Where does “longhand” come from?

I need to flag a critical issue: the etymology chain provided appears corrupted or mismatched. It shows a chain for "long" (English long ← ME long ← OE lang, etc.) but the headword is "longhand," which is a compound word meaning handwriting in cursive script (as opposed to shorthand). The chain doesn't support "longhand" at all—it only traces "long." Without the etymology of "hand" or evidence of when "long" + "hand" were compounded, I cannot write an accurate one-sentence origin summary per your rules. Could you please verify: 1. Is the headword "long" or "longhand"? 2. If "longhand," can you provide the complete chain including "hand"? I won't fabricate a summary that violates the rule "State only what the chain supports."

longhand (English): The written characters used in the common method...

Definitions

  1. The written characters used in the common method...

Ancestry of “longhand”, step by step

longhand traces back through two separate lines of ancestry.

via English long

StepLanguageWordMeaning
1EnglishlongHaving much distance from one terminating point...
2EnglishlongitudeAngular distance measured west or east of the...
3Old Frenchlongitude
4Latinlongitūdōlength, longitude; longness
5Latinlongusfar, long; extended, prolonged; long; tedious,...
6Latinly; used to form adverbs from adjectives
7Latindis-asunder, apart, in two; reversal, removal;...
8Latincalceusshoe
9Latincalxlimestone; chalk; the finish line
10Ancient Greekχάλιξsmall stone, pebble; gravel, rubble

via English Hand

StepLanguageWordMeaning
1EnglishHandThe part of the forelimb below the forearm or wrist in a human, and the corresponding part in many other animals
2Middle Englishhondhand; Alternative form of hound
3Old EnglishhandA hand
4Proto-West Germanichanduhand
5SwedishhandA hand; A hand; the set of cards held by a player
6Old SwedishhandA hand; A direction; A behalf
7Old Norsehǫndhand
8Proto-Germanichanduzhand
Every word from Ancient Greek χάλιξEvery word from Latin dis-Every word from Latin
longhand — Etymology, Origin & Word History | Etymology Explorer