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Executable Science local pilot drafts
Compare a known stationary distribution with matrix iteration and occupation frequencies from a deterministic-seed Markov-chain simulation.
Investigate Do the two computational routes approach the same analytical stationary distribution?
Executable Science local pilot drafts
Integrate y'=-y from zero to one at five resolutions and compare each final value with the analytical exponential solution.
Investigate How does the final-time error change when the step size is halved?
Executable Science local pilot drafts
Implement bounded-memory reservoir sampling and record sample integrity plus marginal inclusion frequencies across a fixed-seed simulation.
Investigate Does the sampler preserve sample size and approach the known per-item inclusion probability?
Executable Science local pilot drafts
Compare sequential sum and math.fsum on a repeated cancellation pattern, with a Fraction reference for the exact represented inputs.
Investigate Which summation strategy preserves the small contributions in this adversarial finite sequence?
Executable Science local pilot drafts
Generate 256 paired synthetic measurements through a declared linear transformation of independent standard-normal draws, with known population covariance.
Investigate Can covariance and correlation implementations be calibrated against a transparent generator?
Executable Science local pilot drafts
Generate paired complete, independently missing, and value-dependent missing observations from a declared standard-normal process.
Investigate How does a known missingness mechanism affect a complete-case mean in this controlled example?
Executable Science local pilot drafts
Generate 128 regression observations with known coefficients, a declared Gaussian noise process, and a fixed train/test split, together with a small reference fit.
Investigate Can another implementation recover the reference fit and evaluate predictions without changing the test split?
Executable Science local pilot drafts
Compare a raw second-moment formula, Welford accumulation, and statistics.pvariance on five large observations with an exact population variance of two.
Investigate How does cancellation affect variance calculations when location is much larger than spread?
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