feat(integrations): add @mem0/eve memory provider

Give Eve agents a first-class Mem0 recall/capture provider so they can use Mem0 in the agent loop instead of MCP.

Co-authored-by: Cursor <cursoragent@cursor.com>

integrations/eve/registry/README.md

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+# Eve registry contribution
+
+These files are the Mem0 side of `eve add memory/mem0`. They are not published in the npm tarball. Copy them into a PR against [vercel/eve](https://github.com/vercel/eve) after `@mem0/eve` is on npm.
+
+Supermemory's version of this change is [vercel/eve#2775](https://github.com/vercel/eve/pull/2775). Eve already asked Mem0 to own the package and open that PR.
+
+## What the Eve PR should do
+
+1. Add a `kind: "memory"` catalog item named `mem0`.
+2. Install `@mem0/eve` and declare `MEM0_API_KEY`.
+3. Write `agent/memory/mem0.ts` from [`mem0.ts`](./mem0.ts).
+4. List Mem0 on [eve.dev/docs/memory](https://eve.dev/docs/memory) next to Supermemory and Upstash.
+
+[`item.json`](./item.json) is the shadcn-registry shape Eve uses for `eve add`. Adapt field names to Eve's current catalog schema if it has moved since this was written.
+
+## Suggested install command
+
+```bash
+eve add memory/mem0
+```
+
+## Suggested docs snippet
+
+```ts
+import { mem0Provider } from "@mem0/eve";
+import { defineMemory } from "eve/memory";
+import { byPrincipal } from "eve/memory/scope";
+
+export default defineMemory({
+  description: "Recall and manage durable context for the current user.",
+  provider: mem0Provider({
+    apiKey: process.env.MEM0_API_KEY!,
+  }),
+  scope: byPrincipal,
+});
+```

integrations/eve/registry/item.json

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+{
+  "name": "mem0",
+  "type": "registry:item",
+  "title": "Mem0",
+  "description": "Hosted semantic memory for Eve agents. Recalls relevant context before each turn, captures completed turns, and exposes search, remember, and forget tools.",
+  "dependencies": ["@mem0/eve"],
+  "envVars": {
+    "MEM0_API_KEY": ""
+  },
+  "files": [
+    {
+      "path": "registry/mem0.ts",
+      "type": "registry:file",
+      "target": "agent/memory/mem0.ts"
+    }
+  ]
+}

integrations/eve/registry/mem0.ts

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+import { mem0Provider } from "@mem0/eve";
+import { defineMemory } from "eve/memory";
+import { byPrincipal } from "eve/memory/scope";
+
+export default defineMemory({
+  description: "Recall and manage durable context for the current user.",
+  provider: mem0Provider({
+    apiKey: process.env.MEM0_API_KEY!,
+  }),
+  scope: byPrincipal,
+});