So far, we've got DeeDubb's notation for the basic flick-tricks.
After a little thinking, I was able to come up with the following notation for grips.
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Grip notation proposal:
Fingers will be labelled the same (upper-case = right, lower = left).
All grip notations are written in curly brackets {...} and only when necessary to define a non-standard or non-intuitive grip.
For basic grips:
TF - Right thumb on front, rest on back.
TU - Right thumb on up, rest on down.
TD - Right thumb on down, rest on up.
TB - Right thumb on back, rest on front (How the wrist is twisted depends on the direction of the following move)
TR, TL - You get the idea...
For basic groups with left hand:
tF, tU, tD, tB, tR, tL (same as right hand)
Piece specific grips are separated by a dash. For consistency, corners use DeeDubb's number method for defining corners. The finger will grip on the side of the corner defined (e.g.: T-R1 means that the right thumb is either on the top or front face of the 1 corner of the R side, depending on the rest of the grip and on moves).
Edges are defined by the face letters (ex: M-BR, t-FL, t-FD, etc...).
Center pieces are defined simply by the face letter (T-F is different than TF. TF is a basic grip, meaning it doesn't matter which piece is held. But T-F means the right thumb must be on the center piece).
The grip defined on specific pieces is maintained until a regrip is defined, or a move/trick requires that it be broken. (ex: {M-UR} R U(M2). This means that the defined grip is broken to perform U.)
Where grip is not defined, a normal grip is assumed (As the cuber feels works for the algorithm).
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Additionally, double moves may be defined with prime to define direction (ex: F2')
Demonstrations of complex finger-tricks:
Kirjava's finger-trick: {t-F, m-B, T-R1, M-R2} (R2' D2 L2' U2)*3
XTownCuber's finger-trick: {M-R4, T-R3} R2 U S'(I2) U2' S(I1) U R2
A random finger-trick: {M-UL, T-UR} S2 D2 S2' {TD} R U R' U' D2(TD2, rD4)
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Now, this is to complete the notation. Beyond this, there will be no additions to the notation in order to keep it simple enough to learn and read. If there is something that this notation absolutely cannot explain, then word descriptions can be added where necessary, be it within the brackets of the grips or tricks, or outside the algorithm. (ex: M'(Use fingernail of right thumb to push back on the inside edge of UB)). And even though there will continue to be exceptions, the notation in it's current state covers most finger-tricks that are used for speedcubing in general, because, for speed cubing, especially at high speeds, overly complex finger-tricks that require lots of notation will usually be unnecessary and/or unfeasible for speedcubing purposes. And so the descriptions of the finger-tricks will usually be simple.
This is my proposal for a "completed" finger-trick notation. What do you think?