In 2012, federal agents learned that Iranian scientist Sirous Asgari was working on cutting-edge metallurgy research at Case Western Reserve University in Cleveland, Ohio. The government suspected that Asgari had lied on his visa application and had transmitted scientific information to Iran in violation of American sanctions laws. Investigators applied for a warrant to search Asgari's emails, and the magistrate judge issued the warrant. After the search, the United States brought criminal charges and a grand jury indicted Asgari. In response, Asgari moved to suppress the emails. The district court held that probable cause did not support the warrant, and that the Leon good-faith exception did not apply. Because the Leon good-faith exception at a minimum applies, we reverse.

*511 I.

Sirous Asgari was born and raised in Iran. He first came to the United States for educational reasons, earning a doctorate from Drexel University in 1997. After earning his doctorate, he returned to Iran and became a professor at Sharif University. His work involves transmission electron microscopy, a process in which a scientist directs electrons at samples to produce highly detailed images.

Asgari traveled to the United States in 2011. In the section of his visa application labeled "[t]he [l]ocation[s] you plan to visit in the U.S.," Asgari listed New York, Florida, Pennsylvania, and Los Angeles. R. 123-1 at 2. Once in the United States, however, he traveled to Cleveland and met with another scientist, a friend and Iranian-American, at Case Western's Swagelok Center for Surface Analysis of Materials. The two began collaborating on research. Early in 2012, Asgari returned to Iran.

In August 2012, Asgari applied for another visa to enter the United States, listing his purpose as "temp[orary] business[/]pleasure" and identifying his destination as an address in New York where his son lived. R. 123-1 at 8. Shortly after he arrived, he claims, he learned about an opening at the Swagelok Center and applied for the job.

Someone told the Federal Bureau of Investigation that an Iranian metallurgist worked at Case Western under an improper visa. Special Agent Timothy Boggs interviewed the Swagelok Center's director who told him about Asgari's previous visit and said that Asgari was on a one-year sabbatical from Sharif University. The director said that the Swagelok Center did some research into corrosion-resistant technology funded by the United States Navy and that an opening had emerged on the project.

Agent Boggs prepared an affidavit and a warrant to search the content of Asgari's personal email account for evidence of two crimes: that Asgari made materially false statements in his visa application, 18 U.S.C. § 1001 (a)(2) ; and that Asgari violated the prohibition on exporting "any goods, technology, or services to Iran," Exec. Order No. 13,059, 62 Fed. Reg. 44,531 , 44,531 (Aug. 19, 1997) ; see 50 U.S.C. § 1705 (a). A magistrate judge issued the warrant ("the 2013 warrant"). Based on information uncovered from this search, the government obtained another warrant in 2015 ("the 2015 warrant") to search Asgari's subsequent emails. A grand jury indicted Asgari on 13 counts of stealing trade secrets, 18 U.S.C. § 1832 (a)(1)-(2), wire fraud, id. § 1343, and visa fraud, id. § 1546(a).

Asgari moved to suppress the evidence obtained from the execution of the warrants. The district court ruled that "[n]othing in the 2013 affidavit used to obtain the search warrant approaches probable cause." R. 113 at 7. It then held that the Leon good-faith exception did not permit the government to use the evidence uncovered from Asgari's email account because (1) the affidavit lacked indicia of probable cause and (2) Agent Boggs made intentionally false statements and misleading omissions in his 2013 affidavit. The court suppressed the emails from the 2015 warrant as ill-gotten gains from the 2013 warrant. The government appealed.

II.

The parties agree that this appeal turns on the evidence uncovered by the execution of the 2013 warrant. If probable cause supports the warrant or if the good-faith exception to the exclusionary rule applies, the government may use the information obtained from that search and the search *512 connected with the 2015 warrant in this prosecution.

Probable cause. The government first argues that probable cause supports the warrant. That may or may not be the case. But it doesn't matter because the Leon good-faith rule applies.

The Leon good-faith rule. If federal investigators conduct a search without probable cause of criminal activity, the search generally violates the Fourth Amendment. The violation usually comes with a remedy: suppression of the evidence found during the search. See Mapp v. Ohio , 367 U.S. 643 , 648, 81 S.Ct. 1684 , 6 L.Ed.2d 1081 (1961). Not always, however. Hiccups sometimes occur in complex as well as run-of-the-mine criminal investigations. The investigators may think probable cause exists, but a court may later disagree. To prevent reasonable errors from leading to disproportionally severe consequences, the Supreme Court in United States v. Leon , 468 U.S. 897 , 104 S.Ct. 3405 , 82 L.Ed.2d 677 (1984), created a "good faith" exception to the exclusionary rule, a safe harbor for reasonable slipups. If a neutral magistrate finds probable cause and issues a warrant, investigators may rely on the magistrate's judgment, and courts will consider the resulting evidence so long as two exceptions to the good-faith rule do not apply. One exception applies to warrant applications "so lacking in indicia of probable cause as to render official belief in its existence entirely unreasonable." Id. at 923 , 104 S.Ct. 3405 (quotation omitted). The other applies when the warrant application contains intentional or reckless falsehoods that mislead the magistrate. Id.

Neither exception applies.

As to the first exception, a reasonable officer could fairly rely on Agent Boggs's 10-page affidavit. This was not the kind of "bare bones" affidavit barred by Leon . Id. at 915 , 104 S.Ct. 3405 . The affidavit begins by identifying Agent Boggs's 23 years of experience at the Federal Bureau of Investigation, his decade working in national security, his expertise in Iranian counter-intelligence operations, and his "specialized training." R. 69-1 at 6; see United States v. Stotts , 176 F.3d 880 , 885 (6th Cir. 1999). It then lists several facts that would permit a reasonable officer to believe that probable cause existed to search for evidence of both crimes.

As to the false statement charge, government records showed that Asgari traveled to the United States in late 2011 and again in late 2012. On neither occasion did Asgari list Cleveland as a destination in his visa applications. Yet Asgari traveled to Cleveland both times and sent or received over 100 emails with colleagues at Case Western before applying for his 2012 visa. After arriving in the United States in 2012, Asgari went to Cleveland and secured a position on the anti-corrosion project. The kind of visa Asgari possessed did not permit him to work or "conduct research that will benefit a United States institution." R. 69-1 at 8 n.3. Had Asgari listed his purpose as conducting research for an institution, he would have had to apply for a different type of visa. All told, these facts provide ample indicia of probable cause that Asgari intended to conduct research that his visa did not allow and that he misled State Department officials about his "true intent when traveling to the United States." Id. at 13.

What about the sanctions violations? Here, too, we do not have a "bare bones" allegation so lacking in probable cause that an investigator could not rely on the warrant in good faith. The affidavit showed that Agent Boggs interviewed the Swagelok Center director. The director informed Boggs that Case Western possessed *513 "twenty (20) very precise and expensive instruments that are run by six (6) full time engineers." Id. at 9. This "instrumentation" was "not available in Iran." Id. at 8. The Center's high-tech tools attracted researchers from government entities such as the National Aeronautics and Space Administration and the Oak Ridge National Laboratory, as well as prestigious academic institutions such as the University of Cambridge. While the Center did not itself conduct classified research, the Center was "open to researchers who may be working" on classified projects. Id. at 9. The affidavit also details the nautical and military applications connected to the research at the Swagelok Center. The director had worked for the United States Department of Defense previously and was a member of the Defense Science Research Council. Three-quarters of the Swagelok Center's budget came from the Department of Defense. The Office of Naval Research funded the research into corrosion-resistant stainless steel to develop materials that the Navy could use to combat the harmful effects of saltwater. This "technology could extend the life of certain U.S. Navy propulsion systems." Id.

The affidavit also reveals evidence suggesting that Asgari may have exploited his position to transmit information back to Iran. A variety of people at the Center had access to the corrosion project's data. Asgari communicated by email with individuals in Iran. Asgari's home institution, Sharif University, had ties to the Iranian government. The university was "under the direct supervision" of the Iranian Ministry of Science, Research and Technology. Id. at 8. The university's funding came from the Iranian government as well as private sources. And other evidence suggested that Asgari lied on his visa application and sought to conceal the true purpose of his travel to the United States. That last fact shows how the two allegations intertwined. By lying on his visa application and coming to Case Western to work, Asgari would facilitate a scheme to send technology to Iran.

The question is not whether we would have found probable cause. It is whether the affidavit was so skimpy, so conclusory, that anyone looking at the warrant would necessarily have known it failed to demonstrate probable cause. That doesn't describe the affidavit or warrant in this case. The sanctions on Iran are broad in scope; probable cause is a lenient standard of proof; and the good-faith exception permits an affidavit to show much less than this one did. Put it all together, and investigators operating in good faith reasonably could have thought the warrant was valid.

Asgari resists this conclusion on several grounds. He starts by focusing on the reality that the State Department may not have required him to list Cleveland on his visa application because "travel plans commonly change." Appellee's Br. 22. But Asgari's travel to Cleveland, his acquisition of a post at Case Western, and his pre-existing and extensive relationship with an Iranian-American scientist there all suggest that Asgari intentionally omitted Cleveland as part of a larger effort to deceive the State Department about the purpose of his visit.

It also does not matter that the Swagelok Center director said the position Asgari filled became available after Asgari filed his visa application. That timeline does not disprove the possibility that Asgari planned to visit Case Western and work there. Plus, he emailed extensively with another scientist at Case Western before the visit. In view of Asgari's travel to Cleveland after coming to the United States, the extensive communication between the two men bolstered the probable-cause *514 determination that Asgari had long-held plans to do research at Case Western, whether in one position or another.

Based on the Swagelok Center director's statements reproduced in the affidavit, Asgari argues that information at the Center was purely "academic in nature and within the public domain," meaning Asgari could not send the Iranians anything they could not get elsewhere. Appellee's Br. 28. Read in context, however, the director's comments suggest only that the Center's research was unclassified, not that every piece of data was available in Iran via a Google search.

Asgari also thinks that his emails home to Iran could not contribute to probable cause because many of his correspondents were students-unlikely collaborators, he says, in trying to circumvent the sanctions on Iran. Maybe; maybe not. A university professor on sabbatical, it's true, often will continue to communicate with students for purely educational reasons, such as to advise ongoing research or offer mentorship. But the students also went to a university with close ties to the Iranian government, the sanctions are far reaching, and it's not unreasonable to think that a graduate student might assist a professor on all of his tasks, including transmitting data back to Iran in violation of American sanctions. The sanctions, bear in mind, broadly ban sending " any goods, technology, or services to Iran," covering much more than cloak-and-dagger espionage. Exec. Order No. 13,059, 62 Fed. Reg. at 44,531 (emphasis added); see also Bassidji v. Goe , 413 F.3d 928 , 934 (9th Cir. 2005) (discussing the sanctions' broad scope).

Asgari fares no better in claiming that the affidavit includes intentional or reckless falsehoods. See Leon , 468 U.S. at 914 , 104 S.Ct. 3405 ; Franks v. Delaware , 438 U.S. 154 , 171, 98 S.Ct. 2674 , 57 L.Ed.2d 667 (1978). The district court identified five errors in Special Agent Boggs's 10-page affidavit, all arising from paragraph 9. Here is the paragraph in full and its footnotes:

ASGARI has established ties to the government of Iran ("GOI"), through his employment with Sharif University. Sharif University, based on Affiant's investigation and training, is a university of higher education in technology engineering and physical sciences in Tehran, and one of Iran's most prestigious universities. 1 Funding for Sharif University is provided by the Iranian Government and through private investments. State run (non-medical) universities of Iran are under the direct supervision of Iran's Ministry of Science, Research and Technology. Sharif University researchers have worked in support of Iranian Navy projects such as autonomous underwater vehicles. 2 On two separate occasions, ASGARI traveled to the U.S. with the stated purpose of visiting his children. The first visit was from December 12, 2011, until February 15, 2012. That visit, ASGARI traveled to the U.S. on a B2 tourist visa. ASGARI arrived in the U.S. on his second visit on November 4, 2012, and remains in the U.S. This visit, ASGARI traveled on a *515 B1/B2 visa, 3 with the stated purpose of visiting his children. On both visits, without disclosure to the DoS, in his applications for visas, ASGARI traveled to Cleveland, Ohio to conduct research at the Swagelok Center for Surface Analysis of Materials (herafter [sic] "SSAM"), Case Western Reserve University (hereafter "CWRU"). The SSAM contains advanced research instrumentation that is not available in Iran. At SSAM, without the Navy's approval or knowledge, ASGARI has conducted research at CWRU that is funded by the Office of Naval Research ("ONR").

R. 69-1 at 8 & ns.1-3.

Not one of the alleged errors sinks to the level of a knowing falsehood or deliberate omission. Two of them count as minor omissions, each the type of missing "fragment" that cannot be characterized as deliberate or reckless. See United States v. Atkin , 107 F.3d 1213 , 1217 (6th Cir. 1997). According to the district court, Agent Boggs should have noted that the State Department doesn't require applicants to list an exact itinerary of their planned travel. But each visa application did ask about Asgari's travel plans in the United States, and in neither instance did he mention any travel to Cleveland. Boggs permissibly mentioned that material fact.

Agent Boggs also did not say that an individual may conduct independent research on the type of visa Asgari possessed, even if the visa holder cannot be employed or do research for an American institution's benefit. This, too, does not count as a deliberate omission. See id. Boggs explained what Asgari could not do (work for pay or for Case Western's benefit) and the reader reasonably could infer that the visa permitted Asgari to do activities short of that.

Two of the errors identified by the district court were not mistakes at all. One: Agent Boggs asserted that Asgari stated in his 2012 visa application that he wanted to travel to the United States to visit his children. In fact, Asgari listed his son's address as his point of contact and the address where Asgari planned to stay. Boggs took this to mean Asgari intended to visit his children, even though Asgari's visa technically allowed him to travel for some mix of pleasure and business. Boggs's characterization may have required an inference, but it is not a falsehood.

The other: Boggs wrote that Case Western had "advanced research instrumentation that is not available in Iran." Boggs's interview notes backed up this statement. The Swagelok Center director said that the instruments were "probably" unavailable to Iranian researchers, though similar equipment existed elsewhere. R. 128-2 at 3. That's not false.

Last of all, Agent Boggs stated that Asgari's employer, Sharif University, worked "in support of Iranian Navy Projects such as autonomous underwater vehicles." R. 69-1 at 8. As proof, Boggs cited a graduate student's dissertation about autonomous underwater vehicles that did not otherwise mention the Iranian Navy. This footnote, the court found, "was included to create a false connection between Asgari and the Iranian Navy" and misled the magistrate judge into believing that Asgari *516 would pass "defense technology" to the Iranians. R. 113 at 11-12. Even if technically inaccurate, the statement does not show a deliberate or reckless disregard for the truth. For one thing, the single, offending sentence was isolated in a footnote. For another, Boggs explained that the student paper used a U.S. Navy drone as the basis for its research. For still another, Asgari offers no evidence to show that Sharif University lacks ties to the Iranian military. In reality, it is an elite national university under direct oversight of the Iranian government.

On appeal, Asgari also points to several additional facts that allegedly suggest Agent Boggs misled the magistrate judge. Asgari identifies a discrepancy between what Boggs testified (that the Center's instruments had the highest resolution in world) and what Boggs's notes recorded (that the Center had "very precise" instruments). R. 128-2 at 1. To state the point is to answer it. Minor differences do not show bad faith, much less intentional or reckless lies.

Asgari claims that the affidavit implied that Asgari's failure to list Cleveland as a location of travel would violate 18 U.S.C. § 1001 (a)(2). Even if Asgari's failure to list Cleveland did not break the law, Asgari's desired reading of the affidavit is forced. At worst, the affidavit was slightly ambiguous about how Asgari made the false statement. The best reading of the affidavit suggests that Asgari violated § 1001(a)(2) when he listed "the purpose of the trip" as the kind of temporary business one is permitted to conduct on a visitor visa.

Because, at a minimum, the affidavit satisfies the Leon good-faith exception, we reverse and remand for further proceedings consistent with this opinion.