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/app/mcp/__init__.py

@@ -0,0 +1,25 @@
+"""The paper-doc MCP server: the same domain layer, spoken as MCP tools.
+
+Three front doors, one domain layer
+-----------------------------------
+The REST API (``app.api``), the MCP server (this package) and the seed script
+(``scripts/seed.py``) all end up in :mod:`app.crud` and validate through
+:mod:`app.schemas`. Nothing about a paper is decided here: a rule fixed in the
+CRUD layer is fixed in the API, in the tools and in the next tool added.
+
+What lives here is only what a *model* needs and a browser does not:
+
+* compact JSON instead of HTTP envelopes, because tool results are paid for in
+  context tokens;
+* paragraphs addressed by **heading** as well as by position, because a model
+  knows the paper says "1. Introduction" and does not know that the template
+  happens to place it at ``sort = 20``;
+* a bulk write, because "generate the paper, then put it in" is one intention
+  and should not be thirty round trips.
+
+Transports
+----------
+Both MCP transports are served from one build: ``stdio`` (what Claude Code,
+Codex and the Harness spawn locally) and ``streamable-http`` (what a client on
+another machine connects to). See ``scripts/mcp_server.py``.
+"""