New Class idea [Geometrician]

[Seraphor]

How about something like this:

No stances.
1 Aetherprobe creates a 10y radial 80 potency HoT field.
2 Aetherprobes create a corridor with a 20% damage reduction field.
3 Aetherprobes form a triangle with Terrain Aspect Bonus and healing potency increase, and allows you to trigger the detonation abilities.

You can therefore tailor your ‘stance’ by placing the aetherprobes, but it will not be a permanent ‘stance’ as your goal would still be your terrain bonus and/or a detonation.
E.g. If you require the shield over the buffs, then you hold off on your third aetherprobe, or use Retrieve to remove one, etc.
This gives it cost-benefit mechanism, and is centred around a prep ‘rotation’ kinda like a MCH, but more adjustable.

You still have your GCDs and unique HoT or Mitigation abilities, so that if you don’t have the field you need up you have something to make do with until you’ve set it up.

The concept is therefore more based around your environment dictating your skills.
While terrain decides your buffs, your use of that terrain (aetherprobes) decides your ‘stance’, in addition to you creating a new ‘terrain’ (fields) for party members to use.
Ergo, it’s ALL terrain manipulation in one form or another, with no conventional ‘stances’, more fitting of a Geomancer class in a mathematician skin.

Obviously the Terrain Aspect Bonus would require them to go back through all maps and either set a terrain type to that entire map, or actually map out new zones within those maps.
So by holding off until 3 aetherprobes are available, at level 60, this excludes all pre-60 dungeons from that requirement.
Adjust Gaia/Stratification to post-60 too.
This would also mimic AST’s access to Diurnal and Nocturnal at varying levels, with only 1 probe (HoT) being available first, then 2 probes (shield) later.

Overall, this still allows you to 'fill in the gaps' left by your co-healer without clashing, but doesn't mimic AST's stances or add in three stances to juggle.


As for the Vector/Cartesian traits.
Instead of simply increasing Axiom skills by so much, the Vector/Cartesian trait could cause the ticks of Logarithms to proc an Enhanced Axiom/Congruence, kinda like BLM’s Thundercloud, THEN increase potencies by 50%/100%.

Vector: (2 probes)
Causes enemies within the field inflicted by Negative Logarithm to provide a 10% chance to proc ‘Enhanced Axiom’ increasing potency of the next Axiom spell by 50%.
Causes party members within the field inflicted by Positive Logarithm to provide a 5% chance to proc ‘Enhanced Congruence’ increasing potency of the next Congruence spell by 50%.

Cartesian: (3 probes)
Causes enemies within the field inflicted by Negative Logarithm to provide a 6% chance to proc ‘Enhanced Axiom’ increasing potency of the next Axiom spell by 100%.
Causes party members within the field inflicted by Positive Logarithm to provide a 3% chance to proc ‘Enhanced Congruence’ increasing potency of the next Congruence spell by 100%.

Plus…
Triangulation:
Using an ‘Enhanced Axiom’ on a target outside of the field resets the cooldown on Aftershock.
Using an ‘Enhanced Congruence’ on a target outside of the field resets the cooldown on Natural Logarithm.

This provides you with a pseudo combo rotation (e.g. Neg.Log>Enhanced Axiom>Reset Aftershock, or Pos.Log>Enhanced Congruence>Reset Nat.Log) which is no more powerful than the kind of crit/mp-free procs that the other healers get but is reliant on and has different effects based on, you guessed it, position (whether or not targets are in or out of the aetherprobe field)
In any of these cases, if the target moves into or out of the field, then the effect stops.
E.g. if a target within the field has Neg.Log, then moves out of the field, further ticks will not be able to proc Vector/Cartesian.
and if a target outside of the field moves into the field as you're casting Enhanced Axiom, it will not reset the cooldown on Aftershock.

[Wayfinder3]

Astrologian has many problems because of it's ability to fit in the slot of both healers, mainly that it's raw utility in it's cards circumvent the fact that the other healers are more efficient at either healing or shielding. Since there are 3, having the 3 healers balanced around 1 being able to shield and the other being able to regen while one can do both makes sense. However problems will arise unless every healer gets the ability to regen or shield or you're going to see ast as that puzzle piece that fits into every comp, or you'll have every NEW healer nearly replicate AST as far as having a watered down version of whm and sch's core kit. Thing is, they already did this with AST.

this would be like making a physical version of red mage and calling it gunblade job. I would rather shields be nerfed to allow for stacking or adjusted in some way, then to see ast continue to fit in the puzzle piece place that it does right now.

Not to be rude but as both me and Caeseisa noted, your proposal is literally a hybrid of a Hybrid and i don't think making a hybrid of 3 jobs 1 of which is already a hybrid is smart job design. if your healer focused more on the concept of AoE, shields in the same vain of sacred soil or regens like asylum, you'd have a unique job idea. AoE domes based effects that can do either shields or regens but not both allow for more diversity while not running into the issue you mentioned with over lapping shields. Sacred soil and Collective unconsious can stack together. you could also have an AoE that causes buffs in the same vain of ley lines but for the raid.