Ability Score Array: For scores, you can determine them however you want for your table, but here I will make use of the standard array- 15, 14, 13, 12, 10, 8

Race:Githzerai from Mordenkainen's Tome of Foes. Although WoTC seems to be moving to make a floating +2/+1 the standard, I decided to stick with the standard racial modifiers for my theory crafting so that this build can be consistent across all tables. The Githzerai gets a +1 to Intelligence and a +2 to Wisdom. Intelligence will be the primary stat for this build and Wisdom will be important to exploration. This race also has access to the Mage Hand cantrip and the Shield spell as part of its innate casting. Mage Hand will help in interacting with suspicious objects from far away and Shield will boost your defense at critical moments. Advantage against being charmed or frightened isnt critical to this build, but nice icing on top of the cake.

Background: The Tomb of Annihilation adventure introduced the Archeologist background, so it would seem silly not to use it. That being said, if you want an option from the PHB, I recommend the Sage, as it gives alot of the same things we want. From Archeologist we get proficiency with Cartographer's or Navigator's tools, proficiency in History and Survival, and a language of our choice. On top of that, the Historical Knowledge feature will help you discern who constructed the ruins you are exploring.

Ability Score Distribution

Strength: 10

Dexterity: 13

Constitution: 14

Intelligence: 15 (+1)

Wisdom: 12 (+2)

Charisma: 8 

Here, Dexterity is the only score which starts out odd but it will get bumped later on in the build when we reach certain levels. Charisma will be our dump stat, as almost nothing in this build relies on it.

In tier 1, we are going to focus on getting a strong foundation in our primary class, Artificer, which will give us many tools to use for exploring dungeons.

Level 1: Artificer 1

To start this build off, we are going to make Artificer our main class. Its tool proficiency, utility magic, and magical infusions offer us a huge utility belt with which to dissect a dungeon down to the finest detail. Level 1 in artificer gives us proficiency in simple weapons, light & medium armor + shields, and several tools - most notably Thieves' Tools which are usually required for picking locks on doors and chests. We also get proficiency in 2 skills. Choose Investigation and Perception as these will be critical to spotting both secret doors and traps.

The most noteable feature we get at 1st level is Spellcasting, where Intelligence is our casting modifier. Artificers have access to Ritual Casting which will be helpful when trying to preserve spell slots. Pick whatever spells you wish, but to be prepared for what a dungeon holds, I recommend taking any of the following options: Absorb Elements, Dispel Magic, Feather Fall, and Identify. 

Level 2: Artificer 2

Here we learn how to Infuse Items. We can learn up to 4 Infusions and can apply 2 at a time. There are many magic items which can be replicated which are great for exploration, but here are my recommendations:

• Enhanced Defense - It is going to take us a while to boost our Dexterity score in this build, so this will help to make up for our +1 modifier. 
• Replicate Item: Goggles of Night - One of the few racial downsides to the Githzerai is no Darkvision. This will help you keep your hands free  while exploring dark places.  
• Homunculus Servant: If you can get the gem for this one, you get a "canary in the coal mine" for sending into unknown territories
• Replicate Item: Mystery Key - This last one is just for fun. Because you can replicate common magic items from any source, the Mystery Key from Xanathar's Guide to Everything gives you a 5% chance to open any lock without relying on your Theives' Tools. The infusion is only lost after it works, and you can get it back after a long rest.

I recommend having the Enhanced Defense and Goggles of Night applied the majority of the time, with the other two saved for if/when you think you need them. For the Mystery Key, I wanted to include it as a fun option, but replicating things like a Cap of Water Breathing or Rope of Climbing may find more use.

Level 3: Artificer 3

The main thing we get from this level is our Artificer Specialty. I am choosing the Armorer subclass for this build for a few reasons: We can use our casting stat for attacking using the armor's weapon, which makes the build less MAD / We will eventually be able to utilize extra infusions for this build

Armor Model: Infiltrator

Choosing this model will allow us to stay at mid or long range using the lightning launcher weapon. Because this weapon is mounted on the armor, it also keeps our hands free for holding a shield and spellcasting. It will also boost our movement speed and help us ignore disadvantage to stealth if/when we can pick up something like half-plate.

Level 4: Artificer 4

Ability Score Improvement: Here we will take our first feat. Staying within the theme and goals of this build, I am choosing the Dungeon Delver feat. On top of our proficiency in the skills, we now get advantage on any Investigation or Perception check made to spot secret doors. Our exploration survival gets a big boost as you now have advantage on saving throws against traps as well as resistance to damage dealt by traps, meaning you are either taking 1/2 or 1/4 damage from those pesky spike pits or poison darts. Although less likely to be impactful unless you are on a time limit, you can also now search for traps without reducing your speed.

In tier 2, we are going to round out some of the more important things we want to get from Artificer for this build (including 6th level infusions) and then move to multiclassing into Rogue which will help to further enhance the skills we have as well as our reactionary defense for combat.

Level 5: Artificer 5

From our subclass, we get Extra Attack, allowing us to use our lightning launcher twice ever turn.

We also get access to 2nd level spell slots from our Spellcasting. Here I recommend picking up Blur and Spider Climb. The former will again boost our ability to stay untouched in combat and the latter will give us a way to avoid treacherous pits and similar areas. Additionally, if you want to replace the Goggles of Night with another infusion, picking up Darkvision is recommended. 

Level 6: Artificer 6

This is the last level for this tier that we are going to take in Artificer, but it was important to reach this point as level 6 is going to give us a double improvement to our abilities to use our Theives' Tools.

Firstly, we get Tool Expertise, which will let you double your proficiency bonus for any ability check made using your tools (including the Dexterity check made with Theives' Tools to pick locks or disarm traps).

Secondly, we get to learn two more infusions and apply one more at a time. Here we will pick up Replicate Magic Item: Gloves of Thievery, as they give a +5 bonus to Dexterity checks made to pick locks. Additionally, we will pick up Enhanced Weapon to keep on the back burner for use with out lightning launcher.

Level 7: Rogue 1

From multiclassing ,we can pick up one skill from the Rogue list. Pick either Sleight of Hand or Stealth.

We also get Expertise, which we are going to use to further boost our Investigation and Perception scores. At this point, there should be very little that will escape our eyes, especially when it comes to finding secret doors thanks to our Dungeon Delver feat. This will also boost your passive Perception score to help avoid being caught off guard.

We also get Theives' Cant as a language and the rogue's Sneak Attack feature. Because your lightning launcher counts as a Simple Ranged weapon, you will be able to use the sneak attack feature with it.

Level 8: Rogue 2

We get Cunning Action, improving our battlefield mobility and giving a consistent use for our bonus action in combat. With the boosted speed from the infiltrator armor, "run-and-gun" is going to be your style

Level 9: Rogue 3

Here we choose our Roguish Archetype. I am choosing the Arcane Trickster. As an Int-base caster, we will be able to acquire more spell slots while multiclassing. Using the wizard spell list, although we are mostly restricted to enchantment/illusion spells, we can still pick up a few from any school of magic. I recommend making the Shield spell one of them (although you can already cast it 1/long rest as a Githzerai, having it known will allow you to use it more often). Later on, Knock would be another good choice in case there simply isnt a lock to pick. One redundancy here is we get Mage Hand, which we already have from our racial features as well, but we can now cast it using Intelligence as our spellcasting ability.

More importantly, we now get Mage Hand Legerdemain, which expands on what we can interact with using our Mage Hand. This further helps to put 30 feet between us and imminent danger.

Level 10: Rogue 4

Ability Score Improvement: One thing that has been missing from helping us survive deadly traps has been proficiency is Dexterity saving throws. Its a little late in the game, but here we will grab the Resilient feat to both bump our Dexterity up to 14 (which is as high as we will need it) and give us that saving throw proficiency.

In tier 3, we will continue to focus on levels in Rogue to try and boost our survival - both in combat and out of combat- by picking up more "dodgy" features like Uncanny Dodge and Evasion. We are going to push Rogue all the way to level 10, as there is not much above 10th level we want from Artificer

Level 11: Rogue 5

Here we get Uncanny Dodge, which will boost our defense in combat and possibly against traps which rely on attack rolls rather than saves (this will depend on your DM as to whether a trap counts as an "attacker" and whether you can see it based on your Passive Perception). But hey, we will take anything we can get

Level 12: Rogue 6

Here we get more skills we can apply Expertise to. We do not need to worry about our Theives' Tools, so we will bump our Survival and the skill we picked up from Rogue (Sleight of Hand or Stealth).

Level 13: Rogue 7

We now have access to Evasion. Beyond helping in all combat encounters, for any traps that allow you to only take half damage you will now either take no damage on a success or 1/4 damage on a failure (due to Evasion + Dungeon Delver).

Level 14: Rogue 8

Ability Score Improvement:Here we are going to take the Telekinetic feat. This gives you a bonus action shove and a +1 to our Int, but most importantly doubles the range of our Mage Hand cantrip, allowing you to put 60 feet between yourself and suspicious things.

Level 15: Artificer 7

We get access to Flash of Genius, which will let you add your Int modifier to an ability check or saving throw that doesn't go the way you want it. Paired with our spellcasting and weapon, we definitely will want to put more weight into improving our Int score.

Level 16: Artificer 8

Almost back to back we get another ASI

Ability Score Improvement: Here we will take the Observant feat. This will finally bring our Int score up to 18. Additionally we now have a +5 bonus to our passive perception.

Note: In the final character sheet, I forgot to add this in, so your final score at level 20 should be a Passive Perception of 29.

In tier 4, we are going to push both Artificer and Rogue to level 10, starting with Artificer. I chose level 10 as the cap for both as Artificer 10 improves our infusions and Rogue 10 lets us pick up an extra ASI.

Level 17: Artificer 9

We now get the Armor Modifications feature from the Armorer, which allows us to apply 2 extra infusions as long as 2 of them go on the armor. In this case, you should be able to apply your Goggles of Night to the Helment, the Enhanced Defense to the armor, and the Enhanced Weapon to your lightning launcher while still being able to apply to other infusions outside of the armor (like the Homunculus Servant and Mystery Key)

We now also able to prepare 3rd level spells through Artificer (we have had 3rd level slots through the Multiclass Spellcaster table for a while now, but could only use them for upcasting). For dungeon exploration and the art-of-not-getting-hit, I recommend picking up Blink, Fly, and Water Breathing when possible.

Level 18: Artificer 10

We get Magic Item Adept, allowing us to attune to up to 4 items at a time. More importantly we now learn two new infusions and can apply one additional infusion (total of 6 applied). The infusions we are going to pick up are

• Winged Boots - This can be applied to our armor and gives us a pretty consistent fly speed.
• Necklace of Adaptation - Great for surviving a lich's Cloudkill or breathing underwater if you didnt want to pick up the spell.

Level 19: Rogue 9

Magical Ambush from Arcane Trickster comes into play. Its impact wont be incredibly strong this late into the game, but is a welcome addition

Level 20: Rogue 10

For our capstone, we get a final ASI

Ability Score Improvement: To keep things simple, I am going to bump Int up to 20, as it carries over to our spellcasting, lightning launcher, and Flash of Genius. That being said, this could also be used to pick up any feat you want if you are comfortable with an 18.

So, I'll admit, this build is a bit of an odd one. There were alot of things that were put off much longer than most builds would, but I really wanted to double-down on the Dungeon Exploration and evasiveness , even if it is ultimately overkill. So lets look over some key aspects

How well do I interact with and survive dungeon encounters?

Lets start with rule number one of dealing with unknown stuff: touch with a 10ft pole. Coincidentally, we have a 10ft pole from our background supplies. We also have a Mage Hand which is invisible, has a range of 60 feet, and can do any of the following: manipulate an object, open an unlocked door/container, stow or retrieve an object (including into/out of containers on other creatures), pour out contents, pick locks or disarm traps.

For magical probing, we also have the Detect Magic spell. If thats still not enough, you can potentially send ahead a Homunculus servant to touch stuff for you. 

For spotting traps, we have a +14 bonus to Perception and a +17 bonus to Investigation thanks to Expertise and we have a passive Perception of 29. If secret doors are what you are looking for, thanks to Dungeon Delver you have advantage on your checks, so effectively a +19 or +22, respectively.

We can pick locks like no other. As mentioned before, we can now do it from 60ft away, but thanks to Tool Expertise, Gloves of Thievery, and potentially Flash of Genius, we are looking at 1d20+12+2(Dex)+5(gloves)+5(Flash of Genius), so the lowest you could roll is a 24 and the highest (assuming you dont use Flash of Genius) is a 37. If somehow that still fails, well you can always fall back on your Mystery Key for a 5% shot

If you somehow still spring a trap, you can use Evasion (if it has a Dex save for half damage), but in any case you will have advantage on the save and will have resistance to the damage dealt by the trap. If what is harming you doesnt technically qualify as a trap, then you still have reactions like Shield, Absorb Elements, or Feather Fall to help get you through it.

For general dungeon exploration Fly, Spider Climb, or your Winged Boots infusion will give you ways to avoid pitfalls (both literally and figuratively). Water Breathing means pools, wells, and underground springs will not impair your exploration. 

How well do I do in combat?

Defensively, with Enhanced Defense you have a 19 AC if you are wearing Half Plate which can be as high as 21 if you are using a shield. You also have access to a myriad of reactions and passive abilities like Shield, Absorb Elements, Uncanny Dodge, and Evasion. Spells like Blur and Blink will also help you not get hit. You also have a +5 ft of movement speed and a flying speed to stay out of the enemy's reach.

Offensively, you are kinda a 1-trick pony. You likely have a few cantrips and attack spells, but most of your spellcasting is focused on utility and defense. With multiclassing, your slots don't get higher than 4th level and you only know up to 3rd level spells, so offensive casting is more or less out.

What you have is your Lightning Launcher, which you can attack with twice per turn. Once per turn, you can apply the extra damage of the lightning launcher and possibly your sneak attack, so if played well you can have one attack per turn dealing 1d6+5(Int)+2(Enhanced Weapon)+1d6(launcher)+5d6(sneak attack) lightning damage (on average 32 damage for the attack).

Your bonus action can be consistently used to either Cunning Action, command your Homonculus Servant, or Telekinetic Shove a creature, so you have options.

But again, I want to stress this character was not built to be optimized for combat. You are an academic that just happens to be able to stay out of danger. That being said, if you wanted to enhance the combat presence, you could potentially drop the +2 Int ASI and replace it with something like Sharpshooter (which will work with you Lightning Launcher) to bump your damage some.

How will I do in social encounters?

This is the main weakness of this build. Charisma starts as your dump stat and never gets built on, so your people skills are so-so.

Thankfully, from the Arcane Trickster, you should be able to prepare a handful of enchantment and illusion spells to make others do what you want, but only if you play into that aspect.

Staff, artifact (requires attunement by a spellcaster)

The Archdruid Grenhildr created this staff using the stone from the elemental plane of earth to house the pieces of a scale of Gormadraug, the Great Prismatic Wyrm. This staff allowed her to harness the great primordial power stored within, but harnessing it comes with a cost. 

This staff allows the user to harness the power of cold fire, a blue flame which burns through moisture as normal fire burns through wood. Water, ice, and living flesh act as kindling for this dangerous primordial flame. 

Random Properties: The staff has the following randomly determine properties

• 2 minor detrimental properties
• 1 major detrimental property
• 1 minor beneficial property
• 1 major beneficial property

Magical Spellcasting Focus

The Staff of Cold Fire grants a +3 bonus to your spell attack modifier and spell save DC. 

Fire Magic

While attuned to this staff, you can cast Burning Hands, Scorching Ray, and Fireball once each using the staff and regain the ability to do so following a long rest. You can also cast these spells using your spellcasting if you have spell slots of the appropriate level.

Summon Cold Fire

Targeting an area of snow, ice or liquid within 60ft, you can summon forth coldfire in a line up to 30 feet long. On initiative count 20 (losing ties), the blue flames spread into nearby spaces if those spaces also are covered in one of the materials listed above. Any creature which starts its turn in such a space or enters it for the first time on a turn takes 1d10 cold damage. A creature can use its action to extinguish a 5ft area of the cold fire. If any space would be subjected to fire damage, the cold fire in the affected spaces is extinguished. Throwing burning oil onto an area also extinguishes the cold fire. Throwing water or another non-burning liquid onto the fire immediately causes the affected area to spread again. 

Once you have used this feature, you cannot do so again until you finish a long rest. 

Primordial Inferno

Whenever you cast a spell of 1st level or higher which deals fire damage using this staff as a spellcasting focus, you can warp the flame into cold fire. When you do so, the spell deals cold damage instead and that damage ignores resistance to cold damage. 

Whenever a creature is damaged by the warped spell, it ignites in coldfire. A burning creature takes 1d10 cold damage at the start of each of its turns until it or another creature uses their action to extinguish the flames. If any creature tries to use a liquid to put out the cold flames, the target immediately takes the damage again and continues to burn. If the burning creature takes fire damage, the creature rolls 1d10 and subtracts the value rolled from the damage dealt, and the cold fire is then extinguished.

A creature reduced to 0 hit points by the damage of a warped spell or burning effect is immediately frozen solid and petrified. The creature remains petrified until it is treated by a Greater Restoration spell or similar magic. If the creature is polymorphed or otherwise shape changed, it is petrified without reverting to its original form. 

You can warp the magic of spells whose total level equals 5, at which point you must finish a long rest before you can do so again. 

Frigid Backfire

When using the Primordial Inferno power of the staff to warp a spell you cast, if you score a critical failure on a spell attack OR if a target succeeds on a saving throw against the spell effect by 5 or more, you immediately take 1d10 cold damage and begin to burn, as outlined in that feature. 

The Invisible Sky City of Aerok Nor

An ancient city of Stargazers, Diviners, and Experimentation. Said to have been pulled into the sky by the gods themselves so that the finest minds could study the stars and work on developing new magics and technologies in a place that only the gods could see.

Its location is unknown, but it was rumoured to be somewhere high above the Great Southern Plains. The Aerokians were careful and warded their city against most teleportation and scrying magics. The only ways to get there were via a single, heavily guarded teleportation circle, or by sailing through the golden archway in the outer ring.

It had bountiful gardens of plenty, luxurious pavilions and walkways, and incredible laboratories and research centres where alchemists, metallurgists, smiths, and theologians would work. The Aerokians believed that their proximity to the gods allowed them the means to be blessed in their endeavours.

Whilst many advancements were made in a variety of fields, the Aerokians very protective of their developments and few of these were shared with the cities on the ground.

What caused the decline of the city is unknown. Could it have been an exotic disease? An experiment gone wrong? A jealous rival city mounting a raid to steal the devices and technological advances made? Or maybe the gods themselves became jealous or fearful of the advances being made in the city and struck down the inhabitants before their power rivaled that of the gods themselves.

Many adventurers and scholars have searched for the city over the years hoping to unearth the long forgotten treasures and clues, however none of those who return have been able to find it, and the fate of those who never made it back is unknown. Did they give up after years of travelling? Did they merely meet an unexpected accident along the way? Did they succeed and then travel to far off lands to claim the inventions as their own? Or could they have found the city but suffered the same fate as the original Aerokians?