diff --git a/R/CalcTraces.R b/R/CalcTraces.R
index e64a807..2262f15 100644
--- a/R/CalcTraces.R
+++ b/R/CalcTraces.R
@@ -1,25 +1,25 @@
-#' Title TODO
+#' Fast Calculation of Matrix Trace and Hilbert Schmidt Norm
 #'
-#' Short Description TODO
+#' Provides multithreaded calculation of trace and Hilbert Schmidt Norm of a matrix PMP (where P is a projection matrix) without explicitly forming PMP.
 #'
-#' Long Description TODO
+#' P here is assumed to have the form I-QQ' for some matrix Q of orthogonal columns
 #'
 #' @param M
-#'        TODO
+#'        a real symmetric R matrix
 #' @param tX
-#'        TODO
+#'        `t((Q %*% (J%*%Q)) - (M %*% Q))`
 #' @param tQ
-#'        TODO
+#'        `t(Q)`
 #' @param J
-#'        TODO
+#'        `crossprod(Q, M)`
 #' @param from_recipient
-#'        TODO
+#'        haplotype index at which to start trace calculation -- useful for distributed computation (experimental feature, more documentation to come TODO)
 #' @param nthreads
 #'        the number of CPU cores to use.
 #'        By default uses the `parallel` package to detect the number of physical cores.
 #'
 #' @return
-#' TODO
+#' a list containing three elements, the first is the trace `tr(PMP)`, the second is the *squared* Hilbert Schmidt Norm of PMP `tr((PMP)'PMP)`, the third is the diag of `PMP`.
 #'
 #' @examples
 #' # TODO
diff --git a/R/CladeMat.R b/R/CladeMat.R
index ad8c6a7..c6982d0 100644
--- a/R/CladeMat.R
+++ b/R/CladeMat.R
@@ -18,17 +18,17 @@
 #'        a matrix with half the number of rows and columns as the corresponding forward/backward tables.
 #'        This matrix is overwritten in place with the clade matrix result for performance reasons.
 #' @param unit.dist
-#'        TODO
+#'        the change in distance that is expected to correspond to a single mutation (typically \eqn{-log(\mu)}) for the LS model)
 #' @param thresh
-#'        TODO
+#'        a regularization parameter: differences distances must exceed this threshold (in `unit.dist` units) in order to used in forming the local relatedness matrix. Defaults to `0.2`.
 #' @param max1var
-#'        TODO
+#'        a logical regularization parameter. When TRUE, differences in distances exceeding 1 `unit.dist` are set to 1 (so that any edge in the latent ancestral tree with multiple mutations on them are treated as if only one mutation was on it).
 #' @param nthreads
 #'        the number of CPU cores to use.
 #'        By default uses the `parallel` package to detect the number of physical cores.
 #'
 #' @return
-#' TODO: this returns from C the list containing neighbourhood, similarity and total clades info, but need full details and list structure.
+#' A list, the first element contains a list of tied nearest neighbors (one for each haplotype). Other elements return other information to allow for efficient removal of singletons and sprigs by [PruneCladeMat()].
 #'
 #' @examples
 #' # TODO
diff --git a/R/FB.R b/R/FB.R
index 51476d3..5d3116b 100644
--- a/R/FB.R
+++ b/R/FB.R
@@ -6,7 +6,7 @@
 #' `Forward` implements the forward algorithm to advance the Li and Stephens rescaled hidden Markov model forward probabilities to a new target variant.
 #' Naturally, this can only propagate a table to variants downstream of its current position.
 #'
-#' For mathematical details please see Section 2 of the kalis paper (TODO: ref).
+#' For mathematical details please see Section 2 of the kalis paper (https://doi.org/10.1186/s12859-024-05688-8).
 #' Note that the precise formulation of the forward equation is determined by whether the flag `use.spiedel` is set in the parameters provided in `pars`.
 #'
 #' @param fwd a `kalisForwardTable` object, as returned by
@@ -111,7 +111,7 @@ Forward <- function(fwd,
 #' variant.
 #' Naturally, this can only propagate a table to variants upstream of its current position.
 #'
-#' For mathematical details please see Section 2 of the kalis paper (TODO: ref).
+#' For mathematical details please see Section 2 of the kalis paper (https://doi.org/10.1186/s12859-024-05688-8).
 #' Note that the precise formulation of the backward equation is determined by whether the flag `use.spiedel` is set in the parameters provided in `pars`.
 #'
 #' **Beta-theta space**
diff --git a/man/Backward.Rd b/man/Backward.Rd
index 761619b..7cc3256 100644
--- a/man/Backward.Rd
+++ b/man/Backward.Rd
@@ -45,7 +45,7 @@ The table is updated in-place.
 variant.
 Naturally, this can only propagate a table to variants upstream of its current position.
 
-For mathematical details please see Section 2 of the kalis paper (TODO: ref).
+For mathematical details please see Section 2 of the kalis paper (https://doi.org/10.1186/s12859-024-05688-8).
 Note that the precise formulation of the backward equation is determined by whether the flag \code{use.spiedel} is set in the parameters provided in \code{pars}.
 
 \strong{Beta-theta space}
diff --git a/man/CalcTraces.Rd b/man/CalcTraces.Rd
index cf94dec..db508ef 100644
--- a/man/CalcTraces.Rd
+++ b/man/CalcTraces.Rd
@@ -2,7 +2,7 @@
 % Please edit documentation in R/CalcTraces.R
 \name{CalcTraces}
 \alias{CalcTraces}
-\title{Title TODO}
+\title{Fast Calculation of Matrix Trace and Hilbert Schmidt Norm}
 \usage{
 CalcTraces(
   M,
@@ -14,27 +14,27 @@ CalcTraces(
 )
 }
 \arguments{
-\item{M}{TODO}
+\item{M}{a real symmetric R matrix}
 
-\item{tX}{TODO}
+\item{tX}{\code{t((Q \%*\% (J\%*\%Q)) - (M \%*\% Q))}}
 
-\item{tQ}{TODO}
+\item{tQ}{\code{t(Q)}}
 
-\item{J}{TODO}
+\item{J}{\code{crossprod(Q, M)}}
 
-\item{from_recipient}{TODO}
+\item{from_recipient}{haplotype index at which to start trace calculation -- useful for distributed computation (experimental feature, more documentation to come TODO)}
 
 \item{nthreads}{the number of CPU cores to use.
 By default uses the \code{parallel} package to detect the number of physical cores.}
 }
 \value{
-TODO
+a list containing three elements, the first is the trace \code{tr(PMP)}, the second is the \emph{squared} Hilbert Schmidt Norm of PMP \verb{tr((PMP)'PMP)}, the third is the diag of \code{PMP}.
 }
 \description{
-Short Description TODO
+Provides multithreaded calculation of trace and Hilbert Schmidt Norm of a matrix PMP (where P is a projection matrix) without explicitly forming PMP.
 }
 \details{
-Long Description TODO
+P here is assumed to have the form I-QQ' for some matrix Q of orthogonal columns
 }
 \examples{
 # TODO
diff --git a/man/CladeMat.Rd b/man/CladeMat.Rd
index 86af088..70836af 100644
--- a/man/CladeMat.Rd
+++ b/man/CladeMat.Rd
@@ -25,17 +25,17 @@ This table must be at the same variant location as argument \code{fwd}.}
 \item{M}{a matrix with half the number of rows and columns as the corresponding forward/backward tables.
 This matrix is overwritten in place with the clade matrix result for performance reasons.}
 
-\item{unit.dist}{TODO}
+\item{unit.dist}{the change in distance that is expected to correspond to a single mutation (typically \eqn{-log(\mu)}) for the LS model)}
 
-\item{thresh}{TODO}
+\item{thresh}{a regularization parameter: differences distances must exceed this threshold (in \code{unit.dist} units) in order to used in forming the local relatedness matrix. Defaults to \code{0.2}.}
 
-\item{max1var}{TODO}
+\item{max1var}{a logical regularization parameter. When TRUE, differences in distances exceeding 1 \code{unit.dist} are set to 1 (so that any edge in the latent ancestral tree with multiple mutations on them are treated as if only one mutation was on it).}
 
 \item{nthreads}{the number of CPU cores to use.
 By default uses the \code{parallel} package to detect the number of physical cores.}
 }
 \value{
-TODO: this returns from C the list containing neighbourhood, similarity and total clades info, but need full details and list structure.
+A list, the first element contains a list of tied nearest neighbors (one for each haplotype). Other elements return other information to allow for efficient removal of singletons and sprigs by \code{\link[=PruneCladeMat]{PruneCladeMat()}}.
 }
 \description{
 Constructs a clade matrix using forward and backward tables.
diff --git a/man/Forward.Rd b/man/Forward.Rd
index dbb7ceb..aa6aad1 100644
--- a/man/Forward.Rd
+++ b/man/Forward.Rd
@@ -40,7 +40,7 @@ The table is updated in-place.
 \code{Forward} implements the forward algorithm to advance the Li and Stephens rescaled hidden Markov model forward probabilities to a new target variant.
 Naturally, this can only propagate a table to variants downstream of its current position.
 
-For mathematical details please see Section 2 of the kalis paper (TODO: ref).
+For mathematical details please see Section 2 of the kalis paper (https://doi.org/10.1186/s12859-024-05688-8).
 Note that the precise formulation of the forward equation is determined by whether the flag \code{use.spiedel} is set in the parameters provided in \code{pars}.
 }
 \examples{