Quote:
Matthew Gano wrote:
I've been thinking about this some more in terms of the . ...
includes the method of entry/connection;
includes the method of remaining connected/musubi and blending; and
includes the method of gaining complete control (an explosive or exponential quality), usually by way of pin or projection. ...
think blending (circle) is part of the formula. ... there must be that (square) in which the harmonized/blended force of nage is explosive or somehow exponentially increased in nature; which happens through the musubi/connection.

Quote:
Kevin Leavitt wrote:
...what are the mechanics of the neutralization. That is, what are the standard conditions that must be in place for neutralization to be in effect?
Certainly irimi is an option, and a good one if you cannot handle the bull!
But are you really blending as you enter during or after the irimi, or is there something else going on?

I have thought about this a great deal  often at greater length out loud than most have patience for. But doing so has brought me to a summation in these terms:
Triangle relates to Irimi and Kuzushi: Balance is deflected to its external limits of stability by direct entry  visualised as a wedge, or plow  kiriotoshi or suriotoshi  fundamentally tangential action. Even in yokomenuchi uchimawari entries, contact of one hand with the advancing strike forms a triangle with the countering hand striking uke, like the wedge or plow  carrying his balance to its uttermost limit.
Circle relates to Tenkan and Tsukuri  Momentum is further directed and converted tangentially or centripetally (tenkan) to alter the plane of rotation or potential rotation (moment) (both fundamentally rightangle concepts i.e  Juji) in three dimensions  that produces three dimensional spiral paths.
Square relates to Juji and Kake  The momentum may be constrained radially or tangentially (respectively, the uprights and crossmembers of the square) and in that regard constrained either inward or outward in affect (the opposed parallels of the square) the to the point of an inevitable release either of projection nagewaza or reduction of the connection (osaewaza youch).
Some more practical observations:
One point of said triangle is directly aimed at uke's center, one at nage's center and one away from both. A triangle is rigid and points in one of these three ways depending on the sense of emphasis on the other two. Uke can cover one or two but never all three, because he only has two points of support.
Triangles literally point the way if you see them. From that example, consider the triangle formed by the connections in the yokomenuchi uchi mawari entry :: uke and nage's joined hands  uke's arm connected at his body  and nage's hand connecting to uke's body in atemi.
If uke's striking energy in the hand is relatively strong  the counteratemi point of the triangle at uke's center shows the way to iriminage or whatever else you find there.
If his connection is relatively strengthened at that point to deflect nage's counterstrike, then the point of the triangle where uke's attacking hand joins nage's blending hand shows the way. It points him further out of his center into sumiotoshi or whatever you like.
Or, if he strengthens both of his points simultaneously (trying to stop and reassess, essentially), the point of the triangle at nage's center shows the way and nage moves his own center out and across  the classic set up for shihonage, kokyunage, or what have you.
Similar relationships (sometimes squashed in a certain dimension) can be found that tie other engagements into the same basic entry principle.
Even when those 3d spirals are squashed into a single two dimensional plane curve there is still strong moment (rotation potential) that wants to break the plane and so there is hidden reserve of physical response along the suppressed plane of motion that is quite literally not perceptible until uke tries to go there, only to find a wall already poised and falling on him.
While the crossing moments and the boundary of gravity and ground are stable ( antoerh set of images for the square), the constraint of the square is only critically stable. If need be, the square figure can still collapse catastrophically into release in shear sideways (image of the square racking sideways and the side toppling together). In reality, it happens along the third plane of spiral orientation, (the image of a stick figure cube racking and collapsing in torsional shear, or the Daitoryu image of asagao  the opening and closing of morning glory blossom) With that additional rotation potential, more reduction/projection/destruction remains to be delivered, if necessary.
In osaewaza, the momentum making up the 3d spiral motion is critically constrained through the connection in a progressively damped fashion (the opposite of releasing it) transforming the momentum of body rotation into moment ( potential for rotation)  simultaneous moments in two planes (thus the square image) bounded by the ground and gravity, making movement structurally impossible.