Automatically granted based on Nuke choice at the end of Lonesome Road:

Sic Semper Tyrannis - You've set the tyrannical Legion ablaze with that most unholy of powers, nuclear fusion. While facing members of the Legion, you penetrate 8 DT, and deal 15% more damage with melee and flame-based weapons while your karma is Bad or Very Bad.

Igne Natura, Renovatur Integra - 200 years after the Great War, two lone nuclear missiles were launched. Not aimed at another country, but at their own land, targeting the last vestiges of civilization, a wicked punishment for the audacity to grow and thrive in this desolate wasteland. You deal +20% damage and +10% critical damage when attacking any members of the NCR or Legion while your karma is Bad or Very Bad.

Oderint Dum Metuant - You've set the toothless NCR ablaze with that most unholy of powers, nuclear fusion. While facing members of the NCR, you penetrate 8 DT, and deal 15% more damage with guns and flame-based weapons while your karma is Bad or Very Bad.

Non Ducor, Duco - Though neither the NCR or the Legion is a perfect solution for the Mojave, neither is worth damaging at the cost of repeating humanity's greatest sin. You've gain +1 Intelligence, Charisma, and Luck while your karma is Good or Very Good.
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Traits:

Ascetic - Through meditation, you've touched the fibers which connect all life, and you've sworn not to sever them; preservation of the beauty of life is the highest moral imperative. You've gained +2 Endurance, and +2 Strength while in combat, but your carry weight is reduced by 50, and you may only fight using non-lethal unarmed techniques.

Assassin's Step - Stealth and discretion come second nature to you, but with your suspicious demeanor, once you've been spotted, it's hard for you to slink back into the shadows undetected. You gain +10 Sneak and +30 AP while sneaking and undetected, but you suffer an inverse penalty to those stats while detected.

Lucky Accident - You've always been lucky, and that's led to being dangerously complacent. Your Luck is increased by 5, but every other SPECIAL stat is decreased by 1. 

Scientific Method - Your dedication to science is admirable, if bordering on obsessive. Standing in front of monitors and taking samples from irradiated puddles has started to take its toll, but it's all in the name of progress. You've gained +2 INT and +20 Science, but you've lost -2 PER and -10 Radiation Resistance, and you've become obsessed with using nothing but the most advanced of weapons.

Trader's Touch - Your understanding of the markets is second-to-none, and you intend to prove it to the entire Mojave. You've gained +20 Barter, +10 Speech, and +2 Charisma. However, your brahmin is long gone, and your caravan's bad luck with raiders has persisted; You suffer -30 AP and Carry Weight, as well as -2 Luck. While you hold more than 10k caps, you also gain +15% XP.
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Available to choose based on choices made during DLC questlines:

Faithful's Exodus - "Yea, though I walk through the valley of the shadow of death, I will fear no evil: for thou art with me; thy rod and thy staff they comfort me." - Psalm 23:4. (Your run speed is increased by 10%, and enemies are 10% less likely to critically hit you, so long as you have your Bible.)

Faithful's Wrath - "And I will execute great vengeance upon them with furious rebukes; and they shall know that I am the LORD, when I shall lay my vengeance upon them." - Ezekiel 25:17 (You deal 15% more damage with holy weapons, and equipment degrades 10% slower, so long as you have your Bible with you.)

Faithful's Fall - "And I looked, and behold a pale horse: and his name that sat on him was Death, and Hell followed with him. And power was given unto them over the fourth part of the earth, to kill with sword, and with hunger, and with death, and with the beasts of the earth."  - Revelation 6:8 (So long as you have your Bible, you are 5% more likely to critically hit, and do 10% more critical damage.)

Elijah's Montresor - Elijah is now trapped in the vault, with the treasure he coveted for so long. You, however, are free to begin again. You gain 20% extra experience, so long as you keep at least something to remind you of the Sierra Madre on you. In pace requiescat, Elijah.

Survivor's Guilt - You survived the hell that was the Sierra Madre, but after all of the deaths you've seen, you feel as though a piece of you has been left behind there forever. As long as you carry a reminder of that place, your AP regenerates 15% faster, and AP costs are reduced by 5%.

The Ties That Bind - Elijah's collars may have brought you together initially, but it's the bonds you made that will keep them in your heart. As long as you carry a reminder of the Sierra Madre, and have at least one teammate, you ignore 5 points of enemy DT, gain an additional 5 points yourself, and have a 5% increased critical hit chance.

Mobius Strip - After experiencing the delirium of the Think Tank first-"hand", it seemed only natural to side with Mobius, and you ended their deranged experiments once and for all. Now, for every 10 points of Science above 50, you regen 5% more AP, and your AP costs are reduced by 5% as well.

Klein Bottle - While the Think Tank may be unreliable and chaotic, they're at least well intentioned. Mobius was clearly the aggressor, so you've taken him out of the equation. Now, when using Energy Weapons, you attack 15% faster, and their strength requirements are lowered by 1.

Scientific Consensus - Against all odds, you've managed to balance the Big Mountain equation. The Big Empty isn't so empty with all these scientists floating around! Your Energy Weapons deal 10% more damage, have reduced spread, and you've gained +10 Science while hacking.

ED-E, My Friend - With a loyal eyebot by your side, you've survived the ravages of The Divide. You've even learned from it's example! You can carry an additional 30 lbs., your chance to set off mines is reduced, and your equipment decays at a 15% slower rate.

The Final Delivery - Ulysses was right about something: One person's decisions can irrevocably change history. While you wear your Courier Duster, you gain a 8% chance to knock opponents down in combat. You gain an additional 3% for carrying 3/6/9 Mini Nukes, up to a maximum of 17.

A Mended Divide - Ulysses once faced you down with malice from across a divide, but you've found common ground and a mutual understanding. While wearing your Courier Duster, you have 20% increased carry weight, and 15% better accuracy in VATS.