diff --git a/layouts/_default/home.html b/layouts/_default/home.html
index 58a6261..efaa84c 100644
--- a/layouts/_default/home.html
+++ b/layouts/_default/home.html
@@ -96,14 +96,16 @@ <h2 class="feature-grid-title">Contributors</h2>
                      would draw a city of two as four times the city of one.
 
                      Strictly proportional area — 6·√count — is where this started,
-                     and it drew Shanghai at a radius of 14.7 against 6 for a city
+                     and it drew Shanghai at a radius of 15.9 against 6 for a city
                      of one. Rendered, that is not a bigger dot, it is the subject
-                     of the map: six of the thirty-six contributors it can place took
-                     the eye and the other cities read as its outliers. So the area is
-                     offset rather than proportional. The first contributor buys a
-                     mark of a fixed size, and each one after adds half that mark's
-                     area again — Shanghai lands at 11.2, still unmistakably the
-                     largest, without being the only thing on the map.
+                     of the map: seven of the forty-eight contributors it can place
+                     took the eye and the other cities read as its outliers. So the
+                     area is offset rather than proportional, and capped: the first
+                     contributor buys a mark of a fixed size, each one after adds half
+                     that mark's area again, and nothing exceeds 10 units. Shanghai
+                     sits on that ceiling against 8.5 for the next city down — still
+                     unmistakably the largest, without being the only thing on the map.
+                     The cap is argued in partials/worldmap-place.html, where it lives.
 
                      That is a compressed scale and it should be said plainly:
                      these dots are comparable, not measurable. Nothing here rests
@@ -138,10 +140,10 @@ <h2 class="feature-grid-title">Contributors</h2>
                          Drawn halfway between the dot's own radius and a common 13, not
                          at the dot's radius, which is where this started. The stylesheet
                          grows the ring by a factor, so a radius of 6 travelled 6 units
-                         where Shanghai's 11.2 travelled 12: the cities of one — most of
-                         the map — got half the movement over the shortest distance, and
+                         where Shanghai's 10 travelled 10: the cities of one — most of
+                         the map — got the least movement over the shortest distance, and
                          read as static dots beside a breathing Shanghai. Averaging with
-                         a constant lifts them to 9.5 and leaves Shanghai at 12.1, so the
+                         a constant lifts them to 9.5 and leaves Shanghai at 11.5, so the
                          smallest cities gain most of the ring they were missing while
                          the rings stay in the order the dots are in: a smaller dot still
                          has a smaller circle. It costs nothing in meaning — the count is
diff --git a/layouts/partials/worldmap-place.html b/layouts/partials/worldmap-place.html
index 8782b7a..b433672 100644
--- a/layouts/partials/worldmap-place.html
+++ b/layouts/partials/worldmap-place.html
@@ -20,6 +20,24 @@
      first contributor buys a mark of a fixed size and each one after adds half that
      mark's area again, which keeps Shanghai the largest dot without making it the
      subject of the map. The long version of this reasoning is in home.html, beside
-     the dot it draws. */}}
-{{- $r := mul 6.0 (math.Sqrt (add 1.0 (mul 0.5 (sub $place.count 1)))) -}}
+     the dot it draws.
+
+     Capped at 10, which is a ceiling and not a scale change: at seven contributors
+     Shanghai reached 12 units against 8.5 for the next city down, and a dot that size
+     is read as the point of the map rather than as one city on it. The cap holds the
+     top still while leaving the bottom alone — a city of one is 6 units and a city of
+     two is 7.3 either way, and those are the marks that cannot afford to lose size,
+     since at 390px wide six units is already only two real pixels.
+
+     Flattening the whole curve was the alternative and it costs more: taking the
+     half-again down to a third would have put Shanghai at 10 too, and brought a city
+     of two to 6.8 — under a pixel apart from a city of one on a phone, which loses the
+     one comparison the dots are actually for.
+
+     What a cap gives up is the difference between two cities above it, and today
+     nothing else is close: the second largest is 8.5, so this bites Shanghai alone.
+     When a second city passes it the two will read as one size, which is the point at
+     which the dots have said all they can and the cards behind them — which list who
+     is in each city, so the count can be counted — are the honest place to look. */}}
+{{- $r := math.Min 10.0 (mul 6.0 (math.Sqrt (add 1.0 (mul 0.5 (sub $place.count 1))))) -}}
 {{- return dict "x" $x "y" $y "r" $r -}}