What she sings doesn't seem to have much signifigance other than to show how intelligent she is, due to her growing up around computers.
1: The Solidus she mentions is the name of one of the three chickens they have on the Nomad. I have no idea what the first string of numbers she sings are meant to be (7892990360), but the second string after the "lalalas" are part of Pi: 33053054882046652. Could be a coincidence, given Pi's many number combinations, but quite unlikely.
2: Part of the Fibonacci sequence it seems
3: Elements, obviously
4: "Stations along the Nose Japanese private railway :
Kawanishi-noseguchi, Kinunobebashi, Takiyama, Uguisunomori, Tsuzumigataki, Tada, Hirano, Ichinotorii, Uneno, Yamashita, Sasabe, Kōfūdai, Tokiwadai, Myōkenguchi"
Much thanks to pockythesupersnack for that one
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