The 637 thing and the chart are taken off Japanese websites I located and ran through babelfish. I'm not sure if they're theory or canon, but they're roughly adding up to what I experienced raising. I don't have the links anymore, as I don't read Japanese and the links were only so helpful without that knowledge. They've been correlated with what I've seen repeated on KI and BG's threads on chocobo raising, by breeders with much better birds than I own, which leads me to believe they're probably pretty well grounded or someone would've ripped into that person 2 replies later as is normal for these sites. Again, I have no idea if the 637 cap is hard or soft, as I haven't been able to reach it. I can say that the tiers for each rank seem to be working just fine, however. These are on unbred eggs you either bought/ISNM'd though, bred eggs show up with different numbers already in them based on date plan and parent stats.
Now, for reference, here's the FFXIcylopedia reference on chocobo raising:
Category:Chocobo Raising - FFXIclopedia - a Wikia Gaming wiki
Notice about halfway down the page there's a chart in plain text that has numbers on it for each care plan? That's what I use. To that, add that a San D'Orian Carrot is worth .5 points to every stat, and the Vomp and Zegham are worth 1 point to the two stats they effect, and 0 points to the stats they don't. Celerity Salad is 4 points to Disc only, and Carrot Paste effects Endurance, but I don't know by how much.