In the months following the 2020 presidential election, Defendant-Appellant Brendan Hunt threatened prominent elected officials in several posts on various social media platforms. In one of those posts, a video published on the website BitChute, Hunt urged viewers to “slaughter” members of the U.S. Congress and stated that he would go to the Capitol himself to “take out these Senators and then replace them with actual patriots.” App’x 1425. Based on this video, a jury convicted Hunt of one count of threatening to assault and murder members of Congress in violation of 18 U.S.C. §115(a)(1)(B). The district court (Chen, J.) sentenced Hunt to a prison term of nineteen months. In this appeal, Hunt challenges the sufficiency of the evidence, a jury instruction, the partial closure of the courtroom due to the COVID-19 pandemic, and his sentence. For the reasons explained below, we AFFIRM the judgment of conviction and the sentence. JOHN WALKER, Jr., C.J. In the months following the 2020 presidential election, Defendant-Appellant Brendan Hunt threatened prominent elected officials in several posts on various social media platforms. In one of those posts, a video published on the website BitChute, Hunt urged viewers to “slaughter” members of the U.S. Congress and stated that he would go to the Capitol himself to “take out these Senators and then replace them with actual patriots.” App’x 1425. Based on this video, a jury convicted Hunt of one count of threatening to assault and murder members of Congress in violation of 18 U.S.C. §115(a)(1)(B). The district court (Chen, J.) sentenced Hunt to a prison term of nineteen months. In this appeal, Hunt challenges the sufficiency of the evidence, a jury instruction, the partial closure of the courtroom due to the COVID-19 pandemic, and his sentence. For the reasons explained below, we AFFIRM the judgment of conviction and the sentence. BACKGROUND Brendan Hunt was incensed by the outcome of the 2020 presidential election. He questioned the legitimacy of the vote count and condemned “deceitful leftists” as “domestic terrorists and enemies of our constitutional republic…[who] will be dealt with one way or another.” App’x 267-68. Beginning in late November 2020, Hunt made threats on various social media platforms against prominent elected officials, including House Speaker Nancy Pelosi, Senate Majority Leader Charles Schumer, and Congresswoman Alexandria Ocasio-Cortez. The threat for which Hunt was ultimately convicted was a video he posted on BitChute, a video-sharing platform similar to YouTube. In the video, titled “Kill Your Senators,” Hunt spoke into the camera: Hey guys, so we need to go back to the U.S. Capitol when all of the Senators and a lot of the Representatives are back there and this time we have to show up with our guns and we need to slaughter these motherfuckers…. If anybody has a gun, give me it. I will go there myself and shoot them and kill them. We have to take out these Senators and then replace them with actual patriots. App’x 1425. In reply to comments on the video and in subsequent videos, Hunt doubled down. Referencing the inauguration of President Biden scheduled for January 20, 2021, he urged: “lets go, jan 20, bring your guns,” App’x 1426; “everyone should come to Washington, D.C. on January 20th wearing masks and camo, concealed carry, body armor and just blast them all away while we still have a chance,” App’x 1427; and “[t]here are really only a hundred of these weakling Senators.…Every single one of them just needs to go,” App’x 1145-46. The video was posted on January 8, 2021. On January 19, 2021, FBI agents arrested Hunt. The government charged him with one count of threatening to assault and murder members of Congress in violation of 18 U.S.C. §115(a)(1)(B) for four statements, among them the BitChute video, made between December 6, 2020 and January 8, 2021. Hunt’s trial was among the first held in-person in the Eastern District of New York following the onset of the COVID-19 pandemic. Consistent with the Eastern District’s plan for the resumption of jury trials during the pandemic, which was developed in consultation with an epidemiologist, the district court adopted several precautions to protect the health of all involved. These measures included requiring masks, implementing social distancing (e.g., the jury was spread throughout the gallery), and limiting the total number of people allowed in the courtroom. To facilitate public access to the trial, the district court set aside two adjacent courtrooms to which live audio and video feeds broadcast the trial in real-time. On the second day of the trial, Hunt’s father passed a note to the district judge through Hunt’s counsel requesting permission to observe proceedings from the trial courtroom. The district court rejected the request, explaining that the courtroom was already over capacity and that Hunt’s father could observe the trial from an adjoining courtroom. The next day, the district court sua sponte suggested that it instruct the jury that public health considerations precluded Hunt’s family and friends from being present in the trial courtroom and that it should not infer anything from the absence of supporters. The defense agreed, and the jury was so instructed. After a six-day trial, Hunt moved for a judgment of acquittal under Federal Rule of Criminal Procedure 29. The district court denied the motion upon finding that the evidence was sufficient for the jury to conclude beyond a reasonable doubt that Hunt had made a constitutionally unprotected true threat to murder members of Congress. United States v. Hunt, 573 F. Supp. 3d 779, 797 (E.D.N.Y. 2021). The district court then charged the jury. Relevant to this appeal, the court explained, with respect to §115(a)(1)(B)’s intent element, that “[t]he Government must prove beyond a reasonable doubt that Defendant acted with the intent to impede, intimidate, or interfere with the officials while they were engaged in the performance of their official duties….” App’x 1412-13. In making this determination, the district court continued, the jury could “consider…whether there is evidence Defendant intended or did not intend any of his statements to reach the officials in question. The Government, however, does not need to prove that the alleged threats actually reached those officials.” App’x 1413. The jury convicted Hunt. On a special verdict form, the jury was asked whether it found Hunt guilty of violating 18 U.S.C. §115(a)(1)(B), the sole count of the indictment, and, if so, which of the four charged statements it found “constituted a true threat…to murder,” thereby satisfying the offense elements. App’x 1418-20. The jury answered that it found Hunt guilty based on the BitChute video, which was a “true threat…to murder.” App’x 1418-19. The jury found that the other three charged threats did not rise to the level of true threats proscribed by §115(a)(1)(B). At sentencing, the district court calculated that Hunt’s Guidelines offense level was 22 and, with no criminal history, his Guidelines sentence range was 41-51 months. This included a twolevel enhancement pursuant to U.S.S.G. §3C1.1 for obstructing or impeding the administration of justice, which the district court determined was warranted because Hunt “testified falsely at trial that he did not intend to retaliate against or interfere with members of Congress.” App’x 1495. The district court sentenced Hunt to a prison term of nineteen months. This appeal followed. DISCUSSION Hunt makes four arguments on appeal. First, invoking the constitutional fact doctrine, he contends that the evidence was insufficient to prove beyond a reasonable doubt that his BitChute video was a true threat unprotected by the First Amendment. Second, Hunt claims that the district court erred by refusing to instruct the jury that, to find him guilty, it had to conclude that he intended his threats to reach the targeted officials. Third, he maintains that the exclusion of his father from the trial courtroom violated his Sixth Amendment right to a public trial. Last, Hunt argues that the district court erred at sentencing by misapplying the perjury enhancement and impermissibly considering a rehabilitative purpose. After carefully considering these arguments, we conclude that each lacks merit. We therefore affirm Hunt’s conviction and sentence. I. Sufficiency of the Evidence Hunt’s statute of conviction, 18 U.S.C. §115, provides that (1) “[w]however…threatens to assault, kidnap, or murder, a United States official” (2) “with intent to impede, intimidate, or interfere with such official…while engaged in the performance of official duties, or with intent to retaliate against such official…on account of the performance of official duties, shall be [guilty].” 18 U.S.C. §115(a)(1)(B). The first element of §115 is satisfied if a threat constitutes a “true threat,” meaning one that “an ordinary, reasonable recipient who is familiar with the context of the [communication] would interpret…as a threat of injury,” United States v. Turner, 720 F.3d 411, 420 (2d Cir. 2013) (first alteration in original) (internal quotation marks omitted), and one that the defendant made at least recklessly by consciously disregarding the “risk that his communication[] would be viewed as threatening violence,” Counterman v. Colorado, 143 S. Ct. 2106, 2111-12 (2023). The second element is purely subjective, turning on the defendant’s intent in making the threats. Turner, 720 F.3d at 420. Where, as here, a defendant contends that the evidence did not establish that his speech was “a true threat of violence” “[un]protected by the First Amendment,” he challenges the sufficiency of the evidence supporting his §115 conviction. Id. at 418-19. Invoking the First Amendment, Hunt asks this court to apply the constitutional fact doctrine, which would require us to review the trial record de novo, and conclude based on that review that the BitChute video was not a true threat. We decline to do so. The constitutional fact doctrine’s requirement that courts “determine for themselves whether the fact-finder appropriately applied First Amendment law to the facts,” United States v. Wheeler, 776 F.3d 736, 742 (10th Cir. 2015), is inapplicable where, as here, the First Amendment is not implicated. Instead, applying the ordinary deferential standard of review, we find that the evidence was sufficient to support Hunt’s conviction. A. Standard of Review and Applicability of the Constitutional Fact Doctrine Ordinarily, we review challenges to the sufficiency of the evidence deferentially, construing the evidence “in the light most favorable to the government, crediting every inference that could have been drawn in its favor,” United States v. Gordon, 987 F.2d 902, 906 (2d Cir. 1993), and affirming the conviction provided that “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt,” Jackson v. Virginia, 443 U.S. 307, 319 (1979). Hunt argues, however, that the constitutional fact doctrine displaces this standard. He would thus have us examine the entire trial record and determine for ourselves whether the prosecution proved beyond a reasonable doubt that he made a true threat in violation of 18 U.S.C. §115(a)(1)(B). The government argues that the doctrine is inapplicable to this case and that we must defer to the jury’s verdict so long as it is reasonable. We have not definitively answered whether the constitutional fact doctrine applies to true threat determinations under 18 U.S.C. §115, see Turner, 720 F.3d at 419, and other circuits that have considered the issue have reached opposing conclusions.1 We now hold that the constitutional fact doctrine does not apply to §115 true threat determinations. Under the constitutional fact doctrine, courts “conduct[] an independent review of the record both to be sure that the speech in question actually falls within the unprotected category and to confine the perimeters of any unprotected category within acceptably narrow limits…to ensure that protected expression will not be inhibited.” Bose Corp. v. Consumers Union of U.S., Inc., 466 U.S. 485, 505 (1984). Courts apply the doctrine and engage in this independent review “to correct errors of law, including those that may infect a so-called mixed finding of law and fact, or a finding of fact that is predicated on a misunderstanding of the governing rule of law.” Id. at 501; see Hernandez v. New York, 500 U.S. 352, 367 (1991) (whether doctrine applies “turn[s] on the Court’s determination that” the question “involve[s] legal, as well as factual, elements”). Thus, the Supreme Court has applied the doctrine when reviewing whether a libelous statement was made with “actual malice,” Bose, 466 U.S. at 514, and whether a confession was voluntarily made, Miller v. Fenton, 474 U.S. 104, 115 (1985), and we have applied it in reviewing convictions for breach of peace and contempt of court, see United States v. Cutler, 58 F.3d 825, 834 (2d Cir. 1995). Distinguishing questions that implicate legal principles, to which the constitutional fact doctrine applies, from ordinary questions of fact, to which it does not, hinges on “the nature of the substantive law at issue.” Bose, 466 U.S. at 501 n.17. In Bose, the Supreme Court offered several reasons for finding that the “actual malice” determination involved legal principles necessitating application of the constitutional fact doctrine. Among these reasons were: (1) “the common-law heritage of the [actual malice] rule,” which “assigns an especially broad role to the judge in applying it to specific factual situations”; (2) that “the content of the rule is not revealed simply by its literal text, but rather is given meaning through the evolutionary process of common-law adjudication”; (3) the First Amendment “values protected by the rule[, which] make it imperative that judges…make sure that it is correctly applied.” Id. at 502. The nature of the substantive law at issue in this case supports letting the jury decide whether there was a true threat without any judicial second-guessing. Section 115(a)(1)(B) criminalizes threats that a reasonable person familiar with the context would view as genuine. Unlike “actual malice” in Bose, which “is given meaning through the evolutionary process of common-law adjudication,” 466 U.S. at 502, the true threat determination will usually hinge on the objective assessment of a reasonable person, and thus requires only “ordinary principles of logic and common experience” rather than legal judgment.2 Id. at 501 n.17. The substantive law at issue here does not implicate the constitutional fact doctrine for two additional reasons. First, the true threat question does not require a “case-by-case [judicial] adjudication…[to] give content to…otherwise elusive constitutional standards,” unlike those situations in which the doctrine applies. Harte-Hanks Commc’ns, Inc. v. Connaughton, 491 U.S. 657, 686 (1989). Second and relatedly, the common law does not “assign[] an especially broad role to the judge” to answer the operative question in this case. Bose, 466 U.S. at 502. To the contrary, the true threat standard spelled out in our cases constrains the role of judges and instead relies upon the sensibilities of ordinary people. In sum, the court is no better equipped than the jury — and is arguably less equipped — to answer whether a statement is a true threat. We therefore conclude that the true threat determination involves no legal principles warranting independent review of the jury’s conclusion. This holding aligns with our well-established view that “whether words used are a true threat” is “a question of fact” for the jury to which we defer. United States v. Amor, 24 F.3d 432, 436 (2d Cir. 1994) (internal quotation marks omitted); accord United States v. Davila, 461 F.3d 298, 304 (2d Cir. 2006); United States v. Malik, 16 F.3d 45, 49 (2d Cir. 1994); United States v. Carrier, 672 F.2d 300, 306 (2d Cir. 1982). B. Whether the Evidence Supported the Verdict As the district court found, the government presented to the jury “evidence[] capable of showing beyond a reasonable doubt that an ordinary and reasonable recipient familiar with the context of the [video] would interpret it as a threat.” Malik, 16 F.3d at 50. Hunt contends that the BitChute video cannot constitute a true threat because it “is incitement protected under the First Amendment…rather than a threat.” Appellant’s Br. 38 (citing Brandenburg v. Ohio, 395 U.S. 444, 447 (1969)). We are unpersuaded by this argument because it is predicated on the erroneous assertion that “when confronted with a particular communication that may be either incitement or a threat…a court must first determine the category to which the statement belongs.” Appellant’s Br. 44. Such a binary sorting is both unsupported by the case law and makes little sense: the offense elements the government must prove are determined by the crime actually charged. Indeed, Hunt’s argument is foreclosed by our holding in Turner that “a threat…need not also constitute incitement to imminent lawless action to be properly proscribed.” 720 F.3d at 425; see id. at 424 (rejecting an appellant’s argument that “his language…c[ould ]not be prohibited unless it constitute[d] incitement within the meaning of Brandenburg”); see also Wheeler, 776 F.3d at 745 (“Allowing defendants to seek refuge in the First Amendment simply by phrasing threats as exhortations would…leave the state powerless against the ingenuity of threateners.” (internal quotation marks omitted)). In this case, the trial evidence provided the jury with an ample basis to find beyond a reasonable doubt that the video constituted a true threat. Hunt emphatically stated his own violent intent. Using the first person, he said: “we have to show up with our guns,” “we need to slaughter these moutherfuckers,” and “I will go there myself and shoot them and kill them.” App’x 1436 (emphasis added). He also reiterated his seriousness in replies to comments posted to the video and in two follow-up videos. Circumstances surrounding the video are relevant as well. See Davila, 461 F.3d at 305 (events that occur close in time may inform how a reasonable person understands a threat). Hunt posted the BitChute video two days after a mob violently attacked the U.S. Capitol in an attempt to prevent certification of the 2020 presidential election. See Trump v. Thompson, 20 F.4th 10, 15 (D.C. Cir. 2021), cert. denied, 142 S. Ct. 1350 (2022). In this context, a reasonable person could conclude that Hunt was serious when he said that “we need to go back to the U.S. Capitol.” App’x 1436. We have no difficulty concluding that the jury reasonably found that Hunt’s BitChute video constituted a true threat to assault or murder. Hunt suggests in his post-argument Rule 28(j) letter that the evidence was insufficient also because the jury was not instructed that, to convict, it was required to find that he acted with at least recklessness as to the “risk that his [video] would be viewed as threatening violence.” Counterman, 143 S. Ct. at 2111-12. It is true that the district court did not so instruct the jury, doubtlessly because our pre-Counterman precedent did not recognize this mens rea requirement and Counterman — the Supreme Court decision adding the requirement — was not announced until well after trial. Assuming that Hunt’s argument is properly before us despite his failure to raise it on appeal, see United States v. Santillan, 902 F.3d 49, 58 n.4 (2d Cir. 2018) (“declin[ing] to consider…argument” raised “for the first time in a [Rule 28(j)] letter”), we hold that any error in instructing the jury as to the mens rea aspect of the true threat element was harmless beyond a reasonable doubt, see Neder v. United States, 527 U.S. 1, 8 (1999) (erroneously omitted jury instruction subject to harmless-error review). The trial evidence, much of which this opinion has already recounted, includes overwhelming evidence that Hunt acted with, at the very least, recklessness as to the risk that his video would be viewed as threatening violence. Because “the evidence in the record could [not] rationally lead to a finding favoring [Hunt] on the omitted element…the error was harmless.” United States v. Jackson, 196 F.3d 383, 386 (2d Cir. 1999). For the same reason, Hunt’s challenge to the sufficiency of the evidence on that element, in light of Counterman, also fails. II. Jury Instruction Hunt also contends that the district court erred by refusing to instruct the jury that, to find Hunt guilty, it had to conclude that Hunt “believed or expected…that his BitChute video would reach or be communicated to members of Congress.” Appellant’s Br. 60. Instead, the district court instructed that, in evaluating whether Hunt had the requisite intent under §115(a)(1)(B), the jury “may consider” whether the evidence showed that he “intend[ed] any of his statements to reach the officials in question.” App’x 1413. The government counters that this issue was not preserved and that, in any event, the district court’s instruction was correct. We review an unpreserved objection to a jury instruction for plain error and a preserved challenge de novo. United States v. Crowley, 318 F.3d 401, 413 (2d Cir. 2003); United States v. Alfisi, 308 F.3d 144, 148 (2d Cir. 2002). Here, Hunt’s claimed error was unpreserved. We thus review for plain error and find none. A. Preservation Federal Rule of Criminal Procedure 30 requires that “[a] party who objects to any portion of [a jury] instruction[] or to a failure to give a requested instruction must inform the court of the specific objection and the grounds for the objection before the jury retires to deliberate.” Fed. R. Crim. P. 30(d). Hunt argues that he raised the issue on four occasions. After careful review of the record, we find that on none of these occasions did Hunt satisfy Rule 30. The first occasion Hunt identifies is his “pretrial request to charge.” Appellant’s Reply Br. 18. This argument is unavailing, however, because “a party does not satisfy [his Rule 30] burden merely by submitting its own proposed language as part of a requested charge.” United States v. Giovanelli, 464 F.3d 346, 351 (2d Cir. 2006) (per curiam). Two of the other occasions are insufficient because they did not involve the jury instructions at all: one addressed the government’s objection to Hunt’s opening statement and the other arose following Hunt’s objection to a witness’s testimony. While the fourth occasion to which Hunt points at least occurred during the charge conference and pertained to the jury instructions, it too falls short because it was materially different from the objection raised here. During the charge conference, the district court acknowledged that Hunt had raised the issue of whether he must “have to intend that [his statement] reach the intended target,” Appellant’s Reply Br. 21 (alteration in original) (quoting App’x 925), but this discussion pertained to the first element of §115(a)(1)(B), true threat, and not the second element, intent to interfere, impede, or retaliate, which is the element that Hunt challenges here. The district court, in rejecting Hunt’s objection, made it clear that his argument only related to the true threat element. The district court responded that a defendant’s threat “doesn’t actually have to reach the intended victim to constitute a threat.” App’x 914 (emphasis added). Hunt’s argument on appeal pertaining to the second element was not preserved, and thus we review for plain error. B. Instruction Not Plain Error The district court’s intent instruction as to the second element was not plain error. For an error in a jury instruction to be plain, “it must, at a minimum, be clear under current law.” United States v. Weintraub, 273 F.3d 139, 152 (2d Cir. 2001) (internal quotation marks omitted). “We typically will not find such error where the operative legal question is unsettled, including where there is no binding precedent from the Supreme Court or this Court.” United States v. Whab, 355 F.3d 155, 158 (2d Cir. 2004) (internal quotation marks omitted). Hunt cites no binding precedent supporting his proposed jury instruction, and we are aware of none. The only Second Circuit case Hunt cites, United States v. Kelner, involved a different offense, 18 U.S.C. §875(c), which prohibits the transmission of threats in interstate commerce. 534 F.2d 1020, 1020 (2d Cir. 1976). In that case, the defendant argued “that there was no ‘communication’ within the meaning of 18 U.S.C. [§] 875(c) because there was no specific person to whom the threat was addressed and to whom [he] intended to cause emotional suffering.” Id. at 1023. We held that the jury was required to find that “the appellant intended to communicate his threat” to the threat’s target in order to satisfy the offense element that the “appellant’s activity [be] properly within the scope of the term ‘communication’” as used in §875(c). Id. (emphasis added). As that offense element is not present in §115(a)(1)(B), Kelner is inapposite to this case. Because Hunt fails to identify “a prior decision from this court or the Supreme Court mandating the jury instruction that [he], for the first time on appeal, says should have been given, we [cannot] find any such error to be plain, if error it was.” Weintraub, 273 F.3d at 152. III. Public Trial Hunt next contends that the district court violated his right to a public trial by excluding his father from the courtroom during the trial. The Sixth Amendment guarantees defendants in a criminal prosecution the right to a public trial. See U.S. Const. amend. VI. “But while the Sixth Amendment creates a ‘presumption of openness,’ ‘[t]he public trial guarantee is not absolute.’” United States v. Laurent, 33 F.4th 63, 95 (2d Cir. 2022) (quoting United States v. Gupta, 699 F.3d 682, 687 (2d Cir. 2012), cert. denied, 143 S. Ct. 394 (2022), and cert. denied sub nom. Ashburn v. United States, 143 S. Ct. 462 (2022). The Constitution permits “closure of a criminal trial courtroom…under limited circumstances.” Ayala v. Speckard, 131 F.3d 62, 69 (2d Cir. 1997) (en banc). As a general matter, courts may constitutionally close a courtroom if: “(1) closing the [proceeding] would advance an overriding interest…; (2) the closure is no broader than necessary to protect that interest; (3) the trial court considers reasonable alternatives…; and (4) the trial court makes findings adequate to support the closure.” United States v. Smith, 426 F.3d 567, 571 (2d Cir. 2005) (citing Waller v. Georgia, 467 U.S. 39, 48 (1984)). Where, as here, a defendant failed to object contemporaneously to a courtroom closure, we review the claim for plain error.3 Laurent, 33 F.4th at 95-96. “Under that standard, before an appellate court can correct an error not raised at trial, there must be (1) error, (2) that is plain, and (3) that affects substantial rights.” United States v. Gomez, 705 F.3d 68, 75 (2d Cir. 2013) (internal quotation and alteration marks omitted). Applying the four-part test set forth in Smith, we find that the district court did not plainly err by excluding Hunt’s father from the trial courtroom. First, excluding the public from the courtroom advanced an overriding interest4: protecting public health during the COVID-19 pandemic. At the time of Hunt’s trial, COVID-19 was understood to pose a serious health hazard, and limiting the risk of transmission by limiting the number of people in the trial courtroom was of paramount concern. See United States v. Allen, 34 F.4th 789, 797 (9th Cir. 2022) (“[L]imiting the transmission of COVID while holding a trial was an overriding interest.”); cf. Roman Cath. Diocese of Brooklyn v. Cuomo, 141 S. Ct. 63, 67 (2020) (“Stemming the spread of COVID-19 is unquestionably a compelling interest….”). Hunt does not dispute this point. Second, the closure was not clearly broader than was necessary. “A courtroom closure is permissible under the second Waller prong so long as there is a positive and proportional relationship between (1) the extent of the closure, and (2) the ‘gravity’ of the interest that assertedly justifies the closure….” Carson v. Fischer, 421 F.3d 83, 89 (2d Cir. 2005) (internal quotation and alteration marks omitted). In evaluating the breadth of a closure, we consider several factors, including the closure’s duration, whether all or just some spectators were excluded, and “whether the public can learn what transpired while the trial was closed.” Smith, 426 F.3d at 571 (internal quotation marks omitted). In this case, the closure was broad in as much as it excluded all spectators for the entirety of the trial. On the other hand, the simultaneous video and audio access available in nearby courtrooms ensured public access to the proceeding, Allen, 34 F.4th at 798, thereby safeguarding “the values the [Sixth] Amendment is aimed to protect,” Carson, 421 F.3d at 92-93. Here, the district court sought to balance the urgent imperative to protect public health and accommodating Hunt’s and the public’s interests in an open trial. See Ansari, 48 F.4th at 402 (It was “eminently reasonable…to maintain social distancing…by [using] an audio and video feed down to the jury assembly area to allow for any spectators…to view th[e] trial.” (internal quotation marks omitted)). As the district court explained, there was no adequate space for Hunt’s father in the trial courtroom because the courtroom was already “at a slightly higher number…than the epidemiologist…had approved.” App’x 265; see App’x 410. Third, the district court considered alternatives to closing the courtroom. Indeed, it “considered and used an alternative to complete[ly]” excluding Hunt’s father by providing a real-time broadcast of the trial. Carson, 421 F.3d at 87 (quoting People v. Carson, 740 N.Y.S.2d 346, 347 (2002)). It also specifically considered excepting Hunt’s father from its prohibition on spectators but determined that doing so was ill-advised. This decision was consistent with the Eastern District’s court-wide plan for resumption of jury trials, which called for admitting “ family members of the defendant” only if there was “available space.” App’x 37. Fourth, the district court made findings on the record to support the courtroom closure and enable appellate review. In Smith, we held that the district court was not required to make particularized findings justifying security measures that worked a partial closure where those measures were taken “to address a generalized threat.” 426 F.3d at 574. Here, too, the closure was made in response to the generalized threat of the COVID-19 pandemic. In any case, the district court explained its rationale for closing the trial courtroom, thereby facilitating our review. See Press-Enter. Co. v. Superior Ct. of California, Riverside Cnty., 464 U.S. 501, 510 (1984). We also note that had Hunt objected, the district court may have made a different decision, and, at the least, it “would have been alerted to” the need to make more specific findings, including as to potential alternatives that may have allowed the defendant’s father to be present in the courtroom. Gomez, 705 F.3d at 75 (holding no plain error where defendant’s counsel “fully acquiesced in the exclusion of [his] family” from the courtroom during jury selection due to space constraints). In short, given the lack of an objection, the district court cannot be faulted for failing to provide more detailed reasoning for its decision. See id. at 76 (“[T]he fairness and public reputation of the proceeding would be called into serious question if a defendant were allowed to gain a new trial on the basis of the very procedure he had invited.”). Finally, the district court mitigated any negative inference the jury might draw as to Hunt’s lack of visible support by informing it that due to the COVID-19 pandemic Hunt’s family and friends were excluded from the courtroom. “Accordingly, even if the exclusion of [Hunt's father]…was error, it cannot be viewed as one that affected the fairness, integrity, or public reputation of judicial proceedings.” Gomez, 705 F.3d at 76. Because the district court did not plainly err in closing the courtroom to the public, we reject Hunt’s unpreserved argument that the district court improperly excluded his father. IV. Sentencing Finally, Hunt contends that the district court erred in two respects during sentencing. First, he argues that it erroneously applied a two-level enhancement for obstruction of justice. Second, he claims that it impermissibly considered a rehabilitative purpose in deciding upon his sentence. We reject both contentions and affirm Hunt’s sentence. This court reviews criminal sentences “for procedural and substantive reasonableness under a deferential abuse-of-discretion standard.” United States v. Singh, 877 F.3d 107, 115 (2d Cir. 2017) (internal quotation marks omitted). “A sentence is procedurally unreasonable if the district court…improperly calculates[] the Sentencing Guidelines range…[or] selects a sentence based on clearly erroneous facts, or fails adequately to explain the chosen sentence.” Id. (internal quotation marks omitted). If a defendant failed to raise a claimed sentencing error below, however, we review for plain error. United States v. Villafuerte, 502 F.3d 204, 207 (2d Cir. 2007). A. Obstruction Enhancement A U.S.S.G. §3C1.1 obstruction enhancement based upon a defendant’s perjured testimony is appropriate if the “sentencing court…find[s] that the defendant 1) willfully 2) and materially 3) committed perjury, which is (a) the intentional (b) giving of false testimony (c) as to a material matter.”5 United States v. Zagari, 111 F.3d 307, 329 (2d Cir. 1997). While “it is preferable for a district court to address each element of the alleged perjury in a separate and clear finding,” United States v. Dunnigan, 507 U.S. 87, 95 (1993), at a minimum, it must “identify the statements on which the perjury finding was grounded,” find that they are material, and “make explicit findings that defendant’s testimony was intentionally false,” United States v. Rosario, 988 F.3d 630, 634 (2d Cir. 2021) (per curiam) (internal quotation and alteration marks omitted). See also Dunnigan, 507 U.S. at 95. Hunt argues that “the district court’s findings are insufficient to sustain the obstruction enhancement” because “it made no finding whatsoever other than that defendant testified and that the jury rejected this testimony” and “did not consider the possibility that” Hunt unintentionally gave inaccurate testimony. Appellant’s Br. 76-77. The government counters that Hunt failed to object to the enhancement below, rendering his claimed error amenable only to plain error review, and that, in any case, the district court’s findings were sufficient. Upon full review of the record, we find that Hunt preserved this issue. In his written objections to the presentence report, Hunt contested the §3C1.1 obstruction enhancement: “That the jury did not credit [his] testimony does not automatically show [that he] lied or obstructed justice.” Resp. to Presentence Investigation Report at 13, United States v. Hunt, 21-CR-86, No. 121 (E.D.N.Y. Sept. 24, 2021). He went on, “[t]here is nothing in the record that suggests how [his] testimony was deliberately untruthful or purposefully calculated to obstruct justice. The jury simply did not find it sufficient to show a lack of intent.” Id. at 14 (citation omitted). Although the government’s argument that this objection differed from the claimed error on appeal is plausible, Hunt’s objection at the sentencing hearing resolves any ambiguity in Hunt’s favor. At the hearing, Hunt argued that “someone could give truthful testimony about a lack of intent and still have that testimony rejected by a jury who didn’t find that that testimony was sufficient to overcome other evidence of…intent.” App’x 1514-15. This argument closely mirrors the objection raised on appeal. Accordingly, we find that Hunt preserved the issue; we thus review it for abuse of discretion rather than plain error. The district court did not abuse its discretion in applying the obstruction enhancement. Contrary to Hunt’s contentions, it made the necessary findings required by U.S.S.G. §3C1.1. The district court identified Hunt’s perjurious statements: his “testimony that he lacked the requisite intent” in making the video. App’x 1495. Although not specifically referenced by the district court, the record reflects that Hunt testified that he “wasn’t sending this message out to anybody” but that he “wanted…to get people talking about when does it cross the line into a necessity to pushback against Government in a way.” App’x 1003-06. The district court found that Hunt’s statements were intentionally false, concluding that the purpose of the testimony “was to prevent him from getting convicted.” App’x 1495-96. The district court then found that the statement was “plainly…material” because Hunt’s intent “was an element of the offense” and that the defendant’s intent to obstruct justice was proven “by a preponderance.” App’x 1495-96. As the district court made the required findings and did not rely on plainly erroneous facts in concluding that the perjury had been established by a preponderance of the evidence, we see no abuse of discretion and hold that it did not err by applying the enhancement. B. Consideration of Rehabilitative Purpose Hunt also challenges the district court’s sentence on the ground that it improperly considered a rehabilitative purpose in sentencing him to prison. Because Hunt did not raise this issue before the district court, our review is for plain error. See United States v. Gilliard, 671 F.3d 255, 258 (2d Cir. 2012). The Sentencing Reform Act of 1984 “precludes sentencing courts from imposing or lengthening a prison term to promote an offender’s rehabilitation.” Tapia v. United States, 564 U.S. 319, 332 (2011) (citing 18 U.S.C. §3582(a)). “A court commits no error,” however, “by discussing the opportunities for rehabilitation within prison or the benefits of specific treatment or training programs,” and “a court properly may address a [defendant]…about these important matters.” Id. at 334. In sentencing Hunt, the district court did not impermissibly consider rehabilitation. Rather, it considered the factors prescribed by 18 U.S.C. §3553(a), including the seriousness of the offense, promoting respect for the law, the need for deterrence, and protecting the public. App’x 1558-60. Hunt points to two instances in which, he argues, the district court impermissibly considered rehabilitation. Neither is problematic. The first was the district court’s statement that “prison ‘will enable’ Hunt ‘to grow up and reflect on [his] actions’” and serve as “‘a form of rehabilitation.’” Appellant’s Br. 78 (modification in original) (quoting App’x 1567). This expression of hope does not indicate that the district court had a rehabilitative motive in determining the proper sentence, and it was plainly permitted by Tapia. See Gilliard, 671 F.3d at 259 (noting that “discussion of rehabilitation” is permissible under Tapia if “the sentence length [is] based on permissible considerations”). Second, Hunt points to the district court’s statement that incarceration was “necessary for Mr. Hunt to fully come to grips with how he got here and how he needs to change” as proof of a rehabilitative purpose. Appellant’s Br. 79 (quoting App’x 1563). Again, we disagree. As the government points out, the district court made the excerpted statement in the context of “the need for specific deterrence,” a sentencing factor prescribed by §3553(a). App’x 1562. We therefore conclude that the district court did not impermissibly consider rehabilitation in determining Hunt’s sentence. CONCLUSION For the forgoing reasons, we AFFIRM the judgment of conviction and the sentence.
