Me again - I've seen references to a story about how Sigyn and Loki met each other in several places, but I can't seem to find a record of it anywhere. Is there a surviving story about that, or is there just a 'mythology fanon' edition that's commonly accepted as fact?
No, there is no surviving story about this from Old Norse literature. I’m not aware of any story about them meeting, so I don’t know where the story that you found comes from. For better or worse, it’s very easy to be completely exhaustive with regard to Sigyn, because there is so little lore about her. Here is a list of every reference to Sigyn in Norse mythology that I have been able to find. Since a lot of people have questions about Sigyn, I’ve decided that while this may be overkill for answering your question, others might find an exhaustive list of sources useful.
Þar sitr Sigyn
þeygi um sínum
‘There sits Sigyn (under Hveralundr, with Loki)
but not, of/concerning her
- Lokasenna (epilogue):
Sigyn, kona Loka, sat þar ok helt munnlaug undir eitrið. En er munnlaugin var full, bar hon út eitrið, en meðan draup eitrit á Loka.
‘Sigyn, Loki’s wife, sat there and held a washbasin under the venom. But when the washbasin was full, she poured the venom out, and meanwhile the venom dripped on Loki.’
- Gylfaginning “About Loki Laufeyjarson”:
Kona hans heitir Sigyn, sonr þeira Nari eða Narfi.
‘His wife is named Sigyn, their son is Nari or Narfi.’
- Gylfaginning “Loki bound”
…en Sigyn, kona hans, stendr hjá honum ok heldr mundlaug undir eitrdropa. En þá er full er mundlaugin, þá gengr hon ok slær út eitrinu, en meðan drýpr eitrit í andlit honum.
‘…but Sigyn, his wife, stands next to him and holds a washbasin under the venom drops. But then when the washbasin is full, she goes and pours out the venom, and meanwhile the venom drips onto his face.’
In the beginning of Skáldskaparmál she is listed among the deities who are present when they host Ægir. Later in the list of kennings for Loki, ver Sigynjar ‘husband of Sigyn’ is mentioned.
- Skáldic Poetry
There are two kennings for Loki in skáldic poetry that refer to him in relation to Sigyn. The first is farmr Sigynjar arma ‘burden of Sigyn’s arms’ from Haustlǫng by Þjóðólfr úr Hvini.
The second is farmr arma hafts galdrs, from Þórsdrápa by Eilífr Goðrúnarson from around the year 1000. This is a compound kenning, and it’s not certain that this is the order of the words; skáldic poetry has extremely open-ended sentence structure and words, which are marked for grammar by their ending, can appear in nearly any order, but in this case three of four words are in the genitive case making it impossible to determine the order by means of grammar. However it clearly follows the same pattern as Þjóðólfr’s Loki-kenning mentioned above. It seems interpretable ‘burden of the arms of (the) magic-deity’ (from haft, literally ‘fetter’ but often refers to the gods, especially in the plural hǫft) or ‘burden of the arms of (the) captive of magic’ (from haftr ‘prisoner, captive’).
On the Skáldic Poetry Project website, they’ve analyzed Eilífr’s verse completely differently, so that the kenning is farmr arma meinsvarra and translated ‘The cargo of the arms of the harm-woman,’ but this is so far unpublished and it’s not clear how the rest of the verse was analyzed (that is, what galdrs and hafts are supposed to mean in that case).
- The Gosforth Cross
The last is not a textual reference but rather the image carved on the Gosforth Cross, a stone cross in Gosforth, England, depicting scenes from Norse mythology, particularly from ragnarök:
These are all of the references that I have ever managed to find to Sigyn. It’s not impossible that I missed something, but here’s how I searched in case anyone wants to look for more: searched “Sigyn” and “Loki” on the Skáldic Poetry Project, searched “Sigyn”, “Sigynjar”, “Sigvin”, and “Sigvinjar” on the Árni Magnússon Institute’s database of Norse/Icelandic texts, looked up “Sigyn” in Finnur Jónsson’s version of Sveinbjörn Egilsson’s Lexicon Poeticum. That’s pretty thorough, but it would not turn up the Gosforth Cross for example, I just happened to know about that.