{"schemaVersion":1,"studyVersion":1,"exhibitId":"chaos","runId":"run-20260917003910210-62944-012","caseLabel":"ε=1e-8 · h=0.0025 · T=1","modelVersion":"chaos-rk4-1.0.0","parameters":{"sigma":10,"rho":28,"beta":2.6666666666666665,"epsilon":1e-8,"step":0.0025,"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":"2026-09-17T00:39:15.850Z","observables":[{"label":"Base integration step h","value":0.0025,"unit":"model time","precision":6},{"label":"Integrated duration","value":1,"unit":"model time","precision":6,"description":"Requested T=1; 400 complete fixed steps."},{"label":"Initial separation","value":9.99999993922529e-9,"precision":8},{"label":"Final separation","value":1.1159947262026489e-8,"precision":8},{"label":"Maximum sampled separation","value":2.010778207352675e-7,"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":801},{"label":"Short-window maximum step difference","value":0.0000028816317582099183,"precision":8,"description":"Same initial state; h versus h/2 at 401 common points through t=1."},{"label":"Short-window endpoint difference","value":1.5881468053876506e-7,"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.","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":1e-8,"step":0.0025,"duration":1,"threshold":1,"compareStep":true},"integration":{"method":"Classical fixed-step RK4","precision":"IEEE 754 binary64","baseStep":0.0025,"baseSteps":400,"requestedDuration":1,"integratedDuration":1,"alignmentResidual":0,"referenceInitial":[1,1,1],"perturbedInitial":[1.00000001,1,1],"halfStep":0.00125,"halfSteps":800,"halfStepInitial":[1,1,1]},"separation":{"initial":9.99999993922529e-9,"final":1.1159947262026489e-8,"maximum":2.010778207352675e-7,"threshold":1,"firstCrossingIndex":null,"firstCrossingTime":null,"zeroSamples":0},"comparison":{"enabled":true,"requestedShortEnd":1,"lastCommonTime":1,"commonSamples":401,"maximumShortDifference":0.0000028816317582099183,"finalShortDifference":1.5881468053876506e-7,"maximumFullDifference":0.0000028816317582099183},"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":[-9.761478567571203,-10.396341198246756,0.9616731694212098],"max":[19.568940680094425,27.183492348736234,47.84076974861856]},"sampling":{"authoritativeTable":"csv.rows contains every computed trajectory state once, at its own time grid.","rows":801,"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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integration step h","value":0.0025,"unit":"model time","precision":6},{"label":"Integrated duration","value":1,"unit":"model time","precision":6,"description":"Requested T=1; 400 complete fixed steps."},{"label":"Initial separation","value":9.99999993922529e-9,"precision":8},{"label":"Final separation","value":1.1159947262026489e-8,"precision":8},{"label":"Maximum sampled separation","value":2.010778207352675e-7,"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":801},{"label":"Short-window maximum step difference","value":0.0000028816317582099183,"precision":8,"description":"Same initial state; h versus h/2 at 401 common points through t=1."},{"label":"Short-window endpoint difference","value":1.5881468053876506e-7,"precision":8}],"diagnostics":{"method":"Double-precision classical RK4. 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.","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":1600}},"build":{"packageVersion":"0.1.0","softwareVersion":"0.1.0+0e6017e6a747.dirty.02665ba9098c","gitRevision":"0e6017e6a747d3c610b956612b4125e232283001","gitDirty":true,"sourceDigest":"02665ba9098c7b8fe2a4b728fbd2b3749b1724fe9999f830d8fa90cb5d8b209b","runtime":"v26.5.1"}}