backend: serve the writing domain to agents as an MCP server

The paper is written by a model now. A browser is the wrong client for that:
the work is "generate the paper, then put it in", and doing it through a form
means a person retyping what a model already produced. So the same domain is
served over the Model Context Protocol, which Claude Code, Codex and the
DeepSeek Harness all speak.

It is a third front door, not a second implementation. Every tool is three
lines around an `app.crud` call and validates through `app.schemas`, exactly
as the REST routes do, so a rule fixed in the CRUD layer is fixed on both
surfaces and a paper written by an agent is indistinguishable from one written
by hand. What `app/mcp/` adds is only what a model needs and a browser does
not:

- 29 tools, prefixed `paper_` `paragraph_` `sentence_` `template_` `field_`,
  because a model picks a tool out of a list by name rather than by reading 29
  descriptions;
- results as compact `None`-free JSON, since a tool result is paid for in
  context tokens and `PaperRead.model_dump()` carries four counts and two
  timestamps into every list row;
- paragraphs addressed by **heading** as well as by position. Storage is
  correct as it stands — a sentence remembers the position it sits at, which is
  what makes a template switch non-destructive — but nobody writing
  "1. Introduction" knows the template places it at `sort = 20`. The server
  translates, and refuses with the real heading list when it cannot, so a model
  that guessed wrong corrects itself in one retry;
- `paper_write` and `paper_write_text`: one intention, one call. The latter
  finds its own sections from Markdown headings or from lines that name a
  template heading, and reports every heading it could not place instead of
  writing half a paper;
- `sentence_search` across papers, for consistency rather than retrieval — a
  paper that says 洪水损失 should not be joined by one that says GUL;
- `paper_delete` refuses once, naming what would go with it. A cascading delete
  has no undo in a tool call.

Two transports, one build. `stdio` is what a client spawns — so nothing in the
process may print to stdout, and diagnostics go to stderr. `streamable-http` is
what a client on another machine connects to, optionally behind a bearer token;
binding a non-loopback address disables the SDK's DNS-rebinding allow-list,
because a LAN client sends whatever Host it knows the server by.

Tools register with `structured_output=False` on purpose: inferred from a
`-> str` annotation the SDK publishes a `{"result": ...}` envelope and sends
the JSON twice, once as `structuredContent` and once as text, and clients that
read only one of the two then disagree about what came back.

`scripts/smoke_mcp.py` drives the whole loop through a real MCP client — the
child process and JSON-RPC over stdin/stdout a client actually uses — and runs
unchanged against a running HTTP server via `--url`. 47 checks pass on both
transports; the REST suite still passes its 45.

backend/scripts/mcp_server.py

@@ -0,0 +1,40 @@
+"""MCP server entry point for paper-doc.
+
+Usage (from anywhere — the script anchors ``sys.path`` itself)::
+
+    backend/.venv/bin/python backend/scripts/mcp_server.py                 # stdio
+    backend/.venv/bin/python backend/scripts/mcp_server.py --check         # 自检
+    backend/.venv/bin/python backend/scripts/mcp_server.py \\
+        --transport http --host 0.0.0.0 --port 8931 --token secret
+
+``stdio`` is what an MCP client spawns: Claude Code, Codex and the DeepSeek
+Harness all run a command and speak JSON-RPC over its stdin/stdout. Two rules
+follow from that, and both are easy to break by accident:
+
+* **Nothing may print to stdout** except the protocol. Diagnostics go to
+  stderr; a ``print`` added here for debugging would corrupt the stream and
+  present as "the server disconnected".
+* **The command must work from any working directory**, because a client's
+  ``cwd`` is its own, not this project's. That is why the path anchor below
+  exists rather than a relative ``import app``.
+
+The CLI itself lives in :func:`app.mcp.server.main` so this file stays a
+launcher: the same arguments are reachable as ``python -m app.mcp`` from
+``backend/``.
+"""
+
+from __future__ import annotations
+
+import sys
+from pathlib import Path
+
+# Running this as a plain script puts scripts/ on sys.path, not backend/, so
+# `import app` would fail. Anchor to the backend directory instead.
+BACKEND_DIR = Path(__file__).resolve().parents[1]
+if str(BACKEND_DIR) not in sys.path:
+    sys.path.insert(0, str(BACKEND_DIR))
+
+from app.mcp.server import main  # noqa: E402
+
+if __name__ == "__main__":
+    sys.exit(main())