Default simultaneous bands

This study measures the default simultaneous band of 25 shipped fit shapes. TMLE and LTMLE default to simultaneous=True. A fit that reports two or more inferential estimates then publishes a max-t multiplier band over all of them. The simultaneous bands section of the inference reference defines the band and lists the other registered studies that measure it.

Each shape is the subject fit of one registered source study. This study refits it with simultaneous=True and changes nothing else. The law, the sampler, the truth oracle, the sample size and the fit function are the source study’s own. The samples are this study’s own: it draws each replication through the source study’s sampler at a seed this study owns.

No canonical implementation is compared. The pinned comparators publish no multiplier band over these families. The zero-row equivalence artifact records the absence of a comparator.

What was tested

setting	declaration
band	the shipped default: 1000 Rademacher draws on the point path and 2000 on the sequential path, seeded by the subject fit’s random_state, over every estimate the fit reports. A ratio band is exponentiated from the log scale
band cell	<shape>__simultaneous_band. Each replication is covered when every truth lies inside the band. The 99% exact interval of the joint coverage must lie inside \([0.92, 0.98]\)
control cell	<shape>__pointwise_joint_control. The same fits, read with their pointwise 95% intervals jointly. The 99% upper endpoint of the joint coverage must lie below 0.95, which shows that the band’s critical value does work
budget	2,400 replications for each shape, and 4,000 for longitudinal_msm. tests/unit/test_simultaneous_cell_design.py computes the control’s power from the family’s correlation before any run, and requires at least 0.99
primary scenario	default_fit: TMLE() with two main-terms logistic learners and random_state=0, and every other argument at its default, on the binary law of the ordinary point-treatment study. Ten-fold pooled cross-fitting, the default binary estimands, \(n = 1000\), 1,000 replications
Monte Carlo inference	exact 99% intervals around every coverage rate, and 99% intervals around every primary endpoint

The table gives each shape, its source study and its size.

shape	source study	what the shape adds	n
default_fit	this study’s primary scenario	the shipped TMLE() defaults	1,000
ordinary_binary	ordinary point-treatment TMLE	ten estimands, with log-scale ratio bands and the PAF	1,000
fold_evaluated	fold-evaluated CV-TMLE	a cross-validated variance beside centered multiplier draws	1,000
weighted	weighted point-treatment TMLE	fixed observation weights and ratios	2,000
learned_weighted	learned weighted point-treatment TMLE	weighted nuisances and a linear fluctuation	2,000
missing_outcome	missing-outcome TMLE	a missing outcome	2,000
missing_outcome_drtmle	missing-outcome DR-TMLE	DR-TMLE with a missing outcome	2,000
drtmle	DR-TMLE for binary complete data	cross-fitted DR-TMLE corrected curves	3,000
multi_arm_drtmle	multi-arm DR-TMLE	nine multi-arm parameters with ratios	2,000
cde_z0, cde_z1	controlled direct-effect TMLE	one band for each intermediate level	2,000
point_msm	point-treatment MSM	three MSM projection terms	2,000
clustered	clustered CV-TMLE	grouped folds and multipliers drawn by cluster	2,000
shift_grid	continuous modified treatment policies	three shifts and two contrasts	2,000
incremental_grid	incremental interventions	three odds multipliers and two contrasts	2,000
stochastic_regimes	known stochastic regimes	a static and a stochastic regime	2,000
deterministic_regimes	deterministic regimes	a static regime and a dynamic rule	2,000
ltmle_crossfit	cross-fitted end-of-study LTMLE	five cross-fitted regimen parameters	2,000
survival_crossfit	cross-fitted survival-curve LTMLE	ten parameters with two exact duplicate pairs	2,000
competing_crossfit	cross-fitted competing-risk LTMLE	twenty parameters with four exact duplicates	4,000
weighted_ltmle	weighted end-of-study LTMLE	observation weights	2,000
weighted_ltmle_crossfit	cross-fitted weighted end-of-study LTMLE	observation weights, cross-fitted	2,000
categorical_ltmle	categorical LTMLE	five categorical regimens	2,000
categorical_ltmle_crossfit	cross-fitted categorical LTMLE	the same, cross-fitted	2,000
longitudinal_msm	longitudinal MSM	two MSM projection terms	2,500

A duplicate is a parameter that equals another one exactly, because the two plans agree at node one. The band covers it twice. The truth of a duplicate is the truth of its twin.

Accuracy against known truth

law	estimand	what was tested	implementation	bias (99% interval)	coverage	SE ratio	result
binary-outcome law, fitted with the shipped TMLE() defaults	atc	average effect on the untreated	cleverly shipped TMLE() default fit	-0.0032 to 0.0020	0.9610	0.9813	pass
binary-outcome law, fitted with the shipped TMLE() defaults	ate	average treatment effect	cleverly shipped TMLE() default fit	-0.0031 to 0.0019	0.9600	0.9812	pass
binary-outcome law, fitted with the shipped TMLE() defaults	att	average effect on the treated	cleverly shipped TMLE() default fit	-0.0032 to 0.0020	0.9590	0.9809	pass
binary-outcome law, fitted with the shipped TMLE() defaults	ey0	counterfactual mean under no treatment	cleverly shipped TMLE() default fit	-0.0020 to 0.0018	0.9400	0.9564	pass
binary-outcome law, fitted with the shipped TMLE() defaults	ey1	counterfactual mean under treatment	cleverly shipped TMLE() default fit	-0.0026 to 0.0011	0.9380	0.9916	pass
binary-outcome law, fitted with the shipped TMLE() defaults	or	marginal odds ratio, reported on the log scale	cleverly shipped TMLE() default fit	-0.0111 to 0.0098	0.9580	0.9807	pass
binary-outcome law, fitted with the shipped TMLE() defaults	rr	marginal risk ratio, reported on the log scale	cleverly shipped TMLE() default fit	-0.0056 to 0.0059	0.9520	0.9761	pass

Theory properties

property	cell	role	what was tested	what must hold	measured	result
simultaneous_coverage	categorical_ltmle__pointwise_joint_control	control	five categorical regimen means and four contrasts: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.6579 to 0.7072	pass
simultaneous_coverage	categorical_ltmle__simultaneous_band	positive	five categorical regimen means and four contrasts: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9101 to 0.9382	fail
simultaneous_coverage	categorical_ltmle_crossfit__pointwise_joint_control	control	five cross-fitted categorical regimen means and four contrasts: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.6864 to 0.7344	pass
simultaneous_coverage	categorical_ltmle_crossfit__simultaneous_band	positive	five cross-fitted categorical regimen means and four contrasts: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9173 to 0.9443	fail
simultaneous_coverage	cde_z0__pointwise_joint_control	control	the controlled direct-effect fit at intermediate level zero: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8260 to 0.8643	pass
simultaneous_coverage	cde_z0__simultaneous_band	positive	the controlled direct-effect fit at intermediate level zero: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9015 to 0.9309	fail
simultaneous_coverage	cde_z1__pointwise_joint_control	control	the controlled direct-effect fit at intermediate level one: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8452 to 0.8817	pass
simultaneous_coverage	cde_z1__simultaneous_band	positive	the controlled direct-effect fit at intermediate level one: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9228 to 0.9488	pass
simultaneous_coverage	clustered__pointwise_joint_control	control	grouped cross-fitted TMLE with cluster multipliers: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8611 to 0.8957	pass
simultaneous_coverage	clustered__simultaneous_band	positive	grouped cross-fitted TMLE with cluster multipliers: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9241 to 0.9499	pass
simultaneous_coverage	competing_crossfit__pointwise_joint_control	control	cross-fitted cumulative incidence of two causes, three plans, two horizons: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.6063 to 0.6574	pass
simultaneous_coverage	competing_crossfit__simultaneous_band	positive	cross-fitted cumulative incidence of two causes, three plans, two horizons: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9232 to 0.9492	pass
simultaneous_coverage	default_fit__pointwise_joint_control	control	the shipped TMLE() defaults on the binary law: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8408 to 0.8777	pass
simultaneous_coverage	default_fit__simultaneous_band	positive	the shipped TMLE() defaults on the binary law: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9365 to 0.9600	pass
simultaneous_coverage	deterministic_regimes__pointwise_joint_control	control	a static regime and a dynamic rule and their contrast: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8523 to 0.8879	pass
simultaneous_coverage	deterministic_regimes__simultaneous_band	positive	a static regime and a dynamic rule and their contrast: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9301 to 0.9548	pass
simultaneous_coverage	drtmle__pointwise_joint_control	control	cross-fitted DR-TMLE over the arm means and the ATE: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8743 to 0.9074	pass
simultaneous_coverage	drtmle__simultaneous_band	positive	cross-fitted DR-TMLE over the arm means and the ATE: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9467 to 0.9681	pass
simultaneous_coverage	fold_evaluated__pointwise_joint_control	control	fold-evaluated CV-TMLE over five estimands: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8461 to 0.8824	pass
simultaneous_coverage	fold_evaluated__simultaneous_band	positive	fold-evaluated CV-TMLE over five estimands: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9411 to 0.9637	pass
simultaneous_coverage	incremental_grid__pointwise_joint_control	control	three incremental odds multipliers and their two contrasts: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8518 to 0.8875	pass
simultaneous_coverage	incremental_grid__simultaneous_band	positive	three incremental odds multipliers and their two contrasts: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9351 to 0.9589	pass
simultaneous_coverage	learned_weighted__pointwise_joint_control	control	weighted point-treatment TMLE with learned nuisances: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8730 to 0.9063	pass
simultaneous_coverage	learned_weighted__simultaneous_band	positive	weighted point-treatment TMLE with learned nuisances: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9443 to 0.9663	pass
simultaneous_coverage	longitudinal_msm__pointwise_joint_control	control	the two terms of the longitudinal MSM projection: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.9038 to 0.9267	pass
simultaneous_coverage	longitudinal_msm__simultaneous_band	positive	the two terms of the longitudinal MSM projection: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9337 to 0.9527	pass
simultaneous_coverage	ltmle_crossfit__pointwise_joint_control	control	cross-fitted end-of-study regimen means and contrasts: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8007 to 0.8413	pass
simultaneous_coverage	ltmle_crossfit__simultaneous_band	positive	cross-fitted end-of-study regimen means and contrasts: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9260 to 0.9514	pass
simultaneous_coverage	missing_outcome__pointwise_joint_control	control	missing-outcome TMLE over the arm means and the ATE: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8553 to 0.8907	pass
simultaneous_coverage	missing_outcome__simultaneous_band	positive	missing-outcome TMLE over the arm means and the ATE: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9232 to 0.9492	pass
simultaneous_coverage	missing_outcome_drtmle__pointwise_joint_control	control	missing-outcome DR-TMLE over the arm means and the ATE: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8672 to 0.9012	pass
simultaneous_coverage	missing_outcome_drtmle__simultaneous_band	positive	missing-outcome DR-TMLE over the arm means and the ATE: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9328 to 0.9570	pass
simultaneous_coverage	multi_arm_drtmle__pointwise_joint_control	control	multi-arm DR-TMLE over nine parameters: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.7860 to 0.8278	pass
simultaneous_coverage	multi_arm_drtmle__simultaneous_band	positive	multi-arm DR-TMLE over nine parameters: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9273 to 0.9526	pass
simultaneous_coverage	ordinary_binary__pointwise_joint_control	control	ordinary in-sample TMLE over ten binary-outcome estimands: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8181 to 0.8572	pass
simultaneous_coverage	ordinary_binary__simultaneous_band	positive	ordinary in-sample TMLE over ten binary-outcome estimands: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9383 to 0.9615	pass
simultaneous_coverage	point_msm__pointwise_joint_control	control	the three terms of the point-treatment MSM projection: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8646 to 0.8989	pass
simultaneous_coverage	point_msm__simultaneous_band	positive	the three terms of the point-treatment MSM projection: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9278 to 0.9529	pass
simultaneous_coverage	shift_grid__pointwise_joint_control	control	three shift policies and their two contrasts: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8316 to 0.8695	pass
simultaneous_coverage	shift_grid__simultaneous_band	positive	three shift policies and their two contrasts: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9346 to 0.9585	pass
simultaneous_coverage	stochastic_regimes__pointwise_joint_control	control	a static and a known stochastic regime and their contrast: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8642 to 0.8985	pass
simultaneous_coverage	stochastic_regimes__simultaneous_band	positive	a static and a known stochastic regime and their contrast: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9388 to 0.9619	pass
simultaneous_coverage	survival_crossfit__pointwise_joint_control	control	the cross-fitted survival curve of three plans at two horizons: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.7407 to 0.7857	pass
simultaneous_coverage	survival_crossfit__simultaneous_band	positive	the cross-fitted survival curve of three plans at two horizons: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9223 to 0.9484	pass
simultaneous_coverage	weighted__pointwise_joint_control	control	weighted point-treatment TMLE over five estimands: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8545 to 0.8899	pass
simultaneous_coverage	weighted__simultaneous_band	positive	weighted point-treatment TMLE over five estimands: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9328 to 0.9570	pass
simultaneous_coverage	weighted_ltmle__pointwise_joint_control	control	weighted end-of-study regimen means and contrasts: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8037 to 0.8441	pass
simultaneous_coverage	weighted_ltmle__simultaneous_band	positive	weighted end-of-study regimen means and contrasts: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9278 to 0.9529	pass
simultaneous_coverage	weighted_ltmle_crossfit__pointwise_joint_control	control	cross-fitted weighted end-of-study regimen means and contrasts: the pointwise 95% intervals of the same fits, read jointly	joint coverage upper endpoint must fall below the nominal rate	joint coverage 0.8150 to 0.8544	pass
simultaneous_coverage	weighted_ltmle_crossfit__simultaneous_band	positive	cross-fitted weighted end-of-study regimen means and contrasts: the max-t multiplier band over every estimand the law reports, from the same-row centered influence curves	joint coverage interval inside the calibration coverage band	joint coverage 0.9269 to 0.9522	pass

Result

Every primary test passed, and every pointwise control fell below 0.95, so each band’s critical value does work. The bands of 22 of the 25 shapes kept their joint-coverage interval inside \([0.92, 0.98]\). The study publishes under the reporting policy, and three bands are red. band-finite-sample owns them in the red-cell ledger.

shape	band coverage	package critical value	oracle band coverage	source pointwise calibration
categorical_ltmle	0.9250	2.680	0.9267 at 2.689	static contrast 0.939
categorical_ltmle_crossfit	0.9317	2.680	0.9325 at 2.689	static contrast 0.946
cde_z0	0.9171	2.312	0.9200 at 2.331	0.942 at Z = 0

The declared diagnostic read each red cell’s rows again at the design critical value, which tests/unit/test_simultaneous_cell_design.py computes. The oracle band also covers below the band edge or at it, so the multiplier is not the main cause. The package critical value averages a little below the design one, and that gap accounts for at most 0.0029 of each coverage. Each source study’s pointwise calibration of the same parameters sits near the lower edge of its own band. The reading is finite-sample, so the default band stays on. tests/unit/test_band_shortfall_reading.py rebuilds every number in the table from the committed rows.

The design critical value of a shape comes from the package’s own influence curves, averaged over the design fits. It is independent of the multiplier draws but not of the curves, so it cannot detect a defect in a curve. The source studies’ pointwise calibration cells are the evidence for the curves.

The first declared run stopped before any joint verdict. One sample of the multi_arm_drtmle shape activated the propensity bound, and the source study’s fit raises on that, because that study publishes bound_active as false for every replication. The band does not depend on that claim, so this study turns the check off and keeps the replication as drawn. A one-off refit of all 2,400 replications found one with an active bound, replication 1862, where one propensity entry reached the bound. A second run ran out of memory at 16 workers, and the published run used 8.

Measured values

Names beginning margin: are thresholds declared before the run. Everything else is measured from the committed results and checked at the precision printed.

quantity	value	source
replicates	1000	primary replications
n	1000	observations per primary replication
independent_tests_total	7	primary tests against truth
independent_tests_passed	7	of those, passing
paired_tests_total	0	external comparisons declared
paired_tests_passed	0	external comparisons passing
property_cells_total	50	repeated-sampling property cells
property_cells_passed	47	cells whose own and family verdicts pass
max_standardized_bias	0.0320	largest absolute primary bias in empirical standard deviations
min_coverage	0.9380	lowest measured primary-study coverage
min_se_ratio_ci_lower	0.9081	lowest bootstrap primary SE-ratio endpoint
max_se_ratio_ci_upper	1.0569	highest bootstrap primary SE-ratio endpoint
properties[simultaneous_coverage/default_fit__simultaneous_band]:coverage	0.9492	joint coverage of the band of the shipped TMLE() default
properties[simultaneous_coverage/default_fit__pointwise_joint_control]:coverage	0.8600	joint coverage of its pointwise intervals
properties[simultaneous_coverage/categorical_ltmle__simultaneous_band]:coverage	0.9250	joint coverage of the categorical LTMLE band
properties[simultaneous_coverage/categorical_ltmle__simultaneous_band]:coverage_ci_lower	0.9101	its 99% lower endpoint
properties[simultaneous_coverage/categorical_ltmle_crossfit__simultaneous_band]:coverage	0.9317	joint coverage of the cross-fitted categorical LTMLE band
properties[simultaneous_coverage/categorical_ltmle_crossfit__simultaneous_band]:coverage_ci_lower	0.9173	its 99% lower endpoint
properties[simultaneous_coverage/cde_z0__simultaneous_band]:coverage	0.9171	joint coverage of the controlled direct-effect band at Z = 0
properties[simultaneous_coverage/cde_z0__simultaneous_band]:coverage_ci_lower	0.9015	its 99% lower endpoint
properties[simultaneous_coverage/drtmle__simultaneous_band]:coverage	0.9583	the highest band coverage, cross-fitted DR-TMLE
properties[simultaneous_coverage/longitudinal_msm__pointwise_joint_control]:coverage	0.9157	the highest control coverage, two longitudinal MSM projection terms
properties[simultaneous_coverage/longitudinal_msm__pointwise_joint_control]:coverage_ci_upper	0.9267	its 99% upper endpoint
margin:confidence_level	0.9900	confidence level of every Monte Carlo interval
margin:alpha	0.0500	nominal size of the reported intervals
margin:nominal_coverage	0.9500	nominal coverage those intervals claim
margin:bootstrap_replicates	10000	resamples behind every bootstrap interval
margin:standardized_bias	0.2500	bias equivalence margin, in empirical standard deviations
margin:coverage_floor	0.9000	validity floor the coverage lower endpoint must clear
margin:over_coverage_ceiling	0.9900	above this, coverage is conservative rather than invalid
margin:se_ratio_sanity_lower	0.8000	SE-ratio screen, lower limit
margin:se_ratio_sanity_upper	1.2000	SE-ratio screen, upper limit
margin:calibration_se_ratio_lower	0.9300	calibration-cell SE-ratio band, lower limit
margin:calibration_se_ratio_upper	1.0700	calibration-cell SE-ratio band, upper limit
margin:calibration_coverage_lower	0.9200	calibration and joint-coverage band, lower limit
margin:calibration_coverage_upper	0.9800	calibration and joint-coverage band, upper limit
margin:type_i_ceiling	0.1000	largest supported type-I rate. No cell of this study reads it
margin:paired_difference	0.1500	paired similarity margin, in pooled empirical standard deviations
margin:rmse_noninferiority	1.1000	largest external-comparison RMSE ratio bound
margin:coverage_noninferiority	-0.0250	smallest external-comparison coverage difference bound
margin:calibration_noninferiority	0.0500	largest external-comparison calibration excess bound
margin:minimum_power	0.8000	rejection lower bound a power cell must clear. No cell of this study reads it
margin:root_n_slope	-0.5000	contraction rate root-n asymptotics predict. No cell of this study reads it
margin:root_n_slope_lower	-0.6250	accepted root-n slope band, lower limit
margin:root_n_slope_upper	-0.3750	accepted root-n slope band, upper limit
margin:excluded_slope	-0.2500	slower rate a root-n interval must exclude

Limitations

limitation	what it means for use
Each shape is measured at one law and one size	The band of another law, size or learner is not measured. Each source study page states the law
The band uses one multiplier seed for every replication	The shipped band seeds its draws with the fit’s random_state, and each source fit fixes it. The cells measure the band as it ships
No comparator	The pinned comparators publish no multiplier band over these families
The design correlations are estimates	The control’s power comes from the curve covariance averaged over ten fits at each shape’s size, or three for the four slowest shapes. The design test holds the power at the joint coverage plus 0.005

Reproduction

The fixture README gives the regeneration command. The manifest records the seeds, margins, shapes, source hashes, and result hashes.