Responses API

Used by Codex-style clients. Both sync and streaming are supported and verified:

curl {base_url}/r/{router}/v1/responses \
  -H "Authorization: Bearer sk-dodo-YOUR_KEY" \
  -H "Content-Type: application/json" \
  -d '{"model": "default", "input": "Reply with exactly the word: pong"}'

# Streaming event sequence

With "stream": true, DodoRouter emits the full item lifecycle a strict Responses-API client expects:

response.created → response.output_item.added → response.content_part.added → one or more response.output_text.delta → response.output_text.done → response.content_part.done → response.output_item.done → response.completed.

Verified with a real Codex CLI streaming run — text renders live in the terminal. An earlier version of this endpoint skipped the output_item.added / content_part.added events, which caused strict clients to log OutputTextDelta without active item and stall; that gap is fixed.