
    UNITED STATES of America, Appellee, v. Tarek MEHANNA, Defendant, Appellant.
    No. 12-1461.
    United States Court of Appeals, First Circuit.
    Nov. 13, 2013.
    
      Sabin Willett, with whom Susan Baker Manning, Julie Silva Palmer, Bingham McCutchen LLP, J.W. Carney, Jr., and Carney & Bassil were on brief, for appellant.
    Alex Abdo, Hina Shamsi, Matthew R. Segal, and Sarah R. Wunsch on brief for American Civil Liberties Union and American Civil Liberties Union of Massachusetts, amici curiae.
    Pardiss Kebriaei, Baher Azmy, and Amna Akbar on brief for Center for Constitutional Rights, amicus curiae.
    Nancy Gertner, David M. Porter, and Steven R. Morrison on brief for National Association of Criminal Defense Lawyers, amicus curiae.
    E. Joshua Rosenkranz and Orriek, Her-rington & Sutcliffe LLP on brief for Scholars, Publishers, and Translators in the Fields of Islam and the Middle East, amici curiae.
    Elizabeth D. Collery, Attorney, Appellate Section, Criminal Division, U.S. Department of Justice, with whom Mythili Raman, Acting Assistant Attorney General, Criminal Division, Denis J. Mclnerney, Acting Deputy Assistant Attorney General, Criminal Division, Carmen M. Ortiz, United States Attorney, John P. Carlin, Acting Assistant Attorney General, National Security Division, and Joseph F. Palmer, Attorney, National Security Division, were on brief, for appellee.
    Before HOWARD, SELYA and THOMPSON, Circuit Judges.
    
      
      . "Mujahideen” (singular: "mujahid”) is defined as "Muslim guerilla warriors engaged in a jihad.” The American Heritage Dictionary of the English Language 1153 (4th ed.2000). At trial, Aboubakr described "mujahid” as meaning “somebody who partakes in fighting.”
    
   SELYA, Circuit Judge.

Terrorism is the modern-day equivalent of the bubonic plague: it is an existential threat. Predictably, then, the government’s efforts to combat terrorism through the enforcement of the criminal laws will be fierce. Sometimes, those efforts require a court to patrol the fine line between vital national security concerns and forbidden encroachments on constitutionally protected freedoms of speech and association. This is such a case.

As if that were not enough, the case presents a welter of other issues. At the risk of singling out one of many, we pay particular heed to the need to appraise the district court’s efforts — in the face of an avalanche of emotionally charged evidence — to hold steady and true the delicate balance between probative value and unfairly prejudicial effect. This appraisal is especially difficult in terrorism cases because it puts two competing rights on a collision course: the government’s right to present its best case in support of its theories of guilt and the defendant’s right to be shielded from untoward prejudice arising out of the introduction of evidence that is, at one and the same time, probative yet inflammatory.

The stage can be set quite simply. In the court below, the government aimed a barrage of terrorism-related charges at defendant-appellant Tarek Mehanna. Following a protracted trial, the jury convicted him on all counts. The defendant, ably represented and supported by a coterie of earnest amici, challenges not only these convictions but also his 210-month sentence. After careful consideration of the massive record, the defendant’s prolific arguments, and the controlling law, we affirm.

I. OVERVIEW

We start with an overview of the charges lodged against the defendant and then outline the travel of the case.

This appeal has its genesis in an indictment returned by a federal grand jury sitting in the District of Massachusetts. In its final form, the indictment charged the defendant with four terrorism-related counts and three counts premised on allegedly false statements. The terrorism-related counts included one count of conspiracy to provide material support to al-Qa’ida (count 1); one count of conspiracy to provide material support to terrorists knowing or intending its use to be in violation of 18 U.S.C. §§ 956 and 2332 (count 2); one count of providing and attempting to provide material support to terrorists, knowing and intending its use to be in violation of 18 U.S.C. §§ 956 and 2332 (count 3); and one count of conspiracy to kill persons in a foreign country (count 4). The remaining counts included one count of conspiracy to make false statements as part of a conspiracy to commit an offense against the United States (count 5) and two counts of knowingly and willfully making false statements to federal officers (counts 6 and 7). See 18 U.S.C. §§ 371, 1001. For the reader’s convenience, we have annexed to this opinion an appendix delineating the pertinent portions of the relevant statutes.

Counts 1 through 3 (the conspiracy and material support charges) were based on two separate clusters of activities. The first cluster centered on the defendant’s travel to Yemen. We briefly describe that trip.

In 2004, the defendant, an American citizen, was 21 years old and living with his parents in Sudbury, Massachusetts. On February 1, he flew from Boston to the United Arab Emirates with his associates, Kareem Abuzahra and Ahmad Abousam-ra. Abuzahra returned to the United States soon thereafter but the defendant and Abousamra continued on to Yemen in search of a terrorist training camp. They remained there for a week but were unable to locate a camp. The defendant then returned home, while Abousamra eventually reached Iraq.

The second cluster of activities was translation-centric. In 2005, the defendant began to translate Arab-language materials into English and post his translations on a website — -at-Tibyan—that comprised an online community for those sympathetic to al-Qa’ida and Salafi-Jihadi perspectives. Website members shared opinions, videos, texts, and kindred materials in online forums. At least some offerings that the defendant translated constituted al-Qa’ida-generated media and materials supportive of al-Qa’ida and/or jihad.

The false statement counts (counts 5 through 7). related to statements that the defendant made during the course of an investigation by the Federal Bureau of Investigation (FBI) into his activities and those of his confederates. This investigation began in or around 2006. The statements specified in the indictment concerned the whereabouts and activities of one Daniel Maldonado, as well as the purpose and ultimate destination of the defendant’s trip to Yemen.

After considerable pretrial skirmishing, not material here, trial commenced. It lasted some 37 days. The district court refused to grant judgment of acquittal on any of the seven counts. The jury convicted the defendant on all of them, and the district court imposed a 210-month term of immurement.

This timely appeal ensued. In it, the defendant challenges his convictions, various evidentiary rulings, and his sentence. We address below the more substantial components of this asseverational array. A few points are not addressed at all because we have found them to be insufficiently developed, patently meritless, or both. In addition, the amici have attempted to raise some issues not preserved by the defendant. We disregard those attempts. The law is settled that amici cannot ordinarily introduce into a case issues not briefed and argued by the appellant. See United States v. Chiaradio, 684 F.3d 265, 284 n. 7 (1st Cir.) (“[W]e adhere to the established principle that an amicus may not ‘interject into a case issues which the litigants, whatever their reasons might be, have chosen to ignore.’ ” (quoting Lane v. First Nat’l Bank of Bos., 871 F.2d 166, 175 (1st Cir.1989))), cert. denied, — U.S. -, 133 S.Ct. 589, 184 L.Ed.2d 386 (2012). This case presents no occasion for departing from this general rule.

II. THE TERRORISM-RELATED COUNTS

The centerpiece of the defendant’s challenge to his convictions on the four terrorism-related counts is his binary claim that these convictions are neither supported by the evidence nor constitutionally permissible.

A. Sufficiency of the Evidence.

We review de novo challenges to the sufficiency of the evidence. See United States v. Gobbi, 471 F.3d 302, 308 (1st Cir.2006). This review eschews credibility judgments and requires us to take the facts and all reasonable inferences therefrom in the light most favorable to the jury’s verdict. See United States v. Sepulveda, 15 F.3d 1161, 1173 (1st Cir.1993). Using this lens, we must determine whether a rational jury could have found that the government proved each element of the crimes charged beyond a reasonable doubt. See id. To withstand a sufficiency challenge, a guilty verdict need not be an inevitable outcome; rather, “it is enough that the finding of guilt draws its essence from a plausible reading of the record.” Id.

To put the defendant’s sufficiency challenge into a workable perspective, it is helpful to trace the anatomy of the four terrorism charges. Count 1 charges the defendant with conspiring to violate 18 U.S.C. § 2339B, which proscribes “knowingly provid[ing] material support or resources to a foreign terrorist organization.” Id. § 2339B(a)(l). To satisfy the intent requirement of section 2339B, a defendant must have “knowledge about the organization’s connection to terrorism.” Holder v. Humanitarian Law Project (HLP), 561 U.S. 1, 130 S.Ct. 2705, 2717, 177 L.Ed.2d 355 (2010). A specific intent to advance the organization’s terrorist activities is not essential. See id.; see also United States v. Al Kassar, 660 F.3d 108, 129 (2d Cir.2011) (identifying “two express scienter requirements: that the aid be intentional and that the defendant know the organization he is aiding is a terrorist organization or engages in acts of terrorism”).

In this case, the defendant does not dispute that al-Qa’ida was and is a foreign terrorist organization (FTO). Nor could he credibly do so. See Redesignation of Foreign Terrorist Organizations, 68 Fed. Reg. 56,860, 56,862 (Oct. 2, 2003); Redes-ignation of Foreign Terrorist Organization, 66 Fed.Reg. 51,088, 51,089 (Oct. 5, 2001); see also United States v. Farhane, 634 F.3d 127, 135 n. 7 (2d Cir.2011). By like token, the record leaves no doubt that the defendant was aware of al-Qa’ida’s status.

Count 2 charges the defendant with conspiring to violate 18 U.S.C. § 2339A, which proscribes “providing] material support or resources ..., knowing or intending that they are to be used in preparation for, or in carrying out,” certain other criminal activities.- Id. § 2339A(a). The intent requirement under section 2339A differs somewhat from the intent requirement under section 2339B: to be guilty under section 2339A, the defendant must have “provide[d] support or resources with the knowledge, or intent that such resources be used to commit specific violent crimes.” United States v. Stewart, 590 F.3d 93, 113 (2d Cir.2009) (emphasis in original). Thus, “the mental state in section 2339A extends both to the support itself, and to the underlying purposes for which the support is given.” Id. at 113 n. 18. As adapted to the circumstances of this case, the government had to prove that the defendant had the specific intent to provide material support, knowing or intending that it would be used in a conspiracy to kill persons abroad. See 18 U.S.C. §§ 956, 2332.

Count 3 is closely related to count 2. It charges the defendant with violating, or attempting to violate, 18 U.S.C. § 2339A. The district court instructed the jury- that it could find the defendant guilty on count 3 under theories of direct liability, attempt, aiding and abetting, or agency. Because the parties’ arguments on appeal target the attempt theory, we focus our attention there.

Material support is defined identically for purposes of sections 2339A and 2339B. Such support may take various forms, including (as arguably pertinent here) the provision of “service[s]” or “personnel.” 18 U.S.C. §§ 2339A(b)(l), 2339B(g)(4). With respect to the Yemen trip, the government accused the defendant of conspiring to provide himself as an al-Qa’ida recruit (count 1); knowing or intending the use of this material support in a conspiracy to kill persons abroad (count 2); and attempting to provide this support, knowing or intending that it would be used in such a conspiracy .(count 3).

■ Count 4 bears a family resemblance to counts 1 through 3, but it has a slightly different DNA. It charges the defendant with violating 18 U.S.C. § 956, which proscribes conspiring in the United States “to commit at any place outside the United States an act that would constitute the offense of murder” if that act had been committed within the United States. Id. § 956(a)(1). For purposes of this statute, it does not matter whether the defendant’s coconspirators are located within the United States or abroad. See id.

We turn next to the government’s proof. In gauging the sufficiency of that proof, we start with the Yemen trip and the cluster of activities surrounding it.

The defendant asserts that this trip cannot bear the weight of his convictions on any of the four terrorism-related counts because the record shows nothing more than that he went to Yemen to pursue Islamic studies. The government counters that the evidence reflects a far more sinister purpose. The salient question — at least with respect to the first three terrorism-related counts — is whether the record, viewed in the light most agreeable to the verdict, supports a finding that the defendant conspired to provide or attempted to provide himself and others as recruits (and, thus, as material support) for al-Qa’ida’s terrorist aims.

The government’s evidence of the defendant’s specific intent with respect to his Yemen trip included his own actions, discussions with others, coeonspirator statements, and materials that the defendant either kept on his computer or shared on the Internet. The defendant contends that this evidence, in the aggregate, showed nothing more than his participation in activities protected by the First Amendment (e.g., discussing politics and religion, consuming media related to those topics, and associating with certain individuals and groups) and, thus, could not support a finding of guilt. See Scales v. United States, 367 U.S. 203, 229-30, 81 S.Ct. 1469, 6 L.Ed.2d 782 (1961); United States v. Spock, 416 F.2d 165, 169-74 (1st Cir.1969). But the defendant is looking at the evidence through rose-colored glasses. We think it virtually unarguable that rational jurors could find that the defendant and his associates went abroad to enlist in a terrorist training camp.

On this point, the defendant’s own statements are highly probative. His cocon-spirators testified that the defendant persistently stated his belief that engaging in jihad was “a duty upon a Muslim if he’s capable of performing it,” and that this duty included committing violence. The evidence further showed that, following United States intervention in Iraq, the defendant concluded “that America was at war with Islam,” and saw American “soldiers as being valid targets.”

Acting upon these views, the defendant and his associates — as early as 2001 — discussed seeking out a terrorist training camp. Following these discussions, the defendant expressed interest in receiving military-type training in order to participate in jihad. The defendant made clear that he wished to engage in jihad if he “ever had the chance” and that he and his associates “would make a way to go.” Together, they “discussed the different ways people could get into Iraq, the different training camps.”

In these conversations, the defendant voiced his desire to fight against the United States military forces in Iraq. He and his associates went “in depth on details” regarding the logistics of reaching such a terrorist training camp.

Coconspirator testimony shined a bright light on the defendant’s intent. This testimony made pellucid that the defendant and his comrades traveled to Yemen “for the purpose of finding a terrorist training camp” and “[ejventually ... get[ting] into Iraq.” The defendant’s particular interest in Iraq was because it was “an area that was being attacked.” He took the position that “there was an obligation for Muslims to stand up and fight against invasion of Iraq and the U.S. forces in Iraq.”

The defendant attempts to characterize these remarks as mere political speech. The jury, however, was entitled to draw a different inference: that the defendant’s comments were evidence of the formation and implementation of a scheme to go abroad, obtain training, join with al-Qa’ida, and wage war against American soldiers fighting in Iraq.

The timing of the trip and the furtiveness with which the defendant acted provide circumstantial support for this conclusion. The record contains evidence that the defendant abruptly suspended his studies in Massachusetts during the school year and kept his plans hidden from his parents. Prior to his departure, he gave his brother a bag of personal belongings and asked his brother to dispose of them. These belongings included “something about how to make a bomb.”

We note that the defendant and his associates purchased round-trip airline tickets. In the travelers’ own words, however, the return portions were for use “[i]f things didn’t work out,” as well as to avoid raising the sort of suspicion often associated with one-way ticketing. And Abuzahra testified at trial that, notwithstanding the return ticket, he did not expect to return to the United States because “[t]he purpose of ... going was to basically fight in a war.”

From this and other evidence, a rational jury could conclude that the defendant did not intend to return to the United States after leaving for Yemen. This intent dovetails with the defendant’s self-proclaimed jihadi agenda and makes the purpose of the trip apparent. ■ '

There was more. The evidence showed that the defendant and his associates had a plan of action for their arrival in Yemen. Abousamra had obtained the name of a contact there “who was going to get them to a military training camp.” When the men traveled to Yemen, they carried. a piece of paper that contained the contact’s name.

To be sure, the Yemen trip did not bear fruit. Once there, the defendant learned to his evident dismay that training camps no longer existed in the area and “that it was nearly impossible for anybody to get any training” there. The contact in Yemen fizzled, telling the defendant and Abousamra that “all that stuff is gone ever since the planes hit the twin towers.” It is consistent with the government’s theory of the case, however, that the defendant, when confronted with this news, expressed disappointment that he had “left [his] life behind” based on faulty information.

The government’s case is strengthened by evidence that the defendant and his associates engaged in a coverup that continued long after the defendant’s return from Yemen. The record reflects that the defendant and his associates repeatedly discussed how to align their stories and mislead federal investigators (in point of fact, they formulated cover stories for their Yemen trip even before the trip began). To facilitate the coverup, the defendant and his cohorts attempted to obscure their communications by using code words such as “peanut butter,” “peanut butter and jelly,” or “PB & J” for jihad and “culinary school” for terrorist training. Relatedly, the defendant encouraged an associate to install an “encryptor” on his computer in order to make it “much harder for [the FBI] to” monitor their online communications.

It is settled beyond hope of peradventure that evidence of participation in a coverup can be probative of elements of the underlying crime such as knowledge and intent. See United States v. Davis, 628 F.2d 188, 192 (1st Cir.1980) (citing Grunewald v. United States, 353 U.S. 391, 405, 77 S.Ct. 963, 1 L.Ed.2d 931 (1957)). This is a commonsense proposition, and “criminal juries are not expected to ignore what is perfectly obvious.” United States v. Echeverri, 982 F.2d 675, 679 (1st Cir.1993).

There is another dimension to this aspect of the government’s case. Although the theory of guilt that we have been discussing centered on the cluster of activities surrounding the Yemen trip, it was bolstered by other evidence.

To begin, the defendant’s desire to engage in jihad did not end with the failed Yemen trip. Early in 2006, the defendant told an associate, Ali Aboubakr, about how he had traveled to Yemen to engage in jihad. The defendant invited Aboubakr to join him if he elected to travel abroad for jihad again. He described “a camp” that they could attend in Yemen, where they would “live with like, 300 other brothers” who “all walk around ... with camo jackets and AK-47s.” The defendant urged Aboubakr, who was then a college student, not to tell his father about his plan.

The defendant’s communication with his “best Mend,” Daniel Maldonado, further evinced his determination to engage in jihad. In December of 2006, Maldonado telephoned the defendant from Somalia. During this call, the two discussed the logistics needed for the defendant to join Maldonado in Somalia, including transportation and travel documents. Maldonado said that he was “in a culinary school” and “mak[ing] peanut butter and jelly.” Maldonado testified that this was code language, familiar to the defendant, denoting that Maldonado was in a terrorist training camp and engaged in jihad.

Percipient witnesses testified that the defendant watched jihadi videos with his associates for the purpose of “gaining] inspiration from the[m]” and “becoming] like a mujahid.” These videos depicted events such as Marines being killed by explosives, suicide bombings, and combat scenes glorifying the mujahideen. The defendant was “jubilant” while watching them.

In a similar vein, the record is shot through with evidence of the defendant’s rabid support for al-Qa’ida, his “love” for Osama bin Laden, his admiration of the September 11 hijackers, and his conviction that the September 11 attacks were justified and a “happy” occasion.

The defendant complains that some of this evidence bears no direct connection to his Yemen trip. This plaint is true as far as it goes — but it does not take the defendant very far. It overlooks the abecedari-an proposition that evidence of a defendant’s general mindset may be relevant to the issue of his intent. See, e.g., United States v. Allen, 670 F.3d 12, 14-16 (1st Cir.2012). The record here is replete with such evidence.

The evidence we have summarized sufficed to ground a finding, beyond a reasonable doubt, that the defendant traveled to Yemen with the specific intent of providing material support to al-Qa’ida, knowing or intending that this support would be used in a conspiracy to kill persons abroad. It likewise sufficed to ground a finding that the defendant attempted to provide such material support, knowing or intending that it would be used in a conspiracy to kill persons abroad. Finally, it sufficed to ground a finding that the defendant, while in the United States, conspired with others in a plan to kill persons abroad. The evidence was, therefore, ample to convict on the four terrorism-related counts.

B. The Defendant’s Rejoinders.

Despite the obvious logic of the government’s position and the wealth of evidence that supports it, the defendant labors to undermine the four terrorism-related convictions. His efforts take two different directions — one a frontal assault and the other an end run. We address each in turn.

1. Scholarly Pursuits. The defendant argues that the only reasonable interpretation of his Yemen trip and the activities surrounding it is an innocent one: he sojourned to Yemen solely for the purpose of studying there. He describes himself as a devoted scholar of Islam and asserts that he visited Yemen, specifically, because the purest form of Arabic is spoken there., In support, he reminds us that he toured a school while in the country.

Relatedly, the defendant suggests that, regardless of his associates’ purpose and intent, he was far more moderate than they. This moderation allegedly included adherence to certain beliefs antithetic to al-Qa’ida canon. Among these beliefs was the doctrine of “aman,” which the defendant describes as “a covenant to obey the law within a country that permits practice of the faith.” As he would have it, his adherence to aman would prohibit him from targeting American troops.

We readily agree that the record contains some evidence supporting the defendant’s alternative narrative. Yet, that evidence does not eclipse the plethora of proof pointing in the opposite direction. When all was said and done, the jury heard and rejected the defendant’s innocent explanation of the events that occurred. It was plainly entitled to do so. See United States v. Olbres, 61 F.3d 967, 972-73 (1st Cir.1995).

To gain a conviction, the government need not “eliminat[e] every possible theory consistent with the defendant’s innocence.” United States v. Noah, 130 F.3d 490, 494 (1st Cir.1997). It is the jury’s role — not that of the Court of Appeals — to choose between conflicting hypotheses, especially when such choices depend on the drawing of inferences and elusive concepts such as motive and intent. See id.; Olbres, 61 F.3d at 972-73.

2. The Alternative Theory of Guilt. The defendant’s second rejoinder represents an attempt to change the trajectory of the debate. He points out that the indictment identifies his translations as culpable activity; that the government introduced copious evidence in support of a theory of guilt based on the translations; that it argued this theory to the jury; and that the jury returned a general verdict. Building on this platform, he argues that even if the evidence of the Yemen trip is sufficient to ground his terrorism-related convictions, those convictions cannot stand because they may have been predicated on protected First Amendment speech.

It is pointless to speak in the abstract of a verdict predicated on protected conduct. The Court of Appeals is not a sorting hat, divining which criminal defendants’ stories fall into constitutionally protected and unprotected stacks. Cf. J.K. Rowling, Harry Potter and the Sorcerer’s Stone 113-22 (1997). Instead, an appellate court’s role is to discern what, if any, errors marred the trial below. This inquiry requires us to focus on the relevant actors in the trial and not to engage in an untethered academic analysis of the verdict itself.

Personification has its limits. Verdicts, not being sentient, cannot err on their own; rather, any errors in a verdict come from the actors who have contributed to it. For example, a trial judge can commit error by instructing the jury that it can convict a defendant for wholly legal conduct. See, e.g., United States v. Tobin, 480 F.3d 53, 56-58 (1st Cir.2007). By the same token, jurors can err by returning a guilty verdict that is unsupported by legally sufficient evidence. See, e.g., United States v. Valerio, 48 F.3d 58, 63-65 (1st Cir.1995).

When it comes to the argument that the defendant makes here — that one of two possible grounds for the general verdict is suspect — the classification of the specific error makes all the difference. If “a mistake about the law” underlies the argument, reversal may be necessary. Griffin v. United States, 502 U.S. 46, 59, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991); see Yates v. United States, 354 U.S. 298, 312, 77 S.Ct. 1064, 1 L.Ed.2d 1356 (1957); Stromberg v. California, 283 U.S. 359, 367-68, 51 S.Ct. 532, 75 L.Ed. 1117 (1931). Such a “legal error” occurs, for instance, when “jurors have been left the option of relying upon a legally inadequate theory” by the trial court’s charge. Griffin, 502 U.S. at 59, 112 S.Ct. 466. If, however, “a mistake concerning the weight or the factual import of the evidence” underlies the argument, the verdict must be upheld as long as the evidence is adequate to support one of the government’s alternative theories of guilt. Id.

With this short primer in place, we turn to the defendant’s asseveration that the district court committed legal error in charging the jury with respect to his translations. At first blush, this asseveration is counter-intuitive because the court below evinced a keen awareness of the First Amendment issues implicated here. Pertinently, the court instructed:

Now, this is important. Persons who act independently of a foreign terrorist organization to advance its goals or objectives are not considered to be working under the organization’s direction or control. A person cannot be convicted under this statute when he’s acting entirely independently of a foreign terrorist organization. That is true even if the person is advancing the organization’s goals or objectives. Rather, for a person to be guilty under this count, a person must be acting in coordination with or at the direction of a designated foreign terrorist organization, here, as alleged in Count 1, al Qa’ida.
You need not worry about the scope or effect of the guarantee of free speech contained in the First Amendment to our Constitution. According to the Supreme Court, this statute already accommodates that guarantee by punishing only conduct that is done in coordination with or at the direction of a foreign terrorist organization. Advocacy that is done independently of the terrorist organization and not at its direction or in coordination with it does not violate the statute.
Put another way, activity that is proven to be the furnishing of material support or resources to a designated foreign terrorist organization under the statute is not activity that is protected by the First Amendment; on the other hand, as I’ve said, independent advocacy on behalf of the organization, not done at its direction or in coordination with it, is not a violation of the statute.

The defendant assigns error to these instructions in three respects. He says that they (i) fail to define the term “coordination”; (ii) incorrectly direct the jury not to consider the First Amendment; and (iii) should have been replaced by a set of instructions that he unsuccessfully proffered to the district court.

Where, as here, preserved claims of error relate to the correctness of a jury instruction as a matter of law, our review is de novo. See United States v. Sasso, 695 F.3d 25, 29 (1st Cir.2012). None of the defendant’s three claims of instructional error survives this review.

Although we agree that coordination can be a critical integer in the calculus of material support, the defendant’s first assignment of instructional error is simply wrong. While the district court did not use the phrase “is defined as,” it nonetheless defined the term “coordination” functionally. It explained to the jury in no fewer than three different ways that independent advocacy for either an FTO or an FTO’s goals does not amount to coordination. This distinction, which the court accurately characterized as “important,” went to the heart of the matter.

Moreover, the district court’s instructions harmonize with the text of the material support statute, which reads: “Individuals who act entirely independently of the [FTO] to advance its goals or objectives shall not be considered to be working under the [FTO]’s direction and control.” 18 U.S.C. § 2339B(h). The context made clear that the government’s “translations-as-material-support” theory was premised on the concept that the translations comprised a “service,” which is a form of material support within the purview of the statute. See id. §§ 2339A(b)(l), 2339B(g)(4). The HLP Court explained that “service,” as material support, “refers to concerted activity, not independent advocacy.” 130 S.Ct. at 2721. The instructions given to the jury embraced this construct.

In sum, the district court’s instructions captured the essence of the controlling decision in HLP, where the Court determined that otherwise-protected speech rises to the level of criminal material support only if it is “in coordination with foreign groups that the speaker knows to be terrorist organizations.” Id. at 2723. If speech fits within this taxonomy, it is not protected. See id. at 2722-26. This means that “advocacy performed in coordination with, or at the direction of,” an FTO is not shielded by the First Amendment. Id. at 2722. The district court’s instructions tracked the contours of this legal framework. The court appropriately treated the question of whether enough coordination existed to criminalize the defendant’s translations as factbound and left that question to the jury. See, e.g., Jones v. United States, 526 U.S. 227, 247 n. 8, 119 S.Ct. 1215, 143 L.Ed.2d 311 (1999). We discern no error.

The second assignment of instructional error is no more robust. The defendant contends that the court below erroneously foreclosed his argument that his activities were constitutionally protected by telling the jury: “You need not worry about the scope or effect of the guarantee of free speech contained in the First Amendment to our Constitution.” ■

This contention is futile. The very next sentence of the instructions makes the district court’s purpose pellucid: “According to the Supreme Court, this statute already accommodates that guarantee by punishing only conduct that is done in coordination with or at the direction of a foreign terrorist organization.” The instructions, read in context, did not tell the jury to blind itself to the protections of the First Amendment. Instead, they appropriately advised the jury that the material support statute, as well as the instructions the district court gave regarding that statute, already accounted for those protections.

In all events, it is a bedrock principle that “[t]he role of the jury in a federal criminal case is to decide only the issues of fact.” Berra v. United States, 351 U.S. 131, 134, 76 S.Ct. 685, 100 L.Ed. 1013 (1956). In line with this principle, the district court- properly barred the jury from embarking on an independent evaluation of First Amendment protections. See United States v. Victoria-Peguero, 920 F.2d 77, 86 (1st Cir.1990); see also United States v. Fincher, 538 F.3d 868, 872 (8th Cir.2008).

The defendant’s third assignment of instructional error calumnizes the district court for failing to give his proffered instructions on the interaction of the material support statutes and the prophylaxis afforded by the First Amendment. We will reverse a trial court’s refusal to give a proffered jury instruction only 'if the proffered instruction is substantively correct, not otherwise covered in substance in the court’s charge, and of sufficient import that its omission seriously affects the defendant’s ability to present his defense. See Chiaradio, 684 F.3d at 281; United States v. Prigmore, 243 F.3d 1, 17 (1st Cir.2001); United States v. McGill, 953 F.2d 10, 13 (1st Cir.1992).

In the case at hand, the defendant’s proffered instructions were not substantively correct but, rather, contained legally flawed propositions. There is nothing to be gained by citing book and verse. A single illustration suffices.

The proffered instruction stated: “the person [providing the alleged support] must have a direct connection to the group [FTO] and be working .directly with the group [FTO] for it to be a violation of the statute.” Contrary to the tenor of this statement, a direct link is neither required by statute nor mandated by HLP.

We add, moreover, that to the extent that the proffered instructions were sound, they were covered in substance by the charge actually given. Here, too, a single example makes the point.

The proffered instructions stated: “[m]ere association with terrorists or a terrorist organization is not sufficient to meet the element of ‘in coordination with.’ ” What the district court told the jury is perfectly consistent with this language. That ends the matter: a defendant has a right to an instruction on his theory of the case, but he has no right to insist that the trial court parrot his preferred wording. See, e.g., United States v. DeStefano, 59 F.3d 1, 2-3 (1st Cir.1995); McGill, 953 F.2d at 12.

The bottom line is that the defendant’s assault on the district court’s jury instructions is without merit. And, having eliminated the defendant’s claims of legal error, we are left only with his claim that the jury’s finding of “coordination” lacked sufficient supporting evidence.

As noted above, that inquiry is foreclosed by Griffin. We already have determined that the cluster of activities surrounding the defendant’s Yemen trip supplied an independently sufficient evidentiary predicate for the convictions on the terrorism-related counts. The defendant’s translation-related activities were tendered to the jury only as an alternative basis for those convictions. Even if that proof is factually insufficient, Griffin dictates that we affirm based on the government’s Yemen theory.

It makes no difference that the absence of facts showing coordination with al-Qa’ida might have resulted in constitutionally protected conduct. The dividing line that the Supreme Court drew in Griffin was based on the distinct roles of judge and jury in our system of justice, not the presence vel non of constitutional issues. We entrust trial judges with the grave responsibility of giving juries a proper view of the law, and when they fail to do so, reversal may be warranted because “there is no reason to think that [jurors’] own intelligence and expertise will save them from that error.” Griffin, 502 U.S. at 59, 112 S.Ct. 466.

On the other hand, jurors are endowed with expertise in factfinding. See id. That presumed expertise is not vitiated even when performing the factfinding task requires them to separate constitutionally protected conduct from illegal conduct. See, e.g., N.Y. Times Co. v. Sullivan, 376 U.S. 254, 279-82, 84 S.Ct. 710, 11 L.Ed.2d 686 (1964). Thus, Griffin wisely teaches that there is no need for courts to save jurors from themselves “when they have been left the option of relying upon a factually inadequate theory, since jurors are well equipped to analyze the evidence.” 502 U.S. at 59, 112 S.Ct. 466 (emphasis in original).

That brings down the final curtain. We have found the defendant’s claims of legal error with respect to his translation activities wanting, and we have no occasion to examine the factual sufficiency of those activities as a basis for his terrorism-related convictions. Even if the government’s translation-as-material-support theory were factually insufficient, we would not reverse: the defendant’s convictions on the affected counts are independently supported by the mass of evidence surrounding the Yemen trip and, under Griffin, we need go no further.

C. Odds and Ends.

The defendant invites us to overturn his conviction on some or all of the terrorism-related counts for a variety of additional reasons. Without exception these reasons are meritless. We dispose of them summarily.

1. Variance. The defendant perceives a fatal variance between the conspiracies charged in counts 1, 2, and 4 and what he visualizes as a hodge-podge of other conspiracies captured by the proof at trial. The accepted rule is that when the government’s case at trial varies from the crime limned in the charging document and that variance is both material and prejudicial, an ensuing conviction must be set aside. See United States v. Boylan, 898 F.2d 230, 246-48 (1st Cir.1990).

We need not tarry. As we have explained, questions about the number of conspiracies that are in play and about their structure typically “present matters of fact suitable for resolution by a jury.” Sepulveda, 15 F.3d at 1190. Hence, variance claims are normally reviewed on appeal as matters of evidentiary sufficiency. See id.

Silhouetted against this backdrop, what we have said about the defendant’s failed sufficiency argument, see supra Part 11(A), not only shows that the government proved the conspiracies that it charged but also refutes the defendant’s variance claim. Based upon a careful perscrutation of the record, we are confident that no material and prejudicial variance exists in this case. The government introduced sufficient evidence to prove each of the conspiracies with which the defendant was charged.

We add, moreover, that the district court’s instructions focused the jury with laser-like intensity on these particular conspiracies. And even though the defendant labored to splinter the government’s proof into a myriad of separate conspiracies, the jury supportably rejected this effort at deconstruction. That ends the matter.

2. Legal Impossibility. The defendant argues that counts 2 and 8 must fail because they depend on a legal impossibility. See United States v. Dixon, 449 F.3d 194, 202 n. 2 (1st Cir.2006) (explaining that “legal impossibility exists when a defendant sets out to achieve an objective which, even if achieved as envisioned, will not constitute a crime”). Specifically, he maintains that he could not have had an intent to provide material support knowing or intending its use to violate either section 956 or section 2332. In terms of section 956, he envisions a legal impossibility because “[pjutative recipients of the ‘personnel’ could not ‘use’ that support, as section 2339A contemplates, to commit a predicate crime requiring conspiracy within the United States, because by definition, those recipients were contemplated to be abroad.” He further argues that legal impossibility results because the government’s theory of the case fell short of making out a conspiracy to commit “an act that would constitute the offense of murder.” 18 U.S.C. § 956(a)(1).

With respect to section 2332, the defendant contends that legal impossibility forecloses conviction because the government did not make out “a contemplated conspiracy or attempt occurring outside the United States to make use of [the defendant’s] or Abousamra’s person to kill some national of the United States.”

These convoluted theories are difficult to follow. We need not wend our way, step by step, through the intricate labyrinth that the defendant constructs. It suffices to say that, in the last analysis, his theories raise questions of factual, rather than legal, impossibility. As such, their resolution depends on the sort of functions that the criminal law commits to juries, namely, how one looks at the facts of the case and what inferences one chooses to draw.

At any rate, dressing up an argument in different raiment rarely improves its prospects. Stripped of rhetorical flourishes, the defendant’s legal impossibility theories are nothing more than creative reformulations of discrete aspects of his previously rejected sufficiency claim. What matters is that the evidence in this case was adequate to prove all of the elements of the terrorism-related counts. See supra Part 11(A). The defendant’s legal impossibility theories therefore fail.

3. Vagueness. The defendant makes a cursory argument that the district court’s “construction” of the material support laws was unconstitutionally vague. To the extent that this argument is preserved, it is foreclosed by HLP, 130 S.Ct. at 2718-22. Consequently, we reject it out of hand.

4. The Certification Requirement. The defendant objects that his convictions on counts 2 and 3 are invalid because of the government’s failure to comply with the certification requirement adumbrated in 18 U.S.C. § 2332(d). This requirement reads: “No prosecution for any offense described in this section shall be undertaken ... except on written certification ... that, in the judgment of the certifying official, such offense was intended to coerce, intimidate, or retaliate against a government or a civilian population.” Id.

The government concedes that no such certification was obtained. In the circumstances of this case, however, the absence of a certification affords the defendant no sanctuary.

To begin, the defendant did not raise this objection in the district court. Our review, therefore, is only for plain error. See United States v. Duarte, 246 F.3d 56, 60 (1st Cir.2001). To make out plain error, the defendant must show “(1) that an error occurred (2) which was clear or obvious and which not only (3) affected the defendant’s substantial rights, but also (4) seriously impaired the fairness, integrity, or public reputation of judicial proceedings.” Id.

There is no plain error here. In the first place, it is doubtful that the certification requirement applies to this case. The defendant was not prosecuted for an offense “described in” section 2332 but, rather, for an offense described in section 2339A (which references section 2332 as a specific-intent element). Given this uncertainty, any error that may have transpired would not be “clear or obvious.”

At any rate, the defendant cannot vault the third hurdle erected by the plain error standard: on this record, he cannot show that his substantial rights were adversely affected by the absence of a certification. The defendant’s convictions under section 2339A were premised on knowledge and intent that his material support would be used for violations of either section 2332 or section 956. On a separate count — count 4 — the jury found that the defendant violated section 956. Thus, his section 2339A conviction was supported by an intent to' violate section 956. This makes it highly unlikely that the inclusion of the reference to section ,2332 had any substantial effect. See Turner v. United States, 396 U.S. 398, 420, 90 S.Ct. 642, 24 L.Ed.2d 610 (1970) (explaining “that when a jury returns a guilty verdict on an indictment charging several acts in the conjunctive, ... the verdict stands if the evidence is sufficient with respect to any one of the acts charged”).

5. Count 3. The defendant mounts a singular attack on count 3, which charged him with attempted violation of section 2339A; that is, attempting to provide material support knowing or intending its use in • a conspiracy to kill persons abroad. The defendant suggests that the government failed to prove that he engaged in the substantial step necessary to under-gird an attempt conviction. This suggestion is plainly unavailing.

We agree with the defendant that a conviction for attempt necessitates proof that the defendant took at least one substantial step toward the actual commission of the charged crime. See, e.g., United States v. Pires, 642 F.3d 1, 8 (1st Cir.2011); Gobbi 471 F.3d at 309. Here, however, the Yemen trip constituted a very substantial step toward the attempted commission of the crime. The defendant suspended his studies, instructed his brother to destroy a bag of his possessions, and flew to Yemen armed with the name of a possible al-Qa’ida liaison. The jury was fully entitled to find that these actions satisfied the “substantial step” requirement.

In an effort to efface this reasoning, the defendant posits that the Yemen trip could not have constituted a substantial step toward the commission of the crime because there was no al-Qa’ida presence in Yemen in February of 2004. Notwithstanding these importunings, we need not decide whether or when alQa’ida pulled up stakes and quit Yemen. Even if we assume arguendo that alQa’ida retreated before the defendant’s trip, the existence of a substantial step would not be called into question. Such a' departure would, at most, have created a factual impossibility; and as we previously have explained, “factual impossibility is not a defense to ... liability ... for inchoate offenses such as conspiracy or attempt.” Dixon, 449 F.3d at 202.

III. THE FALSE STATEMENT COUNTS

The defendant does not contest the sufficiency of the evidence underpinning his convictions on counts 5 (making false statements as part of a conspiracy to commit an offense against the United States) and 7 (making false statements anent the purpose and ultimate destination of the Yemen trip). He does, however, interpose a sufficiency challenge to his conviction on count 6. We turn next to this challenge.

Count 6 charges a violation of 18 U.S.C. § 1001(a)(2), which criminalizes “knowingly and willfully ... mak[ing] any materially false, fictitious, or fraudulent statement or representation” to federal officials. The statements on which this count depends pertain to the whereabouts and activities of the defendant’s friend and compatriot, Maldonado. These utterances were made when FBI agents questioned the defendant in December of 2006. In response to direct queries, the defendant told the agents that he had last heard from Maldonado two weeks earlier and that Maldonado was living in Egypt, working as a website steward. These statements were unquestionably false: the defendant had spoken to Maldonado within the week and knew that Maldonado was in Somalia and training for jihad.

Still, even proof of knowing and willful falsity, without more, is not enough to sustain a conviction under section 1001(a)(2). Targeted statements must not only be false but also materially so. See United States v. Sebaggala, 256 F.3d 59, 64-65 (1st Cir.2001).

The defendant seizes on this additional requirement. He points out that when the agents questioned him, they knew full well where Maldonado was and what he was doing. They also knew that he had spoken with Maldonado by telephone within a matter of days.

Building on this foundation, the defendant argues that the agents were asking him questions to which they already knew the answers for the sole purpose of catching him in a lie. Thus, his argument runs, his false statements cannot be material because the agents knew that his statements were false ab initio and, therefore, were not misled by them. Inasmuch as this argument challenges the sufficiency of the government’s evidence, it engenders de novo review. See Gobbi, 471 F.3d at 308.

The defendant is fishing in an empty stream. To satisfy the materiality requirement of section 1001(a)(2), a statement must have “a natural tendency to influence, or [be] capable of influencing, a governmental function.” Sebaggala, 256 F.3d at 65. But the statement need not actually have influenced the governmental function. It is enough that the “statement could have provoked governmental action.” Id.; see United States v. Edgar, 82 F.3d 499, 510 (1st Cir.1996) (explaining that “the standard is not whether there was actual influence, but whether [the statement] would have a tendency to influence”). Thus, the proper inquiry is not whether the tendency to influence bears upon a particular aspect of the actual investigation but, rather, whether it would bear upon the investigation in the abstract or in the normal course. See United States v. McBane, 433 F.3d 344, 350-51 (3d Cir.2005); Edgar, 82 F.3d at 510.

Under this formulation, the knowledge of the interrogator is irrelevant to the materiality of the defendant’s false statements. See United States v. Land, 877 F.2d 17, 20 (8th Cir.1989). With this in mind, courts have rejected variations of the metaphysical proposition advanced by the defendant with a regularity bordering on the monotonous. See, e.g., United States v. Lupton, 620 F.3d 790, 806-07 (7th Cir.2010); McBane, 433 F.3d at 350-52; Edgar, 82 F.3d at 510; Land, 877 F.2d at 20; see also Brogan v. United States, 522 U.S. 398, 399-400, 402, 118 S.Ct. 805, 139 L.Ed.2d 830 (1998) (finding defendant’s false response to be material where agents knew correct answer at time of questioning, but not elaborating on this point).

In the case at hand, it is clear beyond hope of contradiction that the defendant’s false statements about Maldonado had a natural tendency to influence an FBI investigation into terrorism. After all, Maldonado was hip-deep in terrorism-related antics. During the critical interview, the defendant was plainly attempting to obscure both Maldonado’s participation in terrorist endeavors and the telephone call in which he and Maldonado had discussed jihad and terrorist training. The misinformation imparted by the defendant thus had a natural propensity to influence an FBI investigation into terrorist activity.

To cinch matters, the defendant’s mendacity was undertaken for the purpose of misdirecting the ongoing FBI investigation (or so the jury could have found). This is an important datum: where a defendant’s statements are intended to misdirect government investigators, they may satisfy the materiality requirement of section 1001 even if they stand no chance of accomplishing their objective. See Lupton, 620 F.3d at 806-07. This principle makes eminently good sense: it would stand reason on its head to excuse a defendant’s deliberate prevarication merely because his interrogators were a step ahead of him.

To say more on this point would be supererogatory. The defendant’s challenge to the sufficiency of the evidence on count 6 is a losing proposition.

IV. THE EVIDENTIARY RULINGS

The next leg of our journey takes us through a series of hotly contested eviden-tiary rulings. Although these claims of error are somewhat interrelated, we subdivide them into five segments.

A. Coconspirator Statements.

The challenged evidentiary rulings concern four sets of out-of-court statements attributed to coconspirators and admitted at trial. The first two sets of declarations were made by closely related coconspira-tors and were uttered either before or after the Yemen trip. The remaining two sets comprise remarks of more remote personages, whom the government also alleges were coconspirators. Although the defendant unleashes a torrent of arguments against the admission of these statements, we discern no reversible error.

The principles that govern the admission of coconspirator statements are old hat. Out-of-court statements offered to prove the truth of the matter asserted are generally regarded as hearsay and, thus, inadmissible. See Fed.R.Evid. 801(c), 802. But there are exceptions. Pertinently for present purposes, when such a statement is offered against a party and is shown to have been “made by the party’s coconspir-ator during and in furtherance of the conspiracy,” it is “not hearsay” and therefore admissible. Fed.R.Evid. 801(d)(2)(E).

If a defendant challenges the admissibility of such a statement when it is offered against him, the trial court may provisionally admit the evidence and defer its final ruling until the close of all the evidence. See United States v. Perez-Ruiz, 353 F.3d 1, 12 (1st Cir.2003). This procedure imposes a two-fold obligation upon a protesting defendant: he must object when the evidence is first offered and again at the close of all the evidence. See id.

In evaluating a trial court’s refusal to sustain such a close-of-evidence objection, we ask whether the record adequately evinces “that a conspiracy embracing both the declarant and the defendant existed, and that the declarant uttered the statement during and in furtherance of the conspiracy.” United States v. Piper, 298 F.3d 47, 52 (1st Cir.2002) (internal quotation mark omitted). The party seeking the benefit of the hearsay exception (here, the government) must carry the devoir of persuasion on this inquiry and establish the necessary elements by a preponderance of the evidence. Id. “If these conditions are met, and if there is corroboration in the form of extrinsic evidence of the declar-ant’s involvement in the conspiracy, then the hearsay barrier is avoided and the statement may be admitted.” United States v. Bradshaw, 281 F.3d 278, 283 (1st Cir.2002).

1. Pre-Yemen Statements. With this framework in place, we turn first to cer-. tain statements that preceded the Yemen trip. The Yemen trip did not take place until February of 2004. Abousamra had sought to locate a terrorist training camp in 2002. At that time, Pakistan captured his fancy. He solicited assistance from Hassan Masood, a confederate who had particularized knowledge about that country.

Armed with Masood’s information, Abousamra traveled to Pakistan twice that year. Upon returning, he complained to Masood about the futility of his quest. Abousamra nonetheless noted that this cloud had a silver lining: in his travels, he had come across a sympathetic contact who had urged him to “do whatever [he could] back in America.”

That advice presaged conversations that took place in 2003 among Abousamra, Abuzahra, and the defendant. Fueled by anger over the intervention by the United States in Iraq, the three men agreed in principle to participate in jihad against the United States. They discussed possible ways to implement this consensus, including the assassination of political leaders, attacks on military bases, and incursions at shopping malls.

Ultimately, the trio abandoned any plans for mischief-making in the United States. At that point, Abousamra conversed with Jason Pippin, a person whom he had met through online Salafi-Jihadi forums. Abousamra sought Pippin’s counsel about a possible Yemen trip.

At trial, the government used several of the statements that had been made during the foregoing discussions. The defendant argues that nothing Abousamra said at those times can satisfy the strictures of Rule 801(d)(2)(E). He insists that all the statements preceded the formation of any plan to go to Yemen and, a fortiori, did not take place during the conspiracy. He adds that, even when viewed in the most sinister light, the statements relate to separate conspiracies that he never joined. Because the defendant challenges these statements for the first time on appeal, our review is for plain error. See Duarte, 246 F.3d at 60.

We find no error, plain or otherwise. To begin, we already have rejected the defendant’s atomizing conception that each distinct terrorism-oriented thought must be treated as its own separate conspiracy. See supra Part 11(C)(1). Our rejection is consistent with the truism that a conspiracy may “shift its priorities from time to time without sacrificing its essential identity.” Sepulveda, 15 F.3d at 1191. That the conspiracy shifted its focus from Pakistan to domestic attacks and then to Yemen did not rob it of its essential purpose: waging jihad against the United States. The means may have changed from time to time, but the end remained the same.

Once this essential purpose is understood, it becomes evident that none of the statements at issue predate the formation of the relevant conspiracy. All of the statements follow the discussions between the defendant and his associates in 2001 about terrorist training camps. What is more, the defendant agreed to participate in jihad against the United States before Abousamra’s exploration of domestic attacks and the trio’s investigation into the plausibility of a Yemen trip.

To be sure, Abousamra’s flirtation with Pakistan and his conversations with Ma-sood occurred earlier. But even though these remarks came beforehand, the law is settled that a “statement made by a cocon-spirator, if in furtherance of the conspiracy, is ... admissible against the defendant even if made prior to the defendant’s involvement in the conspiracy.” United States v. Masse, 816 F.2d 805, 811 (1st Cir.1987). Judge Aldrich graphically described the underlying rationale: “[A] conspiracy is like a train. When a party knowingly steps aboard, he is part of the crew, and assumes conspirator’s responsibility for the existing freight....” United States v. Baines, 812 F.2d 41, 42 (1st Cir.1987).

2. Post-Yemen Statements. After Abuzahra bailed out of the Yemen trip, he told Masood his reasons for doing so. For his part, Abousamra recounted his travels in Yemen and beyond to a number of witnesses. These post-Yemen oral histories were admitted at trial. The defendant maintains that by the time these statements were made, the conspiracy had end-' ed as to the declarants: he says that Abu-zahra abandoned the conspiracy by leaving Yemen early and that, by the time Abous-amra spoke, there was no one left with whom he could have been conspiring. Because these fact-laden claims of error were preserved below, we review them for clear error. See Sepulveda, 15 F.3d at 1180.

With respect to Abousamra, the defendant’s attempt to limit the conspiracy to Yemen alone casts the net too narrowly. As we already have explained, the defendant continued to seek opportunities to engage in jihad well after his return from Yemen. See supra Part 11(A). Furthermore, the defendant’s claim ignores entirely the charged conspiracy to provide false information to the government — a conspiracy that continued long after the Yemen trip.

The defendant’s plaint that Abuzahra abandoned the conspiracy is equally asthenic. “[I]n order to withdraw from a conspiracy, a conspirator must act affirmatively either to defeat or disavow the purposes of the conspiracy,” such as by confessing to the authorities or informing his coconspirators that he has forsaken the conspiracy and its goals. Piper, 298 F.3d at 53 (internal quotation marks omitted). Abuzahra took no such affirmative steps but, rather, merely eschewed contact with Abousamra and the defendant upon his return from Yemen. Avoiding contact with one’s coconspirators, without more, is not in any way, shape, or form tantamount to abandoning the conspiracy. Consequently, the record in this case does not support the notion- that Abuzahra abandoned the conspiracy before recounting his travels. See id. (explaining that “[m]ere cessation of activity in furtherance of the conspiracy does not constitute withdrawal from a conspiracy” (alteration in original) (internal quotation marks omitted)).

There is no need to tarry. We conclude, without serious question, that the court below did not clearly err in admitting the post-Yemen statements.

3. At-Tibyan Statements. We next consider the statements of more remote figures alleged to be among the defendant’s coconspirators. Once again, we split the inquiry into two parts. We start with the defendant’s challenge to the admission of instant messages from his at-Tibyan collaborators — messages that tended to show that al-Qa’ida solicited translations from the website’s members.

In the defendant’s view, the evidence showing a link between at-Tibyan and the charged conspiracy consisted of these messages alone — and more was needed in order to invoke the hearsay exception. See Bradshaw, 281 F.3d at 283 (requiring “corroboration in the form of extrinsic evidence”). We need not weigh the substance of this objection. Even if we assume for argument’s sake that the district court erred in admitting the atTibyan messages, the error would be harmless. After all, a conviction will stand, notwithstanding a non-constitutional error, “as long as it can be said “with fair assurance, after pondering all that happened without stripping the erroneous action from the whole, that the judgment was not substantially swayed by the error.’ ” Sasso, 695 F.3d at 29 (quoting Kotteakos v. United States, 328 U.S. 750, 765, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946)).

Our conclusion about the harmlessness of any error is easily explained. In this case, the relevance of the at-Tibyan evidence is limited to the translation theory of guilt. But the Griffin Court’s teachings, when applied here, render that theory of guilt academic. See supra Part 11(B)(2) (explaining why the defendant’s conviction would endure even if the evidence were insufficient to convict on the translation theory). And if we need not consider whether sufficient evidence exists to undergird the translation theory of guilt, it would be pointless to evaluate whether some of that evidence should have been excluded. It follows that any error in the admission of such evidence is perforce harmless. See, e.g., United States v. Mitchell, 85 F.3d 800, 812 n. 11 (1st Cir.1996).

4. Al-Qa’ida Statements. The defendant’s last challenge under Rule 801(d)(2)(E) implicates the district court’s failure to exclude statements of high-level al-Qa’ida leaders. In support, the defendant asserts that any connection between those infamous figures and himself was too attenuated to warrant admission of the statements.

This might be a different case had the challenged statements been admitted for their truth. The government suggested below that these statements qualified for the Rule 801(d)(2)(E) exception because al-Qa’ida leaders “called for individuals to come join al Qa’ida” and the defendant “tried to respond to that call,” but the perimeter staked out by the government’s rationale seems vast. Arguably, any projihadi Muslim publicly announcing his opinions would come within its borders.

Here, however, we can leave the obvious concerns raised by this scenario for another day. It is virtually a tautology to say that in order to require a hearsay exception, a piece of evidence must otherwise satisfy the definition of hearsay. See United States v. Salameh, 152 F.3d 88, 112 (2d Cir.1998). To qualify as hearsay, a statement must be offered for its truth. See Fed.R.Evid. 801(c)(2). The defendant directs us to no statements of al-Qa’ida leaders that were admitted to prove the truth of the matter asserted.

This hardly seems to be an oversight. It would, for instance, defy logic to think that the government offered Abu Musab al-Zarqawi’s invective that “the American administration” has “become an utter liar” to prove itself a perpetual prevaricator. By the same token, it is plain that the government did not offer Osama bin Laden’s hypothesis that “[t]he wounds of the Muslims are deep, very deep, in every place” to prove the depth and ubiquity of Muslim wounds. Because these coconspir-ator statements simply do not fit within the taxonomy of Rule 801(d)(2)(E), the district court did not clearly err in allowing them into evidence over such an objection.

5. Recapitulation. The short of it is that the defendant’s objections to the admission of coconspirator statements are unavailing. Collectively, those objections take too crabbed a view of the relevant conspiracy, joust with harmlessly admitted evidence, and tilt with windmills by addressing statements that do not meet the definition of hearsay. When all is said and done, the objections afford no basis for tampering with the jury’s verdict.

B. Probative Value/Prejudicial Effect.

The next cluster of contested evidentiary rulings relates to the district court’s admission of dozens of terrorism-related pictures, videos, and printed materials. This evidence, the defendant insists, vastly exceeded what was necessary to prove the government’s case, inflamed the jury, and contaminated the verdict.

Federal Rule of Evidence 403 governs this challenge. That rule permits a court to “exclude relevant evidence if its probative value is substantially outweighed by a danger of’ certain pitfalls, including “unfair prejudice” or “needlessly presenting cumulative evidence.” Fed.R.Evid. 403. Within this rubric, the term “unfair prejudice” denotes “an undue tendency to suggest decision on an improper - basis, commonly, though not necessarily, an emotional one.” Old Chief v. United States, 519 U.S. 172, 180, 117 S.Ct. 644, 136 L.Ed.2d 574 (1997) (internal quotation marks omitted).

The role of an appellate court in conducting the triage that Rule 403 contemplates is narrowly circumscribed. “With respect to evidentiary questions in general and Rule 403 in particular, a district court virtually always is in the better position to assess the admissibility of the evidence in the context of the particular case before it.” Sprint/United Mgmt. Co. v. Mendelsohn, 552 U.S. 379, 387, 128 S.Ct. 1140, 170 L.Ed.2d 1 (2008). As a natural corollary of the district court’s superior coign of vantage, that court’s striking of the Rule 403 balance between probative value and prejudicial effect should, not be disturbed unless an abuse of discretion looms. See id. at 384, 128 S.Ct. 1140. In undertaking such review, we afford the district court “especially wide latitude.” United States v. Candelaria-Silva, 162 F.3d 698, 705 (1st Cir.1998) (internal quotation marks omitted). “Only rarely — and in extraordinarily compelling circumstances — will we, from the vista of a cold appellate record, reverse a district court’s on-the-spot judgment concerning the relative weighing of probative value and unfair effect.” Pires, 642 F.3d at 12 (quoting Freeman v. Package Mach. Co., 865 F.2d 1331, 1340 (1st Cir.1988)).

With this deferential standard in mind, we turn to the defendant’s contention that terrorist media admitted at trial incited the jury to irrational decisionmaking. We begin with a frank acknowledgment that the collection of terrorist-related media introduced into evidence was extensive. According to the defendant, the “most disturbing” items referenced beheadings. For example, one witness testified about portions of a video in which Abu Musab al-Zarqawi extolled the decapitation of American businessman Nicholas Berg while images of deceased American soldiers were displayed on screen. Other testimony indicated that the defendant circulated a video depicting the beheading of Wall Street Journal reporter Daniel Pearl.

Of course, the defendant’s Rule 403 challenge goes well beyond evidence of be-headings. He also assails the government’s introduction of more than thirty propaganda video clips, such as al-Qa’ida’s State of the Ummah; statements of Osama bin Laden and Ayman al-Zawahiri in book and interview form; and dozens of images portraying gripping scenes, such as the World Trade Center engulfed in flames and al-Qa’ida leaders exhorting their followers.

The defendant remonstrates that any appropriate use of these materials was overwhelmed by the prejudice inherent in them. This remonstrance lies at the heart of the defendant’s claim of error. We test its soundness.

In this instance, the first half of the probative value/prejudicial effect dichotomy is easily satisfied. Evidence is relevant if it tends to make a material fact more or less likely. See Fed.R.Evid. 401. The persuasiveness of the evidence with respect to such a fact is an appropriate proxy for its probative force. See United States v. Lachman, 48 F.3d 586, 591 (1st Cir.1995).

The government proffered all of the disputed evidence on the theory that the defendant either saw or read it and shaped his worldview accordingly. The evidence was relevant, the government says, for two reasons.

The first reason (stressed by the government at oral argument) is breathtaking in its scope: the government labeled the defendant’s crimes “ideological” and argued that, as a result, his speech and beliefs, as well as the writings and videos that he consumed were integral to the charged crimes. We do not accept this sweeping proposition.

Courts must be wary of the particular perils associated with prosecutions centered on ideology (which include, to use the government’s phrase, prosecutions centered on “propaganda”). An objective observer might well regard the sprawling taxonomy suggested by the government as a thinly disguised effort to saddle defendants indiscriminately with the criminal and cultural baggage of internationally notorious terrorists. The government’s embrace of such a theory smacks of overreaching, and we give that theory no weight.

We have much less difficulty with the government’s second (more traditional) reason for urging a finding of relevance. The government argues convincingly that the defendant’s motive and intent are material facts and that the disputed media have probative value with respect to those facts. Specifically, the government posits that the defendant, inspired by terrorist rants, developed an anti-American animus, which culminated in his decision to travel to Yemen to join in al-Qa’ida’s struggle. The pictures, videos, and literature that he absorbed and endorsed during that evolutionary process, as well as the materials that he used to recruit others to follow a similar path, doubtless bear on his motive and intent. See, e.g., United States v. El-Mezain, 664 F.3d 467, 509-10 (5th Cir.2011) (holding that material seized from the defendant, “including images of violence and videos glorifying Hamas and depicting Hamas leaders, was probative of the motive or intent of the [defendant] to support Hamas”), cert. denied, — U.S. -, 133 S.Ct. 525, 184 L.Ed.2d 338 (2012); United States v. Jayyousi, 657 F.3d 1085, 1108 (11th Cir.2011) (holding that televised interview with Osama bin Laden was properly admitted as “state of mind evidence”); United States v. Abu-Jihaad, 630 F.3d 102, 133-34 (2d Cir.2010) (affirming conclusion that “pro-jihadist contents of the videos were relevant to understanding [the defendant’s] motive and intent”). While no picture, .video, book, or tract spoke directly to the defendant’s purpose in going to Yemen, evidence need not achieve the conspicuousness of a smoking gun in order to have probative value.

Probative value, however, is only one pan of the scale. For Rule 403 purposes, that value must be juxtaposed with prejudicial effect (or, more precisely, with unfairly prejudicial effect). The juxtaposition in this case, the defendant suggests, indicates that the probative value of the evidence is substantially overbalanced.

To prove his point, the defendant argues long and loud that the situation here reprises the situation in United States v. Al-Moayad, 545 F.3d 139 (2d Cir.2008). The defendants there were convicted of, among other things, conspiring and attempting to provide material support to Hamas. Id. at 145. On appeal, they complained about the admission of the testimony of Gideon Black, who gave a graphic, first-hand account concerning a suicide bombing aboard a bus in Tel Aviv. Id. at 152-53. They likewise complained about the testimony of Yahya Goba, who told the jury about an al-Qa’ida training camp that he attended,, recounting Osama bin Laden’s visit there and commenting on a video documenting that visit. Id. at 156-57.

The Second Circuit concluded that this testimony had been improvidently admitted. In reaching this conclusion, the court found the probative value of Black’s testimony infinitesimal: although the government offered the testimony to establish the defendants’ knowledge of Hamas’s violent activities, the “bombing was almost entirely, unrelated to the elements of the charges,” id. at 161, and in all events the defendants had offered to stipulate unqual-ifiedly to their knowledge that Hamas engaged in violent activities, id. at 160-61. Thus, Black’s “extended account of the tragedy could not reasonably be considered part of’ the government’s narrative. Id. at 161.,.

The court offered much the same critique with respect to Goba. A “mujahidin form” required for entry into al-Qa’ida camps mentioned one defendant, and the ostensible purpose of Goba’s testimony was to explain that form’s significance. Id. at 156. Despite the tenuous nature of this link to the case, the district court “never appear[ed] to have assessed the probative value” of the testimony. Id. at 163. Without some “assurance that the court conscientiously balanced the probative value of the testimony against its prejudicial effect,” the “highly inflammatory and irrelevant” testimony and accompanying bin Laden video should have been excluded. Id.

It is hen’s-teeth rare that two cases involving different parties, different facts, and different scenarios will be of much assistance through a comparative analysis of Rule 403. determinations. These determinations are case-specific and it is readily apparent that Al-Moayad and the case at hand are not fair congeners. Although the defendant’s counsel in this case stated at one point that he could “virtually stipulate to the defendant’s state of mind,” no actual stipulation was ever proffered or made.

Perhaps more important, the evidence of which the defendant complains was (unlike the evidence challenged in Alr-Moayad) central to the government’s narrative: the government’s case depended on proving that the defendant’s actions emanated from views that, over time, had aligned with al-Qa’ida’s. The media that he consumed en route to forming those views 'is a salient part of the story.

Moreover, that part of the story was fiercely contested. Although the defendant indicated a willingness to admit that he admired al-Qa’ida’s ideals, he steadfastly disassociated himself from any anti-American actions involving violence. As he put it, his beliefs “would prevent [him] from attacking fellow Americans within the United States or outside of it.” In the same vein, his counsel cast Yemen as nothing more than a “free trip” for the defendant to “do what he wanted to do” — seek out a scholarly community. The challenged evidence helped to tell a different tale — and it tended to make the defendant’s account less believable.

We summarize succinctly. On the pivotal issue of his state of mind with respect to his Yemen trip, the defendant refused to yield an inch. His objections below largely overlooked (or, at least, implausibly discounted) the potential value of the challenged evidence in undercutting his insistence that his motive in going to Yemen was benign. Al-Moayad is, therefore, distinguishable. See El-Mezain, 664 F.3d at 511 (distinguishing Al-Moayad “because evidence of Hamas violence found on the premises of [the defendant] tended to rebut the defendants’ denial that they supported Hamas”).

Even apart from Al-Moayad, the defendant mounts an all-out attack on the Rule 403 balancing performed by the court below. Despite the deferential standard of review, we do not suggest that such decisions are by any means insulated from effective- appellate oversight. Indeed, we have demonstrated our willingness to reverse such rulings when the interests of justice so require. We did so, for instance, in a case in which “there Were no findings on prejudice and probativeness, and a ‘hair-trigger’ decision was made.” Rubert-Torres v. Hosp. San Pablo, Inc., 205 F.3d 472, 479 (1st Cir.2000).

Here, however, the record is replete with manifestations of the district court’s conscientious Rule 403 evaluations. There would be little point in cataloguing each and every illustration of the court’s careful stewardship. One concrete example should suffice.

At oral argument, the defendant emphasized the prejudicial impact of the “Texas BBQ” video — so called because the defendant used that phrase to refer to the remains of American soldiers shown in the video. When the defendant objected to this evidence, the district court entertained arguments on both the importance of the evidence to the government and its potential to inflame the jury. After fully considering these arguments, the court found that the video would be “very probative” in rebutting the defendant’s mantra that his moderate beliefs prevented him from attacking Americans. Relatedly, the court determined that describing the more gruesome elements through witness testimony, rather than publishing the video to the jury, would go “a great distance to minimizing unfair prejudice” and would render the video “significantly less inflammatory.” Such painstaking consideration of a Rule 403 objection hardly can be deemed arbitrary, and the.defendant directs us to no other portion of the record indicating that the district court engaged in anything approaching the thoughtless discarding of Rule 403 issues.

The defendant’s most powerful argument under Rule 403 is fueled by the sheer mass of the circumstantial evidence introduced by the government to show motive and intent. Dozens of terrorist videos, writings, and images are in play here. This raises the specter, skillfully evoked by the defendant and some of the amici, that the cumulative effect of the evidence caused unfair prejudice.

The district court addressed this cumu-lativeness concern on several occasions. We offer two representative vignettes.

On the 10th day of trial, the court noted' its concern “that at some point the evidence becomes so cumulative that unfair prejudice outweighs probative value.” The court found, however, that “we’re not at that point.” On the 25th day of trial, the court overruled an objection that the government’s evidence was so cumulative as to be unfairly prejudicial. The court observed that the very volume of terrorism evidence viewed by the defendant “might have some probative value as to [his] ob: sessiveness” with the subject.

There is a line past which the government’s introduction of relevant evidence for the legitimate advancement of its case goes too far. When that line is crossed, fair play morphs into piling on. But that line is hard to draw, and there is no mathematically precise way in which to plot it.

When we pressed the parties at oral argument as to when and where the district court should have drawn the line, neither side gave us any serviceable guide for determining which particular video, image, or book was the straw that broke the camel’s back. Rather, the parties resorted to generalities.

The parties’ inability to plot a well-defined line is understandable. The point at which relevant and admissible evidence lapses into relevant but cumulative (and therefore inadmissible) evidence is murky. Moreover, it is different in every case. A court simply cannot say with any degree of assurance that thirteen images of Osama bin Laden may safely be admitted, but that the fourteenth image ought to be excluded.

In the last analysis, the lack of a scientifically accurate measuring device reinforces both the importance of the trial judge’s role and the wisdom of affording substantial deference to his balancing decision. In this case, we think it is plain that the question of whether the quantum of evidence introduced by the government crossed the indistinct boundary that separates the permissible from the impermissible is fairly debatable. The district court gave this fairly debatable question careful attention, and we are reluctant to second-guess its judgment. After all, “the very closeness of the question favors the district court’s reconciliation of the competing centrifugal and centripetal forces” that attend the striking of the delicate balance that Rule 403 demands. Pires, 642 F.3d at 12. We hold, therefore, that the district court’s rejection of the defendant’s cumulativeness objections, though not inevitable, was not an abuse of discretion.

Let us be perfectly clear. We are mindful that terrorism-related evidence is often emotionally charged. Courts, with good reason, have on occasion termed such evidence “alarming,” United States v. Benkahla, 530 F.3d 300, 310 (4th Cir.2008), “disturbing,” Salameh, 152 F.3d at 122, and even “blood curdling,” United States v. Mubayyid, 658 F.3d 35, 56 (1st Cir.2011). But much of this emotional overlay is directly related to the nature of the crimes that the defendant has set out to commit. It should not surprise a defendant that proof of his participation in conspiracies to provide material support to terrorist organizations and to kill Americans here and abroad will engender the presentation of evidence offensive to the sensibilities of civilized people. See El-Mezain, 664 F.3d at 511. Terrorism trials are not to be confused with high tea at Buckingham Palace.

The Fifth Circuit wisely observed, in analogous circumstances, that in a terrorism case, “it is inescapable ... that there would be some evidence about violence and terrorist activity.” Id. So it is here.

This brings us to the ultimate question that underlies a claim of error based on Rule 403: whether the district court abused its discretion in holding that the probative worth of the challenged evidence was not substantially outweighed by its prejudicial impact. We think that this question must be answered favorably to the district court.

The government’s evidence plainly packed an emotional punch, but Rule 403 does not ensure that trials — even criminal trials — will be antiseptic affairs. Litigants invariably introduce particular evidence as part of an effort to sway jurors to their point of view. In that sense, “all evidence is meant to be prejudicial.” United States v. Rodriguez-Estrada, 877 F.2d 153, 156 (1st Cir.1989). Rule 403 was never designed to alter that reality. “[I]t is only unfair prejudice which must be avoided.” Id. (emphasis in original).

We cannot say that the district court’s Rule 403 determinations offended this principle. For the most part, the evidence of which the defendant complains served to discredit his claim that his purpose in Yemen was innocuous. This is significant because “[e]vidence which tends to rebut a defendant’s claim of innocent action is unlikely to be unduly prejudicial.” El-Mezain, 664 F.3d at 509. The court below carefully superintended the ebb and flow of the evidence, displayed a high degree of sensitivity in regard to Rule 403 concerns, took pains to minimize the impact of potentially inflammatory bits of evidence, and gave the jury suitably prophylactic instructions. There is no reason to believe, on this record, that the verdict was the result of passion or prejudice.

C. Thumbnails.

The defendant has an additional shot in his sling. He objects here, as he did below, to the admission of “thumbnail” images retrieved from his computer. In support, he argues that such images can exist on a person’s computer without the person’s involvement or knowledge.

The defendant couches this argument in the idiom of Rule 403 — but this may not be a Rule 403 objection at all. Instead, it may properly be viewed either as an objection to the relevance of the evidence, see Fed.R.Evid. 401, or as an objection to the lack of a proper foundation, see Fed. R.Evid. 901.

In the end, it does not matter how we characterize this objection. Regardless, the objection goes to the weight of the evidence, not to its admissibility. One logical inference from the discovery of the thumbnails is that the defendant viewed and approved of such images. See El-Mezain, 664 F.3d at 510. The government was free to argue in favor of this inference, and the defendant was free to argue otherwise. Jurors are not so naive that they must be shielded from choosing among reasonable but competing inferences extractable from proven facts.

To say more would be pointless. The objection to the introduction of the thumbnails was appropriately overruled.

D. Failure to Disclose.

The next disputed evidentiary ruling is of a different genre. In a criminal case, the Fifth Amendment imposes certain disclosure obligations on the government. These disclosure obligations were most famously articulated in the Supreme Court’s watershed decision in Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963).

The Brady Court held that “the suppression by the prosecution of evidence favorable to an accused upon request violates due process.” Id. at 87, 83 S.Ct. 1194. This “no-fault disclosure obligation,” Haley v. City of Boston, 657 F.3d 39, 48 (1st Cir.2011), applies “irrespective of the good faith or bad faith of the prosecution,” Brady, 373 U.S. at 87, 83 S.Ct. 1194.

It is important to remember that in Brady, the Court “wielded a scalpel, not a meat-axe.” Haley, 657 F.3d at 48. “The Justices made it transparently clear that the newly announced no-fault disclosure obligation does not cover all evidence but, rather, only ‘evidence [that] is material either to guilt or to punishment.’ ” Id. (alteration in original) (quoting Brady, 373 U.S. at 87, 83 S.Ct. 1194). This taxonomy includes any evidence that fairly tends to negate guilt, mitigate punishment, or undermine the credibility of government witnesses, including evidence known only to police investigators and not to the prosecutor. See Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). Reversal is warranted if the government improperly withholds Brady material and prejudice results. See id.

The defendant in this case essays a Brady claim. He alleges that defense counsel received a tip that his client had refused a solicitation, relayed through either an undercover agent or a cooperating informant, to engage in criminal acts. He moved to compel production of this evidence. The government responded with a representation that it possessed no such evidence.

The district court held a hearing on this motion. Following the hearing, the court reviewed in camera an ex parte proffer by the government. It then denied the defendant’s motion. It is to this ruling that the defendant takes exception.

The defendant’s position can be stated without much ceremony. He suggests that evidence of his refusal to commit a crime would have reinforced a central theme of the defense: that- although he may have sympathized with al-Qa’ida and spoken glowingly of the virtues of jihad, he nonetheless avoided crossing the line into criminal activity. The defendant further suggests that such evidence would have impeached Abuzahra’s testimony that the defendant was ready and willing to commit terrorist acts.

We have inspected the government’s in camera submission. Due to the confidential nature of this submission, we think it prudent to refrain from any detailed description. For present purposes, it suffices to say that both the content and the timing of the contact disclosed in the government’s in camera submission militate against a finding that the conversation in question constituted Brady material. First, the transcript of that conversation does not show any solicitation of the defendant’s participation in further terrorist acts. Second, given the timing of the contact, even a rebuffed solicitation would have had no real probative value.

We review a district court’s decision that particular evidence does not constitute Brady material for abuse of discretion. See United States v. DeCologero, 530 F.3d 36, 65 (1st Cir.2008).

Because the material withheld by the government was tangential to the issues in the case, we find no abuse of discretion in the district court’s judgment that the material was not “discoverable.”

E. Expert Witnesses.

The last group of contested evidentiary rulings deals with expert witnesses. The defendant sought to present no fewer than eight experts at trial. The district court allowed six of these experts to testify, but excluded the remaining two. The defendant complains about the dual exclusion. We review orders excluding expert witnesses for abuse of discretion. See Kumho Tire Co. v. Carmichael, 526 U.S. 137, 141-42, 119 S.Ct. 1167, 143 L.Ed.2d 238 (1999); United States v. Hoffman, 832 F.2d 1299, 1310 (1st Cir.1987).

The first excluded expert was Dr. Steven Durlauf. The defendant sought to have him present mathematical formulae for the purpose of undermining the opinion of one of the government’s experts, Evan Kohlmann, with respect to the latter’s method of defining who was an al-Qa’ida adherent. The district court rejected this proffered testimony on the primary ground that Kohlmann never claimed that his conclusions comported with, or were based upon, scientific standards. We discern no abuse of discretion.

Under Federal Rule of Evidence 702, a district court pondering whether to admit expert testimony must determine, among other things, whether the proffered testimony is tied closely enough to the facts to “assist the trier of fact.” Daubert v. Merrell Dow Pharm., Inc., 509 U.S. 579, 591-93, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993); see United States v. Shay, 57 F.3d 126, 132-33 (1st Cir.1995). To forge this link, there must be “a valid connection ... between the expert’s testimony and a disputed issue.” Shay, 57 F.3d at 133 n. 5.

Viewed against this backdrop, the district court had a plausible basis for rejecting Dr. Durlaufs testimony. There was simply no “fit” between what Kohlmann described as the basis for his opinion and the criticism of that opinion that Dr. Durlauf proposed to make. Admitting Dr. Durlaufs testimony would, therefore, have been akin to inserting a square peg into a round hole.

The second excluded expert witness was Dr. Brian Glyn Williams. The defendant tendered this witness in a professed effort to rebut Kohlmann’s testimony about both the efficacy of jihadi videos in generating recruits for al-Qa’ida and the purpose behind the production of those videos. The district court determined that this testimony would not be helpful to the jury. This ruling, too, was within the compass of the district court’s discretion.

It is common ground that a trial court may bar expert testimony if that testimony will not assist the jury to sort out contested issues. See Fed.R.Evid. 702; see also Daubert, 509 U.S. at 592-93, 113 S.Ct. 2786; United States v. Tetioukhine, 725 F.3d 1, 6-8 (1st Cir.2013). In this case, whether the jihadi videos discussed by Kohlmann were effective as a recruiting tool was a nón-issue. Rather, the relevant issue was whether the defendant intended to provide material support by helping al-Qa’ida to produce the videos. See, e.g., Al Kassar, 660 F.3d at 129; Jayyousi, 657 F.3d at 1105. Even if the videos were not an effective recruiting tool, this lack of efficacy would not dissipate the defendant’s criminal intent. Seen in this light, Dr. Williams’s proffered testimony had no bearing on the relevant issue and perforce would not have helped the jury to resolve it.

Much the same can be said about Dr. Williams’s proffered testimony about al-Qa’ida’s purpose in making the videos. Within the margins of this prosecution, it was immaterial whether al-Qa’ida’s purpose was for recruiting (as Kohlmann indicated) or to boost morale (as Dr. Williams would have testified). Either way, the videos would constitute material support. Paving' the way for the jury to choose between the witnesses’ competing assessments of al-Qa’ida’s aims would, therefore, have been an empty exercise. See, e.g., United States v. Maxwell, 254 F.3d 21, 25-26 (1st Cir.2001).

We add a coda. The proffered testimony of Drs. Durlauf and Williams was cumulative. One of the expert witnesses who was allowed to testify on the defendant’s behalf, Dr. Marc Sageman, made essentially the same points that the defendant sought to pursue through the two excluded experts. The cumulative nature of the excluded testimony, in itself, adequately underpinned the district court’s exclusionary rulings. See Bobby v. Van Hook, 558 U.S. 4, 12, 130 S.Ct. 13, 175 L.Ed.2d 255 (2009) (per curiam); LaPlace-Bayard v. Battle, 295 F.3d 157, 163-64 (1st Cir.2002).

V. THE SENTENCE

We have one more stop before we reach our final destination. The probation office prepared the presentence report based on the 2011 version of the federal sentencing guidelines, and the district court embraced that premise. The defendant asserts that the court should have used the November 2003 version of the guidelines because the relevant criminal activity was the Yemen trip (which occurred early in 2004).

This bevue is material, the defendant says, because of a key difference between the two editions of the guidelines. That difference came about when the Sentencing Commission amended the guidelines in November of 2004. See USSG § 2A1.5(a) (Nov.2004). The amendment, which remained in place through ensuing editions of the guidelines (up to and including the November 2011 edition), had the effect of boosting the defendant’s base offense level (BOL) by five levels for one of the linchpin counts of conviction. Compare id. § 2A1.5(a) (Nov.2003), with id. § 2A1.5(a) (Nov.2011).

As a general rule, a sentencing court should use the version of the guidelines in effect at the time of the disposition hearing. See United States v. Harotuni- an, 920 F.2d 1040, 1041-42 (lst Cir.1990). But this rule, like every other general rule, admits of exceptions. One such exception obtains when the Ex Post Facto Clause, U.S. Const, art. I, § 9, cl. 3, is implicated. The application of a particular version of the guidelines raises ex post facto concerns if that version increases the level of punishment for a crime above that in place when the crime was committed. See Peugh v. United States, — U.S. -, 133 S.Ct. 2072, 2078, 186 L.Ed.2d 84 (2013).

The district court sentenced the defendant in 2012. Thus, in the absence of ex post facto implications, the then-current edition of the sentencing guidelines (published in November 2011) was the appropriate reference point. See Harotunian, 920 F.2d at 1041-42.

The defendant counters that his culpable activity was complete before the guidelines were amended in 2004. To avoid ex post facto concerns, therefore, the court should have employed the earlier, less draconian, version of the guidelines, promulgated in November 2003. To the extent that this assignment of error poses a question of law, it engenders de novo review. See United States v. Goergen, 683 F.3d 1, 3 (1st Cir.2012); United States v. LaCroix, 28 F.3d 223, 226 (1st Cir.1994). To the extent, however, that it hinges on the sentencing court’s factfinding, it can be disturbed only if that factfinding is shown to be clearly erroneous. See United States v. David, 940 F.2d 722, 739 (1st Cir.1991).

We acknowledge that the defendant’s premise is largely correct: if all of the culpable criminal activity were completed before the relevant guidelines were made more stringent, then the district court would in all probability have had to apply the earlier version of the guidelines. See, e.g., United States v. Bennett, 37 F.3d 687, 698-700 (1st Cir.1994); Harotunian, 920 F.2d at 1042. But the conclusion that the defendant draws from this premise is wrong. The sentencing court determined as a matter of fact, at least impliedly, that the charged conspiracies continued well into 2006. The court similarly determined that the defendant’s culpable conduct continued for that same period of time. These determinations are not clearly erroneous; indeed, they are consistent with the heavy weight of the evidence adduced at trial. See supra Part 11(A).

Seen in this light, the defendant’s assignment of sentencing error falters. Because his culpable criminal activity continued past the point when the November 2004 amendment to the guidelines went into effect, the district court did not err in using the current version of the guidelines. “[T]he guidelines apply to a defendant whose offense begins before the guidelines’ effective date and continues after the effective date.” David, 940 F.2d at 739. When a defendant participates in a conspiracy and the duration of that conspiracy extends past the effective date of a change in the guidelines, the new version of the guidelines ordinarily applies to the whole of the defendant’s culpable conduct. See United States v. Aviles, 518 F.3d 1228, 1230-31 (11th Cir.2008); United States v. Zimmer, 299 F.3d 710, 717-18 (8th Cir.2002); United States v. Regan, 989 F.2d 44, 48 (1st Cir.1993). In such a scenario, no ex post facto concerns are present.

That ends this aspect of the matter. We hold that the district court appropriately referred to the version of the guidelines then in effect — the 2011 version — when sentencing the defendant.

VI. CONCLUSION

Cases like this one present a formidable challenge to the parties and to the trial court: the charged crimes are heinous, the evidentiary record is vast, the legal issues are sophisticated, and the nature of the charges ensures that any trial will be electric. In this instance, all concerned rose to meet this formidable challenge. The lawyers on both sides performed admirably, and the able district judge presided over the case with care, skill, and circumspection. After a painstaking appraisal of the record, the briefs, and the relevant case law, we are confident — for the reasons elucidated above — that the defendant was fairly tried, justly convicted, and lawfully sentenced.

We do not pretend to understand why the defendant chose to go down such a treacherous path. Nevertheless, the jury found that he knowingly and intentionally made that choice, and that finding is both supported by the clear weight of the evidence and untainted by legal error. We need go no further.

Affirmed.

Appendix

18 U.S.C. § 371. Conspiracy to commit offense or to defraud United States

If two or more persons conspire either to commit any offense against the United States, or to defraud the United States, or any agency thereof in any manner or for any purpose, and one or more of such persons do any act to effect the object of the conspiracy, each shall be fined under this title or imprisoned not more than five years, or both.

If, however, the offense, the commission of which is the object of the conspiracy, is a misdemeanor only, the punishment for such conspiracy shall not exceed the maximum punishment provided for such misdemeanor.

18 U.S.C. § 956. Conspiracy to kill, kidnap, maim, or injure persons or damage property in a foreign country

(a) (1) Whoever, within the jurisdiction of the United States, conspires with one or more other persons, regardless of where such other person or persons are located, to commit at any place outside the United States an act that would constitute the offense of murder, kidnapping, or maiming if committed in the special maritime and territorial jurisdiction of the United States shall, if any of the conspirators commits an act ' within the jurisdiction of the United States to effect any object of the conspiracy, be punished as provided in subsection (a)(2).

(b) Whoever, within the jurisdiction of the United States, conspires with one or more persons, regardless of where such other person or persons are located, to damage or destroy specific property situated within a foreign country and belonging to a foreign government or to any political subdivision thereof with which the United States is at peace, or any railroad, canal, bridge, airport, airfield, or other public utility, public conveyance, or public structure, or any religious, educational, or cultural property so situated, shall, if any of the conspirators commits an act within the jurisdiction of the United States to effect any object of the conspiracy, be imprisoned not more than 25 years.

18 U.S.C. § 1001. Statements or entries generally

(a) Except as otherwise provided in this section, whoever, in any matter within the jurisdiction of the executive, legislative, or judicial branch of the Government of the United States, knowingly and willfully—

(1) falsifies, conceals, or covers up by any trick, scheme, or device a material fact;
(2) makes any materially false, fictitious, or fraudulent statement or representation; or
(3) makes or uses any false writing or document knowing the same to contain any materially false, fictitious, or fraudulent statement or entry;

shall be fined under this title, imprisoned not more than 5 years or, if the offense involves international or domestic terrorism. (as defined in section 2331), imprisoned not more than 8 years, or both. If the matter relates to an offense under chapter 109A, 109B, 110, or 117, or section 1591, then the term of imprisonment imposed under this section shall be not more than 8 years.

18 U.S.C. § 2332. Criminal penalties

(a) Homicide. — Whoever kills a national of the United States, while such national is outside the United States, shall—

(1) if the killing is murder (as defined in section 1111(a)), be fined under this title, punished by death or imprisonment for any term of years or for life, or both;
(2) if the killing is a voluntary manslaughter as defined in section 1112(a) of this title, be fined under this title or imprisoned not more than ten years, or both; and
(3) if the killing is an involuntary manslaughter as defined in section 1112(a) of this title, be fined under this title or imprisoned not more than three years, or both.

(b) Attempt or conspiracy with respect to homicide. — Whoever outside the United States attempts to kill, or engages in a conspiracy to kill, a national of the United States shall—

(1) in the case of an attempt to commit a killing that is a murder as defined in this chapter, be fined under this title or imprisoned not more than 20 years, or both; and
(2) in the case of a conspiracy by two or more persons to commit a killing that is a murder as defined in section 1111(a) of this title, if one or more of such persons do any overt act to effect the object of the conspiracy, be fined under this title or imprisoned for any term of years or for life, or both so fined and so imprisoned.

(d) Limitation on prosecution. — No prosecution for any offense described in this section shall be undertaken by the United States except on written certification of the Attorney General or the highest ranking subordinate of the Attorney General with responsibility for criminal prosecutions that, in the judgment of the certifying official, such offense was intended to coerce, intimidate, or retaliate against a government or a civilian population.

18 U.S.C. § 2339A. Providing material support to terrorists

(a) Offense. — Whoever provides material support or resources or conceals or disguises the nature, location, source, or ownership of material support or resources, knowing or intending that they are to be used in preparation for, or in carrying out, a violation of section 32, 37, 81, 175, 229, 351, 831, 842(m) or (n), 844(f) or (i), 930(c), 956, 1091, 1114, 1116, 1203, 1361, 1362, 1363, 1366, 1751, 1992, 2155, 2156, 2280, 2281, 2332, 2332a, 2332b, 2332f, 2840A, or 2442 of this title, section 236 of the Atomic Energy Act of 1954 (42 U.S.C. 2284), section 46502 or 60123(b) of title 49, or any offense listed in section 2332b(g)(5)(B) (except for sections 2339A and 2339B) or in preparation for, or in carrying out, the concealment of an escape from the commission of any such violation, or attempts or conspires to do such an act, shall be fined under this title, imprisoned not more than 15 years, or both, and, if the death of any person results, shall be imprisoned for any term of years or for life. A violation of this section may be prosecuted in any Federal judicial district in which the underlying offense was committed, or in any other Federal judicial district as provided by law.

(b) Definitions.- — -As used in this section—

(1) the term “material support or resources” means any property, tangible or intangible, or service, including currency or monetary instruments or financial securities, financial services, lodging, training, expert advice or assistance, safehouses, false documentation or identification, communications equipment, facilities, weapons, lethal substances, explosives, personnel (1 or more individuals who may be or include oneself), and transportation, except medicine or religious materials;
(2) the term “training” means instruction or teaching designed to impart a specific skill, as opposed to general knowledge; and
(3) the term “expert advice or assistance” means advice or assistance derived from scientific, technical or other specialized knowledge.

18 U.S.C. § 2339B. Providing material support or resources to designated foreign terrorist organizations

(a) Prohibited activities.—

(1) Unlawful conduct. — Whoever knowingly provides material support or resources to a foreign terrorist organization, or attempts or conspires to do so, shall be fined under this title or imprisoned not more than 15 years, or both, and, if the death of any person results, shall be imprisoned for any term of years or for life. To violate this paragraph, ' a person must have knowledge that, the organization is a designated terrorist organization (as defined in subsection (g)(6)), that the organization has engaged or engages in terrorist activity (as defined in section 212(a)(3)(B) of the Immigration and Nationality Act), or that the organization has engaged or engages in terrorism (as defined in section 140(d)(2)) of the Foreign Relations Authorization Act, Fiscal Years 1988 and 1989

(g) Definitions.- — As used in this section—

(4)the term “material support or resources” has the same meaning given that term in section 2339A (including the definitions of “training” and “expert advice or assistance” in that section);
(6) the term “terrorist organization” means an organization designated as a terrorist organization under section 219 of the Immigration and Nationality Act.

(h) Provision of personnel. — No person may be prosecuted under this section in connection with the term “personnel” unless that person has knowingly provided, attempted to provide, or conspired to provide a foreign terrorist organization with 1 or more individuals (who may be-or include himself) to work under that terrorist organization’s direction or control or to organize, manage, supervise, or otherwise direct the operation of that organization. Individuals who act entirely independently of the foreign terrorist organization to advance its goals or objectives shall not be considered to be working under the foreign terrorist organization’s direction and control.

(i) Rule of construction. — Nothing in this section shall be construed or applied so as to abridge the exercise of rights guaranteed under the First Amendment to the Constitution of the United States.

(j) Exception. — No person may be prosecuted under this section in connection with the term “personnel”, “training”, or “expert advice or assistance” if the provision of that material support or resources to a foreign terrorist organization was approved by the Secretary of State with the concurrence of the Attorney General. The Secretary of State may not approve the provision of any material support that may be used to carry out terrorist activity (as defined in section 212(a)(3)(B)(iii) of the Immigration and Nationality Act). 
      
      . This cluster of activities also comprises the foundation for count 4.
     
      
      . Abousamra was charged as a defendant in this case but absconded in December of 2006. For aught that appears, he remains a fugitive.
     
      
      .While “jihad'' is a linguistically protean term that may encompass both violent and nonviolent acts, the record makes clear that the defendant used the term to refer to violent jihad — and that is the meaning that we ascribe to it throughout this opinion.
     
      
      . At the time of trial, Maldonado was serving a ten-year sentence pursuant to his guilty plea for receiving military-type training from an FTO. See 18 U.S.C. § 2339D(a).
     
      
      . The defendant makes a fleeting argument that the district court's "coordination” instruction was directed only to count 1 and that the district court failed to instruct on the coordination element with regard to counts 2 and 3. This argument is disingenuous: it is nose-on-the-face plain that the district court incorporated its "coordination” instruction by reference into its instructions on counts 2 and 3. No more was exigible.
     
      
      . Citing strong circumstantial evidence that the jury rested these convictions on the Yemen trip — for example, the conviction on count 4 was necessarily predicated on the Yemen trip (not the translations), making it highly likely that the convictions on counts 1, 2, and 3 shared the same provenance — the government argues strenuously that any instructional error would have been harmless. See Hedgpeth v. Pulido, 555 U.S. 57, 58, 129 S.Ct. 530, 172 L.Ed.2d 388 (2008) (per curiam) (holding that constitutionally or legally defective jury instruction becomes reversible error only if it "had substantial and injurious effect or influence in determining the jury's verdict” (quoting Brecht v. Abrahamson, 507 U.S. 619, 623, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993))). Inasmuch as we discern no instructional error, we do not reach this argument.
     
      
      . Of course, it is possible that this evidence, even if harmless as to guilt, might have been so incendiary as to offend Federal Rule of Evidence 403. We consider this possibility infra.
      
     
      
      . While this evidence was terrifying, we think that the district court’s handling of it was emblematic of the court's measured approach: the court allowed descriptive testimony but did not permit the video itself to be shown to the jury.
     
      
      . We do not mean to imply that a stipulation would necessarily have dictated the result of a Rule 403 analysis. To .the contrary, "the prosecutor’s choice [not to accept a defendant's stipulation] will generally survive a Rule 403 analysis when a defendant seeks to force the substitution of an admission for evidence creating a coherent narrative of his thoughts and actions in perpetrating the offense for which he is being tried.’’ United States v. Balsam, 203 F.3d 72, 84 (1st Cir.2000) (alteration in original) (quoting Old Chief, 519 U.S. at 192, 117 S.Ct. 644); see United States v. Hammoud, 381 F.3d 316, 342 n. 12 (4th Cir.2004) (en banc) (explaining that where proffered stipulation "would not relieve the Government of the burden of demonstrating that [the defendant] knew that Hiz-ballah engaged in terrorist activity,” it did not have to be accepted), vacated on other grounds, 543 U.S. 1097, 125 S.Ct. 1051, 160 L.Ed.2d 997 (2005).
     
      
      . As an alternative ground for exclusion, the district court pointed out that the defendant had not given the government proper notice of the substance of Dr. Durlauf's proposed testimony. See Fed.R.Crim.P. 16(b)(1)(C). There is no need for us to address this alternative ground.
     
      
      . The seven counts of conviction were grouped for sentencing purposes. See USSG § 3D 1.2. The amendment in question affected count 2, which was one of the counts that had the highest BOL and, thus, figured prominently in the overall sentencing calculus.
     
      
      . We hedge this statement because, as an alternative ground in support of the sentencing court’s use of the 2011 version of the guidelines, the government asks us to apply the so-called “one book” rule. See USSG § 1B1.11(b)(2); Goergen, 683 F.3d at 3. Inasmuch as we conclude that the charged conspiracies extended beyond the effective date of the 2004 amendment, we do not reach this issue.
     