Appendix A — Case dossiers

One dossier per case: identity and provenance, the frozen coordinates under both item models, the case’s gallery, and the matched simulation cell where the case has one. Every field is read from the derived layer at render time; the dataset citation is reproduced verbatim from the frozen citations table. The gallery’s four panels are described once in Chapter 11 and in each figure’s caption.

A.1 C1 — Content-literacy reading comprehension assessment

Warehouse unit gilbert_meta_103 (characterized tier; catalogue status accepted_ambiguous_v1_1). Population: US third-grade students, online content-literacy intervention. 1,914 respondents in total, of whom 500 entered the analysis sample; 29 items; analysis seed 40505369. Identified from: Warehouse catalogue and the primary reference (Relyea et al. 2025 Reading Research Quarterly).

Dataset citation (verbatim from the frozen citations table). Relyea, J. E., Gilbert, J. B., Burkhauser, M., Scherer, E., Mosher, D. M., Wei, Z., … & Kim, J. S. (2025). Asset‐Based Implementation of Structured Adaptations in an Online Third‐Grade Content Literacy Intervention. Reading Research Quarterly, 60(4), e70048.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.860	0.861	skewed	2pl · 500 · 0.9 · skew_pos_strong
Rasch	0.840	0.847	skewed	rasch · 500 · 0.8 · skew_pos_strong

Under 2PL this row matches a simulation cell whose primary KS loss ratio is 0.51 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 2.08 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Under Rasch this row matches a simulation cell whose primary KS loss ratio is 0.72 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 1.92 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Figure A.1: C1 under the Rasch model: aggregate-only gallery for a withheld case. Person-level observed scores, posterior estimates, movement rows, and top-k membership are not distributed. Panel (c) shows the focused-DP posterior density and pointwise 95% band with the broad-DP mean; panel (d) shows the five released movement-quintile summaries. The case-cell aggregate prior-swap KS is 0.108 and the aggregate median absolute movement is 0.136 reference SD. These summaries preserve the published consequence claims without exposing a person row or a deterministic score proxy.

Figure A.2: C1 under the 2PL model: aggregate-only gallery for a withheld case. Person-level observed scores, posterior estimates, movement rows, and top-k membership are not distributed. Panel (c) shows the focused-DP posterior density and pointwise 95% band with the broad-DP mean; panel (d) shows the five released movement-quintile summaries. The case-cell aggregate prior-swap KS is 0.094 and the aggregate median absolute movement is 0.140 reference SD. These summaries preserve the published consequence claims without exposing a person row or a deterministic score proxy.

A.2 C2 — Vocabulary assessment from a content-literacy intervention

Warehouse unit gilbert_meta_100 (characterized tier; catalogue status accepted_core_v1). Population: School students in a cluster-randomized content-literacy intervention. 2,118 respondents in total, of whom 500 entered the analysis sample; 12 items; analysis seed 50516843. Identified from: Source publication: the single empirical example in Gilbert Domingue & Kim (2025) Psychological Methods.

Dataset citation (verbatim from the frozen citations table). Gilbert, J. B., Domingue, B. W., & Kim, J. S. (2025). Estimating causal effects on psychological networks using item response theory. Psychological Methods. Advance online publication. https://doi.org/10.1037/met0000764

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.730	0.792	skewed	2pl · 500 · 0.7 · skew_pos_strong
Rasch	0.764	0.493	skewed	rasch · 500 · 0.8 · skew_pos_strong

Under 2PL this row matches a simulation cell whose primary KS loss ratio is 0.53 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 2.24 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Under Rasch this row matches a simulation cell whose primary KS loss ratio is 0.72 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 1.92 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Figure A.3: C2 under the Rasch model: aggregate-only gallery for a withheld case. Person-level observed scores, posterior estimates, movement rows, and top-k membership are not distributed. Panel (c) shows the focused-DP posterior density and pointwise 95% band with the broad-DP mean; panel (d) shows the five released movement-quintile summaries. The case-cell aggregate prior-swap KS is 0.112 and the aggregate median absolute movement is 0.095 reference SD. These summaries preserve the published consequence claims without exposing a person row or a deterministic score proxy.

Figure A.4: C2 under the 2PL model: aggregate-only gallery for a withheld case. Person-level observed scores, posterior estimates, movement rows, and top-k membership are not distributed. Panel (c) shows the focused-DP posterior density and pointwise 95% band with the broad-DP mean; panel (d) shows the five released movement-quintile summaries. The case-cell aggregate prior-swap KS is 0.072 and the aggregate median absolute movement is 0.078 reference SD. These summaries preserve the published consequence claims without exposing a person row or a deterministic score proxy.

A.3 C3 — Inductive Reasoning Developmental Test (IRDT/TDRI) 3rd version

Warehouse unit tdri (characterized tier; catalogue status accepted_core_v1). Population: Brazilian respondents, mixed ages. 1,803 respondents in total, of whom 500 entered the analysis sample; 56 items; analysis seed 248186030. Identified from: Warehouse catalogue and the primary reference (Golino & Gomes 2015).

Dataset citation (verbatim from the frozen citations table). Golino, H. F., & Gomes, C. M. (2015). Investigando estágios de desenvolvimento do raciocínio indutivo usando a análise fatorial confimatória, o Modelo Logístico Simples de Rasch e o modelo de teste logístico linear (Rasch Estendido). In H. F. Golino, C. M. Gomes, A. Amantes, & G. Coelho, Psicometria Contemporânea: Compreendendo os Modelos Rasch (pp. 283-331). São Paulo: Casa do Psicólogo/Pearson.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.933	0.949	skewed	2pl · 500 · 0.9 · skew_pos_strong
Rasch	0.946	0.535	bimodal	rasch · 500 · 0.9 · bimodal_strong

Under 2PL this row matches a simulation cell whose primary KS loss ratio is 0.51 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 2.08 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Under Rasch this row matches a simulation cell whose primary KS loss ratio is 0.48 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 2.27 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Figure A.5: C3 under the Rasch model: Inductive reasoning, reliability 0.95, shape class Bimodal. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.102. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

Figure A.6: C3 under the 2PL model: Inductive reasoning, reliability 0.93, shape class Skewed. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.164. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

A.4 C4 — Vocabulary check-list

Warehouse unit gcbs_brotherton_2013_vcl (characterized tier; catalogue status accepted_ambiguous_v1_1). Population: Adults, internet sample administered alongside the Generic Conspiracist Beliefs Scale study. 2,495 respondents in total, of whom 500 entered the analysis sample; 16 items; analysis seed 81770971. Identified from: Warehouse catalogue; slug suffix vcl denotes the vocabulary check-list rather than the conspiracist-beliefs scale.

Dataset citation (verbatim from the frozen citations table). Brotherton, R., French, C. C., & Pickering, A. D. (2013). Measuring belief in conspiracy theories: The generic conspiracist beliefs scale. Frontiers in psychology, 4, 279.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.261	0.778	skewed	no match
Rasch	0.772	0.296	bimodal	rasch · 500 · 0.8 · bimodal_strong

Under Rasch this row matches a simulation cell whose primary KS loss ratio is 0.48 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 2.54 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Figure A.7: C4 under the Rasch model: Vocabulary checklist, reliability 0.77, shape class Bimodal. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.190. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

Figure A.8: C4 under the 2PL model: Vocabulary checklist, reliability 0.26, shape class Skewed. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.106. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

A.5 C5 — PIRLS reading extract

Warehouse unit pirlsmissing_sirt (characterized tier; catalogue status accepted_no_primary_v1_1). Population: Fourth-grade students, international assessment. 3,480 respondents in total, of whom 500 entered the analysis sample; 35 items; analysis seed 255968925. Identified from: Warehouse catalogue.

Dataset citation (verbatim from the frozen citations table). Robitzsch A (2022). sirt: Supplementary Item Response Theory Models. R package version 3.12-66, https://CRAN.R-project.org/package=sirt.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.878	0.884	normal	2pl · 500 · 0.9 · normal
Rasch	0.868	0.814	normal	rasch · 500 · 0.9 · normal

Under 2PL this row matches a simulation cell whose primary KS loss ratio is 1.01 (harm flag); in that cell the simulated distribution-goal winner is Gaussian + GR and the individual-score winner Gaussian + PM, and Gaussian + PM carries 1.36 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Under Rasch this row matches a simulation cell whose primary KS loss ratio is 1.03 (harm flag); in that cell the simulated distribution-goal winner is Gaussian + GR and the individual-score winner Gaussian + PM, and Gaussian + PM carries 1.54 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Figure A.9: C5 under the Rasch model: PIRLS reading, reliability 0.87, shape class Normal-consistent. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.048. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

Figure A.10: C5 under the 2PL model: PIRLS reading, reliability 0.88, shape class Normal-consistent. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.026. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

A.6 C6 — NAEP extract

Warehouse unit naep_multilcirt (characterized tier; catalogue status accepted_no_primary_v1_1). Population: US students, national assessment. 1,510 respondents in total, of whom 500 entered the analysis sample; 12 items; analysis seed 46209811. Identified from: Warehouse catalogue.

Dataset citation (verbatim from the frozen citations table). Bartolucci, F., Bacci, S. and Gnaldi, M. (2014), MultiLCIRT: An R package for multidimensional latent class item response models, Computational Statistics and Data Analysis, 71, 971-985.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.709	0.724	normal	2pl · 500 · 0.7 · normal
Rasch	0.703	0.607	normal	rasch · 500 · 0.7 · normal

Under 2PL this row matches a simulation cell whose primary KS loss ratio is 0.99 (harm flag); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner Gaussian + PM, and Gaussian + PM carries 1.59 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Under Rasch this row matches a simulation cell whose primary KS loss ratio is 1.04 (harm flag); in that cell the simulated distribution-goal winner is Gaussian + GR and the individual-score winner Gaussian + PM, and Gaussian + PM carries 2.36 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Figure A.11: C6 under the Rasch model: NAEP extract, reliability 0.70, shape class Normal-consistent. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.140. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

Figure A.12: C6 under the 2PL model: NAEP extract, reliability 0.71, shape class Normal-consistent. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.036. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

A.7 C7 — ENEM 2013 mathematics section

Warehouse unit enem_2013_1mil_mt (characterized tier; catalogue status provisional_grade_b). Population: Brazilian secondary-school leavers, national examination. 999,822 respondents in total, of whom 500 entered the analysis sample; 45 items; analysis seed 219125270. Identified from: Warehouse build record: official INEP ENEM 2013 archive; slug suffix mt denotes matematica; 45 items.

Dataset citation (verbatim from the frozen citations table). Derived RDS built from the official ENEM 2013 INEP zip via enem_2013.R; rows=44991990, unique_ids=999822, unique_items=45, sample_rule=1e6_fixed_seed.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.844	0.785	skewed	2pl · 500 · 0.8 · skew_pos_strong
Rasch	0.657	0.957	skewed	rasch · 500 · 0.7 · skew_pos_strong

Under 2PL this row matches a simulation cell whose primary KS loss ratio is 0.48 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 2.40 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Under Rasch this row matches a simulation cell whose primary KS loss ratio is 0.70 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 2.41 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Figure A.13: C7 under the Rasch model: aggregate-only gallery for a withheld case. Person-level observed scores, posterior estimates, movement rows, and top-k membership are not distributed. Panel (c) shows the focused-DP posterior density and pointwise 95% band with the broad-DP mean; panel (d) shows the five released movement-quintile summaries. The case-cell aggregate prior-swap KS is 0.130 and the aggregate median absolute movement is 0.155 reference SD. These summaries preserve the published consequence claims without exposing a person row or a deterministic score proxy.

Figure A.14: C7 under the 2PL model: aggregate-only gallery for a withheld case. Person-level observed scores, posterior estimates, movement rows, and top-k membership are not distributed. Panel (c) shows the focused-DP posterior density and pointwise 95% band with the broad-DP mean; panel (d) shows the five released movement-quintile summaries. The case-cell aggregate prior-swap KS is 0.088 and the aggregate median absolute movement is 0.143 reference SD. These summaries preserve the published consequence claims without exposing a person row or a deterministic score proxy.

A.8 C8 — Millon Clinical Multiaxial Inventory extract

Warehouse unit mcmi_mokken (transitional tier; catalogue status accepted_no_primary_v1_1). Population: Dutch clinical sample, adults. 1,208 respondents in total, of whom 500 entered the analysis sample; 44 items; analysis seed 11872871. Identified from: Warehouse catalogue.

Dataset citation (verbatim from the frozen citations table). Rossi, G., Elklit, A., & Simonsen, E. (2010). Empirical evidence for a four factor framework of personality disorder organization: multigroup confirmatory factor analysis of the millon clinical multiaxial inventory—III personality disorder scales across belgian and danish data samples. Journal of Personality Disorders, 24(1), 128-150.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.868	0.929	skewed	2pl · 500 · 0.9 · skew_pos_strong
Rasch	0.876	0.701	bimodal	rasch · 500 · 0.9 · bimodal_strong

Under 2PL this row matches a simulation cell whose primary KS loss ratio is 0.51 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 2.08 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Under Rasch this row matches a simulation cell whose primary KS loss ratio is 0.48 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 2.27 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Figure A.15: C8 under the Rasch model: MCMI clinical, reliability 0.88, shape class Bimodal. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.056. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

Figure A.16: C8 under the 2PL model: MCMI clinical, reliability 0.87, shape class Skewed. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.054. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

A.9 C9 — Fraction subtraction test

Warehouse unit frac20 (transitional tier; catalogue status accepted_legacy_v1_1). Population: Students, cognitive-diagnosis benchmark dataset. 536 respondents in total, of whom 500 entered the analysis sample; 20 items; analysis seed 119838441. Identified from: Warehouse catalogue.

Dataset citation (verbatim from the frozen citations table). Tatsuoka, C. (2002). Data analytic methods for latent partially ordered classification models. Journal of the Royal Statistical Society: Series C (Applied Statistics), 51(3), 337-350.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.731	0.890	bimodal	2pl · 500 · 0.7 · bimodal_strong
Rasch	0.899	0.396	non-normal (unclassified)	no match

Under 2PL this row matches a simulation cell whose primary KS loss ratio is 0.71 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 1.62 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Figure A.17: C9 under the Rasch model: Fraction subtraction, reliability 0.90, shape class Non-normal, unclassified. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.094. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

Figure A.18: C9 under the 2PL model: Fraction subtraction, reliability 0.73, shape class Bimodal. (a) Observed proportion correct over the 500 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.076. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

A.10 C10 — Verbal aggression questionnaire

Warehouse unit verbagg (as-found tier; catalogue status accepted_core_v1). Population: Adults, questionnaire study. 316 respondents in total, of whom 316 entered the analysis sample; 24 items; analysis seed 253062181. Identified from: Warehouse catalogue.

Dataset citation (verbatim from the frozen citations table). De Boeck and Wilson (2004), Explanatory Item Response Models, Springer.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.849	0.874	bimodal	2pl · 200 · 0.8 · bimodal_strong
Rasch	0.847	0.683	bimodal	rasch · 200 · 0.8 · bimodal_strong

Under 2PL this row matches a simulation cell whose primary KS loss ratio is 0.73 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + CB and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 1.47 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Under Rasch this row matches a simulation cell whose primary KS loss ratio is 0.76 (strong win); in that cell the simulated distribution-goal winner is DP (focused) + GR and the individual-score winner DP (focused) + PM, and Gaussian + PM carries 1.57 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Figure A.19: C10 under the Rasch model: Verbal aggression, reliability 0.85, shape class Bimodal. (a) Observed proportion correct over the 316 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.073. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

Figure A.20: C10 under the 2PL model: Verbal aggression, reliability 0.85, shape class Bimodal. (a) Observed proportion correct over the 316 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.051. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

A.11 C11 — Story recall task 3 (prose recall scored by detail)

Warehouse unit idcr_martinez_2023_story_recall_3 (as-found tier; catalogue status provisional_grade_b). Population: Adults, Automating and Improving Memory Measurement (AIMM) project at UMD. 235 respondents in total, of whom 235 entered the analysis sample; 32 items; analysis seed 204253420. Identified from: Dataset documentation shipped with the unit: project Read Me and Story Rubric.

Dataset citation (verbatim from the frozen citations table). Derived RDS built from Story Recall 3_itemLevel.csv via idcr_martinez_2023.r; rows=7150, unique_items=32, shared_support_docs=3.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.893	0.893	undetermined	no match
Rasch	0.889	0.653	undetermined	no match

No matched simulation cell is available for this case, so no simulation verdict is transferred to it.

Figure A.21: C11 under the Rasch model: aggregate-only gallery for a withheld case. Person-level observed scores, posterior estimates, movement rows, and top-k membership are not distributed. Panel (c) shows the focused-DP posterior density and pointwise 95% band with the broad-DP mean; panel (d) shows the five released movement-quintile summaries. The case-cell aggregate prior-swap KS is 0.051 and the aggregate median absolute movement is 0.024 reference SD. These summaries preserve the published consequence claims without exposing a person row or a deterministic score proxy.

Figure A.22: C11 under the 2PL model: aggregate-only gallery for a withheld case. Person-level observed scores, posterior estimates, movement rows, and top-k membership are not distributed. Panel (c) shows the focused-DP posterior density and pointwise 95% band with the broad-DP mean; panel (d) shows the five released movement-quintile summaries. The case-cell aggregate prior-swap KS is 0.021 and the aggregate median absolute movement is 0.016 reference SD. These summaries preserve the published consequence claims without exposing a person row or a deterministic score proxy.

A.12 C12 — ZAREKI neuropsychological battery for number processing

Warehouse unit mpsycho_zareki (as-found tier; catalogue status accepted_no_primary_v1_1). Population: Children, clinical neuropsychological assessment. 341 respondents in total, of whom 341 entered the analysis sample; 16 items; analysis seed 153125947. Identified from: Warehouse catalogue.

Dataset citation (verbatim from the frozen citations table). Koller, I., & Alexandrowicz, R. W. (2010) Eine psychometrische Analyse der ZAREKI-R mittels Rasch-Modellen [A psychometric analysis of the ZAREKI-R using Rasch-models]. Diagnostica 56, 57-67.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.561	0.730	undetermined	no match
Rasch	0.425	0.516	bimodal	no match

No matched simulation cell is available for this case, so no simulation verdict is transferred to it.

Figure A.23: C12 under the Rasch model: ZAREKI numerical, reliability 0.42, shape class Bimodal. (a) Observed proportion correct over the 341 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.120. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

Figure A.24: C12 under the 2PL model: ZAREKI numerical, reliability 0.56, shape class Undetermined. (a) Observed proportion correct over the 341 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.144. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

A.13 C13 — Work Design Questionnaire (R package authors survey)

Warehouse unit mpsycho_rwdq (transitional tier; catalogue status accepted_no_primary_v1_1). Population: Adults, R package authors. 1,055 respondents in total, of whom 497 entered the analysis sample; 18 items; analysis seed 261421130. Identified from: Warehouse catalogue.

Dataset citation (verbatim from the frozen citations table). Mair, P., Hofmann, E., Gruber, K., Zeileis, A., & Hornik, K. (2015) Motivation, values, and work design as drivers of participation in the R open source Project for Statistical Computing. Proceedings of the National Academy of Sciences of the United States of America, 112(48), 14788-14792.

Model	rho-bar	marginal_rxx	Shape class	Matched simulation cell
2PL	0.654	0.706	undetermined	no match
Rasch	0.651	0.706	normal	rasch · 500 · 0.7 · normal

Under Rasch this row matches a simulation cell whose primary KS loss ratio is 1.04 (harm flag); in that cell the simulated distribution-goal winner is Gaussian + GR and the individual-score winner Gaussian + PM, and Gaussian + PM carries 2.36 times the selected winner’s distributional loss. The verdict is the simulation’s, read at this row’s coordinates.

Figure A.25: C13 under the Rasch model: Work design, reliability 0.65, shape class Normal-consistent. (a) Observed proportion correct over the 497 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.121. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.

Figure A.26: C13 under the 2PL model: Work design, reliability 0.65, shape class Undetermined. (a) Observed proportion correct over the 497 fitted respondents. (b) Empirical distribution functions of all nine reported estimate sets (color: prior; line type: PM solid, CB dashed, GR dotted), shown over the full observed estimate range. (c) Posterior- mean latent density of the focused DP arm with pointwise 95% band (orange), the broad DP arm (green, dashed) and, as an interpretive overlay rather than a like-for-like estimator, the normal implied by the Gaussian arm’s PM ensemble (blue). (d) Per-respondent movement of the PM score under the prior swap against the default score, with baseline-quintile medians (orange); dashed lines at ±0.10 SD. Between-prior KS on the PM ensembles: 0.060. The shape class shown is the standardized one and is of record; a class name is printed only where the standardized screen returned one. Every panel here is a consequence display: it shows what the choice does to this dataset’s report and not which report is closer to the truth, a question only the matched simulation cells of Part V can address. Frozen run store, seed A.