Cut for the 99% of people who don't care about the upgrade system in FF13
First of all, if you're actually interested in this topic and somehow missed it, you should go read my first post on the basics of the system.
In particular, i'm still trying to work out the mechanics of the experience bonus levels. This has been made easier by advancing in the game a little further to the point where i have more components available and getting access to the Creature Comforts store, which lets you buy some of the components that give you positive bonuses.
I have determined that at least for the 6-12 cases i have tried, the exp bonus level system works the same for all weapons, and for both weapons and accessories. Which is a little strange since different items give different amounts of experience points to different levels. If there's any such difference in the number of bonus points given it's smaller than my tests have been able to detect.
However for the numeric tests i'm mostly restricting myself to the Gladius, just to try and reduce the potential number of variables.
It takes 13 Begrimed Claws to get the Gladius to experience bonus level 1.25. Likewise it takes 8 Chipped Fangs.
I decided to make the initial assumptions that items give whole numbers of bonus points, and that bonus levels occurred at fairly round numbers of bonus points.
If that is true, then if you further assume that the first bonus level (1.25) occurs at 100 bonus points, then you get the result that each Begrimed Claw must have 8 bonus points and each Chipped Fang must have 13-14 bonus points.
Running with that assumption and using the components available from Creature Comforts i end up with the following results:
Bonus Level 1.25: 100 BP
Bonus Level 1.50: 100 BP (200 cumulative)
Bonus Level 1.75: 200 BP (400 cumulative)
Bonus Level 2.00: 100 BP (500 cumulative)
Bonus Level 3.00: 500 BP (1000 cumulative)
Wicked Fang: 26 BP
Thickened Hide: 22 BP
Enigmatic Fluid: 24 BP
Sturdy Bone: 28 BP
Scaled Wing: 24 BP
Each of those values is entirely internally consistent (not surprising, given how i came up with them) but i run into small but obvious errors when i try to combine items. 2 Wicked Fangs and either 2 Enigmatic Fluids or 2 Scaled Wings should get an item exactly to bonus level one, but they don't. I have to add in one Begrimed Claw to push it over the top.
The most likely problem is that i was wrong in my assumption about the number of BP required for bonus level one. (Or that i was wrong in my assumption about the BP values being whole numbers, but the two are kind of synonymous.) If the first level took 1000 BP then i can't narrow the component BP values down to a single number, not without a lot more math at least.
Just for those interested, if 1000 BP was correct (and continuing on by multiplying the BP of each succeeding level by 10) i think i've got the ranges down to the following:
Begrimed Claw: 77-83
Chipped Fang: 134-142
Wicked Fang: 257-263
Thickened Hide: 218-222
Enigmatic Fluid: 239-244
Sturdy Bone: 278-285
Scaled Wing: 239-243
I'm not sure if my next best step is to start making tables of how many of each pair of item it takes to level up, or start trying to solve it like a math puzzle.
(Of course if it turns out that the first bonus level takes something funky like 237 BP to get to then i'm probably just screwed =)