Made a video showing the full chain that's currently available for the Sleeper Simulant Exotic, along with text guide along the way. I know there's a few guides out as is, but for anyone interested in the gameplay alongside, here it is.
https://www.youtube.com/watch?v=l-tl-z7CO3A
It shows all the secret codes you need and progression through the quest. Cut out a lot of the unessential stuff (other than The Archive mission), but the rest is just the new missions available and each step that's required.
To start this quest chain, you must have found the four DVALIN relics that you turn into the Gunsmith for rep. Once you have handed all these in, the first mission will be available.
[b]Pt.1 - Mission on Earth "The First Firewall"[/b] - [i]00:00 in video[/i]
A mission is unlocked on Earth called "The First Firewall". This takes you into Seraphim Vault where you need to fight off a bunch of enemies and kill an ultra named "Kandorak". Once you defeat him, it will drop the item "Curious Transceiver".
[b]Pt.2 - Input Passcode - 4 Passcodes to Input into the Curious Transceiver[/b] - [i]07:11 in video[/i]
The second part involves you entering 4 different passcodes into the Curious Transceiver. It is done by opening the inventory and interacting with the Curious Transceiver item. The passcodes are as follows:
1. Up, Down, Up, Up, Down, Down, Down, Up, Down
2. Up, Down, Up, Up, Down, Down, Up, Up
3. Up, Down, Down, Down, Up, Down, Down, Down, Up, Up
4. Up, Down, Up, Down, Up, Down, Up, Up
[b]Pt.3 - Mission on Earth "Shadow Call"[/b] - [i]08:35 in video[/i]
This mission can only be done solo. It will start you at the bridge up in the Devil's Spire (the same tower in the Cayde's Stash mission). You have a timer of 3.53 to progress through the mission and "Find the Core Component". The Core Component is at the top of the tower where you fight the Echo of Oryx in the original Cayde's Stash mission. You open a chest that spawns 3 yellow-bar wizards, and once you defeat them you complete the quest and find the item "Ikelos Fusion Core".
[b]Pt.4 - Repair Ikelos Fusion Core[/b] - [i]13:30 in video[/i]
This item will also be inside of your inventory and has an interaction to "Repair" it. It has 5 nodes, each with a different task you need to complete to fill them in and repair the fusion core.
1. Dismantle a Legendary or higher Heavy Weapon
2. Complete public event "Defend Warsat" on Earth
3. Complete public event "Defend Warsat" on the Moon
4. Complete public event "Defend Warsat" on Mars
5. Complete "The Archives" mission on Venus on any difficulty
[b]Pt.5 - Reassembled Ikelos Fusion Core[/b] - [i]23:37 in video[/i]
This step is just to go to The Tower and give the core to Banshee-44 (the Gunsmith). Once you give to him it seems to currently stop the quest chain, the rest might be time-gated. So for now it's just waiting, but this is all there is to be currently done.
Update:
[b]Pt.6 - The Sleeper Stirs - Video: https://www.youtube.com/watch?v=wIg_08igCSU[/b]
After you hand in the Reassembled Ikelos Fusion Core and complete that step, the next step became available the following day. This begins the quest "The Sleeper Stirs", where you need to complete a 280 Light Level version of the Fallen S.A.B.E.R Strike on Earth. Once you complete this, you are rewarded with the Sleeper Simulant Weapon Frame, which you then take to Banshee-44 and you are given the Sleeper Simulant Exotic.