Codex tool results are not recorded: the Responses parser ignores custom_tool_call_output #1770

What happens

Cortex records every tool call a Codex session makes, but none of the results. In a recorded
Codex session with 13 tool calls, InferenceExtension.ToolResults was empty on every request:
13 calls, 0 results. agentop's timeline shows each Codex command with no output, and a commit
that a git hook rejected shows no rejection.

Claude Code sessions through the same Cortex are recorded correctly.

Cause

Codex declares its tools as custom (freeform) tools. Codex 0.167 sends one exec tool whose
input is a JavaScript snippet that calls tools.exec_command(...). So every tool result it
sends back is a custom_tool_call_output input item, not a function_call_output item.

responsesInputItem.UnmarshalJSON in core/parse/inference/responses.go only reads
function_call_output:

if raw.Type == "function_call_output" {
	it.ToolResults = append(it.ToolResults, model.InferenceToolResult{...})
}

So custom_tool_call_output items are skipped. The response side already reads Codex's
custom_tool_call items (that's why the calls are recorded), so only the results are missing.
The praxis Rust port (praxis/filters/src/parse/inference/responses.rs) has the same check.

The two item types have the same call_id and output fields. These are the two items from a
captured Codex request, with the snippet shortened:

{"type":"custom_tool_call","call_id":"call_2fmY…","name":"exec",
 "input":"const r = await tools.exec_command({cmd:\"cat a.txt\", …});\ntext(r.output);\n"}
{"type":"custom_tool_call_output","call_id":"call_2fmY…",
 "output":[{"type":"input_text","text":"Script completed\nWall time 0.2 seconds\nOutput:\n"},
           {"type":"input_text","text":"hello\n"}]}

The output is an array of input_text parts, which flattenResponsesContent already reads.

Impact

Anything that reads ToolResults gets nothing for Codex:

• agentop's timeline shows no output for Codex tool calls.
• CPEX builds its tool-result parts from ToolResults (inferenceToCMFParts), so policies and
  redaction on tool output never see Codex's.
• Plugins that learn from or audit sessions see Codex's commands but not what they returned.

Steps to reproduce

1. Route Codex through Cortex (agentop configure codex enable), with Codex 0.167.

2. Run one task that uses a tool:

   mkdir -p /tmp/codex-repro && cd /tmp/codex-repro && echo hello > a.txt
   codex exec --skip-git-repo-check "Run 'cat a.txt' and tell me what it prints." < /dev/null

3. Count tool calls and tool results in the newest Codex session:

   API=http://127.0.0.1:47601
   S=$(curl -s --noproxy '*' "$API/v1/sessions?archived=true" \
     | jq -r '[.sessions[] | select(.agent=="codex")] | max_by(.createdAt) | .id')
   curl -s --noproxy '*' "$API/v1/sessions/$S?limit=5000" | jq -r '
     [.events[] | select(.inference)] as $e
     | "tool calls=\([$e[] | .inference.toolCalls[]?.id] | unique | length)  results=\([$e[] | .inference.toolResults[]?.toolUseId] | unique | length)"'

Expected: results equal tool calls. Actual: results=0.

Environment

• macOS, Darwin arm64
• Cortex / agentop v0.9.5. The same code is on main at 28ab6a78.
• Codex CLI 0.167.0, Responses API through a LiteLLM proxy (wire_api = "responses")

Proposed fix

Read custom_tool_call_output the same way as function_call_output, in the Go parser and
in the praxis port. A PR is ready.

Not covered by that change, and maybe worth separate issues:

• The script plugin's Python SDK (core/plugins/script/sdk/cortex.py) also only matches
  function_call_output, so script plugins don't see Codex tool output either.
• The CPEX README's table of tool-output sources lists only function_call_output.