docs(dox): build out the DOX AGENTS.md hierarchy

Root Child DOX Index assembled, plus a per-module AGENTS.md across the tree
(core/*, infrastructure/*, apps/*, testing/*, and docs/examples/frontend/etc),
each following the DOX section shape: Purpose, Ownership, Local Contracts,
Work Guidance, Verification, Child DOX Index.

apps/AGENTS.md

@@ -0,0 +1,31 @@
+# apps/
+
+## Purpose
+
+Entry-point applications that compose core modules into runnable processes. Each app wires infrastructure and core together; no business logic lives here.
+
+## Ownership
+
+All apps in this subtree. Dependency rule: `apps → core → infrastructure`. Apps may not import sibling app modules.
+
+## Local Contracts
+
+- Apps depend on `core:*` and `infrastructure:*` only — never on each other.
+- Configuration loading, process lifecycle, and entrypoint wiring live here.
+- No domain logic in apps; delegate to core services.
+
+## Work Guidance
+
+Follow the Kotlin rules and anti-patterns in the root CLAUDE.md for all JVM apps. `apps/tui-go` is a separate Go module — see its own AGENTS.md.
+
+## Verification
+
+Each app has its own verification command. See child AGENTS.md.
+
+## Child DOX Index
+
+- `apps/cli` — Clikt CLI; sends commands to `apps/server` over HTTP + WebSocket
+- `apps/desktop` — stub module, not yet implemented
+- `apps/server` — Ktor HTTP API + WebSocket server; orchestrates core kernel
+- `apps/tui-go` — Go/Bubble Tea terminal UI; WebSocket client of `apps/server`
+- `apps/worker` — stub module, not yet implemented