It is true that before the Second Vatican Council some moral theology manuals placed arrival before the offertory as the dividing line in deciding whether one fulfilled the Sunday obligation of assistance at Mass. But after the liturgical reform, with its emphasis on the overall unity of the Mass, modern theologians shy away from such exactitude.
https://www.ewtn.com/library/Liturgy/zliturg9.htm
The reason why there is no authoritative documents is because there is none. There is no document that give guidelines of how late you can be. Imagine how it would affect churchgoers nowadays. Each priest has his own rule of thumb.
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In general, it "counts" as long as you are there during part of the Liturgy of the Word, and then the Liturgy of the Eucharist up until Communion. Generally you should hear at least some of the Gospel; but technically, you're okay even if you're there before the Offertory. Technically.
http://forums.catholic.com/showthread.php?t=446611
https://www.ewtn.com/library/Liturgy/zliturg9.htm
The reason why there is no authoritative documents is because there is none. There is no document that give guidelines of how late you can be. Imagine how it would affect churchgoers nowadays. Each priest has his own rule of thumb.
***
In general, it "counts" as long as you are there during part of the Liturgy of the Word, and then the Liturgy of the Eucharist up until Communion. Generally you should hear at least some of the Gospel; but technically, you're okay even if you're there before the Offertory. Technically.
http://forums.catholic.com/showthread.php?t=446611