Getting Started with multidesign • multidesign

Why multidesign?

In experimental research—particularly neuroimaging, psychophysics, and behavioral studies—data often has a specific structure that standard R data frames don’t capture well:

Observations (trials, time points, scans) arranged as rows in a matrix
Variables (brain regions, sensors, features) arranged as columns
Design metadata (condition, subject, run, block) describing each observation
Variable metadata (ROI name, hemisphere, sensor type) describing each column

Without a unified structure, you end up with separate objects for data and metadata that can easily get out of sync, manual bookkeeping for cross-validation splits, and difficulty handling multi-subject or multi-session experiments.

The multidesign package solves these problems by providing data structures that:

Keep data and metadata together — No more matching row indices between separate objects
Support design-aware operations — Split, subset, and summarize by experimental factors
Handle multi-block data naturally — Multiple subjects, sessions, or modalities
Provide built-in cross-validation — Proper stratification respecting your experimental design

Quick reference: When to use each class

Class	Use when…
`multidesign`	You have a single data matrix with row-wise design information and optional column metadata
`hyperdesign`	You have multiple related matrices (e.g., different subjects or sessions) that share design structure
`multiframe`	Your data is expensive to load and you want lazy evaluation (load on demand)
`multiblock`	You have stacked matrices sharing a row or column dimension (low-level operations)

Most users will start with multidesign and move to hyperdesign when working with multi-subject data.

A complete workflow

Let’s walk through a realistic analysis workflow using simulated neuroimaging-style data.

Step 1: Create your data

Imagine a simple experiment: 2 conditions (face vs. house), 10 subjects, 20 trials per condition per subject, measuring activity in 50 brain regions.

# Simulate data for one subject
n_trials <- 40
n_regions <- 50

# Create the data matrix (trials x brain regions)
X <- matrix(rnorm(n_trials * n_regions), n_trials, n_regions)

# Create the design information
# Each run has 10 trials: 5 face + 5 house
design_df <- tibble(
 condition = rep(rep(c("face", "house"), each = 5), 4),
 trial = 1:40,
 run = rep(1:4, each = 10)
)

# Create column metadata describing the brain regions
column_info <- tibble(
 region = paste0("ROI_", 1:n_regions),
 hemisphere = rep(c("left", "right"), 25),
 network = rep(c("visual", "frontal", "parietal", "temporal", "default"), 10)
)

Step 2: Build a multidesign

Combine your data matrix, design information, and column metadata into a single object:

mds <- multidesign(X, design_df, column_info)
mds
#> 
#> === Multidesign Object ===
#> 
#> Data Matrix: 
#>    40 observations x 50 variables 
#> 
#> Design Variables: 
#>   * condition: 2 levels (face, house)
#>   * trial: 40 levels (1, 2, 3...39, 40)
#>   * run: 4 levels (1, 2, 3, 4)
#> 
#> Column Metadata:
#>   * region: 50 levels (ROI_1, ROI_2, ROI_3...ROI_49, ROI_50)
#>   * hemisphere: 2 levels (left, right)
#>   * network: 5 levels (visual, frontal, parietal, temporal, default)
#> 
#> =======================
#>

The multidesign object keeps everything synchronized. You can extract components with accessor functions:

# Get the data matrix
head(xdata(mds)[, 1:5])
#>            [,1]       [,2]        [,3]         [,4]       [,5]
#> [1,]  1.3709584  0.2059986  1.51270701 -1.493625067 -0.1755259
#> [2,] -0.5646982 -0.3610573  0.25792144 -1.470435741 -1.0717824
#> [3,]  0.3631284  0.7581632  0.08844023  0.124702386  0.1632069
#> [4,]  0.6328626 -0.7267048 -0.12089654 -0.996639135 -0.3627384
#> [5,]  0.4042683 -1.3682810 -1.19432890 -0.001822614  0.5900135
#> [6,] -0.1061245  0.4328180  0.61199690 -0.428258881  1.4324219

# Get the design (without internal .index column)
head(design(mds))
#> # A tibble: 6 × 3
#>   condition trial   run
#>   <chr>     <int> <int>
#> 1 face          1     1
#> 2 face          2     1
#> 3 face          3     1
#> 4 face          4     1
#> 5 face          5     1
#> 6 house         6     1

# Get column metadata
head(column_design(mds))
#> # A tibble: 6 × 3
#>   region hemisphere network 
#>   <chr>  <chr>      <chr>   
#> 1 ROI_1  left       visual  
#> 2 ROI_2  right      frontal 
#> 3 ROI_3  left       parietal
#> 4 ROI_4  right      temporal
#> 5 ROI_5  left       default 
#> 6 ROI_6  right      visual

Step 3: Explore and subset your data

Filter observations by design variables:

# Keep only face trials
mds_face <- subset(mds, condition == "face")
mds_face
#> 
#> === Multidesign Object ===
#> 
#> Data Matrix: 
#>    20 observations x 50 variables 
#> 
#> Design Variables: 
#>   * condition: 1 levels (face)
#>   * trial: 20 levels (1, 2, 3...34, 35)
#>   * run: 4 levels (1, 2, 3, 4)
#> 
#> Column Metadata:
#>   * region: 50 levels (ROI_1, ROI_2, ROI_3...ROI_49, ROI_50)
#>   * hemisphere: 2 levels (left, right)
#>   * network: 5 levels (visual, frontal, parietal, temporal, default)
#> 
#> =======================
#> 

# Keep only run 1
mds_run1 <- subset(mds, run == 1)
nrow(xdata(mds_run1))
#> [1] 10

Select variables (columns) by their metadata:

# Keep only visual network regions
mds_visual <- select_variables(mds, network == "visual")
ncol(xdata(mds_visual))
#> [1] 10
column_design(mds_visual)
#> # A tibble: 10 × 3
#>    region hemisphere network
#>    <chr>  <chr>      <chr>  
#>  1 ROI_1  left       visual 
#>  2 ROI_6  right      visual 
#>  3 ROI_11 left       visual 
#>  4 ROI_16 right      visual 
#>  5 ROI_21 left       visual 
#>  6 ROI_26 right      visual 
#>  7 ROI_31 left       visual 
#>  8 ROI_36 right      visual 
#>  9 ROI_41 left       visual 
#> 10 ROI_46 right      visual

# Keep only left hemisphere visual regions
mds_left_visual <- select_variables(mds, network == "visual" & hemisphere == "left")
ncol(xdata(mds_left_visual))
#> [1] 5

Step 4: Summarize by design factors

Compute summary statistics grouped by design variables:

# Mean activity per condition
mds_means <- summarize_by(mds, condition)
mds_means
#> 
#> === Multidesign Object ===
#> 
#> Data Matrix: 
#>    2 observations x 50 variables 
#> 
#> Design Variables: 
#>   * condition: 2 levels (face, house)
#> 
#> Column Metadata:
#>   * region: 50 levels (ROI_1, ROI_2, ROI_3...ROI_49, ROI_50)
#>   * hemisphere: 2 levels (left, right)
#>   * network: 5 levels (visual, frontal, parietal, temporal, default)
#> 
#> =======================
#> 

# The result is a new multidesign with one row per group
dim(xdata(mds_means))
#> [1]  2 50
design(mds_means)
#> # A tibble: 2 × 1
#>   condition
#>   <chr>    
#> 1 face     
#> 2 house

Step 5: Split for detailed analysis

Split into separate multidesign objects:

# Split by condition
by_condition <- split(mds, condition)
length(by_condition)
#> [1] 2
names(by_condition) <- c("face", "house")

# Each element is a complete multidesign
by_condition$face
#> 
#> === Multidesign Object ===
#> 
#> Data Matrix: 
#>    20 observations x 50 variables 
#> 
#> Design Variables: 
#>   * condition: 1 levels (face)
#>   * trial: 20 levels (1, 2, 3...34, 35)
#>   * run: 4 levels (1, 2, 3, 4)
#> 
#> Column Metadata:
#>   * region: 50 levels (ROI_1, ROI_2, ROI_3...ROI_49, ROI_50)
#>   * hemisphere: 2 levels (left, right)
#>   * network: 5 levels (visual, frontal, parietal, temporal, default)
#> 
#> =======================
#>

Step 6: Cross-validation

Create cross-validation folds that respect your experimental design:

# Leave-one-run-out cross-validation
folds <- fold_over(mds, run)
folds
#> 
#> === Cross-Validation Folds ===
#> 
#>  Number of Folds: 4 
#> 
#> Fold 1: 
#>   * Analysis Set: 30 observations
#>   * Assessment Set: 10 observations
#> 
#> Fold 2: 
#>   * Analysis Set: 30 observations
#>   * Assessment Set: 10 observations
#> 
#> Fold 3: 
#>   * Analysis Set: 30 observations
#>   * Assessment Set: 10 observations
#> 
#> Fold 4: 
#>   * Analysis Set: 30 observations
#>   * Assessment Set: 10 observations
#> 
#> =============================
#> 

# Each fold contains analysis (training) and assessment (test) sets
fold1 <- folds[[1]]
nrow(xdata(fold1$analysis))
#> [1] 30
nrow(xdata(fold1$assessment))
#> [1] 10

If downstream code needs stable source-row identities, ask fold construction to carry them through:

folds_with_ids <- fold_over(mds, run, preserve_row_ids = TRUE)
folds_with_ids[[1]]$assessment$design$.orig_index
#>  [1]  1  2  3  4  5  6  7  8  9 10

Step 7: Run a cross-validation pipeline

Use cross_validate() to execute a complete CV workflow:

# Define a simple "model": compute condition means on training data
fit_fn <- function(analysis) {
 means_by_cond <- summarize_by(analysis, condition)
 list(
   face_mean = xdata(means_by_cond)[1, ],
   house_mean = xdata(means_by_cond)[2, ]
 )
}

# Define scoring: correlation between predicted and actual means
score_fn <- function(model, assessment) {
 test_means <- summarize_by(assessment, condition)

 # Compare model predictions to test data
 face_cor <- cor(model$face_mean, xdata(test_means)[1, ])
 house_cor <- cor(model$house_mean, xdata(test_means)[2, ])

 c(face_r = face_cor, house_r = house_cor, mean_r = (face_cor + house_cor) / 2)
}

# Run cross-validation
cv_result <- cross_validate(folds, fit_fn, score_fn)
cv_result
#> 
#> === Cross-Validation Result ===
#> 
#> Folds: 4 
#> 
#> Metrics:
#>    face_r : mean = 0.0176 , sd = 0.1051 
#>    house_r : mean = 0.0332 , sd = 0.0865 
#>    mean_r : mean = 0.0254 , sd = 0.0626 
#> 
#> ===============================
#>

Examine detailed results:

# Get summary statistics
summary(cv_result)
#> # A tibble: 3 × 6
#>   metric    mean     sd     min    max  median
#>   <chr>    <dbl>  <dbl>   <dbl>  <dbl>   <dbl>
#> 1 face_r  0.0176 0.105  -0.100  0.153  0.00883
#> 2 house_r 0.0332 0.0865 -0.0891 0.113  0.0546 
#> 3 mean_r  0.0254 0.0626 -0.0497 0.0982 0.0266

# Access raw scores
cv_result$scores
#> # A tibble: 4 × 4
#>    face_r house_r   mean_r .fold
#>     <dbl>   <dbl>    <dbl> <int>
#> 1 -0.100   0.113   0.00624     1
#> 2 -0.0103 -0.0891 -0.0497      2
#> 3  0.153   0.0432  0.0982      3
#> 4  0.0280  0.0659  0.0470      4

Working with multiple subjects: hyperdesign

Real experiments typically have multiple subjects. A hyperdesign manages multiple multidesign objects that share common design structure.

# Create data for 3 subjects
subjects <- lapply(1:3, function(subj) {
 X_subj <- matrix(rnorm(n_trials * n_regions), n_trials, n_regions)

 # Add a subject-specific signal
 if (subj == 1) X_subj[1:20, 1:10] <- X_subj[1:20, 1:10] + 0.5
 if (subj == 2) X_subj[1:20, 1:10] <- X_subj[1:20, 1:10] + 0.3
 if (subj == 3) X_subj[1:20, 1:10] <- X_subj[1:20, 1:10] + 0.7

 multidesign(X_subj, design_df, column_info)
})

# Combine into a hyperdesign
hd <- hyperdesign(subjects, block_names = c("subj1", "subj2", "subj3"))
hd
#> 
#> === Hyperdesign Object ===
#> 
#> Number of blocks:  3 
#> 
#> +- Block  1  (subj1)  -----------------
#> |  Dimensions: 40 x 50 
#> |  Design Variables: condition, trial, run 
#> |  Design Structure: 
#> |   * condition: 2 levels (face, house)
#> |   * trial: 40 levels (1, 2, 3...39, 40)
#> |   * run: 4 levels (1, 2, 3, 4)
#> |  Column Design: Present
#> |   Variables:  region, hemisphere, network 
#> 
#> +- Block  2  (subj2)  -----------------
#> |  Dimensions: 40 x 50 
#> |  Design Variables: condition, trial, run 
#> |  Design Structure: 
#> |   * condition: 2 levels (face, house)
#> |   * trial: 40 levels (1, 2, 3...39, 40)
#> |   * run: 4 levels (1, 2, 3, 4)
#> |  Column Design: Present
#> |   Variables:  region, hemisphere, network 
#> 
#> +- Block  3  (subj3)  -----------------
#> |  Dimensions: 40 x 50 
#> |  Design Variables: condition, trial, run 
#> |  Design Structure: 
#> |   * condition: 2 levels (face, house)
#> |   * trial: 40 levels (1, 2, 3...39, 40)
#> |   * run: 4 levels (1, 2, 3, 4)
#> |  Column Design: Present
#> |   Variables:  region, hemisphere, network 
#> 
#> =======================
#>

When rows correspond across blocks

The subjects above contain independent trials in the same order, but a hyperdesign can also store known entities that recur across blocks. Examples include landmarks measured in several configurations or tasks embedded by several models. The matrices remain entities by variables; the entity key is a design column, not an instruction to transpose the data.

configuration_a <- multidesign(
  matrix(c(NA, 0, 1, 0, 0, 1), ncol = 2, byrow = TRUE),
  tibble(landmark = c("A", "B", "C")),
  cells = matrix(
    c(TRUE, TRUE, TRUE, FALSE, FALSE, FALSE),
    ncol = 2,
    byrow = TRUE
  )
)
configuration_b <- multidesign(
  matrix(c(1, 0, 0, 1, 1, 1), ncol = 2, byrow = TRUE),
  tibble(landmark = c("B", "C", "D"))
)

configurations <- hyperdesign(
  list(a = configuration_a, b = configuration_b),
  id = "landmark",
  space = "common"
)

entity_id(configurations)
#> [1] "landmark"
column_space(configurations)
#> [1] "common"

corr <- correspondence(configurations)
corr$global_ids
#> [1] "A" "B" "C" "D"
corr$row_map
#> $a
#> [1] 1 2 3
#> 
#> $b
#> [1] 2 3 4
corr$overlap$pair_n
#>   a b
#> a 3 2
#> b 2 3

aligned <- align_by_id(configurations)
aligned$observed
#>       a     b
#> A  TRUE FALSE
#> B  TRUE  TRUE
#> C  TRUE  TRUE
#> D FALSE  TRUE
aligned$cells[, , "a"]
#>       variable
#> entity     1     2
#>      A  TRUE  TRUE
#>      B  TRUE FALSE
#>      C FALSE FALSE
#>      D FALSE FALSE
aligned$x[, , "a"]
#>       variable
#> entity  1  2
#>      A NA  0
#>      B  1 NA
#>      C NA NA
#>      D NA NA

correspondence(configurations, sort_ids = TRUE)$global_ids
#> [1] "A" "B" "C" "D"

stopifnot(all(vapply(seq_along(configurations), function(i) {
  identical(corr$global_ids[corr$row_map[[i]]], corr$ids[[i]])
}, logical(1))))

The global entity universe uses first-seen order, while each row_map maps local rows into it. Partial overlap is valid, and corr$overlap$connected reports whether the block-overlap graph is connected. A disconnected graph is data for a downstream solver to evaluate, not a construction error.

Row presence and cell observation are deliberately separate. In the aligned result above, landmark D is absent from block a, landmark C is present in a but has an all-FALSE cell-mask row, and landmark A’s first coordinate is observed even though its value is NA. All three may display as NA in the aligned data array. Use observed to ask whether the row exists and cells to ask whether a coordinate was observed. fill controls only presentation; missing values in x never create a mask.

Three related concepts remain separate:

common_vars describes design-column names found in every block: shared schema.
id names the design-column values that link rows across blocks: a join key.
space = "common" asserts that every matrix uses the same column axes; space = "block" declares block-specific variables.

as_multidesign() is a row-stack operation, not an ID join, and therefore refuses space = "block". align_by_id() is the deliberately separate join: it constructs entity-by-variable-by-block arrays for space = "common", while preserving both row presence and cell observation. It does not estimate transformations. Similarly, fold_over(configurations, landmark) holds each entity out of every block in which it occurs. That is a general data split, not Bai–Bartoli/LBW smoothness cross-validation.

Masks under data operations

An explicit cells matrix must be logical, contain no NA, and match x exactly. cell_mask() returns it, while has_cell_mask() distinguishes a stored mask from the legacy unmasked case. Row and column subsets, folds, and variable selection slice the mask with the data. Row stacking preserves masks; if only some inputs are masked, unmasked inputs are promoted to all observed.

Combining masked observations requires an explicit rule. For grouped summaries use aggregate = "mean" (or a scalar-returning function):

replicates <- multidesign(
  matrix(c(1, 10, 3, 30, 8, 80), ncol = 2, byrow = TRUE),
  tibble(landmark = c("A", "A", "B")),
  cells = matrix(
    c(TRUE, FALSE, TRUE, TRUE, FALSE, FALSE),
    ncol = 2,
    byrow = TRUE
  )
)

replicate_means <- hyperdesign(
  list(sample = replicates),
  id = "landmark",
  space = "common",
  aggregate = "mean"
)
xdata(replicate_means[[1]])
#>   [,1] [,2]
#> A    2   30
#> B    8   80
cell_mask(replicate_means[[1]])
#>    [,1]  [,2]
#> A  TRUE  TRUE
#> B FALSE FALSE

summarize_by(replicates, landmark, aggregate = "mean")
#> 
#> === Multidesign Object ===
#> 
#> Data Matrix: 
#>    2 observations x 2 variables 
#> 
#> Observed Cells: 
#>    2 of 4 explicitly observed
#> 
#> Design Variables: 
#>   * landmark: 2 levels (A, B)
#> 
#> Column Metadata:
#>   * .index: 2 levels (1, 2)
#> 
#> =======================
#>

For each output coordinate, the rule receives values whose cell masks are TRUE; a coordinate with no observed inputs remains masked. Duplicate entity keys remain an error when aggregate is omitted. Preprocessing and dimensional reduction reject partial masks because their transformation objects do not specify how a mask changes. All-TRUE masks can pass those boundaries, and a legacy NULL mask remains NULL.

Do not store features × observations in x to satisfy a left-action formula. Generalized Procrustes solvers should transpose at their own API boundary. multidesign carries correspondence and column-space declarations; specialized packages remain responsible for transformations, fitting, gauges, and certificates. Cell-aware fitting likewise belongs to those consumer packages; multidesign only carries and reshapes the mask. Use positional = TRUE only for deliberately positional correspondence with equal row counts.

Leave-one-subject-out cross-validation

# Without specifying variables, fold_over creates leave-one-block-out folds
loso_folds <- fold_over(hd)
length(loso_folds)
#> [1] 3

# Each fold: train on 2 subjects, test on 1
fold1 <- loso_folds[[1]]
length(fold1$analysis)
#> [1] 2
fold1$assessment
#> 
#> === Multidesign Object ===
#> 
#> Data Matrix: 
#>    40 observations x 50 variables 
#> 
#> Design Variables: 
#>   * condition: 2 levels (face, house)
#>   * trial: 40 levels (1, 2, 3...39, 40)
#>   * run: 4 levels (1, 2, 3, 4)
#> 
#> Column Metadata:
#>   * region: 50 levels (ROI_1, ROI_2, ROI_3...ROI_49, ROI_50)
#>   * hemisphere: 2 levels (left, right)
#>   * network: 5 levels (visual, frontal, parietal, temporal, default)
#> 
#> =======================
#>

Within-subject cross-validation

# Fold by run within each subject
run_folds <- fold_over(hd, run)
length(run_folds)
#> [1] 12

Explicit row-based cross-validation

When you already know the held-out rows, use cv_rows() to build a foldlist directly:

row_folds <- cv_rows(
  hd,
  rows = list(
    list(subj1 = 1:2, subj2 = 1:2),
    list(subj1 = 3:4, subj2 = 3:4)
  )
)

row_folds[[1]]$assessment
#> 
#> === Hyperdesign Object ===
#> 
#> Number of blocks:  2 
#> 
#> +- Block  1  (subj1)  -----------------
#> |  Dimensions: 2 x 50 
#> |  Design Variables: condition, trial, run 
#> |  Design Structure: 
#> |   * condition: 1 levels (face)
#> |   * trial: 2 levels (1, 2)
#> |   * run: 1 levels (1)
#> |  Column Design: Present
#> |   Variables:  region, hemisphere, network 
#> 
#> +- Block  2  (subj2)  -----------------
#> |  Dimensions: 2 x 50 
#> |  Design Variables: condition, trial, run 
#> |  Design Structure: 
#> |   * condition: 1 levels (face)
#> |   * trial: 2 levels (1, 2)
#> |   * run: 1 levels (1)
#> |  Column Design: Present
#> |   Variables:  region, hemisphere, network 
#> 
#> =======================
#>

Use preserve_row_ids = TRUE here as well if external correspondence tables or annotations are keyed by original rows:

row_folds_with_ids <- cv_rows(
  hd,
  rows = list(list(subj1 = 1:2, subj2 = 1:2)),
  preserve_row_ids = TRUE
)

row_folds_with_ids[[1]]$assessment[[1]]$design$.orig_index
#> [1] 1 2
row_folds_with_ids[[1]]$held_out$row_ids
#> $subj1
#> [1] 1 2
#> 
#> $subj2
#> [1] 1 2

Collapse to a single multidesign

If you need to analyze all subjects together:

# Collapse hyperdesign to one multidesign
mds_all <- as_multidesign(hd, .id = "subject")
mds_all
#> 
#> === Multidesign Object ===
#> 
#> Data Matrix: 
#>    120 observations x 50 variables 
#> 
#> Design Variables: 
#>   * condition: 2 levels (face, house)
#>   * trial: 40 levels (1, 2, 3...39, 40)
#>   * run: 4 levels (1, 2, 3, 4)
#>   * subject: 3 levels (subj1, subj2, subj3)
#> 
#> Column Metadata:
#>   * region: 50 levels (ROI_1, ROI_2, ROI_3...ROI_49, ROI_50)
#>   * hemisphere: 2 levels (left, right)
#>   * network: 5 levels (visual, frontal, parietal, temporal, default)
#> 
#> =======================
#> 

# The .id column tracks which block each observation came from
table(design(mds_all)$subject)
#> 
#> subj1 subj2 subj3 
#>    40    40    40

Next steps

See vignette("class_overview") for detailed documentation of each class
Explore the function reference for methods like bind_multidesign(), df_to_hyperdesign(), and reduce()
Check out the package website for additional examples

Session info

sessionInfo()
#> R version 4.6.1 (2026-06-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.4 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
#>  [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
#>  [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
#> [10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   
#> 
#> time zone: UTC
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] dplyr_1.2.1            tibble_3.3.1           multidesign_0.1.0.9000
#> 
#> loaded via a namespace (and not attached):
#>  [1] Matrix_1.7-5       jsonlite_2.0.0     crayon_1.5.3       compiler_4.6.1    
#>  [5] tidyselect_1.2.1   assertthat_0.2.1   tidyr_1.3.2        geigen_2.4        
#>  [9] jquerylib_0.1.4    systemfonts_1.3.2  textshaping_1.0.5  yaml_2.3.12       
#> [13] fastmap_1.2.0      lattice_0.22-9     R6_2.6.1           generics_0.1.4    
#> [17] knitr_1.51         desc_1.4.3         chk_0.10.0         bslib_0.12.0      
#> [21] pillar_1.11.1      multivarious_0.3.2 rlang_1.3.0        utf8_1.2.6        
#> [25] cachem_1.1.0       xfun_0.60          fs_2.1.0           sass_0.4.10       
#> [29] otel_0.2.0         memoise_2.0.1      cli_3.6.6          withr_3.0.3       
#> [33] pkgdown_2.2.1      magrittr_2.0.5     digest_0.6.39      grid_4.6.1        
#> [37] lifecycle_1.0.5    vctrs_0.7.3        evaluate_1.0.5     glue_1.8.1        
#> [41] ragg_1.5.2         deflist_0.2.0      rmarkdown_2.31     purrr_1.2.2       
#> [45] tools_4.6.1        pkgconfig_2.0.3    htmltools_0.5.9