{"id":"integer-digital-root","version":"1.0.0","description":"Repeatedly sum the base-b digits of the magnitude of an integer string until a single digit remains.","supported_operations":["integer digital root","repeated digit sum","digital root in a base"],"unsupported_operations":["single-pass digit sum","digital root of a fraction","casting out nines shortcut only"],"semantics":["value is a canonical integer string: 0 or an optional ASCII minus followed by a non-zero leading digit, at most 1000 digits excluding sign.","base is a JSON integer from 2 to 36; when omitted it defaults to 10.","The sign of value is ignored: the digital root is computed on the magnitude |value|.","value 0 has digital root 0 in every base.","The base-b digit sum is repeated until the result is a single base-b digit, i.e. strictly less than base.","digital_root is returned as a JSON integer in [0, base)."],"limits":{"max_digits":1000,"min_base":2,"max_base":36},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["value"],"properties":{"value":{"type":"string","maxLength":1001},"base":{"type":"integer","minimum":2,"maximum":36,"default":10}}},"output_schema":{"type":"object","additionalProperties":false,"required":["digital_root"],"properties":{"digital_root":{"type":"integer","minimum":0}}},"examples":[{"input":{"value":"9875"},"output":{"digital_root":2}}],"execute_url":"/v1/tools/integer-digital-root/versions/1.0.0/execute"}