this evening's brilliance:

[fox]

[k] and [g] are in complementary distribution.
[g]/postnasally
[k]/elsewhere
This distribution is logical. The preceding nasal is highly occluded, causing [g] to become more occluded in its pronunciation as well. This difference allows [g] to be differentiated from [k] when it is preceeded [sic] by a nasal.
Thus the two are allophones.
*A phoneme can have only one phoneme as its allophone. Hence, it is unnecessary to test either [k] or [g] against other suspicious phonemes.

i'm not actually a hundred percent sure that voiced sounds aren't more occluded than their voiceless counterparts. i tend to doubt it, because often if a phoneme has a voiced allophone and a voiceless one, the voiced one will be found intervocalically, and vowels are of course the least occluded sounds we have. but in any event, nasals are completely occluded orally but almost completely unoccluded nasally (obviously); and all the nasals in this corpus are voiced, which is actually what conditions the voiced [g] in place of the voiceless [k].

and it is absolutely not true that "a phoneme can have only one phoneme as its allophone". in the first place, a phoneme can't have another phoneme as an allophone -- they're opposite concepts. i think he means a phoneme can only have one segment as its allophone, i.e. it can only have two allophones, one conditioned and one "elsewhere". this is absolutely untrue, and this kid ought to know it's untrue if he's been paying even a little bit of attention in class; a phoneme can have multiple allophones, and the fact that he's found that this phoneme has two allophones doesn't remotely mean that the segments don't need to be tested against other sounds.

aiee.