-Initially let $T_{\pc,0}$ be the git ref for $\pcn$. And let
-$\set D_0 = \depsreqof{T_{\pc,0}}$.
-For each $E_j$ starting with $j=1$ choose a corresponding intended
-merge base $M_j$ such that $M_j \le E_j \land M_j \le T_{\pc,j-1}$.
-Calculate $\set D_j$ as the 3-way merge of the sets $\set D_{j-1}$ and
-$\depsreqof{E_j}$ using as a base $\depsreqof{M_j}$. This will
-generate $D_m$ as the putative direct contributors for $\pcn$.
+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 XXX FIXME IS THIS THE BEST THING?
+$$
+ \bigforall_{\p \isdep \pc}
+ \pancsof{\tipcc}{\p} \subset \left[
+ \tipfa \p \cup
+ \bigcup_{E \in \set E_{\pc}} \pancsof{E}{\p}
+ \right]
+$$
+
+\subsection{Merge Contributors for $\pcy$}
+
+Merge $\pcn$ into $\tipc$. That is, merge with
+$L = \tipc, R = \tipfa{\pcn}, M = \baseof{\tipc}$.
+to construct $\tipu$.