Triforce
From Speedsolving.com Wiki

Triforce method is a 4x4 speedsolving and novelty method proposed by trangium for the August 2021 Method Development Competition. Its motivation is to avoid OLL parity while still being viable for speedsolving.
Overview
 U/D centers + 1x2x4 block (~24 moves): Solve a 1x2x4 block in dL and the first 2 centers. There are several options on how to split up this step into multiple substeps. One may choose to solve the block first, 2 centers first, centerblockcenter, or even freestyle.
 Solve dM quads (~21 moves): Expand the 1x2x4 block into a 3x2x4 block while preserving the centers. After this step, R, U, and u moves will preserve the block.
 Pair 5 U/D edges + Half Centers (~32 moves): Here, "half centers" means reducing the centers such that they can be solved with R2 and u moves. The best general approach is to get to half centers while pairing up 12 U/D edges, then pairing the rest of the U/D edges by setting up to u moves. Although one can't pair up Eslice edges, the fact that the centers aren't fully solved makes edge pairing more efficient overall. At some point towards the end of this step, place an Eslice edge pair in DR using an R2. This is to set up for the next step, EOLE.
 EOLE (~7 moves, 24 algs): Use one of 24 algs to place all Eslice edges in the E slice while orienting all the U/D edges. Since one only has to recognize EO of five U/D edges, all of which are visible, recognition is extremely fast.
 L6W (~10 moves, 14 algs): Solve the six Eslice wings. It is recommended to first solve the dFR or dBR wings, then proceed with one of 14 algs. Recognition can be tricky, but since there are so few cases, it is definitely viable.
 L6C (~2224 moves, 42122 algs): Solve the 6 remaining corners without disturbing the EO or belt. The recommended approach is to first solve the 2 bottom corners (DCAL, intuitive or 80 algs), then solve the 4 top corners (CxLL, 42 algs). A y rotation should be done before starting the next step.
 5e5x (~19 moves): Use the m' U2 m trigger, along with U and u moves, to solve the remaining 5 edges and 5 centers simultaneously. PLL parity may happen here, but that can be fixed with (R2 u2)3 at the start of 5e5x. The key insight here is that m' U2 m cycles 3 edges and rotates the F center 180 degrees. This step can be completely intuitive but benefits from learning at least a few algs to deal with bad cases. See the full detailed method doc for how to solve 5e5x efficiently.
Pros
 No OLL parity, leading to an efficiency gain of at least 10 moves over Yau
 Edge pairing is less restricted
 Good ergonomics for the majority of the solve: mostly <R, r, 3r, U, u>
Cons
 The 1x2x4 step can be difficult
 A lot needs to be planned in inspection
 A few steps have awkward movesets
 Not that many algs will transfer from CFOP, so one will have to learn lots of new algs exclusively for Triforce
Neutral Points
 No 3x3x3 stage, so one's 3x3x3 abilities won't transfer to 4x4x4. This can be a pro or a con depending on one's 3x3x3 skill.
 Many algorithmic steps, which could be a pro or a con depending on the solver
 Many variants, which means that a solver can choose which variant they prefer, but also means that further developments could quickly render certain variants obsolete
Progression
Step  Beginner Triforce  Intermediate Triforce  Full Triforce 
EOLE  0 algs
Orient edges as they are paired 
12 algs
Force an Eslice edge in BR 
24 algs
Full EOLE 
L6W  2 algs
Solve both dFR and dBR first, leading to L4W 
8 algs
Always solve dBR first 
14 algs
Full L5W 
DCAL  0 algs
Intuitively using R2 U* R2 and CFOP inserts 
017 algs
Learn algs for bad intuitive cases 
80 algs
Full DCAL 
CxLL  9 algs
2look: Orient then permute corners 
920 algs
Learn some easy CxLLs 
42 algs
Full CxLL 
5e5x  1 alg
Parity alg only 
311 algs
Learn from top to bottom on the algsheet 
14 algs
Learn all the listed triggers 
Total  12 algs  3268 algs  174 algs 