This post addresses subgenus & species possibilities for Jim Moore's Osmia series here. The image above is a modification of Jim's ventral photo here, where I've tried my best to accurately label:

a) the six visible abdominal sternites, labelled S1 – S6; b) the laterally visible portions of tergites T1 – T6, and the visible portion of the underside of the distal tergite T7; c) the "inner ventral angle" of the bee's left hind coxa (indicated by the arrow at upper right)
The arrow at lower left points to a transverse line which I believe to be the sulcus separating S2 and S3. But I could be in error there...as that transverse line may just be a groove on a "large S2" (consisting of what I've labelled S2 & S3 together). In that case what I've labelled S4 becomes S3; and S5 becomes S4; etc. Certain aspects of such an "alternative sternite numbering" jibe with parts of various keys and descriptions (but not all)...suggesting my numbering of the sternites might be off. This is touched on below in the course of fleshing out alternative interpretations of the keying process.
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To begin the keying process, consider the first couplet of the Key to Subgenera of Osmia of the Western Hemisphere in Michener(1)(2007), which reads:

1. Hind coxa with strong longitudinal carina along inner ventral angle; parapsidal line somewhat elongate ............ O. (Diceratosmia) —. Hind coxa not carinate; parapsidal line punctiform ...... 2
The primary character here involves the coxal carina. It is illustrated here; in these two matching unlabelled & labelled images; and in Fig. 4 on page 9 of Hurd & Michener(2)(1952).

The secondary "parapsidal line character" is quite subtle and not visible in any of Jim's photos (though it might be discernible with the specimen under a microscope...for more details on this character, see item "2)" here).

Thus the primary question for us is:

Q1) Does the well-defined edge visible on the coxa in Jim's photo represent a "strong carina", or just the normal presentation of the inner hind angle?
Looking at the bee's right coxa, it doesn't appear "strongly" carinate to me...but there are definitely clear edges along the inner ventral angle of each coxa. I find this kind of judgement call for subtle character states a bane of taxonomy! When I encounter such a situation, I usually "try going both ways".

So let's start by interpreting the coxae as "strongly carinate", which leads to subgenus Diceratosmia. Studying the literature (e.g. Michener(1949), Mitchell(3)(1962), Krombein et al(4)(1979)), one finds the only known species of the subgenus reaching California is O. (Diceratosmia) subfasciata subfaciata. Mitchell(3)(1962) describes subfasciata as having:

"...sternum 2 broadly rounded apically, largely covering sterna 3 and 4, apical margins of these exposed, form as shown (fig. 29), 5-8 entirely retracted..."
But in Jim's images, S2 (as least as I'm interpreting it) is short with a straight edge; it does not cover S3 and S4; and S5 in not retracted (although the latter two traits may be subject to how a specimen is "relaxed"). Also, note Mitchell's figure 29 shows subfasciata having S3 with a very wide emargination, whereas in Jim's photo S3 is apically rounded but entire (while S4 is narrowly emarginate).

Further, note that Mitchell's figure 29 shows T7 as deeply (semi-circularly) emarginate at apex...having relatively pronounced and sharp lobes (see also this reference photo), whereas in Jim's photo the apical lobes of T7 (seen from below) are much shorter and blunter. Further yet, Michener(1)(2007) states that in Diceratosmia, the apical margin of S4 has its two lateral edges bicarinate with a central groove between the carinae. But in the 2nd image in this series, you can see Jim's specimen has S4 basically entire, while S5 exhibits the lateral, bicarinate groove attributed to S4 by Michener. (But recall that...if my labelling is in error, and my "S2 & S3" actually constitute a single large S2...then Michener's bicarinately grooved S4 would jibe with Jim's 2nd photo.)

And here's another discrepancy: Mitchell states that in O. subfasciata the lateral ocelli are "subequally distant from the eyes and the vertex margin"...whereas in Jim's specimen they're much closer to the vertex margin.
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As noted above, some the the discrepancies between the characters of subfasciata and Jim's specimen may be due a possible error in my numeration of the sterna...or to extension of the abdomen due to relaxation & preparation of the specimen. Nevertheless, there are enough discrepancies to cast doubt on an ID of Diceratosmia here, and motivate consideration of the alternate lead in Michener's first couplet...namely, that the hind coxa may not be "strongly" carinate on its inner ventral angle. In that case, we'd proceed to couplet 2 in Michener's 2007 key, namely:

2(1). Malar space as long as width of scape; small shining depression in genal area below and behind lowermost point of eye margin .......... O. (Osmia s. str.) —. Malar area shorter than width of scape, except in forms with anterior clypeal margin greatly swollen; no small shiny depression below eye ........... 3
None of the characters above are clearly visible in Jim's photo, though previously my impression was that the malar space was quite short. This is something Jim can hopefully check with the specimen in hand. Let's assume it is indeed short (if not, we'd be at the very speciose subgenus Osmia s. str.).
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Next couplet in Michener's key reads:

3(2). Males ........ 4 —. Females......... 10
The absence of scopa on the sternum tells us this is a male (which, if desired, Jim could verify by checking for 11 flagellomeres).
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That brings us to the critical couplet 4 in Michener's key:

4(3). S2 transverse, posterior margin feebly concave, straight, to slightly convex; S3 not or weakly emarginate medially, exposed from side to side, posterior margin not or gently concave ........... 5 —. S2 large, posterior margin strongly convex; S3 medially hidden by S2, posterior margin broadly emarginate with fringe of long hairs in emargination ........... 7
If my proposed numbering of the sternites in Jim's photo is correct, the clear choice is the first option. Following the key beyond there leads clearly to subgenus Mystacosmia.

If I misinterpreted the transverse line indicated by the arrow at lower left of the photo (and the actual S2 is "my" S2 & S3 together), then "S2 large" fits well...but not so much the rest (i.e. in Jim's photo, the emargination of S3 is not broad, and S3 is not medially hidden by S2). This choice would lead to subgenus Helicosmia, but it doesn't seem well supported here to me.
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As mentioned in my related comments here, Mystacosmia was erected as a monotypic subgenus of Osmia by Snelling(1967), with only one species, Osmia nemoris. Among the diagnostic characters Snelling listed for the subgenus, the following are in excellent agreement with Jim's photos: S2-S5 truncate to weakly convex along apical margins; S6 with apical margin broadly triangular. In not-so-good agreement, he also indicated that T7 was "produced apically, mid-apex deeply emarginate, forming two sharp teeth". But Sandhouse, in her original description of O. nemoris indicates T7 had teeth "very broad at apex", i.e. more blunt, like those in Jim's photo. (There are other disagreements too, for instance Sandhouse indicated the hind basitarsus was toothed; Snelling indicated it was not toothed.) Overall, Sandhouse's description fits Jim's post well.

In summary, if my interpretation of the numeration of the sternites is correct then it seems the best fit here is subgenus Mystacosmia...which by virute of its being montypic, would give species O. nemoris. But it's not as leak-proof a match as I'd like...this might be Diceratosmia if I misinterpreted the coxal carina character; or Osmia s. str. if the malar space is indeed greater than the width of the scape; or Heliocosmia if I got the numbering of the sternites wrong.

It would be much appreciated if an expert could share any insights here (e.g. correct or confirm my interpretation of the coxa character here, sternite numbering, or anything else :-)