{
    "check": {
        "by": ["the ontology resolution gate over the math types and foundations that name the domain"],
        "population": "every math type and foundation layer that names the domain",
        "freshness": "a verdict stands until the domain list or a record that names a domain changes",
        "refusal": "the gate fails on a reference to a domain that does not exist",
        "observation": "none: a math domain is a field of study, and nothing observes it while a run executes",
        "evidence": "fires-and-accepts: a suite plants a math type that names a missing domain, and the bundled references resolve",
        "authority": "the domain list, which every math type and foundation that names a domain cites"
    },
    "records": [
        {"id": "number",
            "studies": "quantity",
            "question": "What can be counted or measured?"},
        {"id": "algebra",
            "studies": "operations and structures",
            "question": "What rules govern transformations?"},
        {"id": "geometry",
            "studies": "space and form",
            "question": "What shapes and spaces exist?"},
        {
            "id": "topology",
            "studies": "continuity and connectivity",
            "question": "What remains invariant under deformation?"
        },
        {"id": "analysis",
            "studies": "change and limits",
            "question": "How do quantities vary?"},
        {"id": "logic",
            "studies": "truth and inference",
            "question": "What statements follow from others?"},
        {"id": "set-theory",
            "studies": "collection and membership",
            "question": "What objects can be constructed?"},
        {"id": "combinatorics",
            "studies": "discrete arrangements",
            "question": "How many configurations exist?"},
        {"id": "probability",
            "studies": "uncertainty",
            "question": "What outcomes are possible and likely?"},
        {
            "id": "information-theory",
            "studies": "information and compression",
            "question": "What patterns can be encoded?"
        },
        {"id": "computation",
            "studies": "procedures and algorithms",
            "question": "What can be generated or solved?"},
        {
            "id": "category-theory",
            "studies": "relationships between structures",
            "question": "How do mathematical worlds connect?"
        }
    ]
}