Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations only declare readOnlyHint=false and destructiveHint=false; the description adds substantially more: exactly which fields become publicly visible (kind, number, title, statement, formulas, status) and which never do (bases, journal, review), that the underlying page is exposed only while the project is public, that write permission is required, and that a history line is recorded. This is exactly the disclosure needed for a tool that publishes unauthenticated content.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Purpose and the exposure constraints are front-loaded and nearly every clause carries information (visibility rules, output forms, identification, permissions, audit). The single run-on paragraph and archaic diction ('a link anybody can open', 'which open the claim in a cloud') make it denser to parse than it needs to be.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema, the description still explains the return values (script once per page, mark around words, iframe card), covers permissions and side effects, and leaves parameter rules to a fully documented schema. Remaining minor gaps: no statement about precedence when both id and project/label are supplied, and no hint about revoking an embed (delete_registry_embed/delete paths) after creation.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so the schema already documents id/days/label/sites/project including the 'or name it by project and label' rule. The description restates that identification rule and only adds a cross-reference ('as for create_term_embed'), which is a pointer rather than new semantics, so the baseline 3 applies.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a concrete verb and resource: it puts one claim of a project on other sites as an embeddable link, and names the three output forms (script, mark, iframe). It is distinguishable from create_term_embed/create_wiki_embed/create_embed_set by the 'claim' subject, though the ornate phrasing ('Put one claim ... on other sites') slows recognition of the exact operation.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives a permission precondition ('Only for somebody who may write in the project') and defers parameter behavior to a sibling ('sites' and 'days' as for create_term_embed). It never states when to use this over create_embed_set or the other create_*_embed siblings, so the routing decision is only implied by the resource name.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.