Okay, time to narrow down this discussion and transition from naming new cores to discussing what already exists. First of all, it's clear from the direction of the thread and IRC that as a community, we greatly prefer offensive cores to stall cores. Although frail offense vs. bulky offense really hasn't been settled, there's no question that we're going to move forward with an offensive core.
Offensive cores posted so far can be broken down into two categories: Attacker+Supporter and Attacker+Attacker. The former encompasses cores such as Klefki+Zygarde, Kyurem-Black+Gothitelle or Entei+Zapdos, while proposed dual attacker cores include Latias+Lucario (to an extent), Tornadus-Therian+Terrakion, and Kyurem-Black+Victini, among others. If we choose an Attacker+Supporter core, we'll likely end up building a Pokemon that both takes advantage of the supporter's utility (be it hazards, trapping, etc.) and defeats what the attacker isn't able to. If we choose a dual attacker core, then our Pokemon will likely either be a pivot that takes the hits from the Pokemon the two attackers cannot take or a third attacker that defeats the same Pokemon.
It's really time to start discussing what's already been posted rather than continue to propose new cores. As such, please spend the end of this thread discussing cores based around the following Pokemon or pairs of Pokemon. Think of the following cores or Pokemon as a sort of "slate" for the end of the discussion, but remember that this thread will conclude by executive decision rather than by poll. The deciding core will come from one of these seven Pokemon or pairs of Pokemon. For single Pokemon (Klefki, Tornadus-Therian, Terrakion, Entei), discuss what partners will work well together with this core. For proposed pairs (Gothitelle+Kyurem-Black, Latias+Lucario, Victini+Kyurem-Black), assess the viability of the core right now and what makes an effective partner for these Pokemon. A lot of this has been discussed already, that's by design!
1. Klefki - I chose Klefki as a Pokemon to focus on because its role is so much different than any Pokemon like it. There are few better disruptors in the game right now than Klefki; Klefki can spread Spikes, halve your opponent's damage with Screens, stop an opponent's sweep with a guaranteed Thunder Wave, or even use the Strategy That Shall Not Be Named (SwagPlay). There are dozens of sweepers that can take advantage of the support Klefki brings; a few Pokemon I'd like to see discussed as Klefki partners are Dragonite and Togekiss, especially the former. Dragonite can use Weakness Policy in conjunction with Klefki's screen support, and Klefki's paralysis support patches up Dragonite's one real weakness. Of course, discuss Klefki in all contexts, but I would like to see Klefki+Dragonite explored before this thread closes.
2. Gothitelle+Kyurem-Black - Looking at the two Pokemon in this core should make their role pretty obvious. Gothitelle traps the walls that Kyurem can't break, then Kyurem smashes and crashes through the opponent's team. As nyttyn pointed out, this core struggles against offense but is absolutely devastating to stall-based teams. What could let this core serve more purposes? What can Gothitelle do for a Pokemon whose role is to do what Kyurem-Black can't? Kyurem-Black doesn't need just one support Pokemon to crush teams because it has two main problems: its premier set does not have the power to break through Pokemon that are not weak to its attacks and it does not have the Speed to avoid hits from faster Pokemon. Although Kyurem-Black is very powerful, its true power in this metagame comes from its coverage and Ability. We cannot do it all with only one partner, especially when Gothitelle+Kyurem-Black still has glaring problems with Fairies and Scizor.
3. Latias+Lucario - This core is missing its wallbreaker, really. It's great at luring Bisharp and providing setup opportunities for Lucario, but Lucario is still a weak link in this core. As strong as Luke is, it's so frail that even resisted hits and Life Orb recoil will add up very quickly. Lucario could really use a partner in crime in this core, but there's a lot of potential with this. Lucario can't take advantage of Latias' Defog, but our Major Third could certainly do so. Lucario also has issues dealing with either Landorus-Therian or Aegislash, especially the latter. Lucario and Latias have moderate synergy together, but there are glaring holes that a third partner could definitely fill.
4. Tornadus-Therian - Tornadus-Therian can fit into numerous cores, from Flying Spam to even semi-stall. Tornadus-Therian has a lot of untapped potential; it's lost its ability to indiscriminately fire off Hurricanes and has had to adjust to being a ridiculously fast U-Turn pivot. However, the utility that Tornadus-Therian provides is nearly unmatched; Knock Off, U-Turn, and Regenerator allow Tornadus-Therian to support the team without requiring a lot of team support itself. The biggest problem with Tornadus-Therian is that I don't think we've found the perfect teammate for it yet. Politoed's viability is slipping, Kingdra almost mandates a Drizzle Pokemon, and Terrakion's synergy with Tornadus-Therian is suspect. There are numerous good ideas with Tornadus-Therian, but we need to decide what sort of Pokemon can benefit most from Tornadus-Therian's utility.
5. Terrakion - Terrakion's a very one-dimensional Physical attacker. It's mostly been paired up with similar Special attackers in this thread, and that seems like a reasonable way to move forward. I'm a fan (although not entirely convinced) of Terrakion+Volcarona or Terrakion+Tornadus-Therian because they can set up against or at least disrupt Physical walls such as Skarmory or Gliscor (Torn-T can't beat Skarm 1v1, but it can Knock Off its Lefties or even go for Confusion hax with Hurricane). Terrakion seems like a great partner for an underappreciated Special attacker, and I'd like to see us design a CAP that can focus on Terrakion's specific shortcomings.
6. Kyurem-Black+Victini - This is definitely the best wallbreaking core posted so far. Nothing comes close to the mixed attacking prowess of Kyurem-Black and Victini. In fact, there are few Pokemon that combine bulk, power, and Speed the way these Pokemon do. My biggest reservation with this thread is that Victini's a fringe Pokemon in OU. It's not a threat commonly prepared for because it can't do everything at once the way Kyurem-Black can. Players simply build teams that handle Victini without specifically having to plan for it. Victini seems like little more than a Mega Venusaur stopper in this core, but its raw power is still intriguing. I'd like to see Victini's viability in a core discussed.
7. Entei - Entei is possibly disparaged more than even Klefki by some users, even though it's successfully carved a niche in this metagame. Entei is not a Pokemon to be taken lightly because you can't deal with it the same way you deal with most Physical attackers. Sacred Fire ruins Intimidators such as Landorus-Therian and Gyarados, even if they take the actual hit pretty well. It's definitely a viable Pokemon in OU because of its ability to spread burn as well as hit hard. Although Entei is commonly seen with a Choice Band throwing around Sacred Fires, I'd like to see non-CB Entei talked about more in this thread.
Don't worry about addressing all seven of these cores or half-cores in one post, just pick out what you'd like to see us build our CAP around and build its case. This thread will close in about 18 hours, as well. At that point, our core will be selected and we'll move on to analyzing it in Concept Assessment 2.