Be careful wall of text and theorycrafting ahead...
As I was looking for information regarding the vis cost of Summae, I found a lengthy debate on what was an acceptable level of Summae. Let's just say that opinions were covering a large range value regarding highest possible Summae level and quality as well as the existence of Roots and Branches, but definitely no agreement
So I decided to find out by myself if I could get a good estimate. I run some simple simulations to measure the impact of various parameters to find out what will be highest level a specialist could achieve, as well as the Summae Level and number of Tractatus available.
Initial hypothesys:
 Each generation start from 0 xp, out of apprenticeship in the Art they want to specialised (no virtue, no flaw).
 Each generation will start at 0, and will study from the highest Summae available (no optimising for the best quality) and will read every Tractatus available on the topics (again, no bonus for any virtues).
 Each generation of specialist will spent the same amount of time studying from raw vis. Each raw vis season will bring an average of 6 XP (no bonus for virtues nor from Aura).
 Once this is done, it is considered that the magus will no more progress on this Art and will spend two years writing a Summae at the highest level possible and every Tractatus he can.
 Then the next generation will take over and will resume where the previous magus left. The next generation will also start from 0 xp.
I used 4 different variable to assess their impact on the maximum level achieveable, number of years to reach it and so on. Those variable are: quality of tractatus, quality of Summae, number of season studying from raw vis and number of new tractatus written by each generation.
To illustrate that, I started with an average Quality of Summae and Tractatus of 8  conservatively low , 16 seasons of study from virtus and a ratio of 100% original tractatus.
The first generation start at 0 xp, no books and no tractatus  they had it rough. After 16 seasons of virtus study, the magus accumulates 90 xp, so a level 12. Then he writes one L6Q8 Summae and 3 Q8 tractatus during 2 years. Between his studies and writting, he spent 6 years.
The second generation starts by reading the Summae and all 3 Tractatus (for a total of 7 seasons) before studying 16 seasons of virtus, accumulating 141 xp, so a level 16. Then writes one L8Q8 Summae and 4 Tractatus. Between his studies and writting, he spent 7 years and 3 seasons.
And so on, I spare you the table.
Here is what I found:
How many "generations" for a magus to reach 40 in an Art.
 The initial generation are quite short, allowing a quick increase of competencies in a short time span. The 10 first generations took less than 130 years to complete. The word generation is in fact misleading and should not be seen as "magus generation" but more as how long a magus interested in the topic at to spend to bring this knowledge to speed and then build on it to leave a legacy.
So after 10 iterations of research improvement and about 130 years, the highest level reach by a magus was 33 (568 xp).
And the 14th generation reach level 41 (878 xp) in 238 yrs. That is of course if every magus was able to start immediately after the previous magus dropped his quill to hand him over the precious books and tractatus. To achieve this level, he had to collect each and every of the 74 tractatus written by his predecessors. However, he would have spent "only" 25 years studying.
Increasing this duration by 50% to 100% gives a more organic growth, so we can assume than 400 yrs after the foundation of the order, there are a few specialists with an Art above 40, with all the implication in terms of higher quality Summae, lower level and so on.
How does Summae quality impact the growth ?
As expected, it has no impact on which generation reaches first the level 40 (it is always generation 14th), but it happens faster. It is the accumulated time saved by each generation allowing the next one to start faster. if instead of Q8, the Summae is Q10, the 14th generation happens 10 years earlier.
How does Tractatus quality impact the growth ?
This has the single biggest impact of all the other parameters. Not only does it shortens the number of generation required to reach level 40, but it shortens every generation length. Going from Tractatus Q8 to Q9 allows generation 12th to reach level 40 after only 187 years of combined research and study, and it only took her 22 years of study and required to go through only 62 tractatus. Generation 14 can reach level 45 after 251 years.
How does ratio of original Tractatus impact the growth ?
Tremendously as well.
If only 80% of the tractatus written by a generation are original (or 20% are lost), everything slowdown. Level 40 is reached by generation 17, after 280 yrs of combined research. Generation 14 will be stuck at level 35.
At 70%, it drops to generation 21 and 349 yrs...
On the other hand, if the ratio of original tractatus is above 100%, it speeds up the process. At 120% ratio production per iteration, generation 12 reach level 40 in 200 yrs.
But how it is possible to have a ratio above 100% ? Well, the assumption is that there is only one specialist writting a Summae and as many tractatus as possible. However, nothing prevent other less skilled magus to write other tractatus. Combined to the specialist output, it will bring the production per iteration above 100%.
Other points to consider:
It is very likely that the initial "specialist"  generation 1  has a score well above what 16 seasons of virtus study will provide. Sure, but the impact is not that significant, it only slightly shorten the study time by a year: if instead of being level 13 (what 16x6 xp will provide), the initial magus is level 20, the next generation will have a Summae level 10 instead of 6, and 4 tractatus instead of 3. Not a big of a head start and in fact, gen 2 will reach a level lower than gen 1 because the xp coming from the Summae, the 4 tractatus and 16 seasons of virtus study brings only 183 xp vs 210 for the gen 1 specialist.
What if they spend more seasons studying from virtus ?
The level 40 will be reach by an earlier generation, but not that much faster. By doubling the number of season spent of virtus study (32 seasons), generation 11 will reach level 40, but it will still take 226 yrs: less generation, but each generation works longer.
Also, by keeping a smaller number of season, I avoid the consideration of virtus spent per magus: 16 seasons at 3 points/season is manageable for the last generations prior reaching level 40, [strike]48 pawns is reasonable for a specialiste to have it saved/collected over time[/strike] 7x16=112 pawns of virtus is already quite high. However 32 seasons x 78 pawns, more than two rooks, it will definitely trigger the discussion on how rich is one saga vs another saga.
Also, keeping this number manageable, I avoid the issue of botch, Twilight and so on. With 16 seasons, statistically, the magus will roll one, two or if really unlucky three times a 0. Hopefully not enough to throw him in final Twilight.
Weakness of this simulation:

Assumption that a generation takes immediately after the previous one has finished writing books: Yes, it is definitely a dodgy hypothesis. To make things "worth", it is possible to add a 5 years lag increment between each generation to simulate the coming of a new researcher, the time to gather all the documents required for the study (at the end, it will only account for an extra 70 yrs)... On the other hand, it is also possible to say that gen n+2 can start getting the basics before gen +1 has produced his material by using gen n documents, which will shorten the cycle.

Assumption about Summae Quality: it is really a worse case scenario with a Q8 Summae. It is likely that now and then, somebody will refine an older Summae bringing it to Q9, 10, possibly 11. It will slightly shorten the initial learning period, but the Summae study time is not the one having the biggest impact on the generation length and it has no impact at all on the final level reach by a generation.

Quality and abundance of Tractatus: since it is the most critical element which drive the speed to level 40, it is worth looking at it. An average Q8 tractatus is a conservative assumption. Considering a magus does not need to be the best specialist on the Art to write a good quality tractatus, it is safe to assume that over time, the quality of tractatus will improve as collections (Florilegea) starts to be compiled. It should normally goes hand in hand with the decrease of tractatus, however since every bits of knowledge is valuable for a specialist, only the worst of the worst will be cut. All in all, contribution of good quality nonspecialist with replace the chaff and a ratio of 100% output per researcher generation is reasonable. And as specialists will know who is their predecessors, they will try to get access to their archive: instead of having to look for one tractatus at a time, by looking for older specialists, they will find whole collections. So I don't find unreasonable for a magus asking nicely a few Redcaps succeeding in getting those collections.
What about Schism war and so on ?
Possibly a delay of a few generations considering the possible loss of tractatus and experts, which means starting from a lower initial knowledge base.
What about virtues ?
I wanted to look at worst case scenario. It is sensible to assume that a true specialist will have an Affinity in the relevant Art. To simplify that, it means that each tractatus will be the equivalent of Q12 instead of Q8. It is a huge boost in learning process and speed up significantly the research curve, allowing Gen12 to break the level 40 limit in just about 176 yrs (the increase of perceived Summae quality is comparatively negligible, shortening the research time by about 10 yrs).
Same can be said for Book Learner (the boost in quality is +3 instead of +4).
That's purely a mathematical construction, it does not reflect the organic growth of the Order ?
I know that ! But it is a close as I could get from reconstructing the knowledge development of the Order.
Keep in mind that it is definitely not skew towards an optimal growth to stay more on the lower curve.
I explained every hypothesis and how each parameters affect the whole development. I will welcome your comments and can run various simulation with other hypothesis if you want to see where it goes.
Conclusion ?
After this long wall of text, what's in for me ? Some useful information  I hope.
 500 yrs after the Order birth, it is safe to assume there is a least one mage specialist in each Arts with a level 40 or even higher, and it might not be unheard of somebody reaching level 50.
 Based on that, you can infer the type of book you can find in the Order (Level 40 magus means L6Q20 are available with just a Com of +0 and some refinement/resonant material bring it to Q21, L15Q11 exists, and it is reasonable to consider higher quality and/or level).
 It takes about 25yrs (100 seasons) to go from 0 to level 40 working only with quality 8 documents and no virtues, with an Affinity, it drops to about 66 seasons (16 yrs and half). Obviously, it will not be reached 16 yrs after gauntlet, but it gives a good idea of the shortest time needed. Multiply by 34 to take in consideration other projects, apprentice and side activities and you round that to 5064 years after gauntlet (and it is starting from 0 which is obviously wrong).
 Even by trippling the study time and recalculating the overall research time spent by each generation, level 40+ specialists exists in 1200.
 If high quality Summae gives a good lift up at the early stage of education, tractatus are key to reach the highest level.
 It will requires collecting 74 tractatus  which is a tall order, but again, between collections, good connections, and (I admit) a fairly substantial amount of virtus, doable. Again, an affinity will cut the need to "only" 50 tractatus. This is definitely YSMV as it depends on how magus are willing to trade, how efficient Redcap services are and so on an so forth. But considering that there is about 1200 magus in the order, if areas of specialty are evenly distributed, that 80 specialists (or a least magus with some solid interest) per Art. If each one write one tractatus, that's enough to supply the required 74 tractatus.
 Book learner is a must have for a true specialist, as it will turn even vain Tractatus of Q5 into decent source of xp.
Should your saga have those high level magus & books ? Hey, that's up to you!
If it is not the case, it says something about how the Order works: less trust, less sharing of knowledge  even from the Bonisagus house, less efficient Mercerre, possibly regular knowledge loss due to some covenants getting destroyed (by whom ?).
Can it have higher level books & better specialist ? Sure. It requires also some assumptions like a more efficient collections of knowledge and easier access to it  the Order is more and more looking like a scholar institution and less like a group of paranoid magic wielding lonely nutcases. Are they ready to become an Academic power like suggested in Transforming Mythic Europe ?