The prefix settle walked every link in the graph three times per merge —
to derive the node set, to build the neighbour table the corroboration
vote reads, and to hunt down the links naming the id being folded. On the
device's mesh that is ~1150 links, three times over, some eighty times:
the largest remaining cost of opening the walk.
All three questions are one table's to answer, and a merge's effect on it
is knowable where it happens. So build it once and keep it: its keys are
the live node set, a fold relabels its own neighbours, and a stub whose
every link ran to its owner takes the owner out with it. Both passes now
walk only the under-specified ids, since a full-width one extends
nothing.
Ties in the shortest-first order break lexicographically too. Length
alone left equal-width ids in whatever order the node set iterated, and
CPython randomizes string hashing per process — so two runs over the same
evidence could take their merges in different orders and, where one fold
changes what a later one sees, settle to different graphs.
Verified byte-identical against the previous algorithm over twelve
randomized graphs, and 6.3x on the settle at that scale.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Jean-Pierre MartineauandClaude Opus 5
714bb15fe6