Reproducible figures, tables and data provenance

A bin count, an efficiency-corrected yield, an integrated cross section and a differential cross section are distinct quantities. Divide a selected count by efficiency and integrated luminosity to estimate the bin's integrated cross section under a simple no-migration model. Divide once more by bin width to obtain an average density within that bin. Unequal widths make the distinction visible: a taller count bar need not imply a proportionally taller density. A plotted bin center also requires a convention; it does not replace the stored edges.

Record whether values are before or after background subtraction, acceptance correction and unfolding. A detector response can mix truth bins, so separate binwise efficiency corrections are not a universal unfolding method. Store statistical and systematic components with enough information to preserve their correlations, along with the ordering of entries. A list of total error bars cannot reconstruct a likelihood for arbitrary theory comparisons. If asymmetric uncertainties are reported, explain whether they are interval endpoints, likelihood changes or another convention.

For a linear conversion z equals A times y, covariance transforms with A on the left and its transpose on the right. Unit conversion therefore squares the numerical scale factor for variances and applies both factors to each covariance. The same rule propagates bin densities into an integrated cross section using bin widths as weights. Forgetting the off-diagonal terms can incorrectly make a common normalization uncertainty shrink when bins are added. Rounding should be delayed until after these operations.

For nonlinear transformations, a Jacobian gives a first-order approximation whose adequacy depends on uncertainty size and curvature. Exact distribution propagation or simulation may be needed near boundaries or for strongly asymmetric ratios. Retain enough numerical precision in machine-readable tables to reproduce the displayed result and avoid covariance matrices made non-positive by coarse rounding. Label whether an uncertainty is a standard deviation, a confidence interval or posterior content, and give the level and construction for intervals.

A useful analysis record links raw or accessible derived inputs to calibration versions, event-selection rules, transformations, fitted models and final numerical artifacts. It includes the source version, relevant configuration, software environment and random seeds when stochastic computations are used. Seeds alone do not guarantee identical execution across changed algorithms or numerical libraries. A content hash can identify the exact input bytes but cannot establish their physical correctness, provenance or permission for use without associated metadata.

Store tables in a documented machine-readable form and link them to figures, descriptions, units and immutable versions. HEPData provides a physics example of structured tables, auxiliary resources and versioned identifiers; its data-release practices illustrate why a citation should identify a particular record version. Independent reproduction should compare physical quantities and tolerances, not merely rerun one plotting command. An exactly reproduced mistake remains a mistake, so residual checks, calibration validation and independent arithmetic belong beside the provenance record rather than being replaced by it.