df2w: an open, empty formula panel is drawn

views/formulas were empty-means-closed, so an open panel over a document
with no formulas built the same RenderModel as a closed one. Option<Vec<_>>
carries both facts in one field; the page hides on null.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01VdfEGXA7aJ6ftMsCc9PJze

context/code/clients.md

@@ -1476,6 +1476,19 @@ what says it is closed**. That is the shape `col_groups` already uses for "this
 grid has no column groups" — an absent list rather than a flag the page has to
 interpret alongside a mode it would then have to understand.
 
+**That shape is only sound where "open" implies "non-empty"**, and help is the
+one place it does — its content is static. `views` and `formulas` borrowed it
+and were wrong: a document with no formulas opened a formula panel that built
+the same `RenderModel` as a closed one, so the page hid it under a mode reading
+FORMULAS (improvise-df2w). Both are now `Option<Vec<_>>` — `None` closed,
+`Some(vec![])` open and empty — one field, so the two facts cannot disagree,
+where a `formula_panel_open` flag beside the rows (the `category_panel_open`
+shape) would have been two. The same mistake as improvise-xg1z: an absence
+spent on encoding a second fact. What the page does **not** yet draw is the
+TUI's empty-state line (`(no formulas — press 'n' to add)`); that string lives
+in `src/ui/formula_panel.rs`, and copying it into `render.rs` would be a second
+home for it.
+
 The rows themselves are `improvise_protocol::help::pages()`, the same ones
 `src/ui/help.rs` draws. `RenderHelpRow` carries a `kind` string
 (`heading`, `keys`, `accent`, …) which is a *semantic* name the page maps to a

context/test-evidence/clients.md

@@ -1130,8 +1130,8 @@ Normal and never closes the panel, exactly as `src/draw.rs` keeps drawing it
 off `view_panel_open` alone. Asserting it hidden would have pinned the browser
 to behaviour the TUI does not have.
 
-The gating rule itself — an empty list is what says a panel is closed, the same
-rule `help` follows — is asserted in Rust as well, by
+The gating rule itself — `None` is what says a panel is closed (it was an empty
+list, the rule `help` follows, until improvise-df2w) — is asserted in Rust as well, by
 `a_closed_panel_projects_no_rows_and_an_open_one_does` and
 `the_tile_bar_is_always_present_and_only_its_cursor_is_modal`, because a browser
 test cannot distinguish "closed" from "the cache is empty" and those two tests
@@ -4177,3 +4177,30 @@ and converged.
 
 **Fault injected:** the same `Binding::Prefix` → `Upstream` reversion. Fails on
 the second press.
+
+### `an_open_empty_panel_is_not_a_closed_one`
+
+improvise-df2w. `views` and `formulas` said "closed" by being empty, so an open
+formula panel over a document with no formulas built a `RenderModel` identical
+to a closed one, and the page hid it while the mode read FORMULAS. The test
+compares the two models whole rather than asserting a field, so it does not
+depend on how the difference is spelled.
+
+**Reproduced:** fails at HEAD before the fix with `left == right` on the formula
+half — the two models were byte-identical. The existing
+`a_closed_panel_projects_no_rows_and_an_open_one_does` could not see it, because
+it fills both caches before opening the panels.
+
+### the formula panel opens over a document with no formulas
+
+The browser half of improvise-df2w, in `harness/tests/contract.spec.js`, over
+`harness/fixtures/tall.improv`, which has no `## Formulas` section. It asserts
+**both** directions, because each rival fails a different one.
+
+**Reproduced:** against a bundle built from the unfixed `render.rs` and
+`app.js`, fails at `#formulas` `toBeVisible()`, immediately after `#mode` reads
+FORMULAS — the exact disagreement the ticket describes.
+
+**Fault injected:** `paintPanel` writing `host.hidden = false` (a page that
+stops inferring closed and simply never hides). Fails at the launch-time
+`toBeHidden()` before the panel is opened.

harness/tests/contract.spec.js

@@ -70,7 +70,7 @@ test.describe("every field the render model projects reaches the screen", () =>
     await expect(page.locator("#categories")).toBeVisible();
     await page.keyboard.press("Escape");
 
-    // `views`: empty unless open, so the page asks no question about the mode.
+    // `views`: `null` unless open, so the page asks no question about the mode.
     await expect(page.locator("#views")).toBeHidden();
     await page.keyboard.press("Shift+V");
     await expect(page.locator("#views li")).toHaveCount(2);
@@ -356,6 +356,27 @@ test.describe("a pointer event reaches the client and its answer is painted", ()
   });
 });
 
+test.describe("an open panel is drawn even when it has nothing in it", () => {
+  // improvise-df2w: `formulas` said "closed" by being empty, so a document with
+  // no formulas could open the panel and never see it. `tall.improv` has none.
+  test("the formula panel opens over a document with no formulas", async ({ page }) => {
+    await page.goto("/app/index.html?doc=df2w-empty.improv&seed=tall.improv");
+    await expect(page.locator("#grid table")).toBeVisible({ timeout: 20_000 });
+    await page.locator("#grid").focus();
+    await expect(page.locator("#formulas")).toBeHidden();
+
+    await page.keyboard.press("Shift+F");
+    await expect(page.locator("#mode")).toHaveText("FORMULAS");
+    await expect(page.locator("#formulas")).toBeVisible();
+    await expect(page.locator("#formulas li")).toHaveCount(0);
+
+    // And closed is still closed: the other direction, which a page that
+    // simply never hid the panel would fail.
+    await page.keyboard.press("Shift+F");
+    await expect(page.locator("#formulas")).toBeHidden();
+  });
+});
+
 test.describe("the selection is on screen", () => {
   // improvise-jq8l: `web/app.js` called `scrollIntoView` NOWHERE, so a selection
   // moved past the bottom of `#grid` simply stayed there, invisible, with no way