The sense inventory in ODE is identical to that in NODE/DIMAP except for two small particulars: the wording of one sense, no. 5(3), is slightly different in ODE (not amounting to anything semantically), and one sense has been eliminated from ODE what would have been a second subsense of this same sense. The wording in NODE was "expressing the target of a shot from a weapon," which ODE's editors do not distinguish from its parent sense. I have followed ODE.
There is only one serious hole in the inventory: no sense corresponding to Quirk's 9.51 and 9.63, or "stimulus" and "reaction" (not really clear why Quirk separates these, as they are the same sense. See below for this addition and discussion of it).
A minor quibble is that ODE doesn't really treat or acknowledge PPs of the "at the sound of the trumpet" type. FrameNet seems to treat these as Time PPs, so for convenience I've treated them that way as well and put the few that occur under 2(2), PointInTime, which is the closest correspondence.
In general, the sense assignments for at were simple and straightforward, perhaps more so than for any other preposition; there was no agonizing about whether a given sentence belonged to this or that sense, and with the addition of the new sense, it was rarely difficult to find a slot in which to classify a particular sentence: there was more than usually close correspondence between the FN Elements and the ODE senses.
Notes from the spreadsheet:
New sense added: (Spreadsheet record 13) As noted above, no standing ODE sense accommodates the very common use of at denoting the thing that provokes an emotional reaction: our outrage at their lies, my surprise at your amazing vocabulary. I think this is a core sense, but as our methodology doesn't permit an easy way to add a core, it seemed most sensible to subsume it under "means." See related discussion below at number (2) under Other Notes.
Other instances of at that may deserve idiomatic treatment
The phrases noted in ODE deserve a look and all probably need to be isolated from regular at PPs. A different use of at that than the one treated in ODE is in sentences beginning with the anaphoric construction "At that, . . ." or less frequently, "At this, . . .", where the meaning is to show that one event triggered another (e.g., At that, he got up and left.). These are probably best classified under the "point in time" sense, 2(2), with the POA being the verb in the main clause.
(1) There is a distinction obvious in the sense inventory that is somewhat obscured in FN and revolves around the semantics of certain verbs. To illustrate: frame Body_movement has the peripheral element Goal, which in the case of verbs (and derivatives thereof) that involve simple motion or location, are realized by sense 1(1): she knelt at the feet of Jesus. However, for other verbs where the complement of the at PP in some sense "receives" the action of the verb, the same element is realized by sense 9(5): she waved at Jesus.
(2) Another case where there is slight bleeding from one sense to another is best seen in frame Emotion_directed, element Stimulus. This element is very often realized with an at PP. As above, in cases where the POA suggests a complement that actually "receives" something, case 9(5) is clearly indicated, and this happens particularly where the complement is personal: She was angry/annoyed/furious/mad/sore at me. However, when the complement is impersonal and the POA suggests emotion that is not necessarily targeted, the sense is 11(6)-1: She was angry/annoyed/delighted/exasperated/upset at the delay.
(3) A problem I note here but that occurs with other possibly all prepositions in FrameNet is the POA (as identified by FN taggers) which in some cases, I think, might skew our data in a particular way by not taking into account the real reason for the use of a particular preposition in other words, its genuine POA, rather than the word it happens to be next to and therefore attached to in FrameNet. Take, for example, frame Judgment_Communication, element Evaluee, lexical item criticism. There are three example sentences:
1) Curators and archaeologists have, however, levelled criticism at the museum for the often tenuous relationship between the objects displayed and the Bible.
2) The hon. Member for Thanet, North (Mr. Gale) referred to the issue of management and targeted his criticism at the management of British Rail.
3) Environmentalists directed strong criticism at world leaders after only 15 minutes was spent discussing the environment at the Group of Seven conference in London.
In each case, the real reason that at heads the PP is because of the verb in use, which I have highlighted: they all are the sort of targeting verbs that fit ODE's sense 9(5), and I wonder that the FN taggers do not identify the verb, rather than the noun, as the POA. "Criticism" could in fact be followed by a number of different PPs, beginning with, e.g., about, for, against, concerning, through, by, and others. In the sentences above, I don't think it's quite accurate to identify criticism as the POA.
A case where FN taggers do in fact identify a verbal POA (even though it is not adjacent to the PP) is in this sentence, illustrating element External_cause in frame Body_movement:
The Spanish officials had swung open their barriers, wishing her good luck and shaking their heads at her foolishness in returning to France.
Here, the FN taggers (correctly, to my mind) identify "shake" as the POA, rather than heads, which is adjacent to the PP. But as you can see, the methodology is inconsistent: one principle for POA identification prevails in the three sentences above, while a different prevails in the other sentence. Conversely, in the following sentence:
To avoid queues at the Theatre box office, patrons wishing to pay by credit card must do so 24 hours in advance of the performance.
A naοve tagger without any particular agenda would identify "queues" as the POA for the at PP here. The FN taggers, however, give "avoid" as the POA (frame Avoiding, element Place). The sense exemplified does not change here; it would be the same, namely 1(1), no matter how the POA is construed.
I'm not sure what the upshot is, but I would think that for your analysis, greater emphasis should be placed on associations of Frames and Frame elements with preps, as opposed to lexical items I think this is what you're doing anyway. If we discover anomalies of a recurring type in other words, elements or lex items that don't seem to conform to a blatant pattern this might be one place to look for the explanation.