfrequency55.18%,DD95.50076%;fixed-.58364/+.06186/+.65153%. Thisis19sessionsNOT26calendar days/monthendforecast; daily constantfractionrebalance approximationignoresadditionalrebalancecosts,whole-shareconstraintsandintradaytails. Stationaryresamplingcanmisscrises; bootstrapfrequencyNOTpredictedliveprobability. Nominalaccountstopriskceiling8.5108and212.77positioncapnotguaranteedfills. Baselinefixedplug-inquarterKelly81.42%capitalisunstableandnotauthorized;confidenceandvenuegapsreduceactualsize0. A favorablemedianunderfixeddoesnotrepairnegativebenchmarkrelativeperformanceorrangeedge. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; stats.py,statistics.json.

NumPyseed2026090504(afterfixed20000payoffbootstrap),10000pathsdrawcontiguous5sessionOHLC/previous-closeblocksfrom2026dailyhistory:166possibleblocks. Start80.34,freezeoneATR5.05324stopandtwoATR10.10649target;openinggapscheckedbeforeintradaylow/high,ambiguousboth-touchstopfirst. Five-sessionterminalp5/median/p95=-14.4015/+1.3419/+14.2585%; targetfirst24.73%,stopfirst42.04%,neither33.23%;95thpercentileclosepathDD17.0213%. Initialcodecheckedlowbeforefavorablestartgap; correctedopeningprecedenceandrerun,numericalfrequenciesunchangedforthisdraw. Theseareunconditionalresampledpathfrequencies, NOTFDAapprovalodds,signalconditionalprofitodds,nextweekforecastoractual15minfillprobabilities. Pathterminaldoesnotassumetradingbarrierexit;touchfrequenciesseparate. Historicalblocksincludevariousregimes/events,overlapandlimitedsample,unseenfuturegapsnotmodeled. On49.14hypotheticalfractionalnotional,5thpercentileterminalwouldlose~7.08 beforecosts, buttailisnotguaranteedlossbound; observedRAREstress22.54larger. ActualquarterKelly0fromnegativehistoricalpayoffs,whole-shareaffordability0andnoentrysignal. TargettwoATR iseven>twoADR, thusnotaapprovedvenueexit. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; artifacts/test.py/stats.json,technicalanalysis. Conclusion simulationcannotrescuefailededge; remainflat.

NumPyseed90504,10000paths perasset: draw3 complete24h logreturnblocks from diagnostic holdout, concatenate72h; BTC/SOL325 blocks,ETH324. ReferenceSep4close,1ADRstop/2ADRtarget widths BTC3.667/7.334%,ETH4.834/9.669%,SOL6.405/12.810%. Hourlyclose target-before-stop frequencies5.57/7.02/3.73%,stopfirst30.27/31.76/24.10%; these are unconditional historical resampling frequencies, not forecast probabilities or intrabar/15minute fill odds. 72h terminal5/95percentiles BTC-6.423/+6.226%,ETH-9.029/+9.244%,SOL-9.596/+9.651%. Separate10-trade scenario draws observed net naturalpayoffs,invests10% of changing fundcapital: medianterminal-.241/-.881/-2.581%,lossfrequency57.70/71.76/93.33%. This is10trades,not monthlydeadline simulation; IIDpaths miss clustering/unknown tails. QuarterKelly is negative for all3 using observed win/payoff distributions, so authorizedsize0 beforecaps. Stop-only ceilings min(235.86,212.77,8.5108/stopwidth) BTC212.77,ETH176.05,SOL132.87; actual fills/fees/gaps can exceed nominal1%loss, these are illustrations not approvals. Premises negative netpayoff and modest72h targetfrequency jointly reject deployment; no target extension to meetfundinggap. Sources https://runway.adityaperswal.workers.dev/data/crypto-bars ; https://fapi.binance.com/fapi/v1/fundingRate ; observations1762-1764 and code risk.py.

NumPy10000circular3tradeblockpaths, each19TSN/20PPC/13JBStrades, allocate10%changingcapital pertrade. Terminal5/50/95 percent TSN[-2.530,-1.243,.220],PPC[-2.709,-.771,1.100],JBS[-.642,.716,2.056]; trade-step95%DD2.627/3.038/1.144%. These conditional historical resamples are not monthend or policy forecasts, actualbarrier-touch odds, or whole-shareexecution. Fullfund278.67 initial10%27.867 cannotbuywholeTSN/PPC, so illustrativenotexecutionplan. Plug-inquarterKellyTSN/PPC0,JBS1.665capitalfraction beforeconstraints demonstratesestimateinstability, notpermission; JBSmeanCIcrosseszero andtrainingabsent. Allauthorizednotional0. Unobservedgaps,15minutechecks, liquidityandcorporateactions remainunmodeled. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; test.py andobservations1724/1727/1730. Avoid translatingbootstrap frequencies into probabilitiesofpoliticalorpolicyoutcomes.