Figure 1. Absolute calibration at matched true information.
Mean estimation error (estimate minus known mutual information) for raw KSG with k = 4, permutation-centred KSG with k = 4, and analytically corrected Gaussian-copula estimates. Solid and dashed lines denote true total information of 0.10 and 0.40 nats, respectively. Each point summarises 200 independently generated parent catalogues; bars are two-sided 95% Student-t Monte Carlo intervals for the mean error. Prefixes within a parent are nested. The Gaussian log-determinant correction is not asserted to be exact after rank transformation. Panel axes are labelled separately. The corresponding full results for all eleven estimator variants appear in the reproducibility tables.

Figure 2. Comparisons between independent samples with equal true information.
Mean error in the estimated information difference, (estimate_B - estimate_A) - (I_B - I_A), for centred KSG with k = 4. The true difference is zero. Baseline estimates use the sample sizes shown on the horizontal axis. The common-size procedure uses N = 78 on both sides, averaging five independently selected, potentially overlapping subsets when a source sample has N = 500; baseline estimates are reused at N = 78. Solid and dashed lines denote common information of 0.10 and 0.40 nats. Bars show 95% Student-t Monte Carlo intervals over 200 independently generated A/B parent pairs. Each pair is reused in the prespecified size comparisons, so separate points are not independent replications. Root-mean-square errors and individual-comparison ordering probabilities are reported separately.

Figure 3. Cumulative profiles under constant generating information.
Mean estimation error across nested prefixes of the same parent catalogue, for raw KSG with k = 4, centred KSG with k = 4, and the centred common-size procedure. All prefixes have the same population distribution and true mutual information. Solid and dashed lines denote truth of 0.10 and 0.40 nats. Each curve summarises 200 independent parent catalogues. The common-size procedure averages five subsets of 78 rows at each prefix above 78. Profile assessment uses whole-catalogue bootstrap intervals for the endpoint difference and range of the mean profile, supplied in the full results table; individual prefixes are never resampled independently. A flat mean profile does not establish accurate absolute information estimates.

Figure 4. Comparisons across dependence geometries at equal information and block dimensions.
Mean difference errors for centred KSG with k = 4 when independent stream-A catalogues from L3 are compared with stream-B catalogues from T3, and when Q1x is compared with Q3. Both sides have block dimensions (4,3), with equal total mutual information as indicated. T3 is an invertible within-block deformation of L3. Q1x and Q3 distribute the information across one and three active pairs, respectively. Baseline and common-N = 78 procedures are defined as in Figure 2. Bars show 95% Student-t Monte Carlo intervals across 200 independent parent pairs. Equal true information is not assumed to imply equal estimator bias across different joint distributions.

Supplementary Figure S1. Prespecified nearest-neighbour sensitivity.
Mean estimation error for permutation-centred KSG at k = 3, 4, 5 and 8, using the same datasets and permutation sequences. Solid and dashed lines denote true information of 0.10 and 0.40 nats. Each point is the mean of 200 independent parent catalogues. These k values were fixed before the main study; no k is selected from its reported performance. Full scalar and profile uncertainty results are included in the accompanying tables.

Reserved-geometry figures.
The reserved H1/H3 versions of Figures 1–3 and S1 use the same definitions and fixed procedures. They are generated from the reserved stage after the development-stage interpretation has been recorded. They assess extension to the absolute-value dependence family, not universal validity for nonlinear dependence.

Table field definitions.
calibration.csv: mean, SD, MCSE, confidence limits and RMSE refer to replicate estimation errors, not raw estimates; mean_estimate is supplied separately. profiles.csv: endpoint is the difference between the last and first mean errors; mean_profile_range is the maximum minus minimum mean error across prefixes. comparisons.csv: mean, SD, MCSE, confidence limits and RMSE refer to errors in estimated between-sample differences. p_b_gt_a is descriptive; correct_order_probability is not defined when the true informations are equal. Ratio summaries retain only positive estimates on both sides and always provide the excluded fraction. P1_paired_changes.csv: a signed mean-error change is not itself evidence of improvement; a negative paired MSE change means lower MSE for P1. B500_paired_changes.csv: mean is the paired signed change from B100 to B500, with absolute changes reported separately. Every interval describes Monte Carlo uncertainty for its stated unit, with no familywise guarantee over the full experiment grid.
