A tool returning a non-finite float fails on the client with an error naming the tool

Initial Checks

• I confirm that I'm using the newest release of my line (verified on 2.0.0)
• I confirm that I searched for my issue before opening this issue

Release line

2.x (current stable). Also reproduces on 1.29.0.

Bug description

A tool returning a non-finite float fails on the client with an error that names
the tool. float("inf"), float("-inf") and float("nan") all reproduce it. A
finite float is fine.

The handler returned an ordinary Python float. The value that fails validation is
produced by the SDK's own outbound serialization.

Steps to reproduce

import anyio
from mcp.client import Client
from mcp.server.mcpserver import MCPServer

server = MCPServer("probe")


@server.tool()
def ratio(a: float, b: float) -> float:
    """Divide a by b."""
    return a / b if b else float("inf")


async def main() -> None:
    async with Client(server) as client:
        print(await client.call_tool("ratio", {"a": 1.0, "b": 2.0}))
        print(await client.call_tool("ratio", {"a": 1.0, "b": 0.0}))


anyio.run(main)

Actual behaviour

The first call returns structured_content={'result': 0.5}. The second raises:

RuntimeError: Invalid structured content returned by tool ratio: None is not of type 'number'

Failed validating 'type' in schema['properties']['result']:
    {'title': 'Result', 'type': 'number'}

On instance['result']:
    None

Uncaught, this arrives as two nested ExceptionGroups out of Client.__aexit__,
84 lines in total, with the line naming the tool last. Catching the RuntimeError
leaves the session usable and later calls succeed.

The value cannot be recovered. validate_tool_result runs unconditionally for any
non-error result (client/session.py:1109, client/client.py:828) with no opt-out,
so the caller never reaches the CallToolResult to read either
structured_content or the text block.

Expected behaviour

Either the value survives the round trip, or the failure names the real cause. At
present the message directs the reader to the handler, which is the one component
behaving correctly.

The SDK already rejects non-finite floats explicitly elsewhere, at
server/request_state.py:128, so refusing them at the point of return with a clear
message would match existing practice.

Root cause

1. func_metadata.convert_result builds structured_content = {'result': inf}.
   Correct so far.
2. _dump_result (server/runner.py:118) serializes with
   model_dump(by_alias=True, mode="json", exclude_none=True). Pydantic's JSON mode
   writes non-finite floats as null, since JSON has no Infinity or NaN and
   ser_json_inf_nan defaults to "null". The SDK does not set that setting
   anywhere.
3. The client validates {"result": null} against the generated output schema
   {"result": {"type": "number"}}, which rejects it.
4. client/session.py:1155 raises, interpolating the tool name.

This is server-side and independent of transport, so it is not specific to the
in-memory client used above.

The emitted JSON stays valid, so this is not an interoperability problem. The
problem is that the value is dropped silently and the diagnostic points at the
wrong component.

Non-finite floats arise from ordinary arithmetic, including division by zero,
overflow, statistics on degenerate input, and numpy interop, so a handler can
produce one without ever writing float("inf").

Why the tests do not catch it

No test returns a non-finite float from a tool. math.inf appears in the suite
only as an unbounded stream buffer size (tests/client/test_stdio.py:149,
tests/interaction/transports/_bridge.py:120) and as a rejected TTL input
(tests/server/test_request_state.py:355). The one -> float division helper,
tests/server/mcpserver/test_tool_manager.py:838, is marked # pragma: no cover.

Not a duplicate of #3100 or PR #3118

#3100 reports the same end state, an output schema that rejects the SDK's own
structured result, but its cause is validation and serialization shapes differing
on aliases and computed fields. This reproduces with a plain -> float return and
no Pydantic model.

PR #3118 moves output schema generation into serialization mode. That does not
change this case: a float serializes as number either way, so null still
fails the schema.

#3224 is also distinct. It concerns nulls injected for absent NotRequired
TypedDict keys, not values destroyed by JSON serialization.

Python & MCP Python SDK

Python 3.13.11
mcp 2.0.0            (also reproduced on main @ 0d921927 and on mcp 1.29.0)
pydantic 2.12.5
Linux x86_64

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AI assistance was used to investigate and draft this report.

从 server/runner.py 中的 _dump_result 开始，跟踪 func_metadata.convert_result 如何到达 client/session.py:1109 和 1155。阅读 server/request_state.py:128 中现有的非有限浮点数拒绝逻辑，然后在相关的 server 或 client 测试旁添加针对 inf、-inf 和 nan 的回归测试。完成的标准是：该值被保留，或被一条能够指出非有限结果的消息拒绝，而不是误导性地将问题归咎于工具。