diff --git a/vein/web/src/app.tsx b/vein/web/src/app.tsx
index c970b5f31..603478127 100644
--- a/vein/web/src/app.tsx
+++ b/vein/web/src/app.tsx
@@ -57,10 +57,15 @@ function countIterations(events: api.RunEvent[], prefix: string): number {
 }
 
 export function App() {
+  // Deep-links: ?wf=<workflow>&run=<runId>&v=<version> select on load and are
+  // kept in sync (replaceState) as the selection changes, so the address bar
+  // is always a shareable link to what's on screen. (?chat is read below and
+  // preserved by the sync.)
+  const [initialUrl] = useState(() => new URLSearchParams(location.search));
   const [workflows, setWorkflows] = useState<api.WorkflowEntry[]>([]);
   const [runs, setRuns] = useState<api.RunSummary[]>([]);
-  const [selectedWf, setSelectedWf] = useState<string | null>(null);
-  const [selectedRun, setSelectedRun] = useState<string | null>(null);
+  const [selectedWf, setSelectedWf] = useState<string | null>(initialUrl.get("wf"));
+  const [selectedRun, setSelectedRun] = useState<string | null>(initialUrl.get("run"));
   const [events, setEvents] = useState<api.RunEvent[]>([]);
   const [running, setRunning] = useState(false);
   // Bumped after a durable resume so the run-view effect re-tails the log
@@ -124,7 +129,10 @@ export function App() {
   // Version picker: which version of the selected workflow the canvas shows.
   // Stored with the workflow it was pinned for, so the pin self-invalidates
   // when the selection changes (no effect-ordering games). null = active.
-  const [versionPin, setVersionPin] = useState<{ wf: string | null; v: string | null }>({ wf: null, v: null });
+  const [versionPin, setVersionPin] = useState<{ wf: string | null; v: string | null }>(() => ({
+    wf: initialUrl.get("v") ? initialUrl.get("wf") : null,
+    v: initialUrl.get("v"),
+  }));
   const viewVersion = versionPin.wf === selectedWf ? versionPin.v : null;
   const setViewVersion = useCallback(
     (v: string | null) => setVersionPin({ wf: selectedWf, v }),
@@ -134,6 +142,22 @@ export function App() {
   // against the active version (Publish always builds on active, Run runs it).
   const viewingOld = viewVersion != null && activeVersion != null && viewVersion !== activeVersion;
 
+  // Mirror the selection into the address bar (replaceState — no history
+  // spam) so the current view is always copy-paste shareable. Unrelated
+  // params (e.g. ?chat) are preserved.
+  useEffect(() => {
+    const p = new URLSearchParams(location.search);
+    const put = (k: string, val: string | null) => (val ? p.set(k, val) : p.delete(k));
+    put("wf", selectedWf);
+    put("run", selectedRun);
+    put("v", viewVersion);
+    const qs = p.toString();
+    const next = `${location.pathname}${qs ? `?${qs}` : ""}${location.hash}`;
+    if (next !== `${location.pathname}${location.search}${location.hash}`) {
+      history.replaceState(null, "", next);
+    }
+  }, [selectedWf, selectedRun, viewVersion]);
+
   // ── Sidebar grouping ─────────────────────────────────────────────────────
   // Workflows grouped by category; groups (and workflows within them) are
   // ordered by most-recent run so the active experiment floats to the top.
diff --git a/vein/web/src/components/EventsPanel.tsx b/vein/web/src/components/EventsPanel.tsx
index 96ab13b06..1bcca640c 100644
--- a/vein/web/src/components/EventsPanel.tsx
+++ b/vein/web/src/components/EventsPanel.tsx
@@ -4,6 +4,7 @@ import { eventTone, statusTone } from "../helpers";
 import { ValueFields } from "./ValueFields";
 import { StepData } from "../flow-to-canvas";
 import { CloseIcon } from "../icons";
+import { EvolveChart } from "./EvolveChart";
 import yaml from "js-yaml";
 
 // ── Events Panel (expandable rows) ─────────────────────────────────────────
@@ -62,6 +63,7 @@ export function EventsPanel(props: {
   return (
     <div class="shell-events" ref={scrollRef} onScroll={onScroll}>
       <div class="events-header">Events ({props.events.length})</div>
+      <EvolveChart events={props.events} onOpenRun={props.onOpenRun} />
       {props.events.map((evt, i) => {
         const hasData = evt.input != null || evt.output != null || evt.error != null;
         const isOpen = expanded === i;
diff --git a/vein/web/src/components/EvolveChart.tsx b/vein/web/src/components/EvolveChart.tsx
new file mode 100644
index 000000000..cb2b7e082
--- /dev/null
+++ b/vein/web/src/components/EvolveChart.tsx
@@ -0,0 +1,241 @@
+import * as api from "../api";
+
+// ── Evolve hill-climb chart ────────────────────────────────────────────────
+//
+// Renders the fitness trajectory of an eval/evolve-loop step from the run's
+// event stream alone — no API beyond the events the panel already has. The
+// loop emits synthetic per-generation events at `<path>#<gen>` whose
+// step.end/step.replayed output carries { gen, fitness, bestFitness, bestGen,
+// directive, version, knownCost, runs } (see eval/evolve-loop's emitGen), so
+// the chart derives everything live: a dashed baseline, the best-so-far
+// staircase, and one dot per generation (filled = new best, amber stroke =
+// explore directive, ✕ = failed generation, pulsing = still running).
+// Clicking a dot opens that generation's run via the same run-ref plumbing
+// the event rows use.
+
+interface GenPoint {
+  gen: number;
+  status: "done" | "replayed" | "error" | "pending";
+  fitness?: number;
+  bestFitness?: number;
+  bestGen?: number;
+  directive?: string;
+  version?: string;
+  knownCost?: number;
+  run?: { workflow: string; runId: string };
+  error?: string;
+}
+
+interface EvolveSeries {
+  baseline?: number;
+  points: GenPoint[];
+}
+
+/** Collect the evolve-loop's per-generation events into an ordered series.
+ *  Returns null when the run has no evolve-loop generation events at all. */
+export function evolveSeries(events: api.RunEvent[]): EvolveSeries | null {
+  const byGen = new Map<number, GenPoint>();
+  let baseline: number | undefined;
+  // Multiple evolve loops in one run is theoretical; pin to the first path
+  // prefix seen so a second loop can't interleave garbage into the chart.
+  let prefix: string | undefined;
+
+  for (const e of events) {
+    if (e.stepType !== "eval/evolve-loop") continue;
+    const hi = e.path.lastIndexOf("#");
+    if (hi < 0) continue;
+    const p = e.path.slice(0, hi);
+    if (prefix === undefined) prefix = p;
+    else if (p !== prefix) continue;
+    const gen = Number(e.path.slice(hi + 1));
+    if (!Number.isInteger(gen) || gen < 0) continue;
+
+    const cur: GenPoint = byGen.get(gen) ?? { gen, status: "pending" };
+    if (e.type === "step.start") {
+      const inp = e.input as { directive?: string; bestFitness?: number } | undefined;
+      if (typeof inp?.directive === "string") cur.directive = inp.directive;
+      // Gen 0's start is briefed with bestFitness === the baseline fitness.
+      if (gen === 0 && typeof inp?.bestFitness === "number") baseline = inp.bestFitness;
+    } else if (e.type === "step.end" || e.type === "step.replayed") {
+      const o = (e.output ?? {}) as Record<string, unknown>;
+      cur.status = e.type === "step.end" ? "done" : "replayed";
+      if (typeof o.fitness === "number") cur.fitness = o.fitness;
+      if (typeof o.bestFitness === "number") cur.bestFitness = o.bestFitness;
+      if (typeof o.bestGen === "number") cur.bestGen = o.bestGen;
+      if (typeof o.directive === "string") cur.directive = o.directive;
+      if (typeof o.version === "string") cur.version = o.version;
+      if (typeof o.knownCost === "number") cur.knownCost = o.knownCost;
+      const r = Array.isArray(o.runs) ? (o.runs[0] as Record<string, unknown> | undefined) : undefined;
+      if (r && typeof r.workflow === "string" && typeof r.runId === "string") {
+        cur.run = { workflow: r.workflow, runId: r.runId };
+      }
+      // A replayed gen 0 that had not yet beaten the baseline still tells us
+      // the baseline (its bestFitness anchor is the baseline itself).
+      if (gen === 0 && baseline === undefined && cur.bestGen === -1 && typeof cur.bestFitness === "number") {
+        baseline = cur.bestFitness;
+      }
+    } else if (e.type === "step.error") {
+      cur.status = "error";
+      cur.error = e.error?.message;
+      cur.fitness = 0;
+    }
+    byGen.set(gen, cur);
+  }
+
+  if (byGen.size === 0) return null;
+  const points = [...byGen.values()].sort((a, b) => a.gen - b.gen);
+  return { baseline, points };
+}
+
+const PAD_L = 34; // room for y labels
+const PAD_R = 14;
+const PAD_T = 12;
+const PAD_B = 20; // room for gen labels
+const X_STEP = 56;
+const PLOT_H = 96;
+
+export function EvolveChart(props: {
+  events: api.RunEvent[];
+  onOpenRun?: (workflow: string, runId: string) => void;
+}) {
+  const series = evolveSeries(props.events);
+  if (!series) return null;
+  const { baseline, points } = series;
+
+  const H = PAD_T + PLOT_H + PAD_B;
+  // x slot 0 is the baseline anchor; generations start at slot 1.
+  const slots = points.length + 1;
+  const W = PAD_L + (slots - 1) * X_STEP + PAD_R;
+  const x = (slot: number) => PAD_L + slot * X_STEP;
+  const y = (fitness: number) => PAD_T + (1 - Math.max(0, Math.min(1, fitness))) * PLOT_H;
+
+  // Best-so-far staircase, anchored at the baseline. Each finished gen's
+  // output.bestFitness is the loop's own computation — no re-deriving.
+  let prevBest = baseline;
+  const stair: string[] = [];
+  if (baseline !== undefined) stair.push(`M ${x(0)} ${y(baseline)}`);
+  points.forEach((p, i) => {
+    const b = p.bestFitness ?? prevBest;
+    if (b === undefined) return;
+    const xi = x(i + 1);
+    if (stair.length === 0) stair.push(`M ${xi} ${y(b)}`);
+    else {
+      if (prevBest !== undefined) stair.push(`L ${xi} ${y(prevBest)}`);
+      stair.push(`L ${xi} ${y(b)}`);
+    }
+    prevBest = b;
+  });
+
+  const bestPoint = points.reduce<GenPoint | null>(
+    (acc, p) => (p.fitness !== undefined && (!acc || p.fitness > (acc.fitness ?? 0)) ? p : acc),
+    null,
+  );
+  const best = prevBest;
+  const gridLines = [0, 0.25, 0.5, 0.75, 1];
+
+  return (
+    <div class="evolve-chart">
+      <div class="evolve-chart-header">
+        <span class="evolve-chart-title">hill-climb</span>
+        {baseline !== undefined && <span class="evolve-chart-stat">baseline {fmt(baseline)}</span>}
+        {best !== undefined && (
+          <span class="evolve-chart-stat evolve-chart-best">
+            best {fmt(best)}
+            {bestPoint && bestPoint.bestGen !== undefined && bestPoint.bestGen >= 0 ? ` (gen ${bestPoint.bestGen})` : ""}
+          </span>
+        )}
+      </div>
+      <svg width={W} height={H} viewBox={`0 0 ${W} ${H}`} class="evolve-chart-svg">
+        {gridLines.map((g) => (
+          <g key={g}>
+            <line x1={PAD_L - 4} y1={y(g)} x2={W - PAD_R} y2={y(g)} class="evolve-grid" />
+            <text x={PAD_L - 8} y={y(g) + 3} class="evolve-ylabel">
+              {g === 0 || g === 1 || g === 0.5 ? g : ""}
+            </text>
+          </g>
+        ))}
+
+        {baseline !== undefined && (
+          <line x1={x(0)} y1={y(baseline)} x2={W - PAD_R} y2={y(baseline)} class="evolve-baseline" />
+        )}
+        {stair.length > 1 && <path d={stair.join(" ")} class="evolve-stair" />}
+
+        {/* baseline anchor */}
+        {baseline !== undefined && (
+          <g>
+            <circle cx={x(0)} cy={y(baseline)} r={3.5} class="evolve-dot-base" />
+            <text x={x(0)} y={H - 6} class="evolve-xlabel">base</text>
+          </g>
+        )}
+
+        {points.map((p, i) => {
+          const xi = x(i + 1);
+          const label = `gen ${p.gen}`;
+          const clickable = p.run && props.onOpenRun;
+          const open = () => clickable && props.onOpenRun!(p.run!.workflow, p.run!.runId);
+          const tip = [
+            label,
+            p.version ? `version ${p.version}` : null,
+            p.fitness !== undefined ? `fitness ${fmt(p.fitness)}` : null,
+            best !== undefined && p.fitness !== undefined
+              ? `Δ best ${fmt(p.fitness - (p.bestGen === p.gen ? (points[i - 1]?.bestFitness ?? baseline ?? 0) : (p.bestFitness ?? 0)))}`
+              : null,
+            p.directive ? `directive: ${p.directive}` : null,
+            p.knownCost !== undefined ? `cost $${p.knownCost}` : null,
+            p.status === "error" ? `FAILED: ${p.error ?? "unknown"}` : null,
+            p.status === "pending" ? "running…" : null,
+            clickable ? "click to open run" : null,
+          ]
+            .filter(Boolean)
+            .join("\n");
+
+          if (p.status === "error") {
+            return (
+              <g key={p.gen} class="evolve-pt" onClick={open}>
+                <text x={xi} y={y(0) + 4} class="evolve-err">✕<title>{tip}</title></text>
+                <text x={xi} y={H - 6} class="evolve-xlabel">{p.gen}</text>
+              </g>
+            );
+          }
+          if (p.status === "pending") {
+            const yy = y(prevBestBefore(points, i, baseline));
+            return (
+              <g key={p.gen} class="evolve-pt">
+                <circle cx={xi} cy={yy} r={4.5} class="evolve-dot-pending"><title>{tip}</title></circle>
+                <text x={xi} y={H - 6} class="evolve-xlabel">{p.gen}</text>
+              </g>
+            );
+          }
+          const improved = p.bestGen === p.gen;
+          const explore = p.directive === "explore";
+          return (
+            <g key={p.gen} class={`evolve-pt${clickable ? " evolve-pt-link" : ""}`} onClick={open}>
+              <circle
+                cx={xi}
+                cy={y(p.fitness ?? 0)}
+                r={improved ? 5 : 4}
+                class={`evolve-dot ${improved ? "evolve-dot-best" : "evolve-dot-miss"}${explore ? " evolve-dot-explore" : ""}`}
+              >
+                <title>{tip}</title>
+              </circle>
+              <text x={xi} y={H - 6} class="evolve-xlabel">{p.gen}</text>
+            </g>
+          );
+        })}
+      </svg>
+    </div>
+  );
+}
+
+/** Best fitness known just BEFORE generation i (where a pending dot hovers). */
+function prevBestBefore(points: GenPoint[], i: number, baseline?: number): number {
+  for (let j = i - 1; j >= 0; j--) {
+    const b = points[j]?.bestFitness;
+    if (typeof b === "number") return b;
+  }
+  return baseline ?? 0.5;
+}
+
+function fmt(n: number): string {
+  return String(Math.round(n * 1000) / 1000);
+}
diff --git a/vein/web/src/styles/components.css b/vein/web/src/styles/components.css
index 267f24332..3c6e25b6d 100644
--- a/vein/web/src/styles/components.css
+++ b/vein/web/src/styles/components.css
@@ -1703,3 +1703,76 @@ body.is-resizing-flyout * {
   font-size: 11px;
 }
 
+
+/* ─── evolve hill-climb chart ────────────────────────────────── */
+
+.evolve-chart {
+  margin: var(--sp-2) 0 var(--sp-3);
+  padding: var(--sp-2) var(--sp-3);
+  background: var(--surface);
+  border: 1px solid var(--border);
+  border-radius: var(--r-md);
+  overflow-x: auto;
+}
+.evolve-chart-header {
+  display: flex;
+  align-items: baseline;
+  gap: var(--sp-3);
+  margin-bottom: var(--sp-1);
+  font-size: 11px;
+}
+.evolve-chart-title {
+  color: var(--text-muted);
+  font-weight: 600;
+  letter-spacing: 0.03em;
+  text-transform: uppercase;
+}
+.evolve-chart-stat {
+  color: var(--text-dim);
+  font-family: var(--font-mono);
+}
+.evolve-chart-best { color: var(--ok); }
+.evolve-chart-svg { display: block; }
+.evolve-grid { stroke: var(--border); stroke-width: 1; }
+.evolve-ylabel, .evolve-xlabel {
+  fill: var(--text-dim);
+  font-size: 9px;
+  font-family: var(--font-mono);
+  text-anchor: middle;
+}
+.evolve-ylabel { text-anchor: end; }
+.evolve-baseline {
+  stroke: var(--text-dim);
+  stroke-width: 1;
+  stroke-dasharray: 4 3;
+  opacity: 0.7;
+}
+.evolve-stair {
+  fill: none;
+  stroke: var(--ok);
+  stroke-width: 1.5;
+  opacity: 0.85;
+}
+.evolve-dot-base { fill: var(--text-dim); }
+.evolve-dot { stroke-width: 1.5; }
+.evolve-dot-best { fill: var(--ok); stroke: var(--ok); }
+.evolve-dot-miss { fill: var(--surface); stroke: var(--accent); }
+.evolve-dot-explore { stroke: var(--warning); }
+.evolve-dot-pending {
+  fill: none;
+  stroke: var(--accent);
+  stroke-width: 1.5;
+  animation: evolve-pulse 1.4s ease-in-out infinite;
+}
+.evolve-err {
+  fill: var(--danger);
+  font-size: 11px;
+  text-anchor: middle;
+  font-weight: 700;
+}
+.evolve-pt-link { cursor: pointer; }
+.evolve-pt-link:hover .evolve-dot { stroke-width: 2.5; }
+@keyframes evolve-pulse {
+  0%, 100% { opacity: 0.35; }
+  50% { opacity: 1; }
+}