submit: reject runs whose output would overwrite an existing fig

Before dispatching to Prefect, check if figs/<stem>.html already exists.
If so, return 409 with a message asking to bump seed/jitter/N/T or delete
the fig. Stem is derived from (generator, embedder, N, T, J, seed), so
embed_args-only changes still collide and are blocked — users must vary
a stem-shaping param to get a distinct output file.

app/web/main.py

@@ -751,6 +751,24 @@ async def submit(request: Request) -> HTMLResponse:
 
     embed_args = build_embed_args(reducer, data)
 
+    # Reject submissions whose output path would overwrite an existing fig.
+    # The stem is fully determined by (generator, embedder, N, T, J, seed) —
+    # embed_args don't affect the filename, so e.g. UMAP(n_neighbors=5) and
+    # UMAP(n_neighbors=15) with otherwise-matching params collide too. Force
+    # the user to change a stem-shaping param (seed is usually cheapest) or
+    # delete the existing fig first.
+    _, emb_file = synthesize_output_paths(
+        generator_path, reducer, num_points, num_timesteps, jitter_scale, seed
+    )
+    if (FIGS_DIR / emb_file).exists():
+        return HTMLResponse(
+            f"<div class='flash err'>a run with these params already exists "
+            f"(<code>{emb_file}</code>). change <code>seed</code> / "
+            f"<code>jitter</code> / <code>N</code> / <code>T</code>, or delete "
+            f"the fig first.</div>",
+            status_code=409,
+        )
+
     parameters: Dict[str, Any] = {
         "num_points": num_points,
         "num_timesteps": num_timesteps,