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/tui-go/AGENTS.md

@@ -0,0 +1,37 @@
+# apps/tui-go
+
+## Purpose
+
+Terminal UI for correx. A Go/Bubble Tea application that connects to `apps/server` over WebSocket and renders session state in a "Soft + blue" visual style.
+
+## Ownership
+
+All sources under `apps/tui-go/`. Separate Go module (`github.com/correx/tui-go`) — independent build and test toolchain from the Gradle/Kotlin apps.
+
+## Local Contracts
+
+- Connects to `apps/server` at the configured WebSocket endpoint; does not import any Kotlin/JVM code.
+- **Receives** `ServerMessage` JSON over WebSocket (session lifecycle, approval requests, clarification requests, narration, proposed workflows, health/metrics).
+- **Sends** `ClientMessage` JSON (StartSession, ApproveToolCall, RejectToolCall, AnswerClarification, SetChatMode, etc.).
+- Protocol types are mirrored in `internal/protocol/` — must stay in sync with `apps/server/src/.../protocol/`.
+- Visual theme: "Soft + blue" (see `internal/app/theme.go`). Reference design lives in `docs/visual/ref/`.
+- Key layout defined in `internal/app/key.go`.
+- Main model in `internal/app/model.go`; update loop in `internal/app/update.go`; rendering in `internal/app/view.go`.
+- Overlays (sessions, tasks, config, ideas) in `internal/app/overlays.go` and sibling files.
+
+## Work Guidance
+
+- Standard Go conventions: `gofmt`-formatted, exported names for cross-package types, unexported for internal.
+- Add new WS message handling in `internal/ws/client.go` → dispatch via Bubble Tea `Msg` types → handled in `update.go`.
+- New UI panels follow the existing card/overlay pattern (see `clarcard.go`, `proposecard.go`).
+- Keep theme constants in `theme.go`; do not hardcode colors elsewhere.
+
+## Verification
+
+```bash
+cd apps/tui-go && go build ./... && go test ./...
+```
+
+## Child DOX Index
+
+No child AGENTS.md (leaf module).