Update, I have no finished Fennekin's analysis to a single point of error in terms of base stats.
HP: 40-41 (Same evidence as Froakie, 19 -> 20 at level 6 indicates either 40 or 41 because it is never 18.) My assumption is it is 40.
ATK: 45-46 (Can be 11 on level 5 without personality. Also can be 9, and the tests on the 9s indicated at least 9.6 was reachable, shrinking range to 45-46.) My belief is it is 45 due to rarity of 11 atk. If it was 46, you'd see 1/8 that way.
DEF: 40-41 (Same evidence as HP 9-> 9 on leveling to 6. Never 8) My assumption is, again, 40.
SPATK: 61-62 (Evidence that it can be as low as 62, but I got one that indicated 76 is reachable with IVs. Therefore, range is 61-62.) My assumption is 61. That being said, I did extensive testing and got 10 trials on the bottom end that put 62 and only one out of about 10 trials on the upper end that indicated 61(76 w/ IVs) instead of 60(Rest only hit 75), so who knows...I could be surprised.
SPDEF: 60-61 (Evidence that it can be as low as 61, but never upper evidence of 61 that I got from SPATK...never lower than 11 on 5.) My guess is 60, but there were plenty of 12->14 on 5->6 leveling that would normally be 1/16 whereas it would be 1/8th with 61.
SPEED: 60-61 (Same evidence as SPDEF.) I am still thinking 60 here.
The overall base expectation is 40/45/40/61/60/60 for a total of 306. Interestingly enough, my expected values for Froakie based on earlier data I posted was 40/56/40/61/43/70 for a total of 310. However, in recent iterations, the totals have rarely been exactly the same early on. So I can buy this.
Time for the chestnut!