Unassigned; IANA's registry runs empty from 10631 to 10800, and 10778 is in that gap.
Between printopia (10631) and gap (10800, Gestor de Acaparamiento para Pocket PCs) IANA assigns nothing, and 10778 is inside that empty stretch. Nmap's scan-derived service list carries it as unknown at a very low frequency. There is no documented application default, no known trojan, and no scanner signature attached to it. Anything answering is a locally configured service.
Expose with care
No registration means no assumptions. Grab the banner and judge the actual protocol.
$ nmap -Pn -sV -p 10778 TARGETSeen this on your network? Beige Box scans your Wi-Fi and shows every open port on every device — and its Ports tool links straight back here.
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Corrections or a missing port? Reply @rimrocksystems.