Stats

Python numpy seed20260908 followingbacktests; training836dailyOHLCvectors normalizedtopriorclose, iidresample10sessions/100000paths from https://query1.finance.yahoo.com/v8/finance/chart/EGTX.ST . Start7.70,stop7.34429,target8.23357; gapstopopen,stoppriorityifboth,takeprofittarget,otherwisecloseafter10. Fees10bp/slip25bp/side. Mean-1.21410%,win37.666%,p05-5.69831%,p95+6.18361%,stops62.245%,targets37.570%,time.185%. Thesearehistoricalvolatilityresampling,NOTFDAprobabilities; iidpathscanmissclusters/novelbinarytails and15minexecution. SeparateassumedUSDlossstress for49.14fund:30%gap14.742,50%gap24.57, both>8.5099riskcap; attheseassumedshocksriskboundnotionals28.3663/17.0198 BEFOREcosts,notrecommendedsizes. Full-lossbound8.5099. Bindingedgefailssoadoptednotional0 regardlessstresscapacity; noestimatedregulatorywinprobability.

1. Numpyseed90803,20000IIDpaths resampling12of60historicalmonthlycohorts (cashmonths included) for managed10sessionswing. Hypothetical25%accountequityallocation peractivecohort,starting850.99; costsincludedinbacktestedreturns, overheadexcluded. SPLV12monthPnL5/50/95percentiles[-16.01794,-5.93852,3.58745]USD,lossfrequency84.3%;USMV[-15.79918,-5.95456,3.46558],84.38%;EFAV[-13.29565,-4.89684,3.25648],83.79%;EEMV[-11.40686,-2.62956,5.53836],69.21%. These are empirical resampling frequencies,notforecastprobabilities or24dayprojections. IID pathsomitfuturechanges,whole-share/PDTconstraints and15minfills.2.Holdoutp/W/L managedSPLV50%/.529017%/1.197975%;USMV45.4545%/.590174%/1.088297%;EFAV48.7179%/.528470%/1.075475%;EEMV55.5556%/.568667%/1.110473%. QuarterKelly max(0,.25*(p-(1-p)/(W/L)))=0forall. Positive2026EEMVp71.4286%,W.967954%,L1.846262% impliesnaive4.233%fraction, butN7andfailedtraining/holdoutrequireactual0.3.Own3operatorliquidationstradeshave33.33%winrate,avgwin7.93994%,avgloss5.26143%,quarterKelly0; censoringprecludesstrategyexitcalibration. Account349.01hurdle=41.01223%of850.99,uniformrequired24daygrowth1.442287%daily; this is requiredreturn,notedge.4.Cap212.7475 andrisk8.5099 cannottransformnegativeexpectedpayoff. Current2shareETFcapacity permits arithmetic, notallocation. Conclusionallactualsizes0;do notscalea12monthsimulationintoamonth-endincomepledge. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; diagnostics.py archived478parts;query_tradesfundquant.

Premises:1 Fullpremiumriskmustfit8.5099;stopdoesnotlimitgaps.2 Basehittargetsneedreachablebidexits,notfairvaluealone.3 Simulatedp/W/Ldependsontestedassumptionsandisnotempiricaledge. Numpyseed20260908,4finalistsx3scenariosx20,000paths=240,000conditionalpaths. HypotheticalTuesdaySep8entryatFridaySep4spot/ask,notforecastofTuesdayquotes. DailyGBM S*=exp(-.5sigma²/252+sigma/sqrt252*Z),expectedspotdrift0,first4or5businessdayclosingchecks throughSep11/Sep14. EuropeanBSexitatquotedIV(orfactor.8),r.04,q0,remainingactualcalendartime,bid=max(value-halfFridayquotedspread,0),fee.20USD. Entry/exitIVcanbedifferentfromphysicalvol. Stophalfaskflooreddowncent,min.01;diagnostictarget2.5*(100ask+.20)/100 givesPATHputs.18,RIOT.205,PATHcall.055. Fractionalcenttargetsnotorders; noassertionofactualtickeligibility. Calendar/IV/normaldiffusion anddividendsassumed; noovernightgapmodel or15minexecution. FourlegsfrozenmeanPnL PATHOct2P12 -3.3336USD,Oct16P11 -.0452,RIOTSep11P19 +1.3894,PATHSep11C18 +.2980. Lowerphysicalvol.8andIV.8turnallnegative(-6.8147,-5.8913,-4.7035,-1.6721). RIOTfrozenp=.1952,W36.6302,L7.1581USD,conditionalquarterKelly.009483:largeaveragewinexceedstargetnet12.3USD,showingdailyovershootdependence. ConservativecappositivePnLatplannedtargetnet changesfourfrozenmeans to-4.5044,-1.3030,-3.3628,-1.2814;all12scenario cappedmeansnegative. This stressisnotclaimtargetordersactuallycapfills,butrejectsbasingbase-hitexpectancyonrareunmodeledovershoots. Actualoptionholdout0,p/W/Lunknown,notzero;quarterKellyforcapitalnotdefensibleandallocation0. Fullriskputs7.20/7.20/8.20,call2.20fitsdollarcapbutdoesnotestablishexpectedreturn. Sources https://runway.adityaperswal.workers.dev/data/option-chain/PATH?feed=indicative ; /RIOT ; https://runway.adityaperswal.workers.dev/data/stock-bars ; code research/validate.py/cap_validate.py .

Numpy RNG90802 after configuration bootstraps,100000paths of4 dailyOHLCvectors from1004training2021–24 days; Yahoo https://query1.finance.yahoo.com/v8/finance/chart/PLAY . Within-dayvectors preserved, IID days destroyserialclustering. Start8.72, fixed1ATRstop8.19121,target9.51318; stop-first/gap-openstop, cappedtarget, fees5bp/slip10bp per side. Netmean-.061527%,win46.983%,p05-6.3454%,p95+8.7693%,stops29.830%,targets17.638%,time52.532%. Premises: costs and barrier path matter; resampled general days do not estimate earnings payoff. Conclusion zero allocation, no Kelly from this generic model. No one-shareloss exceeds8.5099 in finite samples, NOT proof zero gaprisk. Assumed30% gap onfive8.72shares loses13.08; full49.14notional14.742, both exceedrisk. Gap probability unestimated. Strongcountercaseeventconditioning could outperform genericpaths, but small eventholdout uncertainty and negative training alreadyreject.

NumPy seed20260908 resamples20000paths from247overlapping3dailyreturnblocksJan2–Sep7 2026. NoGaussianextrapolation, preserveswithinblocksequence; fixed$212.7475position, nofees/intradayexitsorentryalpha. Simulated1%terminaltail loss BTC25.04,ETH39.35,SOL32.39,LTC25.74,LINK32.66,UNI31.44,XRP25.41dollars; BTCexpectedshortfall32.01,ETH42.84. Probabilitydailyclosepathloss>$8.5099 BTC15.21%,ETH22.73%,SOL28.705%,UNI33.725%. Linear99%terminalVaRsizesBTC72.29/ETH46.01/SOL55.90/UNI57.58areillustrativeexposurebounds,NOTapprovedallocationsorstops. Premises1 25%venuecapnotrisktolerance;2 dailyclosepaths missintradaytailandfuturestructuralbreaks;3 finitehistorical247blocksnot20000independentmarketobservations. Conclusion actualsizezero withoutpositiveindependentedge; futureedge requiresquarterKellyAND plannedriskcapwith15minexitlatency. Strongcounterargumentstopscouldreducelosses, butgaps/latencymaydefeatthem; simulateactualpolicyonlyafteredgegate. Source https://runway.adityaperswal.workers.dev/data/crypto-bars ; code simulate.py,simulation.json. NoapprovalforVaRsizedtrade.

From closedholdoutreturns in9893/9897, https://runway.adityaperswal.workers.dev/data/stock-bars ; numpyseed20260908,20000paths,20trades/path,10%hypotheticalequity fraction each trade,compounded,peak includesinitial1. ATI lossprob9.13%,medianreturn2.446817%,95thpercentileDD1.980979%;IREN99.755%,median-6.268158%,p95DD9.879742%. Descriptive IIDempiricalsimulation, not forecast, not15minstop/targethitodds. Smallselectedsamples missunseencrashes andcorrelatedregimes. ATIpositive simulatedpaths inherit favorableselected2026sample despite negativeearliertraining; cannotoverrulequalificationfailure. Neither10%hypotheticalfraction norpositivepointKelly isproposed. Actualsizingzero; hardposition212.7475,risk8.5099,fund278.67ceilings supply noedge.

1.Numpyseed90800,20000IIDpaths of12historicalmonthlycohorts at25%accountequityperentry,starting850.99;hypotheticalcapallocation,notrecommendation. SPY12cohortPnL5/50/95percentiles[-20.8861,-5.1232,12.0501]USD,loss68.97%;EEM[-13.7421,6.3393,26.3885],loss30.34%. Excludesoverhead,regimechange,PDT,whole-share rounding and15minfills. These are resamplingfrequencies,notfutureprobabilities. 2.Singlecohort25%allocationSPY5/50/95[-4.1860,-.5388,4.7435]USD;EEM[-4.6102,.9456,5.4840]. NexttimeexitOctober5/6cannot bepromisedSeptemberprofit. 3.LaterSPYp47.457627%,W1.04319%,L1.307076%,quarterKelly0. EEMp59.322034%,W1.427398%,L1.476685%,empiricalquarterKelly4.3099%;actual0becausefailedtraining andmeanCIspanszero. Own3operatorliquidationsalso implyquarterKelly0 butarecensored,notforwardcalibration. 4.SPY59cohorts finalexits28stops,8targets,7breakevens,16time;23additionalhalffills. EEM21stops,21targets,3breakevens,14time;23halffills. SyntheticOHLCfrequenciescannotcalibratevenue15minutehitodds. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; observations9811/9813/9814/9815.

Numpyseed90800,100000paths each5sessions,1004training dailyOHLC vectors2021–24 from https://runway.adityaperswal.workers.dev/data/stock-bars ; starts hypothetical35.7 with1ATRstop34.77393 and1.5ATRtarget37.08911. Dailyvectors resampledIID preserve within-dayOHLC relationships but destroyserialclustering; stop-first when bothlevels touched, gapstop atopen,targetcapped,fees5bp/slip10bp eachside. Netmean-.151681%,win47.848%,stop42.670%,target34.503%,time22.827%,p05-3.41830%,p953.57985%. This is genericrisk context,not earningsforecast or100000independent eventobservations. No sampled1shareloss exceeds8.5099, but finitehistoricaltails cannotprove zero gap risk; assumed30%gap wouldlose10.71beforecosts,probabilitynotestimated. Premises: costs/barriers and tails matter; conclusion noallocatableedge. Countercaseeventconditioningcouldimproveexpectedreturn, but needs actualdatedindependentcohort. NoKelly inferred from genericMonteCarlo; adoptedsize0. Do not add protective15minfill claim to dailyOHLC model.

Method: NumPy seed20260908,10000circular3dayblock-bootstrap paths perasset from90dailylogreturns throughSep7,7dayhorizon. Startcompletedclose,stop1ADR20below,target2ADR20above. Observe dailycloses only; execute at simulatedcrossingclose includingovershoot, charge25bpfees and10bpslippage per side. Scenario NOT predictive strategybacktest or15minutevenueexit model. Premises1 empiricalrecentdrift maynotpersist;2 dailychecks missintradaycrossings;3 noqualifiedrulewin/lossdistribution. Conclusion use ranges only to challenge ambitious targets, notsize. BTC/ETH/SOL/LTC targetfirst14.23/17.87/15.60/12.55%,stopfirst17.90/13.69/10.71/15.33%,timeout67.87/68.44/73.69/72.12%. Mean netpayoffs+.8935/+2.3668/+2.9084/+1.3412% reflectsampledrift andunvalidatedmodel, notedge. Fifthpercentile−5.5134/−6.7115/−7.9995/−7.0084%,demonstratinglossbeyondnominalstop. Scenario BTCstop76167.40target84955.62;ETH2368.03/2735.32;SOL97.0262/117.3761;LTC52.3305/60.9550. These arenotorders. Nominalrisk-onlyceilings193.25/151.53/117.63/144.05USD use8.5099risk/(stop%+.7%cost),notgapguarantees;actualallocationzero fromedgegate. Counterexample: strongcatalyst canhit2ADRquickly; noindependentfrequency estimated. Source https://runway.adityaperswal.workers.dev/data/crypto-bars ; observations9492–9495,stats_daily.py. FeeassumptionunderstatescurrentLTCroundtrip1.1145%,reinforcingnoLTCauthorization. One-to-twoADR targets aremeasuredscales,notpromisedpayoffs.

NumPy seed20260908 samples with replacement from the12 net closed holdout returns in observation9305/backtest749, source https://runway.adityaperswal.workers.dev/data/stock-bars . Run20,000 paths of20 sequential trades, mechanically invest10% of contemporaneous portfolio equity each trade, compound1+.1*r. Probability of terminal loss96.985%, median terminal return-7.424605%,95th percentile maximum drawdown14.427294%. This is a stress illustration conditional on the empirical sample, NOT a forecast or proposal; IID resampling misses clustered regime shifts and unprecedented gaps. It does not estimate real stop/target hit odds or15-minute execution. Strongest counterexample is a profitable new post-disposal regime, which this history cannot establish; require prospective evidence. Actual allowed allocation remains zero because quarter Kelly is nonpositive and current signal false. Fund cash278.67, venue position ceiling212.7475 and nominal loss budget8.5099 do not create edge; a hypothetical10% fraction is not justified sizing.

1. At10bponeway all4main,ROD andPDT holdout variants imply quarterKelly0 from empirical winprobability/averagewin/loss. SPY main p13.778409%,avgwin.147373%,avgloss.270744%;TLT p11.363636%,avgwin.126794%,avgloss.194806%. Actualsize0.2.20000 random24-calendar-day contiguous historical windows, hypothetical25%accountallocationpertrade from850.99, yield main PnL5th/median/95th SPY[-7.2522,-4.1051,-.9631],EEM[-5.6375,-3.4835,-1.4568],EFA[-5.6374,-3.4271,-1.1810],TLT[-4.5511,-2.5483,-.2636]USD. Loss frequencies97.66/99.545/99.855/96.34%; zero349.01USD gains in sampledwindows.3.PDTSPY windows[-6.5256,-3.4467,-.8002],loss96.985%,zeroKelly. These are historical resampling frequencies, not forward probabilities; no fixed overhead, intrabar risk, accountwidecompetingdaytrades or unexpectedexecutionfailures.4.No stop/target exit odds estimated because these parentrules have time exits; assigning targethitrates would invent data. Nominalriskcap8.5099 is not a guaranteedgaplosslimit. Conclusion protectcash; no sizing to repair the monthly shortfall. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; seed90708, stats.py; separate20-session blockbootstrapmeanCI recorded.

Numpy seed9070800,100000 five-session IID paths sampled from752 ROIV2022–24 daily returns. Unrestricted gross endpoint mean+.46984%,p05-12.52714%,p95+14.86795%,loss49.822%; these are generic daily risk, not clinical outcome forecasts. Descriptive sensitivity uses Sep4ATR1.1575/price34.945 for stop3.312% and target4.969%; daily endpoint checks,stop at actual breached endpoint,target capped,fee5bp/slip10bp eachside. Base netmean-1.02070%,win45.992%,stopfirst44.685%,targetfirst33.972%,time21.343%; one-sharep05-$3.272. Assumed extra30%firstdaygap probabilities1/5/10% produce means-1.29903/-2.49798/-3.96143%; one-share loss>$8.5099 odds.942/4.949/9.894%. Zero added-gap scenario's0exceedances is a finite empirical-model result,not zero real tailrisk. Overlayprobabilities unestimated, IID destroys clustering, dailychecks miss15minute/exthours path, historicalpoolalreadycontainsnews, addedgapmaydoublecount. Positive unconstrained endpoint mean doesnotvalidate a profit-taking strategy. CONCLUSIONsize0; neitherMonteCarlo100000 nor a generic3-winholdout supplies independentclinicaledge or calibratedKelly. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; scriptsroiv.py/simulation.py archived; freezeprospectively ratherthanretunebarriers.

1. SPY swing holdout p43.75%,averagewin1.197682%,loss0.879921% implies raw quarter-Kelly0.605964% of equity,about$5.16; training Kelly0 and negative cost stress veto allocation. Other four holdout Kelly values0. Actual size0. 2.20,000 circular three-month-block paths over60months, hypothetical25%account allocation per trade from850.99: SPY terminalPnL5th/median/95th[-27.1884,4.2175,35.0681]USD,41.515%loss paths,95thpercentile monthly/realized maxDD4.19024%. Open-trade excursions and fixed overhead excluded. 3.Separate24-calendar-day realized-cashflow windows producePnL[-3.90996,0,3.31432],21.82%loss windows,zero simulated349.01gains; inactivity drives median0. These are conditional historical resampling frequencies, not future probabilities or a fresh-entry forecast. 4.Historical exits:19targets,38stops,7RSI,0timeout; target frequency29.6875%,Wilson95%[19.9050,41.7704], distinct from43.75%winning trades.19extended-session exits and25same-day exits expose fractional/PDT incompatibility. Sampled stop overshoot median0.06613R,max0.32550R; no hard gap-loss bound. Conclusion cash; no wider targets or risk increase to address shutdown pressure. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; stats.py and recorded simulation figures.

Numpyseed9070601,100000four-sessioniidpathsfrom857validtraining2020–23dailyreturns,excludezero/missingadjacentprints. LatestATR/price definesdailyendpointstop-3.0163%/target+4.5245%,checkstop/targetfirst,stopatbreachedendpoint/targetcapped,elsefourthendpoint;costfactor .999*.9995/(1.001*1.0005). Base mean-.225076%,win47.193%,targetfirst4.568%,stopfirst11.943%,time83.489%. On49.14fundnotional mean-$0.11060,p05-$2.05044. Independentassumed20%negativegap atfirstendpoint with1/5/10%windowhazard -> means-.416103/-1.219721/-2.190210%;loss>$8.5099 probability .951/4.947/9.801% atfullfund;thesehazardsarenotestimated. 0/25/50/100%fundsizinggrid recorded8524–8527;0sizehas0dollarloss. Notdatedeventforecast:poolcontainsalltrainingdaysandhistoricalnews,addedgapcoulddoublecount;dailyendpointbarriersmissintraday/15minchecks;100000pathsarenot100000independentevents. Calendarholdout p=.6,avgwin.02035497,avgloss.02779982 -> quarterbinaryKellyNOTIONAL=.25*(p/loss-(1-p)/win)=.482913;risk-unitformula .25*(p-(1-p)/(win/loss))=.0134249 isdifferentunit,notnotionalfraction. UnderstressedcostsnotionalquarterKelly=-.856486 ->clip0. NoKellyestimateadopted:CIcrosses0,coststressnegative;actualsize0. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; code research/analyze.py; observation8521–8527.

1. Position-sizing illustration uses each main-rule holdout's chronological net trade returns, resampling circular four-trade blocks into 10,000 paths of20 trades at hypothetical10% capital allocation, seed90607. AA ending return5/50/95 percentiles -2.9641/+1.5116/+7.6594%; loss frequency31.87%,95th-percentile trade-mark drawdown3.7797%. CENX -5.2178/+.8558/+7.6125%; loss41%,DD95=6.3986%. These are model-conditioned empirical scenarios, not future probability estimates; trade-mark drawdown omits adverse movement within trades and joint same-sector risk. 2. Separate exit simulation samples whole observed five-session OHLC path units from the22/26 matched entry cohorts, seed90707,10,000 draws. With priorADR stop and2ADR target, simulated stop/target/timeout percentages are AA49.74/26.72/23.54 and CENX57.03/19.18/23.79. IID bootstrap target-frequency95% intervals are9.09–45.45% and3.85–34.62%; underlying observed counts are AA11stops/6targets/5timeouts andCENX15/5/6. Sampling repeats evidence;10,000 paths are not10,000 independent events. Stop-first conflict policy and opening-gap fills; no ambiguous historicalbars. Actual 15-minute polling and extended-session depth remain unmodeled. 3. Exact fee-inclusive ADR mean returns are AA-.0762645%,CENX-.7722893%; bootstrap mean95% intervals[-1.9802,1.9385]%/[-2.9093,1.4994]%. Baseline compounded returns-3.9406%/-21.6026%, stress-8.0756%/-25.5751%. Exact figures supersede earlier approximate subtract40bp means; individual trades recorded. 4. Main-rule point quarterKelly numbers.036369/.018490 are binary unit-risk fractions, not stock allocation fractions. Stock-capital conversion under a two-outcome approximation would divide by average fractional loss; those optimistic figures are not adopted. The relevant ADR distribution has negative net mean, so long-only concave expected-log optimum is atzero; moreover base mean intervals spanzero and currententryfails. ApprovedcapitalUSD0, despite fundcash278.67, perpositioncap212.7475, equityrisk8.5099. Two actual operator-liquidation wins with no loss sample cannot substitute. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; analyses600/601,615/616 and exact exit observations8553/8555. No probability assigned to unverified future tariff/war paths. Preserve cash.

Premises1 raw selectedholdout tradesdailyN2/7/13 andhourlyN123/119/109.2 IIDtradebootstrap10000paths seed90607:95%meantradeCI dailyBTC[-6.616,-2.326]%,ETH[-5.083,6.768]%,SOL[-5.466,5.021]%;hourlyBTC[-.848,-.376]%,ETH[-1.100,-.041]%,SOL[-1.112,.257]%.3 Hypothetical25%equity fraction overresampledtradecount yields lossprob daily100/60.36/73.73%,hourly100/98.36/93.45%. Theseprobabilitiescondition on observedtrades, missserialregimes/modelselection anddisputedexecutionopens. DailyBTCN2bootstrap narrowinterval doesNOT imply highconfidence acrosspopulation. Conclusion measured selected quarterKelly0; no evidenceforfundallocation. Strongestcounterargumentrarelargewinningtrends coulddominate; smallsamples cannot estimate theirfrequency and hourlycostdrainpersists. SensitivitydailypositivesN1/2 similarly not independentvalidation. Allquantiles andprobabilities recordedasobservations. Source https://runway.adityaperswal.workers.dev/data/crypto-bars .

Premises1 use2160consecutive joint hourly logreturns Jun9 06 toSep7 05UTC, verifiedno missingprices/hours; shared6h movingblocks preserve shortdependence/crosscoin relation.10000paths72h seed90608.2 Exit first hourlyendpoint <=-1ADR or >=1.5ADR, otherwise72h; ADR14BTC3.1492%,ETH3.8647%,SOL5.8714%, correspondingtargets4.7239/5.7970/8.8071%. Baseline25bpfee+5bpslip eachside. Driftpreserved simulatedmean+.0529/+.4605/+.8165%; NOT signalconditioned or eventcalibrated.3 Remove sample hourlylogdrift1.0681/1.8273/2.0757bp and doublecost =>mean-1.1927/-1.1830/-1.1521%,targetfirst14.14/16.48/8.00%,stopfirst28.32/31.14/18.92%,neither57.54/52.38/73.08%. Simulated1%tailreturns-6.7882/-7.9545/-8.9069% imply hypotheticalnotionals125.36/106.98/95.54 toput8.5099USD atthatquantile, not actualapprovedsize. Nominalstop sizing212.75/190.61/131.50 had9.84/21.44/11.63% simulatedchance ofloss>1%equity underbaselinehourly overshoot. Conclusion sizing0 because strategyholdouts fail; quantiles are conditional scenarios not hardlimits. Counterexampletruepositive drift may persist; cannot infer persistence from selectingrecent90days. Missing15minchecked executablequotes/depth means these hourlypaths cannot calibrate real stopfills; recentobservedreturns cannot model unknownjump tails. Source https://runway.adityaperswal.workers.dev/data/crypto-bars ; https://docs.alpaca.markets/us/docs/crypto-fees .

Premises:1 Simulated precision must preserve majorobserveddependence.2 Forecast loss andvariance calibration are not option profits.3 Position sizing needs actual costedoption p,avgwin,avgloss. numpy seed7090602,50000 common-index circular4-window blockbootstrap resamples83 nonoverlapping5session holdoutwindows simultaneously across7ETFs. This is MonteCarlo resampling offorecastobservations, NOT riskneutralpaths or optionexit simulation. Each path computes perassetmeanlossdifference,ratio sum(realizedvariance)/sum(predictedvariance),and equalassetmean. Pooleddifference-.0272720856,95interval[-.084595064,.028682371]. Bonferroni sevenasset95 intervals onlyTLTuppernegative-.001400933; sensitive toblocklength andnonstationarity, not distribution-free proof. GLDvariance-ratio95[1.432672,2.802439],IBIT[.471998,.800341] show modelerror overwhelms simulationnoise. All83dates/581rows,intervals and7x7correlations recorded. Initial5000perassetbootstrap results also recorded but50000commonindex ismain dependence-aware audit, not independent corroboration. Explicit sizing gate: quarterKelly=max(0,.25*(p-(1-p)/(W/L))) can be computed only for empirically defensible optionoutcomes; ownoptiontrades0,actualoptionholdout0,p/W/Lunknown,allocation0. No winprobability0 is asserted. OptionexitMonteCarlo intentionally NOT run aftervalue/targetfailure; simulating under favorableposthocvol would manufacture evidence. No optionreturn,drawdown,winrate or exitodds claimed. Source venueadjustedstockbars; scripts uncertainty.py/analyze.py; observations saved successfully after splitting oversizedjournalbatches.

1. Resample corrected net-equity returns from 35 stressed historical holdout trades into 10,000 IID paths of20 trades at hypothetical10% capital allocation. Seed90407. End-return5/50/95 percentiles -7.0841/+0.1911/+8.6712%; loss frequency48.38%,95th-percentile trade-mark drawdown8.7577%. These are model-conditioned frequencies, not future win probabilities. Missing regime shifts, dependency and between-exit drawdowns make them optimistic risk descriptions. Four-trade block mean interval[-3.9867,4.7908]% reinforces uncertainty. Source https://runway.adityaperswal.workers.dev/data/stock-bars . 2. Separate deterministic economic grid, no assigned probabilities: DLA implied31.7073/lb from accepted82k/$2.6m; assumed all-in costs13.34,20,28/lb. Accepted82k yields GP1.50612/0.960/0.304m; hypothetical163k yields2.99387/1.90829/0.60429m; hypothetical289k yields5.30815/3.38341/1.07141m. Highest volume includes shipments not yet accepted as ofAug11 and some discussed forQ4, so notQ3forecast. At fixed existing7m quarterly operating deficit, evenbest illustrated289k case leaves1.69185m deficit, though othergrowth andcostchanges could alterthis. Cost13.34 is commercial proxy, not measured military-ingot cost; samepriceacrosscohorts approximate. https://www.sec.gov/Archives/edgar/data/101538/000110465926094035/uamy-20260630x10q.htm ; https://www.sec.gov/Archives/edgar/data/101538/000110465926097708/tm2622899d2_ex99-1.htm . 3. Hardlimits: equity850.99,position212.7475,fund278.67,risk8.5099. Point quarterKelly0.6842% capital(base),0.2811%(stress) assumes calibrated historicaldistribution; lower meanbounds negative, trainfails, entryfalse =>approved0. Two actualoperatorliquidations have no loss sample. No MC result repairs those gaps; no stop/target order proposed.

Premises:1 A numericalpricingcross-checkshouldrecovercash-dividendEuropeanparity.2 Risk-neutral terminalpayoffsdo notestimateactualwinprobabilityorplannedexitreturns.3 Failedvalue/riskgatesbartrade-sizingpaths. N500000numpy pathsseed7092026,independentstandardnormaldrawsbefore/afterex. S46.15,r.04,sigma.4081799262,T14/365,td13.7291667/365,D2.61. Spre=Sexp((r-.5sig²)td+sig sqrt(td)Z1);Spost=max(Spre-D,0);ST=Spostexp((r-.5sig²)(T-td)+sig sqrt(T-td)Z2). Discountpayoffs exp(-rT)max(sign*(ST-K),0). SepK46EuropeanC=.603604336(SE.002064965),P=2.992489208(SE.003961243);C-P=-2.388884872vsanalytic S-PV(D)-Kexp(-rT)=-2.385554805;parityMCSE.005213506,difference-.64SE. AmericanFDcall1.565900includesexerciseprivilege andneednotmatchEuropeanMC. PutFD2.992254closebecauseits earlyexerciseincrement smallhere. AffordableK25/29/30/31putvalues0,.000000871,.000002868,.000015226;zeroK25hitsdoesnotprovezerotailprobability. RiskneutralITM frequencies0,.000002,.000002,.000024are NOTempiricalwinrates. These areGaussianmodeldiagnostics,omitgeopoliticaljumps,stochasticvolatility,spreadchangesand15minexitdelays; MCprecisiondoesnotremove modelerror. Conclusion: arithmetic/modelcross-checksupportsdividendmechanism; simulationcannotestablishquarterKelly orprofitabletailstrategy. Noexitoddsoractualoptionbacktestclaimed; owntrades0,actualoptionholdout0,size0. Sources frozenSep4inputs https://runway.adityaperswal.workers.dev/data/stock-bars?symbols=FRO&timeframe=1Day&feed=iex&adjustment=all ; issuerD https://ml-eu.globenewswire.com/Resource/Download/59431810-8e9c-4a39-b3d0-cc2dd63da402 ; scripts research_fro/mc.py andverify.py.

Premises: the main rule's29later trades have p37.9310%, averagewin2.59139%, averageloss1.60982%; max(0,[p-(1-p)/(win/loss)]/4)=0. Simulate20,000 circular six-calendar-month blocks across68months using numpy seed90704, zero exposure in inactive months. Hypothetical25%equity deployment (not a proposal) from850.99 produces terminal P&L5th/median/95th[-37.41097,-2.61184,+42.27635]USD,54.29%paths ending below start,95th-percentile maxdrawdown5.52915%. Drawdown>1%in99.48%paths is a cumulative-path statistic, not a claimed breach of the per-trade1%nominal risk rule. These are conditional resampling frequencies of selected history, not calibrated forecasts; fixed overhead, quote gaps, account interactions and exact cash distributions excluded. Main historical11target/18stop exits imply37.931%target frequency; win Wilson95%[22.6878,55.9978]%, weak precision. Strongest counterexample: some paths profit; this cannot create a reliable expected payoff. Actual size0; neither shutdown pressure nor349.01shortfall enters probability or sizing. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; observations7818/7821 and stats.py.

Premise1 Python numpy seed260907 jointly resamples4hblocks from878 aligned pre-event Aug1-Sep6 13UTC returns,10000paths48h. Stop1xADR14=BTC3.1492%,ETH3.8647%,SOL5.8714%;target1.5x=4.7239/5.7970/8.8071%. Hypothetical generic barriers from observed range, not validated thesis invalidation. Close-only hourly firstcross and timeout48h, gross overshoot retained; fresh quoted roundtriploss plus10bpslippageeachside. These are assumptions, not venue15min model. Premise2 empiricaldrift average net+.5469/+.7386/+1.3458%; subtracting samplemean turns-.6384/-.6627/-.6992%,netwin35.79/36.17/40.00%. Zero-drift targetfirst10.68/12.38/4.42%,timeouts72.81/68.24/86.43%; stopfirst16.51/19.38/9.15%. Premise3 at212.7475USDcap,zero-drift95thloss8.80/10.74/14.51USD vs8.5099 equity1%; model probabilitybreach8.3/21.49/20.81%. No certainty or hard riskbound, bootstrap understates unseen jumps and ignores future liquidity changes. Conclusion model optimism comes from recent drift, not incident alpha; no simulationprobability used for Kelly and allocationzero. Strongestcounterargument recentuptrend may persist; requires independent signalconditioning, absent. Sources https://runway.adityaperswal.workers.dev/data/crypto-bars ; https://runway.adityaperswal.workers.dev/data/crypto-snapshots ; https://docs.alpaca.markets/us/docs/crypto-fees .

Numpyseed709,100000three-sessioniidpathsfrom170positive-print2026dailyreturns,30bpapproxroundtripdeduction. Descriptivebase mean+.739776%,win53.158%,p05-8.82099%;notanapprovalprobabilityorvalidatedtraderule. Addassumed20%adverseterminalgap independently with0/5/10/20%windowhazard: means+.73978/-.28589/-1.265995/-3.273818%;lossover8.5099on49.14notional .086/3.58/7.014/13.746%. Assumedhazardsarenotestimated;compoundingchoiceisillustrative. Breakevenhazardabout3.7%, showsfragilitynotactualriskestimate. Dailyendpointbarrierproxy at+6.43156%target/-9.62343%stop:targetfirst20.93%,stopfirst4.049%,neither75.021%;cannotcaptureintradayorder,gaps,15minvenueexecutionorbidask. Historicalpoolalreadyincludesnews;addedgapstressmaydoublecountsomehazard. No pathquantitycreatesindependentobservations. Requirededgeunknown,quarterKellynotestimableforevent,size0. Recordsourcesobservations7723 andFDAearlydecisioncounterexample https://ir.telixpharma.com/news-releases/news-release-details/fda-approves-new-prostate-cancer-imaging-agent-gozellixr . NoMonteCarlobuyauthorization.

Premises: 1. Model probabilities are conditional, not empirical option winrates. 2. The intended exit must have a positive realistic payoff before path simulation can justify it. 3. Full premium remains at risk. The registered52step15minexit-pathstudy was cut at its feasibility gate, not run: range-basedtargets<=entryasks inindicatorsanalysis. Do notreplaceit with an expiryhold strategy. Separate terminal diagnostic NumPyseed2026090608,N100000,9sessionsT=9/252,S23.67; ST=Sexp(-.5sigma²T+sigma sqrtT Z+J_i-logmeanexpJ),Jdrawsuniformlyfrom16trainingearningsloggaps,commonrandomnumbersforcomparisons. Baselineevent sigma46.9262%; adverse.5J,.8sigma;diffusionJ0,vol42.5200%. Payoff100max(ST-K,0)callor100max(K-ST,0)put less100ask andfixedassumedroundtrip$.20/$1.30. Ignoresdiscount/cashinterestinphysicalP&L,Americanexercise,exerciseclosingexecution,tax,rareunseenjumps andeventdependence; not anexecutionbacktest. CallsK37.5 ask.05 andputsK17.5 ask.06. Event $.20scenario call mean-$5.189230,win.011% (11/100000),avgwin$92.707951,avgloss$5.20,fullpremiumloss99.989%,MCSE$.004165; putmean-$5.870908,win.552%,avgwin$53.102472,avgloss$6.198248,fullpremiumloss99.39%,MCSE$.017642. Raisingfeeto1.30 shiftsmeans-$1.10. Adversemeans-$5.20/-$6.198126 at$.20;diffusion-$5.20/-$6.197772. All12scenariosrecorded; nonepositive. qKelly=max(0,[p-(1-p)/(W/L)]/4)=0throughout. Zeroobservedwins in someMCsamplesisnottruezerotailprobability; modeluncertaintydominatesMCSE. Risks$5/.06*100pluscostfit8.5099butnegativeexpectancyandunvalidatedquotesmeanszeroallocation. Actualoptionhistorysample0 and owntradehistory0. Source https://runway.adityaperswal.workers.dev/data/option-chain/CHWY?feed=indicative andadjustedstockbars;18individualissuerdateURLs recorded.

Numpy seed9060800; exact script note408, outputs7134/7135. Hypothetical mixture:43.6%late, conditional Gamma mean6.06days, shapes.5/1/2/4; other arrivals zero. For each100000draws, assumed chance>14days ranges.764–5.672%; mean hypothetical40ft storage cost at50USD/day AFTER14days ranges.79–28.18USD despite same targetmean. Maersk OptionA tariff gives mechanical21day40ftstorage350USD,30day800USD; excludes baselinefreight/emergency/otherfees. CRITICAL mapping assumption: vessel lateness is NOT container storage duration, globalJuly is NOT a Gulf customer cohort; these are deliberately uncalibrated sensitivity examples, NOT predicted invoices, port wait distribution, or carrier revenue. Mean cannot identify tail or pricing rent. Maersk published annual freight sensitivity100USD/FFE->700mEBIT maps assumed one-quarter-only uniform effect to175m; seasonal volumes/coverage make simple quarter scaling nonforecast. Existing stock-path MonteCarlo analysis416/strategy420 remains rejected:51.51% conditionalprofitfrequency doesnotjustify sizing. Neither economic simulation gives stock win/loss data; proposedsize0. Sources https://sea-intelligence.com/press-room/406-sharp-reliability-drop-from-asian-port-congestion ; https://www.maersk.com/news/articles/2026/08/31/middle-east-operational-update-44 ; https://www.maersk.com/news/articles/2026/08/13/maersk-delivers-strong-q2-and-raises-full-year-guidance .