On game settings:

Personally I like to start with slowest research speed. That seems counterintuitive, but as the research works the same for you and the majors, and you are a human and not an AI, you can have an edge using this guide. As you progress in the game you will meet the major regimes on your planet. They had the same start as you and want to rule the planet, too. In most of the cases, you will fight one or more of them.

To win against them, you need better military tech than they have, better military unit models, better economy and adjustable Orders of Battle (OOB) to suit your needs.


This is the research tree, click to enlarge.




Every three fully researched techs in a compartment will give you access to research in another, higher level. As you see here, four techs in the Engineering compartment are fully researched, and heavy industry is in progress. Advanced Engineering, Machinery and Applied Engineering are now open to get discoveries in their fields.


To get things going, you need councils: The research based Councils are:

Economic Council: This council is about making your own people happier and more productive.

Here you get general discoveries that improve your civilization score like Hospitals, logistics related ones like Sealed Roads, and discoveries that let you access resources like Metal Soil Filtration.

Military Research Council: This council is about making other people unhappy. Killing their people, destroying infrastructure and throwing nukes at someone else MAKES them unhappy for sure.

Airforce Research Council: This council is about making other people unhappy, but with machines that fly. It also has a logistical aspect, as you can fly stuff around to provide supply to make your people happier.

Model Design Council: This council is about putting your military research councils findings to good use for your people, which is normally bad news for other people. Well, hostile Ai sentinels, arachnids, etc. are not really people.

Staff Council: This council is about making other people unhappy while you combine your model design findings into new OOBs, it delivers OOBs. You want to field light tanks, infantry and RPG troops under one commanding officer? This council develops it.

Applied Science Council: This council is about effectivity of your other research councils. You will produce more resources, need less fuel, build better flying aircrafts and many other things that make your people happier and other people unhappier.

WARNING
All applied techs (Ap) are linear techs, giving a bonus to your other technologies/stats, like mining, armor quality, damage output or education level in relation to the percentage it is researched. Getting applied techs researched to 100% is insanely difficult. Be advised to stop at 50-70% and then switch to other research by calling your applied tech director.

If you mouseover a tech in the tech tree you can see the description of this game mechanic.

If you want to optimize research early on, you should take a look at the Mind Profile!

It comes with research bonuses at 40, 60 and 80% mind, prioritizing this profile to get the feat bonuses is recommended.

The Eternity Movement is your cult of choice as it comes with a research bonus.

Reference: https://www.matrixgames.com/forums/tm.asp?m=4852426

I will just say that Grognerd's Guide is unbeaten.

https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=2307478602

I want to add that a good interior council director can deliver. You might want to check the artworks, as I put some of my Cabinet up there for inspiration.

Also: Sages. You want them. They are 3 FP national stratagems, that roll at cap IV-V and always come with INT skills. This is a Sage:


A little math example to help your decisions:

Low cap leaders come with lower average attribute scores and get less XP per turn. Skills add the attribute value to 100% if skill is 20+.

Leader A has cap II, INT 30. As skill maximum is capped at 2x attribute value, his rolls will be +90 maximum.
He gets 6 xp/turn on average.

Leader B has Cap IV, INT 35. His rolls will be at +105 maximum, He gets 12 XP/turn on average.

Not only has leader B an implemented 6%+ bonus to research, he will level up his relevant skills earlier and get better faster. The only time you should have a low cap researcher is when his skill is maxed out from the start.

The relation of your leaders should always be as high as possible. A relation 100 leader adds 50% to your research efforts!
I recommend giving them regular bonuses, gifts, medals, all those can be found under leader stratagems and most of them will be generated by your interior council director.

You now have a research council. You can call the guy/gal in charge and give him orders.




Here I called the economics director as I want to change priorities. I want to get more BP put into prospecting.

In the Decisions tab, a new decision now is available.




Before we decide, we take a look at Reports - Organisations - Economic Council Overview.


I want to put points from Research, which is at 60% into Prospecting, currently at 25%.

Now comes the fine tuning. See the invested BP at the start of the turn? It is 207 for Research, and 87 BP for Prospecting. See Discovery at 10%? That is 34 BP invested. As you see in research, there is a hard 100 BP cap after which all other invested BP beyond 100BP become ineffective.

We hates that.

Putting Prospecting to 30 % would be an increase of 17 BP, next turn it would be 104BP. As Discovery tells us, 10% is 34, so 1% is 3.4 BP.

Going back to Decisions, I decide to change Research to 56% and Prospecting to 29%, press confirm and now have optimized my Prospecting.

Important information: Never put a priority to 0%.

Here's why: I show you my interior guys' priorities:


It is 10-1-40-44%. And now we take a look at his skill log:


You will see that he made four skill rolls. Not 3, if I put the useless tariffs to 0%. That means he rolled four times on his main skill, each training him to get better at it.

You are not alone with your research endeavors, there are lot of things that can improve your research.

Depending on the dissolution history, you can find derelict ancient mechs, ships, cargo ships, etc. that all add to your research as bonus points as hex perks.

Here is a derelict ancient mech that adds 100 military research bonus points:





But you can also produce scientific hex perks: The Scientific Outpost is a 3 Fate Point zone stratagem, that produces 200 bonus research points. These can be put into every zone once. You need the lucky roll, though.


If you open REP. -> Organisations, in the research councils there is a summary for Research, and in it there is the Research bonus.

Mouseover and doubleclick the underlined words Research bonus as always.

The research bonus points are taken into account as research bonus points all added up from hex perks and then squre root of these. I (or someone at matrix forums, Zgrssd, probably) but I cannot remember who it was in the first place) reverse engineered the formula.

With the 1.07.02 update, your scrapped card points can generate zone stratagems that can add to your research, too. For 10-12 PP you can get those. Mind that those are quite private worker intensive at the moment. Nevermind, got fixed by Vic, now with normal job numbers.

How to get tech advances:
The enemy uses BP, same as you in his councils to generate research points, but you can do these things in addition to that:

Mainframe AI event in a city : Call your governor for 3 PP, let him succeed in a difficult oratory roll vs the GR AI and get a free random tech discovery, but no research. This can be done multiple times, but difficulty raises each time
You can of course put a suiting gov into this place. Can backfire with an army of AI sentinels - handle with care!

If you win the roll with the A.I. after failing it, the sentinels will stop.

Otherwise you need to destroy the A.I., because once you've made it angry it will spawn sentinels in your empire until you kill it or die trying.


Ancient Archives: A 4 FP nation strat card that gives full research of a random tech. 4FP sounds much, but take a look at the negative national and zone strat cards that generate FP...

Breaktrough Now!: Have mind 80+, a faction with mind++ at least. Can generate BN!, a 5PP national strat card that gives 1 random tech discovery, no research.

Corporate Tech: Have a corporation in your zones, have good relation. 50PP, get fully researched random tech.

Corporate help: same as above, 20PP get a free random tech discovery.

Scientific cooperation/exchange/joint effort: Be at peace with a major, have a good diplomatic foreign affairs council director and get free tech from them or give them yours. It helps to view their tech report in Reports - Regimes - XYZ tech report before you do this. Needs at least 3 embedded spies.

As we now covered the basics, now the mastering is in process.

Your leaders cannot have too much XP. Your interior director rolls on national admin Stratagems like Grand Convention, Wargames, Governor Convention, Cabinet Retreat all hand out XP and relationship boosts like Santa on speed.

Artifacts: There are personal artifacts for all research directors available, depending on you digging them from archaeological sites. This Dopaminator artifact here for example:

Here we focus on when to found the different councils and what to prioritize when or if. The following steps in the analysis assume you started at tech level III.
Depending on your tech level and threat level start, you want these council as early as round one or you can wait until your imminent threat level is low around your capital.
Further information about threat level and when to found is to be roughly found in this guide: https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=2314171481

Economic council

At tech level III it is mandatory to get access to energy tech as soon as possible, with solar power preferred over power plant, depending on your access to fuel/biofuel.

Prioritization: You have 100% to distribute over the following priorities:

Discovery - Research - Prospecting - Economical policies
These use the Inventor, Science, Prospecting and Administration skills.

Depending on your profiles and the PP production, I can recommend this average 1st round setup:

Discovery: 65%

Research: 5%

Prospecting: 25%

Economical Policies: 5%

This setup ensures:

• Early game abundance of discoveries without really researching them. This is important, as you do not want to open up the research field too much. Remember: 5.13.1.5. Manual page 331:
  The Tech Fields are divided over a number of Tech Groups. Once you have fully researched 3 Techs in a Tech Group the Tech Group will be Mastered. Once a Tech Group is Mastered it will give you Discovery access to all Techs in its connecting Tech Groups.
  Once solar power/power plant are discovered, call your economical council director and change priorities to research to make your people happy.
  
• An early game prospecting boost, so you can get access to valuable resource deposits early on. Fuel for your future tanks and recent truck stations, rare metals for polymer armors and trade, metal for everything. Mind that this will attempt to increase the prospecting level in your zones with the lowest level of prospecting, and you need metal, IP and machines to build assets.
  
• Economical Policies get a chance to be found. Those are Prospecting Push I and II, the latter requires democracy 60+ and the related regime feat Open Politics, Archaeology Effort, Private Investment requiring Commerce 40+ and the related regime feat Free Market and Attract Free Folk, government 50+ and State companies regime feat.
  As I always go commerce, this ensures a big private industry boost relatively early when you need it the most.

Later in the game when you have a much bigger BP production you might want to have a setup of

Discovery: 10%

Research: 65%

Prospecting: 20%

Ecoomical Policies: 5%

with an emphasis on research. Remember that every point of research flows over to discovery if there is nothing to research. This is valid for all research councils.


Military research council
At tech level III it is mandatory to get access to assault rifles as soon as possible, with HV guns at the low end of your research tree. You want side skirts and combat armor!

Prioritization: You have 100% to distribute over the following priorities:

Discovery - Research.
These use the Inventor and Science skills.

Depending on your luck finding solar power in the economic council research tree, or even having that council in the first place, I can recommend this setup on round 1:

Discovery: 10%
Research 90%

This setup ensures:

• Quick research and no PP wasted switching priorities every other round.
  
• Fast discovery is ensured, because as mentioned above, every point put into research flows over to discovery if no research is available.
  
• You will never have to change the priorities for 99% of the games.

I can recommend choosing this council as your first one if

• you are surrounded by alien life forms that are difficult to overwhelm
  
• you face enemies from the "XYZ territory" origin, as these are AI sentinels, slavers, nomads or arachnids and early game you will have a bad time fighting these off.
  
• you have exeptional good models from the start. Exeptional means the structural design is 105+. The model design council should be your next best choice to implement the military discoveries. A good modelled infantry with assault guns and combat armor is the goal.
  
• you have access to energy generating hex perks but no economic council.

Model Design council
Full disclosure: I am a tanker, not an artillery guy. YMMV.

At tech level III it is mandatory to get access to tanks as soon as possible, with artillery at the low end of your research tree. In the future, you want side skirts, advanced sensors, polymer armor and applied tank techs like fuel optimization, armor optimization, etc, too!
Let's take a look at the model discovery tree here:
You can see I went for tanks and tanks only, as fast as possible.
This can be achieved by not designing anything that will distract us from achieving tank discovery. If you, say, design artillery on the other hand, your field to discover widens to mechanized artillery and anti-tank gun, thus making the discovery of light tanks less probable.

That being said, Prioritization: You have 100% to distribute over the following priorities:
Discover Model - Design Model.
Both use the technician skill.

I can recommend this setup at round 1 to the end of the game:
Discover Model 10%
Design Model: 90%

When the decision to model comes up in your Organisation decisions, do not model until you have discovered light tanks. That's it.

I can recommend choosing this council as your first one if

• you play on a tiny planet and enemies are close. Quick modelling ensures you get an early edge, switching slugthrowers for carbines makes this possible.
  
• your initial models are horse dung. Opening MNG - Model - Design like here shows us the structural design of our units. Everything below 95 is unacceptable! and needs remodelling.

Make sure you design a new model as the last thing you do during your turn, as the field testing might rise during combat!

Applied Science research council
At tech level III it is recommended to wait until you have at least three Engineering and/or Chemistry techs - military and economical council neede for this - researched until you form this council. All applied science techs are linear techs.

I quote from the manual, p.330: "Linear Tech costs X BP per point, but the higher you get the more expensive it will get. At 25 points the cost will have almost doubled and at 50 points it will have quadrupled. At 75 points it will have increased sixteen-fold. 100 will be near impossible to reach."

With that information, you can try to min-max the threshold doorsteps. Please write a comment on your XP with that, how many BP you invested and how many % you gained in a tech. I will update this guide with that data.

That being said, Prioritization: You have 100% to distribute over the following priorities:
Discovery - Research
These use the Inventor and Science skills.

I can recommend this setup at round 1 to the end of the game:
Discovery 10%
Research: 90%

As always, points put into research will flow into discovery when nothing is to research. That will be a rare occasion in all your games with applied science, though.

Be advised to change your Ap research as soon as you reach 50-70%.

Airforce research council:

I want to point out to this good guide: https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=2313512236

Tech III start: Not recommended as first council.
Tech IV start: As you start with an ultralight aircraft model and the tech already discovered, forming this council first is potentially viable.

Staff council

In my book, at tech level III it is recommended to beeline for light tank armies. Everything else is wasted BP. (YYMV though, but I never lost a game when I had light tanks at tech level III). I cannot recommend taking the staff council as first council at tech III.

In a game with tech IV start it could be viable to get a Staff council first when you had extreme luck with

• the light tank structural design
  
• hex perks providing free IP production nearby
  
• an easy to defend metal mine or two
  
• relative peaceful expansion options.

If the first three points are positive, you could go with staff council and try to get light tank armies early in the game.

Prioritization: You have 100% to distribute over the following priorities:

Discover OOB - Operationalize OOB - Occupation and Governance -Postures

All use the High Command skill.

I can recommend this priority setup until you get light tank army:

Discover OOB: 80%

Operationalize OOB: 5%

Occupation and Governance: 1-5% depending on your profiles, as this priority is highly depending on your profiles; democracies have way less O&G stratagems than autocracy.

Postures: 10-14% until you have Blitzkrieg for tanks and Defense postures for dedicaded infantry units.

After you discovered the OOB you want, exchange Discover and operationalize OOB priorities via calling the Staff director.