most women ovulate halfway between periods (so if she has a 30 day schedule, she would ovulate on day 15 instead of day 14 if she has a 28 day schedule). other women ovulate 14 days before their next period is expected. a woman can only become pregnant the day before she ovulates, the day she ovulates, and the day after she ovulates. the egg generally 'bounces around' inside the uterus for 2 weeks before she gets her period. so... if a pregnancy test came up positive 4 days after having intercourse, then the pregnancy was already there before that sex happened. it is very rare that a false positive pregnancy test happens.
i did read your other posts yesterday. i find the situation to be quite odd. if the girl is pregnant and you only had sex with her on may 20th or whatever.. then it is obviously not yours. and if she tries to say it is, all you have to do is take a dna test when the baby is born.
as for the girl not showing you proof of the pregnancy, i would just walk away if you have no emotional commitment to this woman. its obviously not your child and shes obviously messing with your head. if you see her in 5 months and she has a bump for a belly, then you know she wasnt lying. but it is impossible for a pregnancy test to come up positive 4-5 days after sex. after the egg is fertilized it still takes a couple days before it even burrows into the uterine wall. the earliest you can test for pregnancy is 5 days before your missed period... and the % for a positive result (if you are pregnant) is below 50%. so even 9 days after conception most pregnancy tests can pick up the pregnancy hormone.
what exactly is this womans intention? is she trying to trap you or has she made is obvious she doesnt want you to be around her or the baby?? i think shes just scared cuz she made a mistake at the beginning of may and doesnt want to believe who the father of the baby could be so shes hoping its you. i dont really know though. but you should seriously sit the girl down and find out whats going on in her head and find out what role she wants you to play in this situation. if shes trying to tell you its your baby and she wants child support and all that crap, tell her you want a dna test when the baby is born. you wont sign any papers and have any obligation to the child until you know for a fact that it is yours. good luck.