GERARD E. LYNCH, Circuit Judge:

Defendant-Appellant Jasaan Bastian pled guilty in the United States District Court for the Southern District of New York (Kenneth M. Karas, Judge) to conspiracy to distribute crack in violation of 21 U.S.C. §§ 846, 841(a)(1), and 841(b)(1)(A), and to using and possessing a firearm in connection with a drug trafficking offense in violation of 18 U.S.C. § 924(c)(1). He now appeals from his conviction for the firearms offense, contending that the district court's acceptance of his plea based on the possession of a different weapon from the one identified by the grand jury constructively amended his indictment and that the district court's failure to inform him of his rights under the Grand Jury Clause prevented him from entering a knowing and voluntary guilty plea. Reviewing Bastian's unpreserved claims for plain error under Fed.R.Crim.P. 52(b), we conclude that Bastian has not established that his conviction on the basis of a different weapon plainly constituted a constructive amendment of his indictment. We therefore AFFIRM the judgment of the district court.

BACKGROUND

Between 2009 and 2011, Jasaan Bastian participated in a conspiracy to distribute crack cocaine in New York's Sullivan County. Over the course of the drug operation, Bastian distributed between 2.8 and 8 kilograms of crack cocaine. During one sale of 2.3 grams of crack on or around November 23, 2010, Bastian also sold one of his customers a .32 caliber revolver with three rounds of ammunition.

On May 16, 2012, a grand jury indicted Bastian on three counts relating to the trafficking ring. Count One charged Bastian with conspiring, between 2009 and December 2011, to distribute crack cocaine in violation of 21 U.S.C. §§ 846, 841(a)(1), and 841(b)(1)(A). Count Two charged him with being a felon in possession of a firearm in violation of 18 U.S.C. §§ 922(g) and 924(a)(2). Count Three charged him with using and possessing a firearm in furtherance of a drug trafficking crime in violation of 18 U.S.C. § 924(c)(1). Specifically, that count charged that "[b]etween in or about January 2011 and in or about April 2011," Bastian did "in relation to ... the narcotics conspiracy alleged in Count One of this Indictment ... possess a firearm, to wit, an Excel .20 gauge shotgun."1

On October 12, 2012, Bastian pled guilty to Counts One and Three of the indictment before the Honorable George A. Yanthis, United States Magistrate Judge. With regard to Count Three, the prosecutor advised the court, without objection from the defense, that Bastian and the government had "conferred and agreed" that Bastian would plead guilty on the basis of his use and possession of a different weapon from the one specified in the indictment: specifically, a .32 caliber revolver. Bastian subsequently allocuted to the fact that he had possessed and sold the .32 caliber revolver to one of his customers in furtherance of his drug trafficking operation. Based on the proceeding, Judge Yanthis recommended that the district court accept Bastian's plea agreement and, in January 2013, Judge Karas adjudged Bastian guilty on both counts.

At no point before Judge Yanthis or Judge Karas did Bastian challenge the substitution of the .32 caliber revolver as the basis of his conviction under § 924(c)(1), nor did he otherwise challenge the sufficiency of his plea.

DISCUSSION

The Grand Jury Clause of the Fifth Amendment provides that "[n]o person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury." U.S. Const. amend. V, cl. 1. Accordingly, no defendant in the federal courts may "be charged with a capital crime, or indeed with any felony," unless the charge is first brought by a grand jury. Matthews v. United States, 622 F.3d 99, 101 (2d Cir.2010). An indictment satisfying the Fifth Amendment must fulfill two requirements: first, it must "contain[] the elements of the offense charged and fairly inform[] a defendant of the charge against which he must defend," and second, it must "enable[] him to plead an acquittal or conviction in bar of future prosecutions for the same offense." United States v. Rigas, 490 F.3d 208, 228 (2d Cir.2007), quoting United States v. Resendiz-Ponce, 549 U.S. 102, 108, 127 S.Ct. 782, 166 L.Ed.2d 591 (2007). The right to indictment thus simultaneously protects a defendant's ability to prepare his defense and safeguards him from facing double jeopardy for a single crime. See United States v. Dupre, 462 F.3d 131, 140 (2d Cir.2006).

Bastian claims that, by convicting him of Count Three on the basis of a different weapon from that specified in his indictment, the district court constructively amended the grand jury's charges, violating the Grand Jury Clause and requiring a per se vacatur of his conviction. Alternatively, he argues that because he was neither informed of nor waived his right to a new indictment for the amended charge, his ensuing guilty plea was not knowing and voluntary under the law. The government responds first, that Bastian's guilty plea waived his challenges and, second, that Bastian's decision to plead guilty on the basis of a different weapon rendered any ensuing Fifth Amendment violation an "invited error" evading appellate review.

I. Waiver by Guilty Plea

A "defendant who knowingly and voluntarily enters a guilty plea waives all non-jurisdictional defects in the prior proceedings." United States v. Garcia, 339 F.3d 116, 117 (2d Cir.2003); accord United States v. Coffin, 76 F.3d 494, 496 (2d Cir. 1996). A defect qualifies as jurisdictional only if it alleges that "the face of the [defendant's] indictment discloses that the count ... to which he pleaded guilty failed to charge a federal offense," such that the district court "lacked the power to entertain the prosecution." United States v. Kumar, 617 F.3d 612, 620 (2d Cir.2010) (internal quotation marks omitted).

As the language of the rule makes clear, a waiver by guilty plea extinguishes the defendant's rights to challenge only defects in a "prior stage of the proceedings against him." United States ex rel. Glenn v. McMann, 349 F.2d 1018, 1019 (2d Cir. 1965); see also Garcia, 339 F.3d at 117. It does not preclude him from challenging defects in the guilty plea itself, which, as the rule demands, must be "knowing and voluntary" to have preclusive effect. Coffin, 76 F.3d at 496. Before we consider a defendant's non-jurisdictional objections waived, therefore, we must conclude that the defendant "entered a valid plea" under Fed.R.Crim.P. 11. United States v. Calderon, 243 F.3d 587, 589 (2d Cir.2001).

Because Bastian was neither advised of nor waived his rights to a superseding indictment on Count Three, Bastian's claim that the substitution of the.32 caliber revolver as the basis of his § 924(c)(1) conviction constructively amended the grand jury's indictment directly challenges the validity of his ensuing guilty plea. As this Court has noted, absent a valid indictment charging a defendant with criminal conduct, a "waiver of indictment" is "a necessary prerequisite... for entering a guilty plea" for a felony charge. United States v. Grandia, 18 F.3d 184, 187 (2d Cir.1994). The government suggests that Bastian's guilty plea itself served as an implicit waiver of his rights to a grand jury. Yet we have repeatedly held that "a guilty plea ... cannot serve as a waiver of indictment." United States v. Cordoba-Murgas, 422 F.3d 65, 71 (2d Cir.2005); see also United States v. Tran, 234 F.3d 798, 806 (2d Cir. 2000), overruled on other grounds by United States v. Thomas, 274 F.3d 655 (2d Cir.2001) ("[P]leading guilty does not waive a defendant's right to indictment by a grand jury."); United States v. Macklin, 523 F.2d 193, 196 (2d Cir.1975) ("While prosecution by indictment can be waived, the only waiver that could conceivably be found here is the plea of guilty.") (citation omitted). As we have emphasized, the waiver of indictment is an act "deliberately clothed in formal procedure." Macklin, 523 F.2d at 196. At the very least, it "must be made in open court," after defendants have been "informed of the nature of and the cause for the accusation" and the court is "satisfied that [they] waive their rights knowingly, intelligently and voluntarily." United States v. Ferguson, 758 F.2d 843, 850-51 (2d Cir.1985); see also Fed.R.Crim.P. 7(b). While a panel of this Court once recognized an implicit waiver of the right to indictment where the defendants specifically requested the court to amend their charges and "displayed a lively cognition of their rights," Ferguson, 758 F.2d at 851-52, the mere fact of a guilty plea does not obviate Fed.R.Crim.P. 7(b)'s procedural requirements.

Because Bastian's constructive amendment claim challenges the validity of his guilty plea, the plea does not preclude us from considering his appeal.

II. Invited Error

Alternatively, the government insists that, to the extent that Bastian's allocution to possessing the .32 caliber revolver constructively amended his indictment on Count Three, it presents an "invited error" barring judicial review.

Under the invited error doctrine, appellate courts are "especially reluctant" to provide relief on the basis of procedural errors that a defendant himself invited or provoked the district court to commit. United States v. Gomez, 705 F.3d 68, 75 (2d Cir.2013) (internal quotation marks omitted); see also United States v. Wellington, 417 F.3d 284, 290 (2d Cir.2005) ("[D]efendant cannot complain of an error that he himself invited...."). Accordingly, this Court has refused to reverse on the grounds of constructive amendment where, for example, the defendants themselves requested the court to issue instructions amending their indictments, see Ferguson, 758 F.2d at 851-52; cf. United States v. Ionia Mgmt. S.A., 555 F.3d 303, 310 (2d Cir.2009) — sometimes over the objections of the prosecution itself, see Ferguson, 758 F.2d at 851. Denying relief even for plain errors where a defendant deliberately provokes a procedural irregularity, the invited error doctrine seeks to avoid rewarding mistakes stemming from a defendant's own "intelligent, deliberate course of conduct" in pursuing his defense. Ferguson, 758 F.2d at 852; cf. United States v. Coonan, 938 F.2d 1553, 1561 (2d Cir.1991) (refusing to review appellate claims "attempting to evade the consequences of an unsuccessful tactical decision").

We find no such deliberate conduct in this case, where so far as appears in the record, Bastian neither sought nor gained any tactical advantage from giving up his right to indictment. The government does not suggest that Bastian deliberately requested the substitution of the .32 caliber revolver in Count Three, nor that he insisted on allocuting to possession of that weapon over the prosecution's own objections. Rather, the parties apparently "conferred and agreed" to the substitution as a part of a standard plea agreement.2 While Bastian made no efforts to avail himself of his right to a superseding indictment before allocuting to the revolver, his omission strikes us as less a strategic gambit than simply a "failure to take an evidentiary exception ... [as] a matter of oversight." United States v. Yu-Leung, 51 F.3d 1116, 1122 (2d Cir.1995). That oversight may limit the rigor of our review of Bastian's claims, see id. at 1121-22, but it does not prevent us from reaching the merits of his appeal.

We thus proceed to consider whether Bastian's guilty plea under § 924(c)(1) on the basis of a different weapon constructively amended his indictment in violation of the Grand Jury Clause.

III. Constructive Amendment

Because Bastian raises his constructive amendment claim for the first time on appeal, we review it for plain error. See United States v. Writers & Research, Inc., 113 F.3d 8, 12 (2d Cir. 1997); United States v. Vebeliunas, 76 F.3d 1283, 1291 (2d Cir.1996).3 Under the plain error standard, an appellant must demonstrate that "(1) there is an error; (2) the error is clear or obvious, rather than subject to reasonable dispute; (3) the error affected the appellant's substantial rights ...; 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 alteration omitted).4 An error is "plain" if "it is so egregious and obvious that a trial judge and prosecutor would be derelict in permitting it in a trial held today." Thomas, 274 F.3d at 667 (internal quotation marks omitted). We typically do not find plain 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).

In the usual context of a conviction after trial, to establish a constructive amendment, a defendant must show that the trial evidence or jury instructions "so altered an essential element of the charge that, upon review, it is uncertain whether the defendant was convicted of conduct that was the subject of the grand jury's indictment." Rigas, 490 F.3d at 227 (internal quotation marks omitted). A constructive amendment occurs where the actions of the court "broaden the possible bases for conviction from that which appeared in the indictment." United States v. Banki, 685 F.3d 99, 118 (2d Cir.2011), as amended (Feb. 22, 2012) (internal quotation marks omitted). Even if an indictment might have been drawn in more general terms to encompass the ultimate conviction, where "only one particular kind of [criminal conduct] is charged ... a conviction must rest on that charge and not another." United States v. Zingaro, 858 F.2d 94, 99 (2d Cir.1988) (internal quotation marks omitted). While a constructive amendment typically contemplates a jury trial, we have also recognized the challenge in the context of a guilty plea that, by its terms, amends the charges brought by the indictment. Fama v. United States, 901 F.2d 1175, 1177 (2d Cir.1990); see also United States v. Tello, 687 F.3d 785, 791 (7th Cir.2012); United States v. Iacaboni, 363 F.3d 1, 7 (1st Cir.2004).

Not every divergence from the terms of an indictment, however, qualifies as a constructive amendment. We have "consistently permitted significant flexibility in proof" adduced at trial to support a defendant's conviction, "provided that the defendant was given notice of the core of criminality to be proven" against him. United States v. D'Amelio, 683 F.3d 412, 417 (2d Cir.2012) (emphases in original) (internal quotation marks omitted); see also United States v. Agrawal, 726 F.3d 235, 259-60 (2d Cir.2013). So long as the indictment identifies the "essence of [the] crime" against which the defendant must defend himself, discrepancies in "the particulars of how a defendant effected the crime" do not constructively amend the indictment. D'Amelio, 683 F.3d at 418. Ultimately, whether an indictment has been constructively amended comes down to whether "the deviation between the facts alleged in the indictment and the proof [underlying the conviction] undercuts the[] constitutional requirements" of the Grand Jury Clause: allowing a defendant to prepare his defense and to avoid double jeopardy. Rigas, 490 F.3d at 228.

In this case, Bastian argues that the government's substitution of the .32 caliber revolver for the Excel 20-gauge shotgun identified in the "to wit" clause of his indictment constructively amended his charges under Count Three. In support of this position, Bastian directs us to several Seventh Circuit cases holding that variations from the specific weapon named in an indictment constructively amend a grand jury's charges under 18 U.S.C. § 924(c)(1). In United States v. Leichtnam, for example, the Seventh Circuit held that allowing a jury to convict a defendant charged with possessing a firearm, "to wit: a Mossberg rifle," on the grounds that he "intentionally used or carried a firearm" constructively amended his indictment. 948 F.2d 370, 374-75, 379 (7th Cir.1991) (emphasis in original); see also United States v. Carter, 695 F.3d 690, 698 (7th Cir.2012) ("Because the [indictment] charged the defendants with using the specific Ruger pistol ..., the jury [must] conclude that the defendants used the Ruger pistol (and not just any firearm)...."). Similarly, the Tenth Circuit has held that an indictment charging a defendant with unlawfully possessing "any ammunition and firearm ..., that is[,] a Hi-Point 9 mm pistol" under 18 U.S.C. §§ 922(g) and 924(a) was constructively amended by jury instructions allowing conviction on the basis of unlawfully possessing a .38 caliber bullet. United States v. Bishop, 469 F.3d 896, 901, 903 (10th Cir. 2006), abrogated on other grounds by Gall v. United States, 552 U.S. 38, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007).

A handful of out-of-Circuit cases, however, cannot establish that the district court plainly erred in accepting Bastian's guilty plea where the law in this Circuit remains silent on the issue. See Whab, 355 F.3d at 158. Bastian himself admits that the Second Circuit "has not squarely addressed" whether the substitution of a different firearm constructively amends an indictment under § 924(c)(1). And, as the government notes, several cases from both this Court and other Circuits counsel to the contrary.

As a preliminary matter, we have never suggested that a "to wit" clause binds the government to prove the exact facts specified in a criminal indictment. In Dupre, for example, we held that the government did not constructively amend an indictment charging defendants with wire fraud on the basis of, "to wit, ... caus[ing] an investor to wire approximately $2,000 ... from... Ohio to New York" by presenting conclusive evidence only of wire transfers originating in other states. 462 F.3d at 140-41 & n. 10 (emphasis omitted). Similarly, in D'Amelio, we concluded that an indictment charging a defendant with "us[ing] a facility and means of interstate commerce ..., to wit, ... a computer and the Internet," to entice a minor into sexual activity was not constructively amended by jury instructions listing "both the Internet and telephone" as potential grounds for the defendant's conviction. 683 F.3d at 414, 417 (emphasis omitted). "[W]here the indictment charge[s] a single course of conduct," we explained, a mere deviation from the "to wit" clause does "not permit conviction for a functionally different crime" and therefore does not meaningfully broaden the indictment. Id. at 423.

With regard to § 924(c)(1) specifically, while this Court has never considered whether a weapon identified in a "to wit" clause qualifies as an essential element of the indictment, several cases suggest a flexible approach toward the identities of weapons in federal firearms charges. In United States v. Patino, we considered a claim that the government constructively amended an indictment charging the defendant with using "a gun on or about November 4, 1990 ... during and in relation to" a kidnapping on the basis of evidence and jury instructions tying the defendant's conviction to three additional weapons seized a week later. 962 F.2d 263, 264-65 (2d Cir.1992). Dismissing the defendant's argument that the terms of the indictment limited the permissible evidence to the specific gun he used during the November 4 kidnapping itself, we observed that courts "have rejected claims that the type of firearm alleged in the indictment is an essential element under Section 924(c)(1) and have affirmed convictions where the evidence showed a different type of weapon." Id. at 266. Similarly, in United States v. Danielson, we concluded that the deviation between an indictment charging unlawful possession of "ammunition ..., to wit, 7 rounds of.45 calibre ammunition" under 18 U.S.C. § 922(g) and evidence proving unlawful possession of only "shells, rather than the entire rounds," did not alter the "core of criminality" identified in the indictment. 199 F.3d 666, 669-70 (2d Cir.1999). The "essential element of the offense charged," we noted, was that the defendant unlawfully "possessed ammunition ..., not the precise nature of that ammunition." Id. at 670.

Other Circuits have adopted a similarly liberal approach toward constructive amendment claims in the specific context of § 924(c)(1). Those courts have consistently concluded that evidence or jury instructions tying a defendant's § 924(c)(1) conviction to his possession of "any firearm" or "any type of gun" did not constructively amend indictments that identified specific weapons as the bases of the charges. See United States v. Robison, 904 F.2d 365, 368-69 (6th Cir.1990); United States v. McIntosh, 23 F.3d 1454, 1457 (8th Cir.1994); see also United States v. Redd, 161 F.3d 793, 796 (4th Cir.1998) (deeming sufficient evidence that defendant possessed "a firearm") (emphasis in original) (internal quotation marks omitted). As the Sixth Circuit explained, "because the specific type of firearm used or possessed by the [defendant] is not an essential element of the crime," the "district court's instructions [allowing a conviction on the basis of a different gun] were a variance, not a constructive amendment." Robison, 904 F.2d at 369; see also Redd, 161 F.3d at 796 ("Because the type of firearm is not an essential element of the crime charged, the government merely had to produce evidence at trial from which the jury could find beyond a reasonable doubt that Defendant had used a firearm during the robbery....") (emphasis in original) (internal quotation marks omitted); McIntosh, 23 F.3d at 1458.

Arguably, these cases are distinguishable from the facts at hand. In Patino, the specific terms of the indictment — charging a gun used "on or about November 4 ... during and in relation to" a kidnapping charge, 962 F.2d at 264 — plausibly encompassed the three additional guns introduced into evidence, which had been seized on November 11 and used as "protection" during the ransom scheme, id. at 265. In every case involving an explicit deviation from the language of the indictment, the "alternate" weapons introduced at trial unquestionably traced back to the same criminal transaction identified in the charge. See, e.g., Robison, 904 F.2d at 369 (tying § 924(c)(1) conviction to different guns seized during same arrest); cf. Danielson, 199 F.3d at 670-71 (tying conviction to possession of ammunition "shells" seized during same arrest). In most cases, indeed, the only evidentiary deviation involved the indictment's mistaken description of a discrete firearm. See, e.g., Redd, 161 F.3d at 794-95 (finding no constructive amendment where evidence confirmed use of "silver" revolver, rather than "black" revolver, during specific sequence of robberies); McIntosh, 23 F.3d at 1457 (finding no constructive amendment where evidence proved possession of different brand of .357 magnum gun than alleged in indictment); United States v. Munoz, 150 F.3d 401, 408 (5th Cir.1998) (finding no constructive amendment where evidence showed that shotgun seized by police was 12-gauge, not 20-gauge as alleged in indictment). In short, in the typical case rejecting a claim of constructive amendment, the divergence between the indictment and the proof was limited to the description of a firearm allegedly possessed on a particular occasion.

In Danielson, however, we specifically distinguished such minor differences of detail from cases where the challenged evidence or jury instructions tied a defendant's conviction to "behavior entirely separate from that identified in the indictment." 199 F.3d at 670. As we have previously noted, a constructive amendment occurs where the government introduces proof of "a complex of facts distinctly different from that" charged by the grand jury, not where it merely amends details pertaining to "a single set of discrete facts" set forth in the indictment. D'Amelio, 683 F.3d at 419 (internal quotation marks omitted).

In this case, Bastian's plea allocution did not simply involve a different description or manufacturer of gun than those identified in the indictment. It involved a completely different type of gun, used on different dates for different purposes and in different criminal transactions. Where the grand jury charged Bastian with possessing an Excel 20-gauge shotgun between "about January 2011 and ... April 2011," Bastian allocuted to possessing a .32 caliber revolver during a drug sale on November 23, 2010. While the indictment alleged the possession of the weapon over a three-month period, inferrably for potential use, the allocution referred to possession on a single occasion, for purposes of sale. To the extent that Bastian's indictment on Count Three "stated no single set of operative facts" that could "alert [him] that at trial he would face ... evidence" regarding the .32 caliber revolver, United States v. Wozniak, 126 F.3d 105, 111 (2d Cir. 1997), Bastian's ultimate conviction on the basis of the revolver arguably raised the concerns about fair notice and double jeopardy that the constructive amendment doctrine seeks to avoid. See also United States v. Ford, 872 F.2d 1231, 1236 (6th Cir.1989) (finding constructive amendment where jury instructions tied 18 U.S.C. § 924(e) charge to distinct criminal incident occurring eleven months before facts of indictment); United States v. Brown, 560 F.3d 754, 764 (8th Cir.2009) (suggesting that 18 U.S.C. § 924(c)(1) conviction based on firearms possession occurring a week after and involving separate parties from incident alleged in indictment would constitute constructive amendment).

Reviewing Bastian's challenge as we do for plain error, however, we cannot fault the district court for failing to parse such novel distinctions in Bastian's favor. As Bastian admits, this Court has never held that substituting a different weapon than that charged in the indictment constructively amends a § 924(c)(1) charge and indeed our cases have suggested that, in general, it does not. Because the "operative legal question is unsettled," Whab, 355 F.3d at 158 (internal quotation marks omitted), we cannot conclude that Bastian's conviction on the basis of a different weapon plainly violated his right to indictment under the Grand Jury Clause. For the same reason, we cannot conclude that, because the district court did not elicit a proper waiver of that right, it plainly failed to ensure that Bastian's guilty plea was knowing and voluntary; if it is unclear whether Bastian had a right to a superseding indictment, it cannot have been plain error for the court not to have advised him of such a right, or sought its waiver. See United States v. Cook, 722 F.3d 477, 481 (2d Cir.2013) (reviewing unpreserved claim that guilty plea was not knowing and voluntary for plain error). At most, the district court failed to identify a novel legal issue that neither party brought to its attention, an omission that does not meet the standard of a plain error calling for relief from this Court.

CONCLUSION

For the foregoing reasons, we AFFIRM the judgment of the district court.