Drop the JSON export, or paste it. The page recomputes every SHA-256 in your browser, checks the link from each record to the one before it, and compares the declared head. Nothing is uploaded.
What this proves: these records were not edited after they were written, none is missing from the middle of the chain, and each signature matches the published ECDSA P-256 key carried in the export. What it does not prove: that the key belongs to a named legal entity. Key publication is the next step.