+generate $D_m$ as the putative direct contributors of $\pcn$.
+
+However, the invocation may give instructions that certain direct
+dependencies are definitely to be included, or excluded. As a result
+the set of actual direct contributors is some arbitrary set of patches
+(strictly, some arbitrary set of Topbloke tip commit sets).
+
+\subsection{Direct contributors for $\pc = \pcy$}
+
+The sole direct contributor of $\pcy$ is $\pcn$.
+
+\subsection{Recursive step}
+
+For each direct contributor $\p$, we add the edge $\pc \hasdirdep \p$
+and augment the ordering $\hasdep$ accordingly.
+
+If this would make a cycle in $\hasdep$, we abort . The operation must
+then be retried by the user, if desired, but with different or
+additional instructions for modifying the direct contributors of some
+$\pqn$ involved in the cycle.
+
+For each such $\p$, after updating $\hasdep$, we recursively make a plan
+for $\pc' = \p$.
+
+
+
+\section{Execution phase}
+
+We process commit sets from the bottom up according to the relation
+$\hasdep$. For each commit set $\pc$ we construct $\tipfc$ from
+$\tipzc$, as planned. By construction, $\hasdep$ has $\patchof{L}$
+as its maximum, so this operation will finish by updating
+$\tipca{\patchof{L}}$ with $\tipfa{\patchof{L}}$.
+
+After we are done with each commit set $\pc$, the
+new tip $\tipfc$ has the following properties:
+\[ \eqn{Tip Sources}{
+ \bigforall_{E_i \in \set E_{\pc}} \tipfc \ge E_i
+}\]
+\[ \eqn{Tip Dependencies}{
+ \bigforall_{\pc \hasdep \p} \tipfc \ge \tipfa \p
+}\]
+\[ \eqn{Perfect Contents}{
+ \tipfc \haspatch \p \equiv \pc \hasdep \py
+}\]
+
+For brevity we will sometimes write $\tipu$ for $\tipuc$, etc. We will start
+out with $\tipc = \tipz$, and at each step of the way construct some
+$\tipu$ from $\tipc$. The final $\tipu$ becomes $\tipf$.
+
+\subsection{Preparation}
+
+Firstly, we will check each $E_i$ for being $\ge \tipc$. If
+it is, are we fast forward to $E_i$
+--- formally, $\tipu = \text{max}(\tipc, E_i)$ ---
+and drop $E_i$ from the planned ordering.
+
+Then we will merge the direct contributors and the sources' ends.
+This generates more commits $\tipuc \in \pc$, but none in any other
+commit set. We maintain
+$$
+ \bigforall_{\p \isdep \pc}
+ \pancsof{\tipcc}{\p} \subset
+ \pancsof{\tipfa \p}{\p}
+$$
+\proof{
+ For $\tipcc = \tipzc$, $T$ ...WRONG WE NEED $\tipfa \p$ TO BE IN $\set E$ SOMEHOW
+}
+
+\subsection{Merge Contributors for $\pcy$}
+
+Merge $\pcn$ into $\tipc$. That is, merge with
+$L = \tipc, R = \tipfa{\pcn}, M = \baseof{\tipc}$.
+to construct $\tipu$.
+
+Merge conditions:
+
+Ingredients satisfied by construction.
+Tip Merge satisfied by construction. Merge Acyclic follows
+from Perfect Contents and $\hasdep$ being acyclic.
+
+Removal Merge Ends: For $\p = \pc$, $M \nothaspatch \p$; OK.
+For $\p \neq \pc$, by Tip Contents,
+$M \haspatch \p \equiv L \haspatch \p$, so we need only
+worry about $X = R, Y = L$; ie $L \haspatch \p$,
+$M = \baseof{L} \haspatch \p$.
+By Tip Contents for $L$, $D \le L \equiv D \le M$. OK.~~$\qed$