Where does “reachability” come from?

I need to pause here because the etymology chain provided doesn't actually support "reachability" as a coherent word formation. The chain shows: - reach (English) ← rechen (ME) ← hrǣċan (OE) - Then jumps to Latin -abilitas, -ibilis, and PIE roots (ker-, -yeti) The problem: "reachability" would be "reach" + "-ability," but the chain doesn't show "-ability" deriving from this Latin suffix chain in connection with the reach/rechen/hrǣċan lineage. The Latin elements appear disconnected from the English verb's actual etymology. I cannot write an accurate one-sentence summary that "names every language in the chain in order" without either: 1. Inventing a connection between the OE verb and the Latin suffix elements, or 2. Creating intermediate steps not supported by

reachability (English): The condition of being reachable; The extent to...

Definitions

  1. The condition of being reachable; The extent to...

Ancestry of “reachability”, step by step

reachability traces back through two separate lines of ancestry.

via English ability

StepLanguageWordMeaning
1EnglishabilitySuitableness; The quality or state of being able;...
2Middle Englishabilitesuitability, aptitude, ability
3Old Frenchableté
4Latinhabilitāsability, aptitude, fitness
5Latinhabilisable to have/possess/maintain; having sufficient...
6Latin-ilis-ile
7Proto-Italic-elis
8Proto-Indo-European-elis
9Proto-Indo-European-lósForms agent nouns from verbal roots

via English reach

StepLanguageWordMeaning
1EnglishreachTo extend, stretch, or thrust out; To give to...
2Middle Englishrechen
3Old Englishrǣċanto reach
4Proto-Germanicrakjanąto stretch, to straighten
5Proto-Indo-Europeanh₃roǵéyetito straighten, to make straight, to cause to be...
6Proto-Indo-European-éyetiForms causative imperfective verbs from roots;...
7Proto-Indo-European-yetiCreates transitive imperfective verbs from roots

Words derived from “reachability

Every word from Proto-Indo-European -lós