{"schemaVersion":1,"studyVersion":1,"exhibitId":"chaos","runId":"run-20260917003910210-62944-004","caseLabel":"ε=0 · h=0.005 · T=1","modelVersion":"chaos-rk4-1.0.0","parameters":{"sigma":10,"rho":28,"beta":2.6666666666666665,"epsilon":0,"step":0.005,"duration":1,"threshold":1,"compareStep":true},"numericalMethod":"Double-precision classical RK4. Fixed h; half-step samples compared at indices i and 2i. Residual: requested versus integrated time-grid endpoint.","softwareVersion":"0.1.0+0e6017e6a747.dirty.02665ba9098c","createdAt":"2026-09-17T00:39:15.412Z","observables":[{"label":"Base integration step h","value":0.005,"unit":"model time","precision":6},{"label":"Integrated duration","value":1,"unit":"model time","precision":6,"description":"Requested T=1; 200 complete fixed steps."},{"label":"Initial separation","value":0,"precision":8},{"label":"Final separation","value":0,"precision":8},{"label":"Maximum sampled separation","value":0,"precision":8},{"label":"First sampled threshold crossing","value":"Not observed","precision":6,"description":"First d(t) > 1; conditional on this run and sample grid."},{"label":"Full exported sample rows","value":401},{"label":"Short-window maximum step difference","value":0.00004641730006565268,"precision":8,"description":"Same initial state; h versus h/2 at 201 common points through t=1."},{"label":"Short-window endpoint difference","value":0.0000024289507761028697,"precision":8}],"warnings":["Finite RK4 trajectories approximate this model; separation does not prove all properties of chaos or predict actual weather.","The diagnostic residual checks time-grid alignment only. It is not a bound on integration error.","201 base samples have zero separation. They remain zero in the data and are omitted from the logarithmic plot.","The separation threshold was not exceeded in this observation window.","Step comparison fixes the initial state; its short-window difference is not a certified error estimate. Long-time divergence is recorded separately."],"sourceIds":["M7","M12"],"result":{"exhibitId":"chaos","modelVersion":"chaos-rk4-1.0.0","parameters":{"sigma":10,"rho":28,"beta":2.6666666666666665,"epsilon":0,"step":0.005,"duration":1,"threshold":1,"compareStep":true},"integration":{"method":"Classical fixed-step RK4","precision":"IEEE 754 binary64","baseStep":0.005,"baseSteps":200,"requestedDuration":1,"integratedDuration":1,"alignmentResidual":0,"referenceInitial":[1,1,1],"perturbedInitial":[1,1,1],"halfStep":0.0025,"halfSteps":400,"halfStepInitial":[1,1,1]},"separation":{"initial":0,"final":0,"maximum":0,"threshold":1,"firstCrossingIndex":null,"firstCrossingTime":null,"zeroSamples":201},"comparison":{"enabled":true,"requestedShortEnd":1,"lastCommonTime":1,"commonSamples":201,"maximumShortDifference":0.00004641730006565268,"finalShortDifference":0.0000024289507761028697,"maximumFullDifference":0.00004641730006565268},"equilibria":[{"point":[0,0,0],"rhsNorm":0},{"point":[8.48528137423857,8.48528137423857,27],"rhsNorm":1.4210854715202004e-14},{"point":[-8.48528137423857,-8.48528137423857,27],"rhsNorm":1.4210854715202004e-14}],"bounds":{"min":[-9.761478916021503,-10.396341828460208,0.9616965589987955],"max":[19.568940536464705,27.183492321560227,47.83639340839442]},"sampling":{"authoritativeTable":"csv.rows contains every computed trajectory state once, at its own time grid.","rows":401,"baseRowStride":2,"sceneCap":2500,"plotCap":2000,"sceneStride":1,"plotStride":1,"missingCells":"Empty cells on odd half-step rows mean no coarse sample was computed there. Values are never interpolated. Without comparison all half-step fields are 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Fixed h; half-step samples compared at indices i and 2i. Residual: requested versus integrated time-grid endpoint.","warnings":["Finite RK4 trajectories approximate this model; separation does not prove all properties of chaos or predict actual weather.","The diagnostic residual checks time-grid alignment only. It is not a bound on integration error.","201 base samples have zero separation. They remain zero in the data and are omitted from the logarithmic plot.","The separation threshold was not exceeded in this observation window.","Step comparison fixes the initial state; its short-window difference is not a certified error estimate. Long-time divergence is recorded separately."],"tolerance":1.4210854715202004e-14,"residual":0,"iterations":800}},"build":{"packageVersion":"0.1.0","softwareVersion":"0.1.0+0e6017e6a747.dirty.02665ba9098c","gitRevision":"0e6017e6a747d3c610b956612b4125e232283001","gitDirty":true,"sourceDigest":"02665ba9098c7b8fe2a4b728fbd2b3749b1724fe9999f830d8fa90cb5d8b209b","runtime":"v26.5.1"}}