Cross-surface AI memory: markdown vault + filesystem MCP beats memory products

User wanted Claude Code and Claude web/desktop to share memory. Research finding: the three memory systems (claude.ai server-side, Claude Code local files, API memory tool) have zero native sync as of mid-2026; the only bridge is MCP. Free/local solution that works: a git-versioned markdown vault with an INDEX.md containing recall/save/sort rules, wired to Claude Code via a CLAUDE.md pointer and to Claude Desktop via the stock @modelcontextprotocol/server-filesystem entry in claude_desktop_config.json. Key gotchas: paid memory layers (mem0 etc.) extract facts and provably lose operational state like campaign ledgers; capture must be instruction-driven ambient, not left to model discretion; and mark sensitive notes with private:true frontmatter so a future cloud bridge never syncs them.