Is there even a possibility I am the father?

[Skeptigall]

I am trying to determine if it is possible I am the father of my ex-girlfriend's pregnancy. In two years we rarely used condoms, mostly she took the pill. She had irregular periods, but I know the exact date of last possible fertilisation and results of ultrasound.
I have spent hours and hours trying to discover whats the maximum possible variance on Gestational Age trying to support her claim. I actually want the child, but I've got a lot to doubt.

Timeline 2014 -
October 10 : away on holiday, low on birth control pills so she purchases different brand of similar composition to usual
October 15 : Due to an argument, girlfriend [GF] tells me to put a 28-day reminder of her period in my calendar.
October 26 : GF decides to move out, we have unprotected sex for the last time. This is also the last time we have seen each other. But we communicate constantly.

November 12 : 28-day Alert

November 22-25 : GF is away with a male friend. She claims no sexual activity.

December 7 : GF remarks noticeable swelling and tenderness of her breasts.
December 8 : GF takes a home pregnancy test, result : negative.
December 10 : 28-day Alert

December 21 : GF takes another home pregnancy test : positive
December 22 : GF takes another HPT : positive
December 23 : GF has transvaginal ultrasound. Results (full text below): 12.5mm Gestational Sac ~equiv. 4week3days Age of Gestation

January 5 : She comments to me that a 2nd ultrasound failed to identify an embryo, she will have another in 2 more weeks
January 10 : She maintains that she has not been with anyone else. We resolve to continue that discussion only after we determine a viable pregnancy. I don't wanna stress her.

So my question stands : Is there any possibility that I am actually the father? What are the chances?

Thanks so much,
SkeptiGall

FULL TEXT U/S REPORT
WITHIN THE FUNDUS OF THE GRAVID UTERUS IS A SINGLE GESTATIONAL SAC WITH A DIAMETER OF 1.25CM EQUIVALENT TO 4.3 WEEKS AGE OF GESTATION. NO EMBRYONIC POLE SEEN YET. SECONDARY YOLK SAC IS SEEN.

THE CHORIODECIDUAL REACTION IS THICK, ECHOGENIC AND REGULAR. MINIMAL SUBCHORIONIC HEMORRHAGE SEEN.
MYOMEMETRIUM IS HOMOGENEOUS WITH NO FOCAL LESIONS.

CERVIX IS CLOSED. NO ADNEXAL MASSES SEEN. CUL DE SAC IS INTACT.

IMPRESSION : EARLY INTRAUTERINE PREGNANCY OF ABOUT 4.3 WEEKS AGE OF GESTATION.
VIABILITY UNDERTERMINED.

[AnnieBrooke]

I am also a little confused.  What exactly is a 28-day alert, and if it came about "due to an argument," what was it supposed to do to solve the argument?  If it were a notation that her period was due than, wouldn't the main thing be for her to have such an alert on her own calendar?  Why would it be on your calendar?

[RockRose]

BTW - there's way too much information in your post that makes it difficult to wade through and find the pertinent information.  Fights,  28 day reminders,  trips with men,  when she moves out,   etc.,  are not helpful in determining whether you are the father of a viable embryo.

All that is needed are the dates of the transvaginal ultrasounds,  what was found during those ultrasounds,  and the date of your last unprotected sex.

[RockRose]

I agree with Annie.

The ultrasound on Dec. 23 that indicated a sac at 4.3 weeks gestation but nothing but the sac was seen - would indicate she became pregnant around Dec. 9th if it's a viable pregnancy.  Two weeks later,  which would be 6.3 weeks, you can expect to see a heartbeat but nothing at all was found in the sac  from what I can tell.

I don't think this is a viable pregnancy,  and if it is,  it's certainly not yours - the timing is very far off.

If it's a failed pregnancy and she has somehow not miscarried the sac yet,  it's possible it was your baby that never did begin to develop properly.