docs(api-reference): align API docs & openapi.json with v3 spec (#5848)

docs/api-reference/organizations-projects.mdx

@@ -14,7 +14,7 @@ Organizations and projects are **optional** features. You can use Mem0 without t
 
 ## Key Capabilities
 
-- **Multi-org/project Support**: Specify organization and project when initializing the Mem0 client to attribute API usage appropriately
+- **Multi-org/project Support**: Organization and project are resolved automatically from your API key via `/v1/ping/` — no org or project params are accepted by `MemoryClient.__init__`. Use a project-specific API key to target a particular project.
 - **Member Management**: Control access to data through organization and project membership
 - **Access Control**: Only members can access memories and data within their organization/project scope
 - **Team Isolation**: Maintain data separation between different teams and projects for secure collaboration
@@ -79,7 +79,7 @@ new_project = client.project.create(
 
 ### Update Project Settings
 
-Modify project configuration including custom instructions, categories, and language preferences:
+Modify project configuration including custom instructions, categories, language preferences, retrieval criteria, and memory decay:
 
 ```python
 # Update project with custom categories
@@ -98,6 +98,17 @@ client.project.update(
 # Use the input language for memory storage and retrieval
 client.project.update(multilingual=True)
 
+# Set retrieval criteria to control which memories are surfaced in search
+client.project.update(
+    retrieval_criteria=[
+        {"name": "relevance", "description": "How directly relevant this memory is to the current topic or user query", "weight": 3},
+        {"name": "access_frequency", "description": "How often this memory has been accessed or surfaced recently", "weight": 1}
+    ]
+)
+
+# Enable Memory Decay (boosts recently-accessed memories at search time)
+client.project.update(decay=True)
+
 # Update multiple settings at once
 client.project.update(
     custom_instructions="...",
@@ -109,6 +120,34 @@ client.project.update(
 )
 ```
 
+#### Set Retrieval Criteria
+
+`retrieval_criteria` is a per-project list of dictionaries (`List[Dict]`) that shapes how memories are ranked and filtered during search. Each dictionary has three fields: `name` (identifier), `description` (interpreted by the LLM to score each memory), and `weight` (relative influence on the final score). Use this to focus retrieval on intent-aligned or signal-specific memories:
+
+```python
+client.project.update(
+    retrieval_criteria=[
+        {
+            "name": "joy",
+            "description": "Measure the intensity of positive emotions such as happiness, excitement, or amusement expressed in the memory. A higher score reflects greater joy.",
+            "weight": 3
+        },
+        {
+            "name": "curiosity",
+            "description": "Assess the extent to which the memory reflects inquisitiveness or interest in exploring new information. A higher score reflects stronger curiosity.",
+            "weight": 2
+        },
+        {
+            "name": "access_frequency",
+            "description": "How often this memory has been accessed or surfaced recently.",
+            "weight": 1
+        }
+    ]
+)
+```
+
+Pass an empty list to clear all criteria and restore default retrieval behaviour.
+
 #### Toggle Memory Decay
 
 `decay` is a per-project boolean that turns on [Memory Decay](/platform/features/memory-decay) — a search-time ranking bias that reinforces recently-accessed memories and gently dampens stale ones. The flag is `false` by default; set it via the same project-update endpoint: