Switch Codex Responses to the shared provider package

docs/IMPLEMENTATION.md

@@ -393,7 +393,7 @@ Positional arguments after flags are joined into the optional initial task deliv
 
 - OpenAI-compatible chat completions, streamed via `@intx/inference`
 - JSON-schema tool definitions for director-layer tools (`ask_operator`, `present`, `submit_output`) and agent tools (`manage_tasks`, `tool_search`, `use_skill`, `search_agents`, …)
-- Codex Responses (`codex-responses-adapter.ts` `buildRequest`): ChatGPT Codex is Responses-only. `instructions` is exactly the supplied Corbits system prompt (including an empty string), omitted when unset. `input` contains only the converted conversation turns, preserving their roles and order without a synthetic developer bridge. There is no official-prompt fetch, cache, or startup refresh. It requires `store: false` (`store: true` → 400) and rejects `previous_response_id`. Multi-turn continuity is full `input` replay; encrypted reasoning captured via `include: ["reasoning.encrypted_content"]` is resent as a `reasoning` item. `prompt_cache_key` (session id) is the cache-routing signal. `parallel_tool_calls` is sent `false` (serial at this surface); the reactor already fans out a multi-call batch concurrently. `max_output_tokens` is omitted (backend rejects it).
+- Codex Responses (`@corbits/codex-provider` via `codex-responses.ts`): ChatGPT Codex is Responses-only. The host system prompt is wrapped with product identity as a leading `developer` input item; conversation turns follow in order. There is no official-prompt fetch, cache, or startup refresh. It requires `store: false` (`store: true` → 400) and rejects `previous_response_id`. Multi-turn continuity is full `input` replay; encrypted reasoning captured via `include: ["reasoning.encrypted_content"]` is resent as a `reasoning` item. `prompt_cache_key` (session id) is the cache-routing signal. `parallel_tool_calls` is sent `false` (serial at this surface); the reactor already fans out a multi-call batch concurrently. `max_output_tokens` is omitted (backend rejects it).
 
 ### State Persistence
 

package.json

@@ -80,6 +80,7 @@
     "tar": "^7.5.1"
   },
   "dependencies": {
+    "@corbits/codex-provider": "github:corbitsdev/corbits-codex-provider",
     "@corbits/openai-responses": "github:corbitsdev/corbits-openai-responses",
     "@corbits/xai-provider": "github:corbitsdev/corbits-xai-provider",
     "@intx/agent": "workspace:*",

src/config/index.ts

@@ -41,7 +41,7 @@ import {
   CODEX_RESPONSES_PROVIDER,
   CODEX_ACCOUNT_ID_OPTION,
   CODEX_SESSION_ID_OPTION,
-} from "../provider/codex-responses-adapter.js";
+} from "../provider/codex-responses.js";
 import {
   GROK_RESPONSES_PROVIDER,
   GROK_SESSION_ID_OPTION,