v1.1.1: omit empty inputSchema.properties at registration

Same json.lua empty-table → [] gotcha that bit `ping` in v1.0.0-rc1
(project_json_empty_table_gotcha memory) bit again — this time on
tool inputSchemas with `properties = {}`. Symptom: spec-strict MCP
clients (Zod et al.) reject tools/list with:

  expected: record, code: invalid_type,
  path: [tools, N, inputSchema, properties],
  message: "Invalid input: expected record, received array"

Fix: in `lmcp:tool()`, normalise the registered inputSchema —
when `properties` is an empty Lua table, drop the key entirely.
JSON Schema permits omitting `properties` on `type: "object"`
(means "any object, no constraints" — exactly what a no-arg tool
wants).

Clone-before-mutate so the caller's table isn't trampled (matters
when a server author shares one schema across multiple
registrations).

Smoke tested locally with 3 tools (empty, default-nil, populated):
- `properties = {}` → emitted as `{"type":"object"}`
- nil schema → same default, same output
- populated properties → emitted intact with full shape

Discovered against hertz-tools live (lxc_list, network_status had
`properties = {}` — hertz hotfixed by hand before this commit;
this protects every future tool author from the same trap).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

lmcp.lua

@@ -163,10 +163,29 @@ end
 --     structuredContent (issue #13; spec-strict clients get first-class
 --     structured access)
 function lmcp:tool(name, description, params_schema, handler, opts)
+    -- Normalise empty inputSchema.properties → nil. JSON Schema allows
+    -- omitting `properties` on a `type: "object"` schema (means "any
+    -- object, no constraints"). Without this, an empty Lua properties
+    -- table goes through json.lua's is_array → emitted as `[]` →
+    -- spec-strict clients (Zod et al.) reject with
+    -- `expected: record, received: array`. The same gotcha already
+    -- bit `ping` in v1.0.0-rc1 (project_json_empty_table_gotcha
+    -- memory). v1.1.1 fix.
+    local schema = params_schema or { type = "object" }
+    if type(schema.properties) == "table" and next(schema.properties) == nil then
+        -- Clone the schema and drop the empty `properties` key. Avoids
+        -- mutating the caller's table (in case they re-use it across
+        -- registrations).
+        local clean = {}
+        for k, v in pairs(schema) do
+            if k ~= "properties" then clean[k] = v end
+        end
+        schema = clean
+    end
     self.tools[name] = {
         name = name,
         description = description,
-        inputSchema = params_schema or { type = "object", properties = {} },
+        inputSchema = schema,
         handler = handler,
         annotations  = opts and opts.annotations  or nil,
         outputSchema = opts and opts.outputSchema or nil,