I can see some segments intersect in your file (if that happens, the "dance" is expected with hair dynamics).
I see no tip / hairkey inside the cube though.
But honestly I am having trouble reproducing this.

The Distance setting will prevent the base of the hair from penetrating the cube, but not the tips

For me, even the tips subbornly refuse to penetrate the cube, so not quite sure how you achieved this?
Will also check code, but assume the Deflect Emitter option makes sure hair keys are deflected, not sure if it is ensured that the whole path is outside

comb the hair so that some hair tips penetrate the cube.

Neat trick. I can't do it (yet).
Agree with @Philipp Oeser (lichtwerk) - once a hair strand intersects host geometry, or hair strands intersect with each other, the hair will 'dance' under dynamics. Collision avoidance is in play. Pulling the hair tip though host geometry - that's the bug! - the circumstances under which that neat trick gets pulled. I can't do it yet with @Graham Cripps (craigievar) file or other files. Hmmm.

Hi Gary and Philip

To duplicate the bug, the trick is to comb just the hair tips of the hair on top of the cube out and then back towards the cube so they are bent back on themselves in an upside-down U shape and the hair tips penetrate the top polygon of the cube. On the sides the hair will usually fall down when the simulation starts, however it can get stuck and start dancing too. I don't think this penetration should happen, if Deflect Emitter is active (as it is by default) no part of the hair should penetrate the cube at all when combing.

This hair issue has caused me problems many times, especially when animating hairy animals where the hair should look wild. It can be overcome by combing the offending hairs back out, if you can find them! But his will also effect neighbouring hairs and can ruin the whole hair-style.

Thanks for your time

Graham

It can be overcome by combing the offending hairs back out, if you can find them! But his will also effect neighbouring hairs and can ruin the whole hair-style.

Tip: if you can find the offending hair, just select that one entirely (select a point, then Ctrl++ a couple of times), combing then affects only the selected hair without ruining the whole hair style

Hi @Graham Cripps (craigievar)
Very clear instructions. Thank you for that. I think I followed them properly; look at the video I've attached. I cannot comb the hair tip through the single-face plane. Nor grabbing it via G and constraining it to follow the normal direction. Immaterial if the plane has been set up as a soft-body collision surface. The only way I could emulate your description of the bug was by deselecting Deflect Emitter. Turning that on again caused the hair tip to snap back to the positive normal side of the face.
Not sure what is going on at your end. It seems, for you, that Deflect Emitter is a no-op. Have you tried this on another machine?

Hi Garry

I really appreciate your efforts in looking into this.

First of all YES, I can duplicate this on another machine.

Thanks for the video - very informative, I think, for me, this identifies the problem - thank you.

It seems it is not so much the tips - or rather the control points of the tips, but the section of the strand between the control points. I have attached some screen shots including views inside the cube, where you can see how the stands have penetrated the corners. There do not appear to be any control points inside the cube however. Then a final test I set up a single hair and combed it so part of the stand penetrated the corner of the cube, I cannot get any control points inside, but it can be seen a section of strand has cut the surface of the cube. This is enough, turn on Hair Dynamics, run the animation and the hair will dance!

The circumstances described here closely parallel T67958. In particular, the discussion in that report from Jan 27, 2020 onward, initiated by @Sybren A. Stüvel (sybren) after the new hair collision commit by @Luca Rood (LucaRood) ( rBd42a7bbd6ea57c69293d3bf978aae2c0e4241b57 ). Note remarks by @Germano Cavalcante (mano-wii) and @Sebastian Parborg (zeddb) regarding the Single Sided setting. Think that this report can be regarded as a duplicate of that.