GERARD E. LYNCH, Circuit Judge.

Narcisa Veliz Novack ("Novack") and her brother Cristobal Veliz ("Veliz") appeal from judgments of conviction entered following a two-month jury trial in the United States District Court for the Southern District of New York (Kenneth M. Karas, Judge). Both were convicted of numerous offenses, including one count of racketeering in violation of the Racketeer Influenced and Corrupt Organizations Act ("RICO"), 18 U.S.C. § 1962(c), and one count of RICO conspiracy, 18 U.S.C. § 1962(d).1 Those charges arose from defendants' participation in an association-in-fact RICO enterprise with the primary purpose of assaulting Novack's husband, Ben Novack, and her mother-in-law, Bernice Novack, in order to gain control of their assets. Defendants raise a host of challenges to their convictions and their sentences of life imprisonment, most of which we reject in a summary order issued simultaneously with this opinion. See United States v. Veliz, 800 F.3d 63, No. 13-914-cr, 13-953-cr, 2015 WL 4923625 (2d Cir. Aug. 19, 2015). This opinion addresses Veliz's challenges to his witness tampering convictions, which warrant greater discussion.

Veliz was convicted of two counts of witness tampering in violation of 18 U.S.C. § 1512(b)(3), which provides that "[w]hoever knowingly uses intimidation, threatens, or corruptly persuades another person, or attempts to do so, or engages in misleading conduct toward another person, with intent to ... hinder, delay, or prevent the communication to a law enforcement officer or judge of the United States of information relating to the commission or possible commission of a Federal offense" shall be guilty of a crime.2 Those charges arose from two occasions on which Veliz solicited associates to murder Alejandro Garcia — whom Veliz had hired to assault Ben and Bernice Novack — in order to prevent Garcia from communicating information about those crimes to law enforcement.

First, Veliz argues that his conduct did not violate § 1512(b)(3) because solicitation to murder does not constitute the use or attempted use of "intimidation, threat[s], or corrupt[] persua[sion]." We reject that argument, because solicitation of a third party to murder a witness constitutes attempted corrupt persuasion under the statute.

Second, Veliz contends that the evidence was insufficient to show, as required by § 1512(b)(3), "that there was a reasonable likelihood that a relevant communication would have been made to a federal officer." Fowler v. United States, 563 U.S. 668, 131 S.Ct. 2045, 2048, 179 L.Ed.2d 1099 (2011) (second emphasis added). That argument fails because the evidence that Veliz had committed multiple related crimes across multiple states was sufficient to support. the jury's finding that communication with a federal investigator was reasonably likely.

Third, Veliz argues that his witness-tampering convictions must be vacated because the district court's jury charge erroneously instructed that § 1512(b)(3) could be violated by the use or attempted use of "physical force," in addition to "intimidation, threat[s], or corrupt[] persua[sion]." Reviewing that unpreserved challenge for plain error, we reject Veliz's argument because he has not shown a reasonable probability that the challenged instruction affected the jury's verdict.

Finally, Veliz contends that the inclusion of the term "physical force" in the jury charge constructively amended the indictment. Again reviewing for plain error, we reject that argument because the government's theory of guilt was consistent from indictment to summation and the jury clearly based its verdict on the conduct charged in the indictment. Accordingly, for the reasons given in this opinion and in the accompanying summary order, we affirm the judgments of conviction.

BACKGROUND

We recount the facts and procedural history of the case only as relevant to the witness tampering charges. Because the jury found Veliz guilty of those charges, "we view the evidence in the light most favorable to the government." United States v. Mergen, 764 F.3d 199, 202 (2d Cir.2014) (internal quotation marks omitted).

In February and March of 2009, Veliz traveled from New York to Florida to orchestrate an assault on Novack's 86-year-old mother-in-law, Bernice Novack. After several aborted attempts, Veliz hired an acquaintance, Alejandro Garcia, to carry out the attack. On the night of April 4, 2009, Veliz drove Garcia to Bernice Novack's home in Fort Lauderdale with instructions to "give her a good beating and to knock off [sic] her teeth." Trial Tr. 870. Despite those chilling but limited instructions, there was sufficient evidence for the jury to conclude that Veliz and Novack intended that the assault on Bernice Novack would be fatal, so that her wealth would be inherited by Novack's husband Ben, whom Novack and Veliz intended to kill or incapacitate in turn, leaving Novack in control of the assets of both victims. Garcia, lurking behind trash cans until Bernice Novack arrived, followed her into the garage and beat her to death with a wrench. Veliz then paid Garcia for his participation, and the following day told him that he had done a "good job." Trial Tr. 371.

Shortly after the attack on Bernice Novack, Veliz recruited Garcia for a "larger job" that entailed assaulting Ben Novack at a convention in New York. Trial Tr. 374-75, 381. The purpose of the assault, Veliz explained, was to disable Ben Novack so that Veliz and Novack could take control of his business, and to punish him for his sexual abuse of Novack. In early July 2009, Veliz, Garcia, and Joel Gonzalez (whom Garcia had enlisted in the plot on Veliz's instructions) drove from Florida to New York, purchased weapons and other tools for use in the assault, and checked in at a hotel near the Hilton Hotel in Rye Brook, New York, where the attack would take place. In the early morning of July 12, 2009, Novack let Garcia and Gonzalez into the Novacks' room, and directed them to her sleeping husband. The two assailants, with Novack's encouragement, then tied up Ben Novack, cut out his eyes, and beat him to death with a pair of dumbbells. In the weeks following the attack, Novack secured control of assets of Ben and Bernice Novack.3

On August 13, 2009, Westchester County Police officers investigating the Ben Novack murder questioned Veliz at his apartment in Philadelphia. During that interview, the officers observed a Western Union receipt for $500 addressed to Alejandro Garcia in Miami. Two weeks later, Veliz told one of the investigating officers that he had discovered that Garcia was the perpetrator. On November 18, 2009, Garcia was arrested in Miami on unrelated theft charges. After learning of the arrest, the investigating officers traveled to Florida to question Garcia about Ben Novack's murder. Garcia initially refused to cooperate. In January 2010, the Federal Bureau of Investigation joined the investigation of Ben Novack's murder.

Veliz, unaware of the arrest, believed that Garcia had fled to Nicaragua, his home country. In late 2009, to prevent Garcia from resurfacing and revealing Veliz's involvement, Veliz approached Yader Tinoco, an associate who had played an ancillary role in the killings. Veliz told Tinoco that Garcia "was opening his mouth," and asked him to "go to Nicaragua... [s]o you can go hush his mouth." Trial Tr. 1830. Tinoco declined. Undeterred, Veliz in late 2009 or early 2010 contacted Melvin Medrano — who had assisted in planning the attack on Bernice Novack — in Nicaragua through a mutual acquaintance, Juan Carlos Castillo. On a three-way conference call, Veliz stated that he "wanted to know where [Garcia] was," and that he "was worried because [Garcia] could talk to the cops about something they have done." Trial Tr. 1874. Veliz asked Medrano "to work [Garcia], to make him disappear," which Castillo interpreted to mean "to have him killed." Id. Medrano agreed, but with Garcia in jail in Miami, nothing came of Veliz's solicitation.

In April 2010, after pleading guilty to the Florida theft offense, Garcia was transferred to the Southern District of New York, where he admitted his role in the crimes and implicated his accomplices, including Veliz and Novack. Pursuant to a plea agreement, Garcia pleaded guilty on June 28, 2010 to one count of interstate domestic violence in connection with the death of Ben Novack. Gonzalez eventually pleaded guilty as well, and he, Garcia, and several other coconspirators agreed to testify as cooperating witnesses against Veliz and Novack.

Veliz and Novack were indicted in the Southern District of New York on July 7, 2010. A superseding indictment filed on April 3, 2012 (the "Indictment") charged Veliz with, among other crimes, two counts of witness tampering, alleging that Veliz violated § 1512(b)(3) in "the fall of 2009" and again in "January and February of 2010" by "solicit[ing] an associate to murder [Garcia] in order to prevent [Garcia] from reporting information to law enforcement authorities concerning the murders of Bernice Novack and Ben Novack." J.A. at 83-84. The witness tampering allegations were also charged against Veliz as two predicate racketeering acts in support of the substantive and conspiracy RICO charges.

The jury found Veliz guilty of both witness tampering counts (as well as other crimes), and also found the corresponding predicate acts to be proven. Veliz and Novack, who was also convicted as described above, were sentenced to life imprisonment.

DISCUSSION

A. Sufficiency of the Evidence: Intimidation, Threats, or Corrupt Persuasion

Section 1512(b)(3) penalizes "[w]hoever knowingly uses intimidation, threatens, or corruptly persuades another person, or attempts to do so, or engages in misleading conduct toward another person, with intent to ... hinder, delay, or prevent the communication to a law enforcement officer or judge of the United States of information relating to the commission or possible commission of a Federal offense." 18 U.S.C. § 1512(b)(3).

On appeal, Veliz does not dispute that the evidence at trial was sufficient to permit the jury to find beyond a reasonable doubt that he solicited Garcia's murder in order to prevent him from communicating with law enforcement. Instead, he argues that his conduct did not violate § 1512(b)(3) because solicitation to murder does not constitute the use of intimidation, threats, or corrupt persuasion.4 Under the statute, Veliz maintains, a defendant must intend that an effort to intimidate, threaten, or corruptly persuade reach, directly or indirectly, the person whose cooperation with law enforcement the defendant seeks to prevent. Veliz asserts that he had no such intent because he certainly did not want Garcia to learn of the murder plot, and that a surreptitious effort to eliminate the witness by killing him is not covered by § 1512(b)(3).

In response, the government argues that under § 1512 a "threat" means "an expression of intention to inflict evil, injury, or damage on another." United States v. England, 507 F.3d 581, 589 (7th Cir.2007), quoting Webster's Third Int'l Dictionary 2382 (1981). According to the government, Veliz's conduct satisfies that definition because he expressed to Tinoco and Medrano an intent to inflict injury on Garcia. Under this reading, it does not matter that Veliz never intended that Garcia perceive the expression; it suffices that Veliz intended that someone perceive it.

The government cites England for the proposition that a defendant may "threaten" a witness in violation of § 1512 even absent an intent that the witness perceive the threat. The dictionary definition of "threat" adopted in England — "an expression of intention to inflict evil, injury, or damage on another," 507 F.3d at 589 (internal quotation marks omitted) — would appear on its face to cover a case like this one. But the facts of England, and therefore the actual holding of the case, are far narrower. England was charged with witness tampering under § 1512(a)(2)(A) — which punishes "[w]hoever uses physical force or the threat of physical force against any person, or attempts to do so," 18 U.S.C. § 1512(a)(2)(A) — based on his request to his father to "relay a message" to a potential witness that England would murder him if he testified. England, 507 F.3d at 584. The Seventh Circuit rejected England's argument that he had not threatened the witness because the witness never received the message. Because England intended (and indeed specifically requested) that the threat be conveyed to the witness, however, the Seventh Circuit was not confronted with the question whether the defendant's statement would have violated the statute absent such an intent.

This Court has not addressed what meaning of "threat" Congress intended in § 1512(b)(3). The word "threat" can mean, as the government contends and as the England court suggested, the mere "expression of intention to inflict evil, injury, or damage on another," without any intent that the threat be communicated to the person threatened in order to influence that person's behavior. Indeed, the word has been so interpreted in at least one other federal criminal statute. It has long been a crime to mail a letter "containing any threat to take the life of ... the President of the United States," or to "otherwise make[] any such threat against the President." 18 U.S.C. § 871(a). That statute has consistently been held to apply not only to statements addressed to the President himself, but also to the announcement to random listeners of an intention to kill the President. See, e.g., United States v. Patillo, 431 F.2d 293, 297-98 (4th Cir.1970); United States v. Jasick, 252 F. 931, 932-33 (E.D.Mich. 1918). It would do no violence to the English language to say that someone who announced an intention to kill a witness, or to have him killed, had "threatened" the witness — just as Jasick, who announced an intention to kill President Wilson, had threatened the President.

The context here, however, is arguably different. Section 871(a) aims to protect the President by permitting the prosecution of those who pose a danger to our highest elected official, as indicated by their threatening words. In § 1512(b)(3), by contrast, the act of "threatening" is linked to other verbs — "uses intimidation" and "persuades" — which suggest an effect on the person to whom the threat is communicated. Moreover, the effect in question is specifically described, and must be intended by the threatener: the threat must be made with the intent to prevent the communication of information to a law enforcement officer or judge. It can thus be plausibly contended that, in the full context of § 1512(b)(3), the threat itself (as opposed to its execution) must be intended to prevent the communication of information, which it cannot do unless the threat is communicated either to the witness or to another person with the intent that that person somehow interfere with the witness's giving of information.

We need not decide here, however, whether a solicitation to murder a witness constitutes "threatening" within the meaning of § 1512(b)(3), because in any event Veliz's conduct falls within the statute as the attempted "corrupt[] persua[sion] [of] another person." Veliz attempted to persuade Tinoco and Medrano to act in such a way as to prevent Garcia from communicating to the authorities information about the Novack murders.

By its plain language, § 1512(b)(3) forbids "corruptly persuad[ing] another person, or attempt[ing] to do so, ... with intent to ... prevent the communication... of information relating to ... a Federal offense." 18 U.S.C. § 1512(b)(3) (emphasis added). The statute conspicuously avoids the use of language that would require that the person threatened or persuaded be the person with information to provide to the authorities. Congress did not, for example, prohibit the use of corrupt persuasion of another person with the intent to prevent that person from communicating with law enforcement. Moreover, in a parallel provision of § 1512(b) — which prohibits the same conduct with intent to withhold testimony or documents in an official proceeding — Congress expressly provided to the contrary: subsection (b)(2) prohibits corrupt persuasion of "another person" with the intent to cause "any person" to withhold evidence. 18 U.S.C. § 1512(b)(2). We can think of no logical reason to read subsection (b)(3) differently in this respect.5 Because the potential object of the persuasion is not limited to the person whose communication the defendant seeks to prevent, an attempt to persuade one person (here, Tinoco or Medrano) to prevent another person (here, Garcia) from communicating information about a crime to a law enforcement officer by killing him violates the statute.

That persuasion, moreover, was clearly "corrupt." We have defined "corrupt persuasion" under § 1512(b) to mean persuasion "motivated by an improper purpose." United States v. Thompson, 76 F.3d 442, 452 (2d Cir.1996); accord, United States v. Gotti, 459 F.3d 296, 343 (2d Cir.2006). The qualifying term "corruptly" clarifies that the statutory prohibition is "limited to constitutionally unprotected and purportedly illicit activity." Thompson, 76 F.3d at 452 (alterations and internal quotation marks omitted).6 Veliz was "motivated by [the] improper purpose," id., of preventing through violence Garcia's cooperation with law enforcement, and Veliz attempted to persuade his associates to engage in the "illicit activity," id., of murder. Few acts are as "wrongful," Arthur Andersen, 544 U.S. at 705, 125 S.Ct. 2129, or demonstrate such "conscious ... wrongdoing," id. at 706, 125 S.Ct. 2129, as soliciting the murder of a potential witness in order to conceal one's involvement in two other murders.7

While it is a question of first impression for this Court whether solicitation to murder constitutes "corrupt persuasion," we note that the Third Circuit has addressed the question, and reached the same conclusion we do, on highly similar facts. See United States v. Davis, 183 F.3d 231 (3d Cir.1999), as amended, 197 F.3d 662 (3d Cir.1999). Davis was convicted under § 1512(b) after he "suggested that [his associate] should kill [a cooperator] and asked [his associate] for a gun so that Davis himself could kill [the cooperator]." Id. at 250. On review, the Third Circuit held that Davis had attempted to corruptly persuade his associate by urging him "to violate his legal duty not to kill [the suspected cooperator] or aid in [the cooperator's] death." Id. It found "irrelevant" the fact that Davis had no direct contact with the cooperator, since the statute required only "that a defendant corruptly persuade `another person' with the requisite intent. That person need not be the witness." Id. Thus, just as we conclude here, the Third Circuit held that Davis violated § 1512(b)(3) by corruptly persuading another person by urging him to "violate his legal duty," with the intent to prevent a communication to law enforcement by a third-party witness concerning a federal offense.

Veliz contends that interpreting § 1512(b)(3) to cover solicitations to murder "ignores the organizational structure of § 1512[,] which delineates separate offenses for witness intimidation utilizing physical force, i.e., § 1512(a)(2)(A), and those that do not, i.e., § 1512(b)(3)." Veliz Reply Br. 26-27. Thus, Veliz seems to argue, the government charged his conduct under the wrong subsection of § 1512.

It is true that the different subsections of § 1512 prohibit different conduct intended to interfere with a federal investigation or proceeding. Subsection (a)(1) covers the "kill[ing] or attempt[ed] kill[ing] [of] another person"; subsection (a)(2) the use or attempted use of "physical force or the threat of physical force against any person"; subsection (b) the use or attempted use of "intimidation, threat[s], ... corrupt[] persua[sion] ... or misleading conduct"; subsection (c) certain conduct relating to a "record, document, or other object"; and subsection (d) the "intentional[] harass[ment] [of] another person." 18 U.S.C. § 1512(a)-(d). But we reject the argument that § 1512 permits no overlap among its various subsections. For example, using the two subsections identified by Veliz, a defendant's statement to a witness that he will be murdered if he testifies might constitute a "threat of physical force" under subsection (a)(2), as well as a "threat[]" under subsection (b). Compare England, 507 F.3d at 588-90 (affirming conviction under subsection (a)(2) where defendant threatened to murder witness), with United States v. Hertular, 562 F.3d 433, 443-44 (2d Cir.2009) (affirming conviction under subsection (b)(3) where defendant "threatened the lives of DEA agents" to prevent their communication with other law enforcement officials). Similarly, a defendant who follows a witness's every move might be guilty of "intimidation" under subsection (b) or "harass[ment]" under subsection (d). See United States v. Chaggar, 197 Fed.Appx. 704, 707 (9th Cir.2006) (holding that "harassment" of witness under subsection (d) was a lesser-included offense of "intimidation" of the witness under subsection (b)). The fact that Veliz's conduct might also violate a separate prohibition under § 1512 therefore is not dispositive.8

Moreover, it is not obvious that solicitation to murder is covered under a different subsection of § 1512. While Veliz's conduct arguably falls within subsection (a)(1) as an "attempt[ed] kill[ing]," courts interpreting § 1512 have hesitated to conclude that a solicitation to murder a witness, without more, constitutes an attempt. See United States v. Irving, 665 F.3d 1184, 1202 (10th Cir.2011) (declining, in light of additional "substantial step[s]," to decide "whether [defendant's] active solicitation of someone to kill [a witness] would be sufficient in itself to establish a substantial step under the law of attempt, such that [defendant] could be convicted of witness tampering" under subsection (a)(1) (emphasis omitted)); United States v. Rovetuso, 768 F.2d 809, 822-23 (7th Cir.1985) (same).9 Veliz could have similarly argued that his conduct was not covered by the statute had he been charged with the attempted "use[] [of] physical force" under subsection (a)(2).

Veliz does not make clear whether he contends that solicitation to murder a potential witness falls entirely outside the reach of § 1512, or only that it is outside subsection (b)(3). But to the extent he takes the former position, we reject it as well. Section 1512 was enacted as part of the Victim and Witness Protection Act of 1982, with the purpose of "provid[ing] additional protections and assistance to victims and witnesses in Federal cases." Pub. L. No. 97-291, 96 Stat. 1248 (1982). We find it inconceivable that in such a statute, which prohibits a broad constellation of methods of wrongfully impeding witness cooperation, Congress did not intend to reach the conduct at issue here. The apparent comprehensiveness of § 1512 also reinforces our conclusion that the text of subsection (b)(3) encompasses solicitation of a third party to murder a potential witness.

Finally, although the government has not argued the "corrupt persuasion" theory on which we rely, "it is well-settled that a reviewing court may affirm on any grounds for which there is a record sufficient to permit conclusions of law." United States v. Glover, 957 F.2d 1004, 1013 (2d Cir.1992) (internal quotation marks omitted). There can be no question that the theory was available to the jury based on the Indictment and the court's instructions, both of which recited the entire text of § 1512(b)(3), including "corruptly persuades" as well as "intimidates or threatens," and did not limit the jury's consideration to one or another of these verbs. Indeed, the district court instructed the jury on the meaning of "corruptly persuades," defining the term as "to act knowingly and with a wrongful, immoral or evil purpose to convince or induce another person to engage in certain conduct." Trial Tr. 5062. The Indictment, both in the witness tampering counts and in the parallel racketeering act specification in the RICO counts, did not distinguish among the three operative verbs, specifying only that the manner in which Veliz "attempt[ed] to intimidate, threaten, and corruptly persuade another person" was that he "solicited an associate to murder [Garcia]." J.A. 69-70, 83-84. Nor did the government's (or for that matter Veliz's) summation focus on the wording of the statute. Rather, the government argued only that the evidence supported the factual conclusion that Veliz attempted "to get Mr. Tinoco and Mr. Medrano to kill Alejandro Garcia." Trial Tr. 4717. The evidence was amply sufficient to permit the jury to conclude that Veliz did exactly that, and as a matter of law, that conduct violated § 1512(b)(3).

B. Sufficiency of the Evidence — Federal Nexus

Veliz next argues that the evidence was insufficient to support a finding of the federal nexus required by § 1512(b)(3).10 While the statute requires "a specific intent to interfere with the communication of information," United States v. Genao, 343 F.3d 578, 586 (2d Cir.2003), under § 1512 "no state of mind need be proved with respect to the circumstance ... that the law enforcement officer is an officer ... of the Federal Government," 18 U.S.C. § 1512(g)(2); see also Fowler v. United States, 563 U.S. 668, 131 S.Ct. 2045, 2049, 179 L.Ed.2d 1099 (2011) (explaining that § 1512 applies where defendant seeks to prevent a communication "to law enforcement officers in general rather than to some specific law enforcement officer").

In Fowler, the Supreme Court held that a defendant who does not intend to interfere with a communication specifically to federal law enforcement has violated § 1512 "only if it [was] reasonably likely under the circumstances that ... at least one of the relevant communications would have been made to a federal officer." Id. at 2052. A "reasonable likelihood" need not be "more likely than not," but it must be "more than remote, outlandish, or simply hypothetical." Id. Veliz contends that that standard is not met here because his prosecution "is a classic state case consisting of classic state charges," and thus, at the time he solicited Garcia's murder, it was not foreseeable that the crimes would be investigated federally. Veliz Br. 50.

As an initial matter, we conclude that although Fowler concerned the murder of a witness in violation of subsection (a)(1)(C), the "reasonable likelihood" test likewise applies to subsection (b)(3). "Fowler was a prosecution under § 1512(a)(1)(C), which, like § 1512(b)(3), is an investigation-related provision aimed at protecting the communication of information to law enforcement." United States v. Shavers, 693 F.3d 363, 378-79 (3d Cir. 2012), vacated and remanded on other grounds, ___ U.S. ___, 133 S.Ct. 2877, 186 L.Ed.2d 902 (2013). And before Fowler, we applied the same federal nexus test to both subsections "because the elements of subsection (b)(3) are similar to the elements of subsection (a)(1)(C)." United States v. Diaz, 176 F.3d 52, 91 (2d Cir. 1999).11

Fowler "le[ft] it to the lower courts to determine whether, and how, the [`reasonable likelihood'] standard applies" to the conduct at issue in that case. 131 S.Ct. at 2053. This Court has not had previous occasion to apply that standard. Prior to Fowler, we had held that to satisfy the federal nexus requirement under § 1512(a)(1)(C) "the government must adduce evidence from which a rational juror could infer that the victim plausibly might have turned to federal officials." United States v. Lopez, 372 F.3d 86, 92 (2d Cir. 2004) (emphasis in original), vacated and remanded on other grounds, 544 U.S. 902, 125 S.Ct. 1613, 161 L.Ed.2d 273 (2005). That burden could be carried "by showing that the conduct which the defendant believed would be discussed in these communications constitutes a federal offense, so long as the government also presents additional appropriate evidence." Id. at 91, quoting United States v. Bell, 113 F.3d 1345, 1349 (3d Cir.1997). We declined to comprehensively define "additional appropriate evidence," because it "by its nature will require careful, case-by-case analysis." Id. (internal quotation marks omitted). But we provided as examples of such evidence "proof that there was a federal investigation in progress at the time" of the witness tampering, or "that the defendant had actual knowledge of the federal nature of the offense." Id. (internal quotation marks omitted).

Since Fowler, the Fourth Circuit has continued to follow that framework, holding that "the federal nexus element of § 1512(a)(1)(C) `may be inferred by the jury from the fact that the offense was federal in nature, plus additional appropriate evidence.'" United States v. Ramos-Cruz, 667 F.3d 487, 497 (4th Cir.2012), quoting Bell, 113 F.3d at 1349. We likewise conclude that the "federal offense" plus "additional appropriate evidence" framework remains valid in light of Fowler. While Fowler may have increased the likelihood that must be demonstrated, it does not follow that a "reasonable likelihood" cannot be shown through the same means that we previously permitted "plausibility" to be shown.

Under that framework, sufficient evidence supports the jury's finding that Garcia's communication with federal law enforcement was reasonably likely.12 Veliz was, of course, convicted of federal offenses based in part on Garcia's information. And contrary to Veliz's assertions, those offenses were not merely "classic state charges." Fowler cautions us, in our federal nexus inquiry, not to afford undue weight to the mere fact that the defendant was convicted of a federal crime. A state crime often "will violate federal criminal law as well ... because of the frequent overlap between state and federal crimes," and we must avoid "transform[ing] a federally oriented statute into a statute that would deal with crimes, investigations, and witness tampering that, as a practical matter, are purely state in nature." Fowler, 131 S.Ct. at 2051-52. But Veliz's offenses were not "purely state in nature" — he committed multiple related crimes across multiple states, with multiple accomplices that a jury found to constitute an association-in-fact RICO enterprise. That is a long way from a murder-weapon-that-traveled-in-interstate-commerce theory of federal jurisdiction. Given the ongoing and interstate nature of the offenses, the jury reasonably found that federal involvement was "more than remote, outlandish, or simply hypothetical." Id. at 2052. Moreover, at the time of Veliz's second act of witness tampering, a federal investigation into his crimes had in fact commenced.

One difference between Fowler and the instant case bears note: unlike the potential witness in Fowler, Garcia was not murdered and did in fact subsequently communicate with federal law enforcement. Arguably, the very fact that communication with federal officials took place months after Veliz's solicitations lends some support to a finding that the communications were reasonably likely at the time of the solicitations. But we need not decide what weight, if any, may be given to the fact that Garcia ultimately cooperated with federal law enforcement. Nor need we explore what gap, if any, exists between Fowler's "reasonable likelihood" standard and our previous "plausibility" formulation. Whatever the contours of that standard, in this case we have no difficulty concluding, based on the nature of the offenses, that sufficient evidence supported the jury's finding.

C. Jury Instruction: Physical Force

Veliz challenges the district court's jury instruction regarding the witness tampering predicate racketeering acts, which stated in relevant part:

J.A. 180-81 (emphasis added).13 Veliz notes that the term "physical force" does not appear in § 1512(b)(3). Instead, the term "physical force" is used in subsection (a)(2) of § 1512, which punishes "[w]hoever uses physical force or the threat of physical force against any person, or attempts to do so." 18 U.S.C. § 1512(a)(2). Thus, Veliz maintains, his witness tampering convictions and the findings with respect to the witness tampering predicate acts must be vacated because the instruction erroneously permitted conviction on a ground not found in the statute under which he was charged. See United States v. Ekinci, 101 F.3d 838, 840 (2d Cir.1996) (reversing conviction where "jury charge included an element that is not found in the statute"). The government concedes that the instruction "mistakenly used the term `physical force,'" Gov. Br. 159, but argues that any error was harmless because the term was only a "superfluous elaboration" of the conduct that could violate § 1512(b)(3), id. at 164.

Because Veliz did not challenge the jury instruction below, we review his claim for plain error. See United States v. Ghailani, 733 F.3d 29, 52 (2d Cir.2013). Under that standard, for this Court to correct an error Veliz must show that "(1) there is an error; (2) the error is clear or obvious, rather than subject to reasonable dispute; (3) the error affected [his] substantial rights, which in the ordinary case means it affected the outcome of the district court proceedings; and (4) the error seriously affects the fairness, integrity or public reputation of judicial proceedings." United States v. Marcus, 560 U.S. 258, 262, 130 S.Ct. 2159, 176 L.Ed.2d 1012 (2010) (internal quotation marks and alterations omitted).

Veliz has not met that standard because he has not demonstrated that the purported error affected his substantial rights. "In the ordinary case, to meet this standard an error must be `prejudicial,' which means that there must be a reasonable probability that the error affected the outcome of the trial." Id. No such probability has been shown here. The government presented to the jury only one factual theory of guilt of witness tampering. The Indictment charged that Veliz violated § 1512(b)(3) by soliciting Garcia's murder, the evidence offered at trial supported that theory and no other, and the government argued in its summation that that is what occurred. We can therefore conclude with confidence that the jury convicted Veliz of witness tampering based on a finding that he solicited Garcia's murder. Veliz offers no reason to doubt that the jury would have returned the same verdict had it been instructed that "physical force" was not an element of the statute. Thus, on plain error review, Veliz's jury instruction challenge fails because he was convicted of conduct covered by the statute and the challenged instruction did not affect the verdict. The "fairness, integrity, or public reputation of judicial proceedings," Marcus, 560 U.S. at 262, 130 S.Ct. 2159, is not undermined by affirming a conviction for conduct that was charged in the Indictment, that the jury found occurred, and that as a matter of law constitutes a violation of the statute referenced in the Indictment.

D. Constructive Amendment

Relatedly, Veliz contends that the inclusion of the term "physical force" in the jury instruction constructively amended the Indictment. Tracking the text of the statute, the Indictment alleged that Veliz violated § 1512(b)(3) by "attempt[ing] to intimidate, threaten, and corruptly persuade another person" — not by attempting to use "physical force." J.A. 83-84.14 Veliz argues that the jury charge, by instructing that he could be found guilty based on the use of "physical force," permitted conviction based on conduct not alleged in the Indictment.15 We review the constructive amendment claim for plain error because Veliz did not raise it below. See United States v. Bastian, 770 F.3d 212, 219 (2d Cir.2014).

A constructive amendment occurs when "the jury charge operates to broaden the possible bases for conviction from that which appeared in the indictment." United States v. McCourty, 562 F.3d 458, 470 (2d Cir.2009) (internal quotation marks omitted). To prevail on such a claim, Veliz must demonstrate that the "jury instructions ... so modify essential elements of the offense charged that there is a substantial likelihood that the defendant may have been convicted of an offense other than that charged in the indictment." United States v. Vilar, 729 F.3d 62, 81 (2nd Cir.2013) (internal quotation marks and emphasis omitted).

We have "consistently permitted significant flexibility in proof" of the charges, so long as the Indictment provided the defendant "notice of the core of criminality to be proven" at trial. United States v. D'Amelio, 683 F.3d 412, 417 (2d Cir.2012) (internal quotation marks and emphasis omitted). "The critical determination is whether the allegations and the proof substantially correspond." United States v. Danielson, 199 F.3d 666, 670 (2d Cir.1999) (internal quotation marks omitted).

On plain error review, we reject Veliz's unpreserved constructive amendment claim for essentially the same reason that we reject his argument that the jury charge permitted conviction on a ground not covered in the statute. The government's theory of the witness tampering charges was entirely consistent from indictment to summation. The Indictment alleged that Veliz twice "solicited [an associate] to murder [Garcia]," J.A. 83-84, witnesses testified that Veliz sought to "hush [Garcia's] mouth" and "to make [Garcia] disappear," Trial Tr. 1830, 1874, and the government argued in summation that those statements were solicitations to murder Garcia. Thus, as discussed above, in finding that Veliz violated § 1512(b)(3), the jury must have found that he had solicited Garcia's murder — the precise conduct alleged in the Indictment that does in fact violate § 1512(b)(3). Moreover, Veliz does not point to any evidence that he engaged in any conduct other than attempting to persuade Tinoco and Medrano to kill Garcia that might have constituted the use of "physical force" against Garcia, or against anyone else, to keep Garcia from communicating with law enforcement. There is therefore not a "substantial likelihood that [Veliz] may have been convicted of an offense other than that charged in the indictment." Vilar, 729 F.3d at 81 (internal quotation marks omitted).

Since the jury clearly found proven conduct that violates the statute charged in the Indictment, and the Indictment gave the defendant clear notice of the conduct to be proved, any error in the jury instruction did not "affect[] the outcome of the district court proceedings" or "the fairness, integrity or public reputation of judicial proceedings," Marcus, 560 U.S. at 262, 130 S.Ct. 2159.

CONCLUSION

For the reasons given in this opinion and in the accompanying summary order, we AFFIRM the judgments of conviction.