As I see it, there are about 6 different things we can work on in order to strengthen our position:
- Atraxas (via Calc Hearts, Material Integration, Evolution, Cryptek assistance, some Libraries, Training, etc.)
- Our Direct Reports (Advisors, Assistants, and Private Army; potentially also Fleet; potentially elite Mechanicus)
- The Homeworld (sending tech and techniques over for them to analyze and improve)
- Research (what Atraxas personally knows, plus what the Shogi elite Mechanicus know)
- The Shogi System (infrastructure, Megastructure, Defense forces, Education, Health, Styles, Economy, etc.)
- Everything else - particularly Diplomatic office as a way of reducing Suspicion
Now, each one of these tends to assist each of the others. Atraxas' massive improvement in Calc-Hearts over Turns 8->10 should give him around 100x capacity to perform Research, and better in Martial/Intrigue/Stewardship. This translates to better searching and better Augments for assistants, more ability to send Tech to the Homeworld, more ability to increase Research, and more ability to assist the Shogi System. Our direct reports free Atraxas to concentrate on the most interesting stuff and assist the Shogi System and Diplo Office, and the Mechanicus speed Research (which often gets sent to the Homeworld...). The Homeworld gave Atraxas the Calc-Heart designs and can provide so much wonderful gear - but only if we send the right tech their way for them to
make said gear. Research makes many Atraxas-boosters and direct-report-boosters
and Shogi-boosters (and one or two Diplo-boosters) possible, and helps the Homeworld.
The two oddballs here are - in my view - the Shogi System and the Diplomatic Office.
The Shogi System actually
doesn't help the others much. Rather, it is
primarily our way of "affecting the universe at large." Now, don't get me wrong - it needs to surpass a certain threshold to "pay for our Research and other activities," it needs to surpass a currently-much-higher threshold to "keep us alive and in good shape and the quest going," and getting it high enough will eventually boost Research helpfully (Megastructure direct bonuses; ability to buy Relics affordably; ability to have Humans do the pesky Deep-Warp Research that Exatari
can't). But, still, in a lot of ways it's the
worst strengthening method for boosting the others - and the
best for affecting the world at large. You see, this is the path to stabilizing the Erymist Sector, building fleets of ships, and so on; it relies upon all prior strengthening methods, but is the mechanism for projecting them out into the world.
Meanwhile, the Diplomatic Office is boosted by a very small and select subset of the other categories. Library-Information and Veil-Tech levels are both helpful to Atraxas' personal Diplomatic ability. The Neural Learning device might help? Hiring, training, and augmenting Diplo Advisors will help the whole office. And raising the prominence and wealth of Shogi will open doors and allow us to be much more free with our gifts. But that's about it, sadly. On the other hand, it clears the primary blockers for nearly-all Shogi System upgrades and many Research upgrades - and quite a few other upgrades (see: Streamline The Code Of Law, which is an upgrade to
all of Atraxas and Diplo-Office and Shogi-System and Direct-Reports).
TL;DR: post-Invasion Shogi System upgrades should actually be done a bit less urgently than I'd previously envisioned - though only a turn or two likely - and we should probably try to boost the Diplo Office a bit harder a bit sooner (probably also post-invasion).
Also note, for the record, that our set of Research Multipliers given TL12 in everything we know about looks something like:
Calc-Hearts x3, Information TL12 plus Veil Physics TL12 (+200%*2.2) x5.4, All-LMs x24, Radiant Scholars plus Improved Exatari Statline plus 3E Calc-Hearts x? (estimated x5)
Total: x3x5.4x24x5=x1944.
(Probably more depending on the limits to the last unknown-modifier-chain.)
The GM has specified that the Homeworld's time-to-implement a full TL12 tech-tree has a soft-cap of roughly 40 years. That is, even if we could theoretically fully research TL12 in 4 years, the Homeworld will still have researchers poke the tech for a few decades, and industry take a few decades more to fully put all the new theories and tools into practice. On the bright side, this should mean that a full TL12 implementation will eventually take only a fraction of the overall Exatari Research Capacity.
The GM has
also stated that, after TL12, the difficulty goes up by a much faster exponential, and most Research Multipliers get logarithmically less effective. If we got all reasonably-available Research Multipliers as far as we could (up to TL12) and put the whole Exatari Research
everything on a tech, we'd tech up TL12->TL16 in 500 years. Right now, I think we'd want our first two to be Weight (auto-discover all Tier 2-and-3 Meta Libraries relatively quickly) and Veil Materials (TL12 gives 4E items; every +4 TLs gives x2 E capacity).