diff --git a/library/components/map-controls/MapControlButton.vue b/library/components/map-controls/MapControlButton.vue
index c35713b24..b3f341455 100644
--- a/library/components/map-controls/MapControlButton.vue
+++ b/library/components/map-controls/MapControlButton.vue
@@ -68,6 +68,11 @@ useShadowStyles(`
 /* shape="square" on a STANDALONE button: their 4px corners, our fill and shadow kept.
    A button inside .map-toolbar--square is overridden back to 0 by the toolbar's rules. */
 .mcb--square{ border-radius:4px; }
+/* shape="rounded-square" — the HEADER-BAR button form (design rule, 2026-09-30): map controls stay ROUND,
+   but a button in a dashboard HEADER is a rounded square at the SAME radius as the gallery's vertical
+   tabs. --vtl-radius is that ONE shared variable (VerticalTabsLayout .vtl-tab), so the header button
+   and the tabs can never drift; 8px is only the fallback for a context that never set it. */
+.mcb--rounded-square{ border-radius:var(--vtl-radius,8px); }
 
 /* ★ REDUCED MOTION, OWNED BY THIS COMPONENT. A page-level rule cannot reach into a shadow root,
    and no generated leaf ships one anyway (measured: 0 across the whole tree), so a component
@@ -93,7 +98,7 @@ defineProps({
    * strip it back off -- the two rule sets compose rather than compete, and the toolbar wins by
    * being the more specific selector.
    */
-  shape:    { type: String,  default: 'round' }
+  shape:    { type: String,  default: 'round', validator: (v) => ['round', 'square', 'rounded-square'].includes(v) }
 })
 
 defineEmits(['click'])
@@ -123,7 +128,7 @@ defineEmits(['click'])
   -->
   <button
     class="mcb"
-    :class="{ dark: isDark, active, 'mcb--square': shape === 'square' }"
+    :class="{ dark: isDark, active, 'mcb--square': shape === 'square', 'mcb--rounded-square': shape === 'rounded-square' }"
     :title="title"
     :aria-label="title || undefined"
     :disabled="disabled"
diff --git a/library/components/map-controls/MapInfoButton.vue b/library/components/map-controls/MapInfoButton.vue
index 559f7c018..8f27e81d3 100644
--- a/library/components/map-controls/MapInfoButton.vue
+++ b/library/components/map-controls/MapInfoButton.vue
@@ -29,6 +29,9 @@ const { t } = useI18n()
 
 defineProps({
   isDark: { type: Boolean, default: false },
+  // 'round' (default) is the map-control form. 'rounded-square' is the dashboard HEADER form (the ⓘ
+  // sits in a header bar beside Share, not in a map's control column) — forwarded to MapControlButton.
+  shape: { type: String, default: 'round' },
 })
 
 // ★ AN UNANSWERED CONTROL ADDS NO CHILD TO THE COLUMN. The button renders only once a host has answered
@@ -68,7 +71,7 @@ onBeforeUnmount(() => { window.removeEventListener('dxmaps:mapinfo-host', ask) }
 </script>
 
 <template>
-  <MapControlButton v-if="hosted" ref="btn" data-control="map-info" :is-dark="isDark" :title="t('mapInfo.open')"
+  <MapControlButton v-if="hosted" ref="btn" data-control="map-info" :is-dark="isDark" :shape="shape" :title="t('mapInfo.open')"
     aria-haspopup="dialog" aria-expanded="false" @click="openInfo">
     <svg xmlns="http://www.w3.org/2000/svg" width="18" height="18" viewBox="0 0 24 24" aria-hidden="true" focusable="false">
       <circle cx="12" cy="12" r="10" fill="none" stroke="currentColor" stroke-width="2" />
diff --git a/library/components/map-controls/ShareButton.vue b/library/components/map-controls/ShareButton.vue
index d66f2939c..a34e6a376 100644
--- a/library/components/map-controls/ShareButton.vue
+++ b/library/components/map-controls/ShareButton.vue
@@ -45,6 +45,9 @@ useShadowStyles(`
   -webkit-mask:linear-gradient(#000 0 0) content-box,linear-gradient(#000 0 0);-webkit-mask-composite:xor;mask-composite:exclude;
   opacity:0.6;animation:share-ring-turn 5s linear infinite;}
 .share-wrap:hover::before{opacity:0.95;}
+/* ROUNDED-SQUARE header form (design rule, 2026-09-30): the wrap and its rotating ring take the vertical
+   tabs' radius, so a circular ring can never wrap a square button. --vtl-radius is the one shared var. */
+.share-wrap--rounded-square,.share-wrap--rounded-square::before{border-radius:var(--vtl-radius,8px);}
 /* The ring itself rotates, so the colours travel around the button in every browser. */
 @keyframes share-ring-turn{to{transform:rotate(360deg);}}
 @media(prefers-reduced-motion:reduce){.share-wrap::before{animation:none;}}
@@ -333,7 +336,11 @@ const { t, tm, rt } = useI18n()
 
 const props = defineProps({
   isDark: { type: Boolean, default: false },
-  embedPath: { type: String, default: '' }
+  embedPath: { type: String, default: '' },
+  // 'round' (default) is the map-control form. 'rounded-square' is the dashboard HEADER form: the
+  // trigger button AND its rainbow ring take --vtl-radius (the vertical tabs' radius) instead of 50%,
+  // so a header Share button matches the header ⓘ and the tabs. Every existing consumer keeps 'round'.
+  shape: { type: String, default: 'round' }
 })
 
 /* ---- state ---- */
@@ -512,12 +519,13 @@ function bindAnchor(el) {
 <template>
   <!-- :ref is a FUNCTION, deliberately — it must run during render, before MapControlMenu's
        mounted hook latches its area. See bindAnchor() in <script> for why onMounted is too late. -->
-  <div :ref="bindAnchor" class="share-wrap" data-share-root>
+  <div :ref="bindAnchor" class="share-wrap" :class="{ 'share-wrap--rounded-square': shape === 'rounded-square' }" data-share-root>
     <MapControlButton
       ref="btnEl"
       data-control="share"
       :is-dark="isDark"
       :active="isOpen"
+      :shape="shape"
       :title="t('buttons.share')"
       @click="toggle"
     >
diff --git a/plugin-designs/doxa-maps-spa/src/tabInfo.js b/plugin-designs/doxa-maps-spa/src/tabInfo.js
index aa2c94037..cf58f2a7b 100644
--- a/plugin-designs/doxa-maps-spa/src/tabInfo.js
+++ b/plugin-designs/doxa-maps-spa/src/tabInfo.js
@@ -67,6 +67,13 @@ export const TAB_INFO = {
   },
   'dashboard-plus-grid': {
     storageKey: 'dashboard-plus-grid',
+    // ⓘ IN THE HEADER, NOT FLOATING (design rule, 2026-09-30). Big Picture draws its own ⓘ as a rounded-square
+    // header button beside Share (DashboardTopBar), announcing itself through MapInfoButton's control
+    // bridge. trigger:'control' hands this MapInfo to that header button and SUPPRESSES the floating ⓘ
+    // whenever it is on screen (fail-open: the grace period keeps the floating one off while the composite
+    // loads, so there is no flash, and it still shows if the header control never appears). The pos below
+    // stays as the FALLBACK placement for that floating button (a leaf without the header control).
+    trigger: 'control',
     // top 46px is the empty END of Big Picture's filter area at every width (1 row at 1440, 2 at 1024,
     // 3 at 800), but that bar is a positioned layer (z-index 55) painted above the button, which left it
     // unclickable (rega, 1440). raise lifts the BUTTON over the bar; the pointer stays under it.
diff --git a/plugin-designs/research-dashboard/src/components/dashboards/DashboardTopBar.vue b/plugin-designs/research-dashboard/src/components/dashboards/DashboardTopBar.vue
index e9f2cca5e..00c598195 100644
--- a/plugin-designs/research-dashboard/src/components/dashboards/DashboardTopBar.vue
+++ b/plugin-designs/research-dashboard/src/components/dashboards/DashboardTopBar.vue
@@ -95,6 +95,10 @@ import SearchBar from '@map/components/search/SearchBar.vue'
 // DashboardBreadcrumb is NOT imported here — it renders bus.filterSet, i.e. selection state, which
 // this header must not show (see the ★ rule at the top). It remains exported from ./index.js.
 import ShareButton from '@map/components/map-controls/ShareButton.vue'
+// The header ⓘ ("What can this map do?"). It reuses the map-control MapInfoButton in its HEADER form
+// (shape="rounded-square"): the same control bridge announces to the tab's MapInfo (trigger:'control'
+// in doxa-maps-spa/src/tabInfo.js), which suppresses the gallery's floating ⓘ — exactly one ⓘ, fail-open.
+import MapInfoButton from '@map/components/map-controls/MapInfoButton.vue'
 import { lbl } from '@map/composables/useFacetAggregation.js'
 
 const dash = inject('dashboardData', null)
@@ -216,24 +220,26 @@ useShadowStyles(`
   .rd-topbar .rd-ttl{ font-weight:800; font-size:var(--fs-lg,13px); letter-spacing:.2px; color:var(--rd-header-ink,#f3f3f1); }
   .rd-topbar .rd-ttl .dot{ color:var(--rd-accent,#e67e22); }
   .rd-topbar .rd-spacer{ flex:1; }
-  /* SHARE in this bar (reported 2026-09-28: "too large"). ShareButton is the map toolbar's 40px round button
-     (36px under 768px) + a 2px rainbow ring, so it measured 44px in a 38px bar: taller than the bar itself.
-     Here it takes the bar's own control scale instead: 28px + the ring = 32px, the search box's height, with the
-     icon at the search icon's 15px. Scoped to .rd-topbar, so the map toolbars keep their 40px button. */
-  .rd-topbar .share-wrap .mcb{ width:28px; height:28px; position:relative; }
-  .rd-topbar .share-wrap .mcb svg{ width:15px; height:15px; }
-  /* ★ THE BUTTON GOT SMALLER TO LOOK RIGHT; THE THING A FINGER HAS TO HIT DID NOT HAVE TO. Shrinking the
-     control to 28px (32 with the ring) also shrank the TAP TARGET to 32px, and this repo states its own
-     floor in two places — DataTable.vue:294 "44px is the accessible tap target; anything smaller is a miss
-     on a phone", and LegendDesktop.vue:124 sizing rows to keep it. A transparent box centred on the button
-     restores the target without moving a pixel of the drawing: it is absolutely positioned, so it changes
-     no layout, and it is part of the button, so it takes the same clicks.
-     ★ 44 WIDE, 38 TALL, AND THE SHORTFALL IS DELIBERATE RATHER THAN OVERLOOKED. The bar is 38px
-     (--rd-topbar-h), so 44 vertical cannot fit inside it: the extra 3px each side would hang over the
-     filters row below and start eating taps meant for a filter — trading one miss for another. 44x38 is
-     the largest target that costs nothing. Closing the last 6px needs a taller bar, which is a look
-     decision already made in the other direction, so it is asked rather than assumed. */
-  .rd-topbar .share-wrap .mcb::after{
+  /* HEADER BUTTONS — the ⓘ + Share, rounded squares at the vertical tabs' radius (design rule, 2026-09-30).
+     The rounded-square SHAPE is not set here: it comes from each button's shape="rounded-square" prop
+     (library MapControlButton → border-radius:var(--vtl-radius)), so the header button and the gallery's
+     tabs share ONE radius variable and can never drift. This bar only sizes them to its own control scale
+     and restores the tap target — the same treatment the Share button already had, now covering both so
+     the ⓘ matches it exactly. Scoped to .rd-topbar, so the map toolbars keep their 40px round buttons.
+     Reported 2026-09-28 ("too large"): ShareButton is a 40px round map control + a 2px rainbow ring, 44px
+     in a 38px bar. Here both take 28px (+ Share's ring = 32px, the search box's height), icon 16px. */
+  .rd-topbar .rd-header-btns{ display:inline-flex; align-items:center; gap:8px; flex:0 0 auto; }
+  .rd-topbar .rd-header-btns .mcb{ --map-btn-size:28px; position:relative; }
+  .rd-topbar .rd-header-btns .mcb svg{ width:16px; height:16px; }
+  /* ★ THE BUTTONS ARE 28px TO LOOK RIGHT; THE THING A FINGER HAS TO HIT IS NOT. This repo states its own
+     44px floor twice — DataTable.vue:294 ("44px is the accessible tap target; anything smaller is a miss
+     on a phone") and LegendDesktop.vue:124. A transparent box centred on each button restores the target
+     without moving a pixel of the drawing: absolutely positioned, so it changes no layout, and part of the
+     button, so it takes the same clicks.
+     ★ 44 WIDE, 38 TALL, AND THE SHORTFALL IS DELIBERATE. The bar is 38px (--rd-topbar-h), so 44 vertical
+     cannot fit inside it: the extra 3px each side would hang over the filters row below and start eating
+     taps meant for a filter — trading one miss for another. 44x38 is the largest target that costs nothing. */
+  .rd-topbar .rd-header-btns .mcb::after{
     content:''; position:absolute; left:50%; top:50%; transform:translate(-50%,-50%);
     width:44px; height:var(--rd-topbar-h,38px);
   }
@@ -340,12 +346,18 @@ useShadowStyles(`
     <!-- CSV export MOVED to the people-groups table header (DashboardDataTable), below the map —
          card BUILD-CSV-EXPORT-MOVE-TO-TABLE-HEADER-ALL-FIELDS. It exports THAT table, so it now
          lives on that table's header bar, which stays docked even when the table is collapsed. -->
-    <!-- SHARE the WHOLE dashboard (decided 2026-09-20): "if we could actually embed this on a
-         partner site from one share button... they can embed this map on all their partner
-         websites." Reuses the SAME ShareButton the upg-100 MFE ships (no hand-rolled variant); the
-         embed path is THIS profile's tree-relative leaf, which ShareButton joins to the served tree
-         root — so the snippet it hands out works from whatever host the tree was dropped on. It
-         sits where the CSV button used to be, the top-right of the dashboard. -->
-    <ShareButton :embed-path="SHARE_EMBED_PATH" />
+    <!-- HEADER BUTTONS (design rule, 2026-09-30): a rounded-square ⓘ to the LEFT of a rounded-square Share.
+         DOM order [ⓘ, Share] gives ⓘ at the logical START — left in English, and RIGHT of Share in
+         Arabic, because this flex row reverses its main axis under dir=rtl. Both are the SAME reusable
+         header-button form, shape="rounded-square" (radius = the vertical tabs' --vtl-radius).
+         SHARE the WHOLE dashboard (decided 2026-09-20): "if we could actually embed this on a partner
+         site from one share button." Reuses the SAME ShareButton the upg-100 MFE ships (no hand-rolled
+         variant); the embed path is THIS profile's tree-relative leaf, which ShareButton joins to the
+         served tree root. The ⓘ reuses MapInfoButton — it renders ONLY once the tab's MapInfo answers
+         (fail-open: no host, no ⓘ, same as before), so a standalone leaf with no gallery is unchanged. -->
+    <div class="rd-header-btns" data-header-btns>
+      <MapInfoButton shape="rounded-square" />
+      <ShareButton :embed-path="SHARE_EMBED_PATH" shape="rounded-square" />
+    </div>
   </header>
 </template>