docs(integrations): add Synap long-term memory integration

docs/integrations/synap.md

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+---
+catalog_title: Synap
+catalog_description: Add persistent, cross-session long-term memory to ADK agents
+catalog_icon: /integrations/assets/synap.png
+catalog_tags: ["data"]
+---
+
+# Synap integration for ADK
+
+<div class="language-support-tag">
+  <span class="lst-supported">Supported in ADK</span><span class="lst-python">Python</span>
+</div>
+
+The [`maximem-synap-google-adk`](https://pypi.org/project/maximem-synap-google-adk/)
+plugin connects your ADK agent to [Synap](https://maximem.ai), a managed
+long-term memory layer for AI agents. Synap automatically extracts and
+structures knowledge from conversations — facts, preferences, episodes,
+emotions, and temporal events — and retrieves only what is semantically relevant
+to the current query.
+
+## Use cases
+
+- **Persistent cross-session memory**: Give your ADK agents long-term memory
+  that survives across sessions and deployments — no manual bookkeeping.
+- **Multi-tenant isolation**: Memory is scoped to `user_id` and `customer_id`,
+  ensuring strict isolation in multi-user deployments.
+- **Semantic recall**: Server-side extraction surfaces only what is relevant to
+  the current query, keeping prompts short and tokens efficient.
+
+## Prerequisites
+
+- A [Synap](https://synap.maximem.ai) account and API key
+- [Gemini API key](https://aistudio.google.com/app/api-keys) (or any other
+  model provider configured with ADK)
+
+## Installation
+
+```bash
+pip install maximem-synap-google-adk maximem-synap
+```
+
+Set the following environment variable:
+
+```bash
+export SYNAP_API_KEY="your-synap-api-key"
+```
+
+## Use with agent
+
+`create_synap_tools(...)` returns two `FunctionTool` instances —
+`search_memory` and `store_memory` — that the agent can call to recall and
+persist memories on demand.
+
+```python
+import os
+
+from google.adk.agents.llm_agent import Agent
+from maximem_synap import MaximemSynapSDK
+from synap_google_adk import create_synap_tools
+
+sdk = MaximemSynapSDK(api_key=os.environ["SYNAP_API_KEY"])
+
+synap_tools = create_synap_tools(
+    sdk=sdk,
+    user_id="alice",
+    customer_id="acme_corp",
+)
+
+root_agent = Agent(
+    model="gemini-2.0-flash",
+    name="memory_assistant",
+    instruction=(
+        "You are a helpful assistant with long-term memory. "
+        "Use search_memory to recall what you know about the user. "
+        "Use store_memory to save important new facts the user mentions."
+    ),
+    tools=synap_tools,
+)
+```
+
+Run with:
+
+```bash
+adk run path/to/your_agent
+```
+
+Teach the agent something on the first turn (e.g. *"I'm allergic to peanuts"*),
+then ask about it on a later turn — Synap retrieves the relevant memory
+automatically, even across separate `adk run` invocations.
+
+## Available tools
+
+| Tool | Description |
+|------|-------------|
+| `search_memory` | Semantic search over the user's stored memories. Takes a natural-language query and returns the most relevant facts, preferences, and episodes. |
+| `store_memory` | Persist an explicit fact in the user's long-term memory. The agent calls this when the user shares something worth remembering. |
+
+## Resources
+
+- [Synap documentation](https://docs.maximem.ai)
+- [ADK integration guide](https://docs.maximem.ai/integrations/google-adk)
+- [`maximem-synap-google-adk` on PyPI](https://pypi.org/project/maximem-synap-google-adk/)
+- [Open source integration package](https://github.com/maximem-ai/maximem_synap_sdk/tree/main/packages/integrations/synap-google-adk)
+- [Synap Dashboard](https://synap.maximem.ai)