Re: Phalanx V-formation...exploit?
As horse vs heavy inf goes, at around cataphract level at the latest the cavalry could usually be used to simply push into and grind down an infantry formation by the virtue of superior mass and armour; the Byzantine "blunt wedge" tactic was apparently designed specifically for this approach.
'Course, they never had to deal with pikes and AFAIK usually walked or at most trotted into the attack - the point was to roll over the infantry, not shatter them with the shock of the charge.
Even far lighter horse could also be very lethal in a frontal charge against even heavy spearmen if they could gain enough of a psychological superiority that the infantry line dithered and therefore created an opening for the cavalry to plunge into - if horse could break into the ranks of infantry in this fashion they were usually able to push deeper (laying about them with their wepaons of course) with their mates piling into the breach after them, which tended to be a Very Bad Thing for the infantry concerned as AFAIK it usually led to psychological collapse right fast.
Pikemen, however, were frontally AFAIK pretty much a no-go for anything short of plate-clad Late Medieval gendarmes, where both he man and the horse were all but invulnerably armoured in solid steel. I understand French gendarmes were in fact able to penetrate and downright ride through Swiss pike squares in some battles - it just didn't have much effect, as the infantry didn't lose heart and simply closed the ranks over the casualties.
Anything else just doesn't have the survivability to hit the wall of braced pikes and get through alive. The "international standard" for pike set to receive horse in the "pike and shot" period at least was the front ranks crouching, with pike-butts firmly planted in the ground and one foot on top of it for good measure, and the pike-tipe at the level of the horses' chest. The successive ranks held theirs level at different heights, IIRC mainly shoulder- and waist-height. Unless distrupted by missile fire or failure of morale, this "hedge" of pikes was practically inviolable to any cavalry short of the very heaviest plate-clad type.
As working simple solutions tend to be ones pretty much everyone who uses the same techniques and tools develops through empirical experience and basic hit-and-miss experimentation, I would be very surprised if the same basic "pike-hedge" system for seeing off cavalry did not develop among Hellenistic pikemen quite early on - and period cataphracts and their horses frankly didn't have enough armour to survive a head-on clash with set pikes, that much I'm certain of. Scale and lamellar, good armour as they generally are otherwise, just don't cut it for that purpose.
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