ok so I get that each sector can support a colony and each colony needs to be one sector apart, what is the annexing and forward basing do though? Is forward basing forfitting the resources of that sector so you can annex others?
Annexing a sector means you wish to make that sector into a province and add it to your colony, you can only do this with sectors that are connected to your own borders. Forward bases are for sectors that aren't connected to your borders but you would still like to "claim" and perhaps annex in the future. So by establishing a forward base your are pretty much laying claim to that sector by building a mini-base there with some militia forces, so other player's/AI can't annex or claim the sector for themselves unless they want to declare war on you; however, you will not gain the resources until you annex the sector.
I see the word "claim" used a lot, but how does that work? I need an in depth explanation of "claiming".
Where does it show what factions have a claim on a sector?
Is it best to double down or to go broader? Like if I see a sector with 2 production and 1 or no growth, is there anything wrong with adding a growth exploit there? Is there any advantage for adding another production exploit?
How much output do annexed sectors actually generate per resource icon? How much do I lose by exploiting energy on a sector with one energy icon vs a sector with two icons?
Do annexed sectors incur any additional food upkeep or is this determined by the colony size alone?
A correction, sectors are claimed by being adjacent to other sectors which you own. Be they colonies, and their sectors, or Forward Bases. Military presence in a sector has no factor into the claiming of it.When you walk an army over the little "pin" in the center of the sector, you now have a claim on that sector. But, multiple players are allowed to have a claim on the same sector, which is where things can get tricky if you annex it without permission.
Note that there may be other ways to claim a sector, like just walking into it at all might, I haven't done any real testing. It's also possible just being adjacent to a colony "claims" it, for example.
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Terrain:
Forest - Food/Production ; Mountain - Production/Energy ; Ruins - Energy/Research ; Fertile Plains - Food/Research
Climate:
Arcadian - Food/Energy ; Arctic - Production/Research ; Fungal - Food/Research ; Arid - Energy/Production
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It's important to note that terrain upgrades come much earlier in the tech tree than climate ones so always look at terrain first unless you're in the late game.