Mehtad

The Mehtad is a 4x4 speedsolving method proposed by Yash Mehta. It is one of the first feasible methods to solve a 4x4 using the ZZ method, because the edges are oriented and the line (in fact 3 of 4 cross pieces) are already solved. It builds upon the ideas of the Yau Method and the first three steps of the solve are in fact identical to Yau.
Some commonly used techniques compatible with the Mehtad method include:
 Solving 3 half centers out of the 4 last centers before fully solving them in order to increase fingertrickability for the remainder of the last 4 centers step. With the half centers technique, the solver can finish off the centers without destroying the partial cross by using only Rw and U moves rather than 3Rw, Rw, 2L, and U moves, essentially making the remainder of this step 2gen.
 Pairing edges using EO 62 edge pairing, also called the ‘’’Pairing Mehtad’’’. Basically, right after the last 4 centers are solved, solve one more edge piece using no specific technique and put it in the bottom, then pair up 3 edge pairs at once by slicing one way, followed by 3 edge pairs while restoring the slice. In Mehtad, however, there will be some extra moves while inserting the second set of 3 edges. The last 2 edge pairs are solved using an algorithm, while orienting the final few unoriented edges.
Overview
 Solve 2 opposite centers .
 Solve 3 of the cross dedges, called the sesquiline.
 Solve the remaining 4 centers, maintaining the partial cross or the sesquiline by keeping it on the left side and using only Rw, 3Rw, 2L, and U moves.
 Pair up the one dedge without messing up the sesquiline and insert it in the correct orientation on the bottom of the cube
 Solve 6 edges at once using an advanced version of 62 pairing, or any other method that orients at least 3 of the 6 edges thus formed.
 Solve the final two edges with one algorithm, and orient the few remaining edges.
 Solve F2L + LL (3x3) and PLL Parity.
The Steps
 First 2 Centres: Two opposite centres are made on the 4x4. These centres must be the ones preferred to be the top and the bottom colours during the 3x3 stage.
 SesquiLine: Three of the bottom colour edges are to be formed using the freedom of 4 unmade centres. The pair of opposite edges will form the line. It is not mandatory that the third edge is a bottom colour edge, but doing the bottom colour edge has its own benefits in the 3x3 stage, and also doesn’t hamper recognition.
 Last 4 Centres: The final 4 centers are solved, maintaining the partial cross or the sesquiline by keeping it on the left side and using only Rw, 3Rw, 2L, and U moves. Techniques like half centres may be used to aid this step. All the steps thus far are identical to Yau.
 Edge 4: One random edge is solved with no specific method, and placed in the bottom in the orientation (i.e. is the edge is solved in FR and the ‘empty’ piece on the bottom is in DF, the edge may be inserted using F’ if it is unoriented, and D R’ if it is oriented).
 Pairing Mehtad: Now 6 edges are paired at once using the ‘Pairing Mehtad’. With the desirable orientation (the orientation you solve ZZ in), the pair of the FLu dedge is put in FRd, and this is followed by a Uw3. Again, the pair of the FLu dedge is put in FRd, and this is followed by a Uw3. For the third time, the pair of the FLu dedge is put in FRd. This is followed by a Uw’ slice pairing 3 edges. Note that you are a y2 away from your desired orientation, and the edge orientation recognition should be just as easy since we have the same rules. For the restoration of the slice, the three new edges will be replaced by the relevant edges to be formed, and the edges removed will be oriented correctly. For an unpaired dedge in UF to be inserted in FR, depending on the orientation of the FR edge and the way the UF edge has to be inserted, one of (R U R’), (U’ F’ U F), (F R’ F’ R)* or (U’ R’ F R F’)* will be used. [The starred algorithms also affect the UR or UL edges’ orientation respectively, hence ensure there is no paired edge in this position.] This should be done while inserting the FR edge, the FL edge (using mirrored algs), followed by a (Uw3)x2, and the nowFR slot. When followed by a Uw, this restores the edges, ensures 3 oriented paired edges on the top layer, and 3 paired edges on the E slice.
 EOL2E: With 4 unoriented paired edges in the bottom and 3 in the top; we have 2 unpaired edges in FL and on top, and 3 paired edges with unknown orientation in the E slice. The 3 orientations are check while or right after restoring the slice, and it is determined whether the number is odd or even. The top layer unpaired edge is brought in UR and bottom layer ‘Empty’ edge is put in DL, and with L’ U, the two unpaired edges are brought to the top. Now, depending on the relative position of the two unpaired edges (opposite dedge exchange or adjacent dedge exchange) and the parity of number of unoriented edges (odd or even, 0/2 or 1/3), the final edges are solved using one of 4 algorithms, that both pairs the remaining dedges and misorients exactly one of the two newly formed paired edges in case of an odd parity, to have an even number of misoriented edges. Now, there can only be 0, 2 or 4 misoriented edges, and all of the must be in DL, FR, BR or UF. These edges are oriented in a few moves. An advanced solver can learn ~20 algorithms to simultaneously pair the dedges and orient all misoriented edges at once in one algorithm. In the case that all edges are paired before reaching this step, if we do not have a parity, we will still have less than or equal to 4 misoriented edges. However, in case of a parity, where we may have 1/3/5 unpaired edges, we will need an OLL parity algorithm to deal with this rare case. The OLL parity algorithm will be much shorter since F2L doesn’t have to be preserved. An advanced solver can learn ~8 algorithms to orient all edges at once. Due to small number of edges to orient, relatively low number of algorithms and enough time during the previous step to lookahead to this step, this step should have low to none recognition time, and good execution speed due to the algorithmic approach.
 ZZ3x3: With all edges oriented and a sesquiline already formed, the ZZ approach may be followed to make up for any lag caused in the edge pairing compared to the Yau method. After ZZF2L which is faster than the traditional F2L, one will obtain an LL with all edges oriented and no OLL parity. One other particular strength this offers is with the COLL/EPLL alg set to solve the last layer, the PLL parity can be incorporated in the EPLL step itself, only increasing the number of algorithms from 4 to 9, and in the new ones, the move set will still be <R, U, r, u> which is quite comfortable to do. This gives a 2 look LL, instead of the occasional 4look set in Yau.
Pros
 EO and sesquiline is already done when you start the 3x3 step.
 Always get an OLL skip.
 Certain LL alg sets like COLL/EPLL work especially well with this method.
Cons
 It can be hard to find the first 3 cross edgesEO edges.
 Removing paired dedges in edge pairing involves preframed moves.
 Centers are a little bit harder.
Walkthrough solves
Coming soon.