When Aaron Stein was studying nuclear nonproliferation at Middlebury College's Monterey graduate program, the students would sometimes construct what they thought would be the best possible nuclear inspection and monitoring regimes.

Years later, Stein is now a Middle East and nuclear proliferation expert with the Royal United Services Institute (as well as the Geneva Centre for Security Policy and the Atlantic Council). And in April, he told me that the Iran nuclear deal, the broad strokes of which had just been announced, looks an awful lot like those ideal hypotheticals he'd put together in grad school.

"When I was doing my nonproliferation training at Monterey, this is the type of inspection regime that we would dream up in our heads," he said at the time. "We would hope that this would be the way to actually verify all enrichment programs, but thought that would never be feasible."

Stein concluded it would make "an excellent deal" — if the negotiators could turn those broad strokes into a formal, finalized agreement. This week, they did exactly that.

The full, final Iran nuclear deal "exceeds in all areas," Stein said on Tuesday. "It makes the possibility of Iran developing a nuclear weapon in the next 25 years extremely remote."

Like many observers, I doubted in recent months that Iran and world powers would ever reach this stage; the setbacks and delays had simply been too many. Now here we are, and the terms are astoundingly favorable to the United States. Arms control and nuclear nonproliferation experts are heralding it as a huge success.

Iran is giving up the bulk of its nuclear program

The deal requires Iran to surrender some crucial components of its nuclear program, in part or even in whole. Here are the highlights:

Iran will give up about 14,000 of its 20,000 centrifuges.

Iran will give up all but its most rudimentary, outdated centrifuges: Its first-generation IR-1s, knockoffs of 1970s European models, are all it gets to keep. It will not be allowed to build or develop newer models.

Iran will give up 97 percent of its enriched uranium; it will hold on to only 300 kilograms of its 10,000-kilogram stockpile in its current form.

Iran will destroy or export the core of its plutonium plant at Arak, and replace it with a new core that cannot produce weapons-grade plutonium. It will ship out all spent nuclear fuel.

Iran would simply not have much of its nuclear program left after all this.

A shorthand people sometimes use to evaluate the size of Iran's nuclear program is its "breakout time." If Supreme Leader Ayatollah Ali Khamenei woke up tomorrow morning and decided to set his entire nuclear program toward building a nuclear warhead — to "break out" to a bomb — as of today it would take him two or three months. Under the terms of the deal, his program would be so much smaller that it would take him an entire year to build a single nuclear warhead.

"I was shocked to read that they got them to agree to let us walk around their centrifuge production facilities. That's amazing."

These terms are not abject surrender. Iran is allowed to keep a small nuclear program, and it won some concessions of its own. For example, what little uranium enrichment is allowed will be done at Iran's facility at Natanz — a hardened, reinforced-concrete structure that was once used for covert enrichment and that the US had hoped to close.

Iran will also be allowed to do some research at Fordow, another hardened facility the US had wanted to close, though the research is restricted and will be barred from using fissile material. These are not big concessions, and they matter mostly for their symbolic value, but it's something.

Still, when you look at many of the specifics laid out in the deal, the hard numbers and timetables and the detailed proscriptions, those all tend to be quite favorable to the United States.

The result is pretty clear, Stein said: "The intention of this agreement is to take the weapons option off the table for the next 25 years, and the agreement does that."

The core issue that the deal really nails

The deal is strong on many terms, but it strongest on what was always going to be among the most crucial: inspections.

Whatever number of centrifuges Iran has or doesn't have, whatever amount of uranium it's allowed to keep or forced to give up, none of it matters unless inspectors have enough authority to hold Tehran to its end of the deal — and to convince the Iranians that they could never get away with cheating. To say the US got favorable terms here would be quite an understatement; the Iranians, when it comes to inspections, practically gave away the farm.

"I would give it an A," Stein said, in April, of the framework. When I asked why: "Because of the inspections and transparency."

There are two reasons inspections are so important. The first is that super-stringent inspections are a deterrent: If the Iranians know that any deviation is going to be quickly caught, they have much less incentive to try to cheat, and much more incentive to uphold their side of the deal.

"I would give it an A"

The second is that if Iran were to try a build a nuclear weapon now, it likely wouldn't use the material that's already known to the world and being monitored. Rather, the Iranians would secretly manufacture some off-the-books centrifuges, secretly mine some off-the-books uranium, and squirrel it all away to a new, secret underground facility somewhere. That would be the only way for Iran to build up enough of an arsenal such that by the time the world found out, it would be too late to do anything about it.

Really robust inspections would be the best way stop that from happening. They would prevent Iran from sneaking off centrifuges or siphoning away uranium that could be used to build an off-the-grid nuclear weapons program, without the world finding out.

Under this deal, the inspections are so strong, Stein said, that if Iran tried to cheat on the deal, "the likelihood of getting caught is near 100 percent."

The inspections issue has not gotten much political attention. When I spoke to Jeffrey Lewis, the director of the East Asia Nonproliferation Program at Middlebury's Monterey Institute of International Studies, back in March before the framework was announced, he seemed worried that negotiators would not focus on it much. Rather, overwhelming political focus in Washington and Tehran on issues like Iran's number of allowed centrifuges seemed likely to push inspections from the top priorities.

Lewis suggested that a top item on his wish list would be inspections so robust that inspectors don't just get to visit enrichment sites like Natanz and Fordow, but also centrifuge factories. That, he said, "would be a big achievement."

Sure enough, Lewis got his wish and then some: centrifuge factory inspections is one of the terms in the framework, and it's pretty robust. For the next 20 years, inspectors would have "continuous surveillance at Iran's centrifuge rotors and bellows production and storage facilities."

That's part of why, when I asked Lewis to grade the final deal this week, he gave me the same answer that Stein had: "I would give it an A."

"I was shocked to read that they got them to agree to let us walk around their centrifuge production facilities. That's amazing," Stein said in April, when the first terms came out. That provision is now part of the final deal.

It's not just centrifuge factories. Inspectors will have access to all parts of Iran's nuclear supply chain, including its uranium mines and the mills where it processes uranium ore. Inspectors will also not just monitor but be required to pre-approve all sales to Iran of nuclear-related equipment. This provision also applies to something called "dual-use" materials, which means any equipment that could be used toward a nuclear program.

"The inspections and transparency on the rotors, and the bellows, and the uranium mines is more than I ever thought would be in this agreement," Stein added.

How the deal prevents Iran from going nuclear for the next 25 years

When I talked to Stein this week, we discussed the scenario that this deal is all about: What happens if Iran decides it wants to build a nuclear bomb? I asked him to walk me through how that would happen, and how effective this deal would be at stopping it.

"They would do Fordow 2.0," he said, referring to the underground Fordow facility where Iran had previously conducted secret and illegal nuclear development. In other words, they would build another underground bunker and do it there. Iran is a big country, and even very strong inspections can't spot every hole in the ground. But they would need two things for this, and both in large supply: uranium ore and centrifuges. This is where the deal comes in.

First, Stein explained, "They would siphon off uranium from an undeclared mine." But under the deal, "that's not really possible."

"Iran only has two mines," he said — both of which will be under heavy inspections and monitoring. "It does not have rich uranium deposits, despite its claims to the contrary. We should know — we helped develop those fields in the 1970s.

"If all of a sudden a barrel of uranium at a conversion facility doesn't show up, we'd know," he explained. "They [inspectors] have an accounting of what comes out of the ground; they have an accounting of what has been refined at the processing plant. They have an accounting of what's been converted, then they have an accounting of what shows up at Natanz, and then they have an accounting of what comes out the back end."

But for the sake of seeing through the hypothetical, let's say that somehow, magically, Iran is able to sneak away the large amounts of uranium ore necessary for a bomb. Then what?

"Then they would build centrifuges without us knowing, because a centrifuge facility is tiny," Stein said. "You don't really pick them up; we've never really been able to find them when they are up."

The deal addresses this, as well: Not only will inspectors keep tabs on every single centrifuge in the country, but they will have eyes on the centrifuge factories, on machines that could be used to make a centrifuge, even on imports of technology that could be used to build a machine that could be used to build a centrifuge.

"The snapback thing is really clever"

"In the agreement, they have to account for all of their flow forming machines [that can be used to build a centrifuge], give us a list of where they are, and then put them under monitoring," Stein said. "The counter to that is they just won't tell us, they won't declare everything. That's to be expected, so don't trust that." That's where the deal's monitoring of things like "dual use" technology, that can have non-nuclear as well as nuclear uses, comes into play.

Meanwhile, Iran will have a relatively small program of approved centrifuges and energy-grade uranium. But all of this will be under constant monitoring, making it essentially impossible for Iran to use them for anything nefarious without the world knowing pretty quickly.

But let's keep the hypothetical going. Let's say that Iran breaks the restrictions on centrifuges or uranium and that the inspectors or US intelligence, inevitably, find out. What happens then?

What happens is that international sanctions — the sanctions that so hurt Iran's economy that it came limping up to the negotiating table — come back. This was always going to be a very difficult part of the deal; the sanctions are so powerful because they come from the European Union and from the United Nations, backed even by China and Russia, all of whom are more skittish than the US about punishing Iran. So how do you make sure they'll go along with reimposing sanctions? How do you make that threat so severe and so certain that Iran won't dare test it?

The solution they came up with is an elaborate mechanism they're calling "snapback."

"The snapback thing is really clever, I had to read it a couple of times to make sure it said what I think it said," Jeffrey Lewis, the Middlebury nuclear expert, told me.

If the US thinks Iran is cheating, the first step is taking it to a special commission of the seven countries that signed the deal plus the European Union. "But wait," you're saying, "can't Russia or China just use this process to stall or outright block the US?" Nope, they can't, because if the US is still unhappy, after a few weeks it can kick the issue up to the UN Security Council.

"But wait," you say again, "won't Russia and China just veto anything the US brings up there?" Nope, they can't meddle there either. If the US complains to the Security Council, and after 30 days the Security Council does nothing — and the US can ensure it does nothing by vetoing any resolutions — then under the deal the sanctions will automatically come back into force.

"It sounds like the US can blow up the deal any time it wants and revert to sanctions," Lewis said. And there's a good reason for that: "That's just how things are anyway."

But say all of that happens — say that Iran cheats on the deal, we inevitable catch them, all the sanctions come back, and somehow Iran keeps chugging away anyway on illegal nuclear development. This seems unlikely — if this is Iran's plan, they just signed a deal making it far more difficult to do it — but it's worth imagining. What then?

"The military force issue would come back," Stein said. In other words, it would take us back where we were a few years ago, with the US threatening military action against Iran. It is worth again recalling that that ended with Iran agreeing to nuclear negotiations in which it willingly gave up the bulk of its nuclear program, so it seems to want to avoid this scenario.

But if this worst-case scenario should happen, then the deal is still a net positive for the US. "I think the US hand is actually strengthened in this, to be honest with you," Stein said. "A full accounting of where everything is [gleaned from invasive inspections and monitoring] is a wonderful targeting mechanism for the Pentagon."

This is about the best we could ask for

The terms in the agreement are just about the best that we could hope for — even better, in some ways, than many had thought possible. The concessions from Iran are painful and many; the concessions by the US minor and few; the details surprisingly robust.

"As a framework it's very good," Mark Fitzpatrick, the director of the Non-Proliferation and Disarmament Program at the International Institute for Strategic Studies, tweeted in April when the broad terms were revealed. He added, "A sharp critic of Iran and skeptic of the talks told me after the announcement that it seemed to be heavily tilted in favour of the West."

The Arms Control Association issued a statement saying that the "historic" agreement "promises to lead to one of the most consequential and far-reaching nuclear nonproliferation achievements in recent decades."

Daryl Kimball, the Arms Control Association's chief, told the Guardian, "The deal is a major nuclear nonproliferation breakthrough that promises to prevent the emergence of another nuclear-armed state and head off a nuclear arms race in the world's most volatile region."

Andrea Berger of the Royal United Services Institute called it "an incredible achievement that much of the nuclear community will enthusiastically support." And on and on.

The way that all of this works is quite technical. But once you understand things like enrichment and inspections regimes and sanctions snapback, you see that the deal is actually pretty simple. Lewis put it well when we spoke:

I see it as a really straightforward measure to slow down an enrichment program that was going gangbusters. So you ask, "Does it slow it down?" Yes. "Does it slow it down in a way that is verifiable?" Yes. "Does it slow it down more than bombing it would?" Yes. "Okay, good deal."

Watch: President Obama's remarks on nuclear deal with Iran