chore(spec): regenerate liveness state-counts, strictness counts and the connector reference page on the merged tree

Main moved the rest_api liveness row, the api/ strictness count and the
connector page's front-matter description; each regenerated with its own
generator (gen:liveness-counts, gen:strictness-ledger, gen:docs on a build of
the merged tree), never hand-merged. The retirement's rows are unchanged.

Co-Authored-By: Claude <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01QcAS3qiYYZNezaxZxaUdMV

Author: claude

content/docs/references/integration/connector.mdx

@@ -1,6 +1,6 @@
 ---
 title: Connector
-description: Connector protocol schemas
+description: "Defines the standard connector specification for external system integration."
 ---
 
 {/* ⚠️  AUTO-GENERATED — DO NOT EDIT. Run build-docs.ts to regenerate. Hand-written docs live in the module folders under content/docs/. */}

docs/audits/2026-07-unknown-key-strictness-ledger.counts.md

@@ -257,7 +257,7 @@ directory rather than per file.
 | Dir | Sites |
 |---|---|
 | `ai/` | 78 |
-| `api/` | 432 |
+| `api/` | 431 |
 | `identity/` | 32 |
 | `integration/` | 5 |
 | `kernel/` | 247 |

packages/spec/liveness/state-counts.md

@@ -62,9 +62,9 @@ for both corollaries.
 | `metadata_endpoints` | 7 | 0 | 0 | 2 | 0 | 9 |
 | `batch_endpoints` | 5 | 0 | 0 | 2 | 0 | 7 |
 | `route_generation` | 0 | 0 | 0 | 4 | 0 | 4 |
-| `rest_api` | 12 | 0 | 0 | 14 | 0 | 26 |
+| `rest_api` | 12 | 0 | 0 | 12 | 0 | 24 |
 | `realtime_subscription` | 0 | 0 | 0 | 6 | 0 | 6 |
 | `sharing_rule` | 16 | 0 | 0 | 0 | 1 | 17 |
 | `connector` | 29 | 0 | 0 | 30 | 1 | 60 |
 | `analytics_cube` | 17 | 0 | 0 | 10 | 0 | 27 |
-| **total** | **936** | **5** | **1** | **154** | **9** | **1105** |
+| **total** | **936** | **5** | **1** | **152** | **9** | **1103** |