Feature Request / Bug: Claude lacks introspective tooling for its own memory state

**Title:** Claude has no introspective access to its own memory state — active project context degrades silently across sessions

**Repo:** anthropic/claude-cookbooks (or appropriate memory/context tooling repo)

**Summary**

Claude currently has two memory surfaces: a synthesized `userMemories` blob generated by Anthropic from past conversations (read-only, no Claude-side control), and a `memory_user_edits` list writable only by the user. Claude has no way to:

- Know what is or isn't in the synthesized memory blob
- Flag when stored context is stale or incomplete
- Track active project state across sessions without user re-narration
- Surface its own retrieval failures (i.e., know when it is reconstructing from training vs. from actual conversation history)

**Concrete failure mode observed**

User has an ongoing multi-session project (G14 Linux setup on Arch). When asked to continue from a specific step, Claude performed 3 `conversation_search` calls, failed to surface the relevant session, and reconstructed the setup guide from general training knowledge — presenting it as continuity when it was actually a cold reconstruction. The user had no way to know this had happened. Claude had no way to flag it.

**What's missing**

A lightweight introspection primitive — something like a `memory_status` tool — that would let Claude:
1. Check what project states are currently tracked
2. Flag retrieval uncertainty explicitly
3. Recommend what the user should write into `memory_user_edits` to prevent future context loss

The `memory_user_edits` tool is user-side only. There is no Claude-side equivalent. The asymmetry means Claude is navigating with a map it cannot read.

**Suggested resolution**

Either:
- Expose a read-only `memory_inspect` tool that returns current synthesized memory summary
- Or document a canonical pattern for users to maintain project-state ledgers in `memory_user_edits` — and have Claude proactively suggest this when it detects retrieval failure

Tagging for visibility: (or whoever owns memory/context tooling on the product side)

**Filed by:** @basyt005 / darthcoder
**Related:** anthropic/claude-cookbooks#414