feat: AI docs update (#40183)

* feat: AI docs update

* Update Rule003Spelling.toml

apps/docs/content/guides/ai/vector-indexes.mdx

@@ -26,7 +26,15 @@ Indexes can be used to improve performance of nearest neighbor search using vari
 | `<#>`    | negative inner product | `vector_ip_ops`                                                                      |
 | `<=>`    | cosine distance        | `vector_cosine_ops`                                                                  |
 
-Currently vectors with up to 2,000 dimensions can be indexed.
+For pgvector versions 0.7.0 and above, it's possible to create indexes on vectors with the following maximum dimensions:
+
+- vector: up to 2,000 dimensions
+- halfvec: up to 4,000 dimensions
+- bit: up to 64,000 dimensions
+
+You can check your current pgvector version by running: `SELECT * FROM pg_extension WHERE extname = 'vector';` or by navigating to the [Extensions](/dashboard/project/_/database/extensions) tab in your Supabase project dashboard.
+
+If you are on an earlier version of pgvector, you should [upgrade your project here](/dashboard/project/_/settings/infrastructure).
 
 ## Resources
 

apps/docs/content/guides/ai/vector-indexes/hnsw-indexes.mdx

@@ -37,7 +37,30 @@ create index on items using hnsw (column_name vector_ip_ops);
 create index on items using hnsw (column_name vector_cosine_ops);
 ```
 
-Currently vectors with up to 2,000 dimensions can be indexed.
+For pgvector versions 0.7.0 and above, it's possible to create indexes on vectors with the following maximum dimensions:
+
+- vector: up to 2,000 dimensions
+- halfvec: up to 4,000 dimensions
+- bit: up to 64,000 dimensions
+
+You can check your current pgvector version by running: `SELECT * FROM pg_extension WHERE extname = 'vector';` or by navigating to the [Extensions](/dashboard/project/_/database/extensions) tab in your Supabase project dashboard.
+
+If you are on an earlier version of pgvector, you should [upgrade your project here](/dashboard/project/_/settings/infrastructure).
+
+## Example with high-dimensional vectors
+
+For vectors with more than 2,000 dimensions, you can use the `halfvec` type to create indexes. Here's an example with 3,072 dimensions:
+
+```sql
+CREATE TABLE documents (
+    id bigint GENERATED BY DEFAULT AS IDENTITY PRIMARY KEY,
+    content text,
+    embedding vector(3072)
+);
+
+CREATE INDEX ON documents
+    USING hnsw ((embedding::halfvec(3072)) halfvec_cosine_ops);
+```
 
 ## How does HNSW work?
 

supa-mdx-lint/Rule003Spelling.toml

@@ -336,6 +336,7 @@ allow_list = [
     "dotenv",
     "e.g.",
     "gte-small",
+    "halfvec",
     "hCaptcha",
     "https?:\\/\\/\\S+",
     "i.e.",