docs: improve consistency

Author: seratch

docs/agents.md

@@ -300,7 +300,7 @@ agent = Agent(
 )
 ```
 
-## Tool Use Behavior
+## Tool use behavior
 
 The `tool_use_behavior` parameter in the `Agent` configuration controls how tool outputs are handled:
 

docs/handoffs.md

@@ -12,7 +12,7 @@ If you pass plain `Agent` instances, their [`handoff_description`][agents.agent.
 
 You can create a handoff using the [`handoff()`][agents.handoffs.handoff] function provided by the Agents SDK. This function allows you to specify the agent to hand off to, along with optional overrides and input filters.
 
-### Basic Usage
+### Basic usage
 
 Here's how you can create a simple handoff:
 

docs/realtime/guide.md

@@ -11,7 +11,7 @@ Realtime agents allow for conversational flows, processing audio and text inputs
 
 ## Architecture
 
-### Core Components
+### Core components
 
 The realtime system consists of several key components:
 
@@ -64,9 +64,9 @@ Additional configuration options you can set on `RealtimeRunner(config=...)` inc
 
 See [`RealtimeRunConfig`][agents.realtime.config.RealtimeRunConfig] and [`RealtimeSessionModelSettings`][agents.realtime.config.RealtimeSessionModelSettings] for the complete typed configuration.
 
-## Tools and Functions
+## Tools and functions
 
-### Adding Tools
+### Adding tools
 
 Just like regular agents, realtime agents support function tools that execute during conversations:
 
@@ -94,7 +94,7 @@ agent = RealtimeAgent(
 
 ## Handoffs
 
-### Creating Handoffs
+### Creating handoffs
 
 Handoffs allow transferring conversations between specialized agents.
 

docs/running_agents.md

@@ -263,7 +263,7 @@ async def main():
         # California
 ```
 
-#### Automatic conversation management with Sessions
+#### Automatic conversation management with sessions
 
 For a simpler approach, you can use [Sessions](sessions/index.md) to automatically handle conversation history without manually calling `.to_input_list()`:
 

docs/sessions/advanced_sqlite_session.md

@@ -1,4 +1,4 @@
-# Advanced SQLite Sessions
+# Advanced SQLite sessions
 
 `AdvancedSQLiteSession` is an enhanced version of the basic `SQLiteSession` that provides advanced conversation management capabilities including conversation branching, detailed usage analytics, and structured conversation queries.
 
@@ -297,7 +297,7 @@ CREATE TABLE turn_usage (
 Check out the [complete example](https://github.com/openai/openai-agents-python/tree/main/examples/memory/advanced_sqlite_session_example.py) for a comprehensive demonstration of all features.
 
 
-## API Reference
+## API reference
 
 - [`AdvancedSQLiteSession`][agents.extensions.memory.advanced_sqlite_session.AdvancedSQLiteSession] - Main class
 - [`Session`][agents.memory.session.Session] - Base session protocol

docs/sessions/encrypted_session.md

@@ -1,4 +1,4 @@
-# Encrypted Sessions
+# Encrypted sessions
 
 `EncryptedSession` provides transparent encryption for any session implementation, securing conversation data with automatic expiration of old items.
 
@@ -75,7 +75,7 @@ session = EncryptedSession(
 )
 ```
 
-### TTL (Time To Live)
+### TTL (time to live)
 
 Set how long encrypted items remain valid:
 
@@ -169,7 +169,7 @@ items = await session.get_items()  # Only returns non-expired items
 result = await Runner.run(agent, "Continue conversation", session=session)
 ```
 
-## API Reference
+## API reference
 
 - [`EncryptedSession`][agents.extensions.memory.encrypt_session.EncryptedSession] - Main class
 - [`Session`][agents.memory.session.Session] - Base session protocol

docs/sessions/index.md

@@ -619,7 +619,7 @@ The community has developed additional session implementations:
 
 If you've built a session implementation, please feel free to submit a documentation PR to add it here!
 
-## API Reference
+## API reference
 
 For detailed API documentation, see:
 

docs/sessions/sqlalchemy_session.md

@@ -1,4 +1,4 @@
-# SQLAlchemy Sessions
+# SQLAlchemy sessions
 
 `SQLAlchemySession` uses SQLAlchemy to provide a production-ready session implementation, allowing you to use any database supported by SQLAlchemy (PostgreSQL, MySQL, SQLite, etc.) for session storage.
 
@@ -70,7 +70,7 @@ if __name__ == "__main__":
 ```
 
 
-## API Reference
+## API reference
 
 - [`SQLAlchemySession`][agents.extensions.memory.sqlalchemy_session.SQLAlchemySession] - Main class
 - [`Session`][agents.memory.session.Session] - Base session protocol

docs/usage.md

@@ -85,11 +85,11 @@ class MyHooks(RunHooks):
         print(f"{agent.name} → {u.requests} requests, {u.total_tokens} total tokens")
 ```
 
-## API Reference
+## API reference
 
 For detailed API documentation, see:
 
 -   [`Usage`][agents.usage.Usage] - Usage tracking data structure
 -   [`RequestUsage`][agents.usage.RequestUsage] - Per-request usage details
 -   [`RunContextWrapper`][agents.run.RunContextWrapper] - Access usage from run context
--   [`RunHooks`][agents.run.RunHooks] - Hook into usage tracking lifecycle
+-   [`RunHooks`][agents.run.RunHooks] - Hook into usage tracking lifecycle

docs/visualization.md

@@ -1,4 +1,4 @@
-# Agent Visualization
+# Agent visualization
 
 Agent visualization allows you to generate a structured graphical representation of agents and their relationships using **Graphviz**. This is useful for understanding how agents, tools, and handoffs interact within an application.
 
@@ -10,16 +10,16 @@ Install the optional `viz` dependency group:
 pip install "openai-agents[viz]"
 ```
 
-## Generating a Graph
+## Generating a graph
 
 You can generate an agent visualization using the `draw_graph` function. This function creates a directed graph where:
 
 - **Agents** are represented as yellow boxes.
-- **MCP Servers** are represented as grey boxes.
+- **MCP servers** are represented as grey boxes.
 - **Tools** are represented as green ellipses.
 - **Handoffs** are directed edges from one agent to another.
 
-### Example Usage
+### Example usage
 
 ```python
 import os
@@ -68,14 +68,14 @@ draw_graph(triage_agent)
 This generates a graph that visually represents the structure of the **triage agent** and its connections to sub-agents and tools.
 
 
-## Understanding the Visualization
+## Understanding the visualization
 
 The generated graph includes:
 
 - A **start node** (`__start__`) indicating the entry point.
 - Agents represented as **rectangles** with yellow fill.
 - Tools represented as **ellipses** with green fill.
-- MCP Servers represented as **rectangles** with grey fill.
+- MCP servers represented as **rectangles** with grey fill.
 - Directed edges indicating interactions:
   - **Solid arrows** for agent-to-agent handoffs.
   - **Dotted arrows** for tool invocations.
@@ -86,16 +86,16 @@ The generated graph includes:
 `agents` package (verified in **v0.2.8**). If you don’t see MCP boxes
 in your visualization, upgrade to the latest release.
 
-## Customizing the Graph
+## Customizing the graph
 
-### Showing the Graph
+### Showing the graph
 By default, `draw_graph` displays the graph inline. To show the graph in a separate window, write the following:
 
 ```python
 draw_graph(triage_agent).view()
 ```
 
-### Saving the Graph
+### Saving the graph
 By default, `draw_graph` displays the graph inline. To save it as a file, specify a filename:
 
 ```python