feat(mockups): restyle the shared filter sheet, and give the segment bar a job

docs/site-map.md

@@ -1018,6 +1018,7 @@ This file is generated by `npm run docs:update` (or `npm run sitemap:update` dir
 - `/mockups/favourites-review-console` - Route discovered from app directory Source: `src/app/mockups/favourites-review-console/page.tsx`.
 - `/mockups/favourites-set-board` - Route discovered from app directory Source: `src/app/mockups/favourites-set-board/page.tsx`.
 - `/mockups/favourites-set-navigator` - Route discovered from app directory Source: `src/app/mockups/favourites-set-navigator/page.tsx`.
+- `/mockups/filter-sheet-restyle` - Route discovered from app directory Source: `src/app/mockups/filter-sheet-restyle/page.tsx`.
 - `/mockups/medication-prescribing` - Route discovered from app directory Source: `src/app/mockups/medication-prescribing/page.tsx`.
 - `/mockups/mode-dropdown` - Route discovered from app directory Source: `src/app/mockups/mode-dropdown/page.tsx`.
 - `/mockups/phone-inpage-navigation` - Route discovered from app directory Source: `src/app/mockups/phone-inpage-navigation/page.tsx`.

mockups/README.md

@@ -127,3 +127,35 @@ has to be unpicked afterwards.
 The facet engine, chips, band and sheet shell are imported from the round-one study rather than
 copied — the ~1KB bitmask table would otherwise be duplicated against a finite `mockups` bundle
 budget, and two studies quoting different numbers for the same catalogue would discredit both.
+
+### Round three — restyle, and a job for the segment bar (2026-08-12)
+
+Runnable study at [`/mockups/filter-sheet-restyle`](../src/app/mockups/filter-sheet-restyle/page.tsx). Rounds one and
+two settled the information architecture; this one is about craft, drawn on the **formulation** sheet because that is
+the specimen that stresses the layout hardest — four domain themes, twelve domains, twelve mechanisms, four presets, thirteen domain chips, and the longest title in the app.
+
+**The segment bar carries scope, not a verb.** Round two used it for "narrow these / start a new search", which is a
+mode set once and rarely changed — a poor use of the most valuable strip in the sheet. Here it is
+`These results 2 | All mechanisms 12`, with live counts on both segments. That is a decision the reader makes
+constantly and which nothing in the product currently answers: filtering two results by twelve domains is close to
+pointless, and today the only way to reach the full set is to clear the query and lose it. It also makes the empty
+state recoverable — the commit button becomes "Show N in all mechanisms" instead of a dead end.
+
+| Style                | Shape                                                                                                       | Best for                             |
+| -------------------- | ----------------------------------------------------------------------------------------------------------- | ------------------------------------ |
+| A — Refined clinical | Shipped structure, craft fixed: tinted header, eyebrow/title/live-count, ghost close, uniform counted chips | Cheapest adoption, no new containers |
+| B — Themed cards     | Each theme a card with icon, label and the library's own description, tinting when it holds a selection     | Many options without a word cloud    |
+| C — Dense list       | Full-width rows, proportion bar, right-aligned count column, sticky group headings                          | Scanning to a known domain           |
+
+Three defects the study documents, all verifiable in source:
+
+1. **Biological, Social and Cultural match zero of the twelve mechanisms.** They are offered as domain chips and can
+   never return anything. Counts expose this on sight; without them it is invisible.
+2. **`formulationDomainGroups` already exists** in `src/lib/formulation.ts` — four themes, each with a written
+   description — and the sheet ignores it, rendering one flat ragged wrap of twelve chips.
+3. **`formulationSearchPresets.slice(0, 4)` of five** means "If it is not perfect" is unreachable from the filter.
+
+One deliberate departure from the services study: the per-option count here is the **intrinsic** count (how many
+mechanisms carry that domain), not "the total if I added this". Domains are a single OR group, so the union contract
+reports the unchanged total for an empty domain — Cultural would read `7`, indistinguishable from a full one. The
+commit button remains the thing that predicts the outcome.

src/app/mockups/filter-sheet-restyle/page.tsx

@@ -0,0 +1,13 @@
+import type { Metadata } from "next";
+
+import { FilterSheetRestyleMockupsPage } from "@/components/filter-sheet-restyle-mockups";
+
+export const metadata: Metadata = {
+  title: "Filter sheet restyle · three styles - Clinical KB",
+  description:
+    "Three style directions for the shared filter sheet, drawn on the formulation specimen, with the segmented bar repurposed as a result-scope control.",
+};
+
+export default function FilterSheetRestyleMockupPage() {
+  return <FilterSheetRestyleMockupsPage />;
+}

src/app/mockups/mockups-layout-client.tsx

@@ -37,6 +37,10 @@ export function MockupsLayoutClient({ children }: { children: ReactNode }) {
   // beside it — that is the concept under judgement, so the shared composer
   // above it would be a second, real search bar competing with the proposal.
   const isServicesFilterOptionsMockup = pathname === "/mockups/services-filter-options";
+  // Draws its own formulation band and an in-frame filter sheet in every device
+  // frame; the shared composer would read as a second, real search bar over a
+  // study about the control that opens from that band.
+  const isFilterSheetRestyleMockup = pathname === "/mockups/filter-sheet-restyle";
   const isPhoneInPageNavigationMockup = pathname === "/mockups/phone-inpage-navigation";
   // Draws its own composer in every frame, and the notice under study is the one
   // the shared composer renders — showing both would put two different privacy
@@ -94,6 +98,7 @@ export function MockupsLayoutClient({ children }: { children: ReactNode }) {
         !isSearchBandDirectionsMockup &&
         !isServicesFilterRefinedMockup &&
         !isServicesFilterOptionsMockup &&
+        !isFilterSheetRestyleMockup &&
         !isTherapyNavigationMockup &&
         !isWarningConsolidationMockup &&
         !isWarningLineMockup &&
@@ -111,6 +116,7 @@ export function MockupsLayoutClient({ children }: { children: ReactNode }) {
         !isSearchBandDirectionsMockup &&
         !isServicesFilterRefinedMockup &&
         !isServicesFilterOptionsMockup &&
+        !isFilterSheetRestyleMockup &&
         !isPhoneInPageNavigationMockup &&
         !isTherapyNavigationMockup &&
         !isWarningConsolidationMockup &&