Plaintiff-appellant Tannerite Sports, LLC (“Tannerite”) appeals from an order of dismissal and a judgment entered by the United States District Court for the Southern District of New York (Scheind-lin, /.). On appeal, we ask whether federal pleading standards, when applied to New York law, require a plaintiff asserting a defamation claim to allege facts demonstrating that the defendant made a false statement. We then consider whether Tan-nerite’s defamation complaint alleged that defendant NBCUniversal News Group (“NBC”) made false statements regarding Tannerite exploding rifle targets (“Tanner-ite targets” or “targets”).
*240Because we answer the first question in the affirmative and the second in the negative, we AFFIRM the district court’s dismissal of the complaint and its entry of judgment.
BACKGROUND
I. The Broadcast
“Right how, I ani basically holding-á bomb in my hand,” proclaimed television reporter Jeff Rossen, speaking against backdrop images of high-powered firearms and flame-engulfed cars. App’x at 89. “And you’ll never believe where I got this,” he continued. Id. “A sporting goods store, no questions asked.” Id. As the television camera zoomed in, he added that “the key ingredient here that causes the explosion has been used by terrorists to kill Americans.” Id. Lifting two white containers for viewers to see, Rossen declared that “[t]his morning, you’re about to see what happens when this gets in the wrong hands.” Id.
So began' a report on NBC’s Today Show considering the dangers of Tannerite exploding rifle targets. Tannerite’s “targets” consist of separately packaged chemicals—-ammonium nitrate and pyrotechnic grade aluminum powder—that detonate when mixed together and then shot with a high-velocity bullet. The targets enhance long-range recreational shooting, as the explosion provides an exciting acknowledgment that the target has been hit. Or, as Tannerite’s 2Ó14 Product Guide states, “[sjtrike your target and the gratification is instant.” App’x at 24.
. Unfortunately, but somewhat obviously* the targets pose dangers if misused. Tan-nerite’s own product guide recommends that the targets be detonated “away from populated areas,” and notes that improper use of the targets “may start fires, may be less safe to handle, and [may cause] erratic performance.” App’x at 25. And, because the targets contain. ingredients that explode, they can be used to-do harm rather than enhance recreation.
The Today Show’s report emphasized these risks, to put things mildly. When Rossen’s introduction concluded,' the scene changed abruptly to a small building in a country setting. Following a moment of serenity, the building exploded in a column of fire. A voice-over noted the presence of “dangerous and powerful explosives.” App’x'at 89. Viewers saw a montage of structures and cars bursting into flame.
After’ displaying more destruction, Ros-sen turned his focus to “[t]he lead manufacturer” of the targets: Tannerite. Id. He described Tannerite targets’ “key ingredient,” ammonium nitrate, as “a favorite of terrorists^] used in the Oklahoma City bombing, and to kill U.S.’ troops in Afghanistan.” Id. He noted that “[t]he FBI even issu[ed]- [an] intelligence bulletin in 2013,” stating that “it has potential use as [an] explosive[] in IEDs by criminals and'ex:-tremists.”3 Id.
NBC’s broadcast emphasized the easy accessibility of Tannerite targets. It noted their presence at' “most sporting goods stores”, and online. Id. Rossen stated that he “went shopping and bought it by the cartload,” and his “producer bought forty pounds’ worth online, enough to blow up a house.” Id.
Next came an interview with -Travis Bond, a firearms expert. Bond stated that Tannerite is “extremely dangerous” and the “equivalent of buying explosives off the shelf.” Id. A voice-over relayed Bond’s view that “Tannerite is getting around the *241law on a technicality, separating the two [chemical] ingredients, even though they’re sold together.” Id. The video showed Bond cutting open separately-wrapped packets of chemicals contained within a package of Tannerite and mixing them together in a single container. After Bond mixed the chemicals, he stated, “[t]his is now classified by ATF as an explosive.” Id.
The report bemoaned the product’s minimal regulatory supervision. Rossen interviewed Senator Richard Blumenthal, who argued that the products should be regulated more rigorously. Rossen then read Tannerite’s response: that the product is safe when used properly and that “[o]nly girly-men want to regulate Tannerite rifle targets.” App’x at 89.
Back in the studio, Rossen, holding two cartons of Tannerite targets, turned to the Today Show anchors and noted that, “after buying all of these products, we are handing it over to experts,” but assured them that • it is “not dangerous being in the studio right now. Of course, I wouldn’t do that to you.” Id. He added, “[a]nd you need the catalyst. But it is incredibly dangerous when you think about it ,.. and how this is used overseas by terrorists,” Id. An anchor added, “[a]nd in some cases here as well, by the way.” Id.
II. The Article
An NBC internet article called “Bombs for sale: Targets containing dangerous explosive being sold legally” provided a similar account. App’x at 37. The article discussed injuries caused- by the “exploding targets.” Id. It stated that the “key ingredient” of the targets “is ammonium nitrate, the same substance used in the Oklahoma City bombing ... and in IEDs ... used against U.S. troops in Afghanistan.” App’x at 38. It noted that “[g]un enthusiasts biiy it for target practice because it explodes when you shoot it, letting you know you’ve made the shot.” Id.
The article again noted Bond’s view that “Tannerite is getting around the law on a technicality by separating the two ingredients in its explosive—ammonium nitrate and aluminum powder—even though the two are sold together,” and quoted Bond as saying that “once it’s mixed, it’s classified as an explosive.” let. Like the video report, the article discussed Senator Blu-menthal’s views embracing greater regulation, and printed Tannerite’s response that additional regulation would be inappropriate.
III. Proceedings Below
Tannerite sued NBC for defamation.4 The complaint alleged that NBC defamed Tannerite in both the article and video by stating or suggesting, among other things, that the “targets are dangerous bombs as sold on store shelves,” which was false because “[plaintiffs rifle targets are not bombs,” and, in any case, “are inert as sold in stores” and therefore not dangerous in that setting. App’x at 17-19.
NBC moved to dismiss, and .the district court granted the motion. Tannerite Sports, LLC v. NBCUniversal Media LLC, 135 F.Supp.3d 219, 236 (S.D.N.Y. 2015). The district court stated that a plaintiff wishing to recover under New York defamation law must allege, among other things, that the defendant made “a false statement about the plaintiff.” Id. at 232. The court explained that “[t]ruth or falsity is determined by the common law standard of substantial truth,” and that “[a] statement is substantially true and not actionable if the published statement could have produced no worse an effect on the *242mind of a reader than the truth pertinent to the allegation.” Id. at 233 (internal quotation marks and citations omitted).
The district court ruled that Tannerite had not alleged that NBC made false statements. The court stated that “[t]here is no question that ‘Tannerite-brand binary exploding rifle targets’ explode. That is their purpose.” Id. at 235 (emphasis in original). Consequently, even if NBC’s “uses of the word ‘bomb’ [did not] me[et] the precise definition of the word.... the gist or substance ... [was] true in light of the many meanings that reasonable audiences associate with the word.” Id. (internal quotation marks and citations omitted). The court also wrote that neither publication “suggested that Tannerite’s exploding rifle targets are dangerous before the component ingredients are mixed, or that proper use of the products causes destruction or injury.” Id. at 236. The court noted that the video demonstrated how the product’s ingredients must be mixed, and both the video and article stated that the product does not become an explosive until its ingredients are mixed together. Id. The court also concluded that NBC’s reports clearly described dangers from misuse, as opposed to proper use, of the products. Id.
In the same order, the court also denied Tannerite’s motion for leave to amend. Id.
Tannerite appealed the district court’s order granting NBC’s motion to dismiss and denying the motion to amend, as well as the judgment order that followed soon after.
DISCUSSION
We review de novo a district court’s order granting a motion to dismiss. Williams v. Priatno, 829 F.3d 118, 121 (2d Cir. 2016).
I. Consideration of Substantial Truth at the Motion-to-Dismiss Stage
Tannerite first argues that the “substantial truth” of a defendant’s statement is not a proper basis for dismissal of a defamation complaint, inasmuch as “substantial truth” is an affirmative defense that must await summary judgment. We consider this argument before addressing whether NBC’s statements were, as the district court ruled, substantially true.
A. Substantial Truth
“Substantial truth” is the standard by which New York law, and the law of most other jurisdictions, determines an allegedly defamatory statement to be true or false. See Masson v. New Yorker Magazine, Inc., 501 U.S. 496, 516, 111 S.Ct. 2419, 115 L.Ed.2d 447 (1991) (“The common law of libel takes but one approach to the question of falsity, regardless of the form of the communication. It overlooks minor inaccuracies and concentrates upon substantial truth.” (citations omitted)); see also Franklin v. Daily Holdings, Inc., 135 A.D.3d 87, 21 N.Y.S.3d 6, 12 (1st Dep’t 2015). In Franklin, the Appellate Division explained that “[t]o satisfy the falsity element of a defamation claim, plaintiff must allege that the complained of statement is ‘substantially false.’” 21 N.Y.S.3d at 12. Thus, “[i]f an allegedly defamatory statement is ‘substantially true,’ a claim of libel is legally insufficient and ... should [be] dismissed.” Id. (internal quotation marks omitted; ellipsis and second alteration in original) (quoting Biro v. Conde Nast, 883 F.Supp.2d 441, 458 (S.D.N.Y. 2012)).
“[A] statement is substantially true if the statement would not have a different effect on the mind of the reader from that which the pleaded truth would have produced.” Id. (internal quotation marks and citations omitted) (quoting *243Biro, 883 F.Supp.2d at 458); see also Fleckenstein v. Friedman, 266 N.Y. 19, 23, 193 N.E. 537 (1934). “When the truth is so near to the facts as published that fine and shaded distinctions must be drawn and words pressed out of their ordinary usage to sustain a charge of libel, no legal harm has been done.” Fleckenstein, 266 N.Y. at 23, 193 N.E. 537 (quoting Cafferty v. S. Tier Pub. Co., 226 N.Y. 87, 93, 123 N.E. 76 (1919)). When a court interprets a publication in an action for defamation, “[t]he entire publication, as well as the circumstances of its issuance, must be considered in terms of its effect upon the ordinary reader.” Silsdorf v. Levine, 59 N.Y.2d 8, 13, 462 N.Y.S.2d 822, 449 N.E.2d 716 (1983); see also Aronson v. Wiersma, 65 N.Y.2d 592, 594, 493 N.Y.S.2d 1006, 483 N.E.2d 1138 (1985); Stepanov v. Dow Jones & Co., 120 A.D.3d 28, 34, 987 N.Y.S.2d 37 (1st Dep’t 2014).
The “substantial truth” standard finds basis in the realities and purposes of defamation law. In Tolbert v. Smith, we explained that “a statement need not be completely true, but can be substantially true” because fact and fiction may not be crisply delineated categories in defamation cases. 790 F.3d 427, 440 (2d Cir. 2015) (quoting Chau v. Lewis, 771 F.3d 118, 129 (2d Cir. 2014)). And the New York Court of Appeals has justified the standard by reference to underlying purposes of defamation law, explaining that “[t]he libel law is not a system of technicalities, but reasonable regulations whereby the public may be furnished news and information, but not false stories about any one.” Cafferty, 226 N.Y. at 93, 123 N.E. 76. This system of “reasonable regulation” would be damaged by an overly technical or exacting conception of truth in publication. Id.
B. Falsity Required to Plead Defamation Under Contemporary New York Law
If this case were governed by traditional common-law rules, Tannerite would be correct in describing “substantial truth,” or simply “truth,” as an affirmative defense. “At common law the majority position [was] that ... the plaintiff must allege falsity in his complaint,” but that, if the plaintiff so alleges, “the falsity of a defamatory communication is presumed” and that “truth is an affirmative defense which must be raised by the defendant and on which he has the burden of proof.”5 Re*244statement (Second) of Torts § 581A cmt. b (Am. Law Inst. 2017). But “[m]any contemporary cases have announced ... nontraditional requirements [that] are now necessary to sustain a libel claim,” and one of the new requirements is that “the plaintiff must prove .., [that] the publication was false.” Dan B. Dobbs, Paul T. Hayden & Ellen M. Bublick, The Law of Torts § 519 (2d ed. 2016).
New York is one jurisdiction embracing such a rule. Falsity is an element of defamation under contemporary New York law.6 In summarizing the tort, some New York courts present the more-traditional formulation that “[m]aking a false statement that tends to expose a person to public contempt, hatred, ridicule, aversion or disgrace constitutes defamation.” Thomas H. v. Paul B., 18 N.Y.3d 580, 584, 942 N.Y.S.2d 437, 965 N.E.2d 939 (2012) (citing Geraci v. Probst, 15 N.Y.3d 336, 344, 912 N.Y.S.2d 484, 938 N.E.2d 917 (2010); Foster v. Churchill, 87 N.Y.2d 744, 751, 642 N.Y.S.2d 583, 665 N.E.2d 153 (1996)). Oth*245•er opinions; such as that in Stepanov, provide a contemporary description that delineates very specifically the acts and effects to be proven:
To prove a claim for defamation, a plaintiff must show: (1) a false statement that is (2) published' to a third party (3) without privilege or authorization, and that (4) causes harm, unless the -statement is one of the types of publications actionable regardless of harm. ■
120 A.D.3d at 34, 987 N.Y.S.2d 37 (emphasis added) (citing Dillon v. City of N.Y., 261 A.D.2d 34, 38, 704 N.Y.S.2d 1 (1st Dep’t. 1999)). Regardless of the precise formulation,.these opinions, and others addressing the issue, include falsity as an element of defamation. See, e.g., Town of Massena v. Healthcare Underwriters Mut. Ins. Co., 98 N.Y.2d 435, 444, 749 N.Y.S.2d 456, 779 N.E.2d 167 (2002) (noting that “[a] party alleging defamation must allege that the statement is false”); Brian v. Richardson, 87 N.Y.2d 46, 50-51, 637 N.Y.S.2d 347, 660 N.E.2d 1126 (1995) (“The essence of the tort of libel is. the publication of a statement about an individual that is both false and defamatory.”); Immuno AG. v. Moor-Jankowski, 77 N.Y.2d 235, 245, 566 N.Y.S.2d 906, 567 N.E.2d 1270 (1991) (“[A] libel plaintiff has the burden of showing the falsity of factual assertions.... ”).
Numerous cases illustrate that falsity is an element of a New York defamation claim, -and that a plaintiff in New York courts generally must identify how the defendant’s statement was false to survive a motion to dismiss. .
In Silsdorf v. Levine, the plaintiff, a former mayor of his town who lost his reelection bid, sued the publishers of a letter that had disparaged Kim during the campaign. 59 N.Y.2d 8, 462 N.Y.S.2d 822, 449 N.E.2d 716 (1983). In ruling on a motion to dismiss, the New York Court of Appeals considered the defendants’ argument that “plaintiff has not: challenged the •accuracy of the letter’s factual statements.” Id. at 14, 462 N.Y.S.2d 822, 449 N.E.2d 716. Had the defendants been correct on that- point, the court noted, “the opinions complained of could not form the basis for a defamation cause of action.” Id. But the court concluded that the plaintiffs “affidavit in opposition to the motion'to dismiss assails virtually every statement of fact contained in the letter as either a ‘gross distortion’ or ‘misrepresentation of fact.’ ” Id. The court then gave a list, of specific examples of the, plaintiffs allegations of falsity. A sampling is instructive:
Defendants’ letter characterizes plaintiffs administration -as “one-man rule”, brought about by plaintiffs disregard of the board’s authority and unilateral actions taken in violation'of village ordinance, and board directive. In response to these statements, plaintiff alleges-that he did not, as stated in the letter, relieve board members of their.responsibilities, thus thwarting the democratic process; rather, following a dispute, he merely withdrew authority he had previously delegated to board members and immediately delegated that authority to others .... Further, defendants’ statement that plaintiff permitted a ferry to dock in violation of a board directive is alleged to be entirely untrue, inasmuch as plaintiff never authorized or permitted such landings.
Id. at 14-15, 462 N.Y.S.2d 822, 449, N.E.2d 716. In view of .these explanations as to why particular statements were false, the court ruled that the action could be sustained.
Similarly, in Fleischer v. NYP Holdings, Inc., the Appellate, Division affirmed the dismissal of a complaint for failure to state a claim because it did not allege falsity. 104 A.D.3d 536, 961 N.Y.S.2d 393 (1st *246Dep’t 2013). The plaintiff contended that a newspaper article falsely stated “that a popular Soho restaurant was closed because of her regular complaints.” Id. at 394. The court observed, however, that the fact “that the inspections” leading to the restaurant’s closure “resulted from plaintiffs complaints ... is an inference well supported by the record, including plaintiffs own allegations.” Id. She had thus failed to allege falsity, and her complaint failed to state a claim.
In Kraus v. Brandstetter, the Appellate Division dismissed a defamation claim as legally insufficient under similar circumstances. 167 A.D.2d 445, 562 N.Y.S.2d 127 (2d Dep’t 1990). The plaintiff, Kraus, a hospital administrator who had been fired, alleged that staff members under her control had been told that “your boss is going to get fired.” Id. at 129. The court explained that “in order to be actionable in defamation, a statement must be both false and defamatory.” Id. at 130. And “[s]ince [the defendant] stated that Kraus was going to be fired in the future, and Kraus was subsequently fired ..., the challenged statement was substantially true, and therefore, not defamatory.” Id.
Plaintiff disputes the principles discussed above, arguing instead that “substantial truth” is an affirmative defense that must await summary judgment. The argument relies on Garcia v. Puccio, 17 A.D.3d 199, 793 N.Y.S.2d 382 (1st Dep’t 2005). In Garcia, a school’s principal told the parent of a student that a particular teacher had been accused of using corporal punishment in the past. Id. at 383. The teacher sued the principal for defamation. The principal moved to dismiss, arguing that the statement was substantially true, because the fact of previous accusations was “undisputed,” and “plaintiff has the burden of showing the falsity of factual assertions.” Id. (citation omitted).
The trial court denied the motion to dismiss, and the Appellate Division affirmed. Id. at 383-84. The Appellate Division stated that “defendants’ reliance upon the apparent truth of [the disputed] statement is premature at this point inasmuch as a claim of truth or substantial truth, like a claim of qualified privilege, is an affirmative defense to be raised in defendants’ answer.” Id. The court noted that “[i]t would be error to give conclusive effect to defendants’ position of truthfulness before any affirmative defense to that effect has been raised in their answer.” Id. at 384.
Garcia fails to show, however, that truth may only be raised as an affirmative defense. In Garcia, the defendant’s statement of past accusations, though “technically” true, allegedly omitted necessary context—which was that the accusations were expunged after review. Id. at 383-84. Consequently, the court in Garcia faced a situation like that in Franklin: a statement technically true, but shorn of context, created a false impression of the plaintiff, while a report of the statement with its context perhaps would not have done so. See Franklin, 21 N.Y.S.3d at 12-13. In both cases, the plaintiff alleged that a statement would have had “a different effect on the mind of the average reader” had it been supplemented with certain context. See id. at 12. That is, of course, equivalent to alleging that the statements were not substantially true. See id. (“[A] statement is substantially true if the statement would not have a different effect on the mind of the reader from that which the pleaded truth would have produced.”) (internal quotation marks omitted). Such a pleading suffices to state a claim.
Although the opinion in Garcia stated that “truth or substantial truth ... is an affirmative' defense to be raised in defendants’ answer,” that language is best understood as referring only to cases where *247the truth or falsity of the defendant’s statement depends on material outside the complaint. In such a situation, the outside material may be presented by the defendant at summary judgment so the court may determine whether a legitimate question exists as to its truth or falsity.7 In sum, despite the language of Garcia, falsity is an element of a defamation claim under New York law.
C, Federal Pleading Standards
Having established that falsity—or lack of substantial truth—is an element of a New York defamation claim, it follows that a plaintiff must plead facts demonstrating falsity to prevail on a motion to dismiss the complaint in federal court.
To survive a motion to dismiss in federal court, a complaint must contain “enough facts to state a claim to relief that is plausible on its face.” Bell Atl. Corp. v. Twombly, 550 U.S. 544, 570, 127 S.Ct. 1955, 167 L.Ed.2d 929 (2007). A claim is facially plausible “when the plaintiff pleads factual content that allows the court to draw the reasonable inference that the defendant is liable for the misconduct alleged.” Ashcroft v. Iqbal, 556 U.S. 662, 678, 129 S.Ct. 1937, 173 L.Ed.2d 868 (2009). “These federal pleading rules and standards, ineluding the Supreme Court’s interpretation of Rule 8, prevail in all civil actions, including diversity litigation.” Biro v. Conde Nast, 807 F.3d 541, 544 (2d Cir. 2015) (internal quotation marks and citations omitted). Consequently, a federal court sitting in diversity must test state-law claims against the standard in Twombly and Iqbal. See, e.g., Cnty. of Erie v. Colgan Air, Inc., 711 F.3d 147, 149-50 (2d Cir. 2013).
Consistent with these principles, when falsity is an element of a state defamation claim, federal courts have required plaintiffs to plead facts that, if proven, would allow a reasonable person to consider the statement false. Swindol v. Aurora Flight Scis. Corp., 832 F.3d 492, 494-95 (5th Cir. 2016); Clark v. Viacom Int’l Inc., 617 Fed.Appx. 495, 509-10 (6th Cir. 2015); Price v. Stossel, 620 F.3d 992, 1000, 1003 (9th Cir. 2010). In particular, several courts of appeals have affirmed dismissals of defamation claims because the material in the complaint cannot be reasonably understood except as being true or substantially true. See Martin Marietta Materials, Inc. v. Kansas Dep’t of Transp., 810 F.3d 1161, 1185 (10th Cir. 2016); Turkish Coal. of Am., Inc. v. Bruininks, 678 F.3d 617, 626 (8th Cir. 2012). At least one court issued such a ruling even under earlier, less-stringent pleading standards. Quinn v. Ocwen Fed. Bank FSB, 470 F.3d 1240, 1244, 1246 (8th Cir. 2006).
Because falsity is an element of New York’s defamation tort, and “falsity” refers to material not substantially true, the complaint in this case must plead facts that, if proven, would establish that the defendant’s statements were not substantially true.8 In determining the sufficiency of Tannerite’s complaint, we may consider documents attached to it, such as the text of the article posted to NBC’s website and the video and transcript of the television report. See Chambers v. Time Warner, Inc., 282 F.3d 147, 152 (2d. Cir. 2002) (“[T]he complaint is deemed to in-*248elude any written instrument attached to it as an exhibit or any statements or documents incorporated in it by reference.”).
II. Substantial Truth of NBC’s Statements
Tannerite argues that its complaint adequately pled several ways in which NBC’s report was not substantially true. We consider these arguments in turn.
A. Tannerite Targets are not “Bombs”
Plaintiff first notes that NBC’s publications repeatédly compare Tannerite targets to “bombs.” Rossen stated, when first describing Tannerite targets, that he was “basically holding a bomb in [his] hand.” App’x at 91. Travis. Bond, the firearms expert interviewed by NBC, opined that Tannerite is “extremely dangerous, like a bomb for sale on the shelf.” App’x at 38. Other comparisons of the targets to bombs abound within NBC’s two publications.
Tannerite’s complaint states. that “[p]laintiff s rifle targets are not bombs.” App’x at 18. In briefing this appeal, Tan-nerite opposes the district court’s view of what constitutes a “bomb,” contending that the court appeared to believe that a “bomb” is' any “object with an explosive nature under certain conditions.” Appellant’s Br. at 24-25. Tannerite disputes what it understood to be the court’s capacious view:
The district court does not have to accept Appellant’s definition of “bomb” but should not substitute its own, when its own would encompass anything that could explode, including a firecracker, a champagne bottle, an oxygen tank, a battery, or potato in a microwave.
Appellant’s Br. at 25,
Given its discussion of oxygen tanks, batteries, and potatoes, Tannerite appears not to grasp a distinction the district court clearly recognized and employed: the difference between objects that merely happen to explode, and those designed or intended to explode. Only the latter are designated as “bombs.” Credible definitions of the term “bomb” capture this distinction. See United States v. Graziano, 616 F.Supp.2d 350, 359-60 (E.D.N.Y. 2008) (ruling, based on dictionary definitions, that under 18 U.S.C, § 921(a)(4)(A), “an incendiary bomb” is “simply any container or device that contains an incendiary material that is designed to be dispersed in a violent or rapid manner upon ignition, impact, and/or detonation, including in the form of heat or fire.”) (emphasis added), aff'd, 391 Fed.Appx. 965 (2d Cir. 2010); see also Bomb, Oxford English Dictionary (2016) (defining “bomb,” inter alia, as “a case filled with explosive, inflammable material, poison gas, or smoke, etc., fired from a gun, dropped from, aircraft, or thrown or deposited by hand”) (emphasis added); Bomb, Webster’s Third New International Dictionary, Unabridged (2017) (defining “bomb” as “a projectile or other device carrying.an, explosive charge fused to detonate under certain conditions ... and that is ... set into position &t a given point (such as dynamite) with varying effects (such as concussion, or fire-flinging, or the release of gases)....”) (emphasis added). These authorities either explicitly state that a bomb must be “intended” or “set” to explode, or clarify that bombs only come about through conditions that must be created intentionally by humans, such as “a case filled with explosive, inflammable material.”
As the district court recognized, the primary purpose, of a Tannerite exploding rifle target is to explode. See Tannerite Sports, 135 F.Supp.3d at 235. Tannerite’s product guide explains the intended use of the targets:!
*249Tannerite brand binary targets have changed the sport and practice of long-range shooting. Now, even at hundreds of yards, the experience of a hit seems close and personal.. Audibly, a well placed bullet produces a thunderous report that underlines your accuracy. Visually, the plume of a direct strike-circles like a round of high fives among friends. And all this sound, fury, reward—and fun—while improving your game,
App’x at 24. The guide also clarifies that the'targets are “intended for use with high powered center-fire rifles,” and explains how to detonate the targets properly. App’x at 25. Neithér the product guide, nor the remainder of the complaint, explains any other purpose of the targets beyond their use for explosion in target practice. The target’s singularity of explosive purpose—the fact that it is “is designed to be dispersed in a violent or rapid manner upon ... detonation,” Graziano, 616 F.Supp.2d at 360—marks it as a kind of bomb.
Unlike Tannerite targets, most other items listed in plaintiffs’ brief do not explode by design or purpose. Oxygen tanks and batteries primarily serve the non-explosive purposes of providing oxygen and electricity, respectively. It is unlikely that a potato’s-purpose is explosion, given that potatoes usually reside underground and seldom explode absent human prompting. As plaintiffs brief suggests, potatoes typically explode only during microwave cooking—a process intended to allow consumption of the potato rather than creation of explosions in the microwave.9
To be sure, the items Tannerite lists could be described as “bombs” if, in a perversion of their ordinary uses, someone intended to use them to cause explosions. But Tannerite-targets- stand out from potatoes, oxygen tanks, and batteries in that the targets’ primary purpose is explosion. For that reason, the district court- correctly ruled that NBC’s description of the product as a “bomb” was, at the least, substantially true.
B, Tannerite Targets are not “Bomb[s] on a Shelf’
Tannerite’s most emphatic argument is that, even if its targets are sometimes “bombs,” they cannot accurately be called “bomb[s] on a shelf,” which is how NBC’s publications described them. Appellant’s Br. at 24-27. Tannerite argues that this characterization ignores the product’s “binary” packaging, which keeps its two ingredients separately wrapped “while they are on the shelf,” thus preventing the targets from reaching their “active state.” Appellant’s Br. at 26. Tannerite explains that “[t]he main reason to create a binary target is ... so it cannot explode on a store shelf.” Appellant’s Br. at 26, Tanner-ite worries that “a reasonable viewer could conclude,” from NBC’s statement that the product is a “bomb on a shelf,” that “it would not be safe to shop at a store that stocked it, for fear of being hurt if it were to explode,” Appellant’s Br. at 26. And, given that no such risk exists, Tannerite argues -that the publications are not substantially true.'
Tannerite’s argument fails because each of NBC’s publications made clear that the target’s ingredients must be removed from the packaging, mixed, and shot before they explode. As noted, the court considers “[t]he entire publication, as well as the circumstances of its issuance,” to interpret *250its meaning. Silsdorf, 59 N.Y.2d at 13, 462 N.Y.S.2d 822, 449 N.E.2d 716.
NBC’s written article states that Tan-nerite is an “exploding target[ ],” App’x at 38 (emphasis added), and that it “explodes when you shoot it,” id. It explains that Tannerite “separat[es] the two ingredients in its explosive,” and quotes Bond, the firearms expert, as saying that “once it’s mixed, it’s classified as an explosive.” Id. The article never mentions any detonation of the product in a store.
Similarly, the video states that consumers “use it for target practice,” and “when you shoot it, it explodes.” App’x at 89. It shows Bond mixing the ingredients of the target, after which he states, “[t]his is now classified ... as an explosive.” Id. The video shows the. product exploding repeatedly in outdoor settings, either stating or implying that it has been shot, and never shows any explosion in a store. Finally, at the end of the video segment, Rossen holds the product and states that it is “not dangerous being in the studio right now,” and that “you need the catalyst” before the targets become explosive. Id. Given these statements, no reasonable viewer could have understood either publication, taken as a whole, to mean that Tannerite targets could explode within a retail outlet.
C. Gun-Rights Enthusiasts Oppose Sale of Tannerite Targets
Tannerite also argues that NBC’s report was not substantially true to the extent it stated that “gun-rights enthusiasts oppose” the targets. Appellant’s Br. at 33. This argument appears to refer to the interview of Bond, who stated that, although he is “a huge supporter of the Second Amendment,” he believes the targets are “extremely dangerous,” and the “equivalent of buying explosives off the shelf.” App’x at 89. Tannerite may also have in mind NBC’s publication of Bond’s view that “Tannerite is getting around the law on a technicality.” Id. The complaint states that NBC’s assertion that “Bond[] opposes the sale of Tannerite-brand targets ... is false” because “Bond himself owns a gun store that sells Tannerite-brand targets.” App’x at 17.
Tannerite does not explain why someone’s willingness to sell a product means that he must believe the product to be safe or otherwise commendable. Even if it were true (although it has certainly not been established at this stage) that Bond actually sells the product, and that he takes no precautions to protect the public from it, that does not mean he lied about holding a negative view of the product’s safety. Among other possibilities, the need to make a living, or the possession of inconsistent beliefs, could account for any apparent conflict between Bond’s views and his actions.
Nor does the balance of either of NBC’s publications suggest that “gun-rights enthusiasts oppose” Tannerite targets. The beginning of the video report, for example, states that “[g]un enthusiasts say they use [Tannerite] for target practice.” App’x at 89. In short, the facts alleged in the complaint would not, even if proven, establish that NBC published a false statement.
D. Tannerite is Not Associated with Terrorists
Tannerite contends that the district court failed to address an additional basis of its defamation claim: NBC’s suggestion that terrorists were associated with the company or had used the targets.
Tannerite contends that it properly pled this basis of its defamation claim in the proceedings below. Tannerite first highlights the following paragraph in the complaint:
*251[NBC’s] report and video ... contained one or more written false statements that were intended to impugn Plaintiffs rifle targets and Plaintiffs reputation in the sporting industry. A true and exact copy of screenshots of an Internet article describing falsities in the [NBC] report is attached as Exhibit E.
App’x at 18. In Tannerite’s view, the complaint alleged that any association of the targets with terrorists was false because Exhibit E, the cited article, suggested as much. Tannerite also points to a passage in the district court’s opinion noting a sentence in Tannerite’s memorandum opposing the motion to dismiss, which stated that NBC “falsely implied] that TAN-NERITE SPORTS is in cahoots with overseas terrorists.” App’x at 176.
These scattered, cryptic references do not amount to proper pleading. First, attaching the internet article to the complaint does not substitute for making a specific allegation that NBC falsely associated Tannerite with terrorists. It is true that parties may sometimes incorporate facts from outside documents into pleadings. See Chambers, 282 F.3d at 152-53. But that allowance does not permit vague, general references to documents outside the complaint in place of specific allegations putting the court and the defendant on notice of the particular claims asserted. See Fed. R. Civ. P. 8(a) (“A pleading that states a claim for relief must contain ... a short and plain statement of the claim showing that the pleader is entitled to relief....”) (emphasis added). Vagueness as to the complained-of conduct is particularly inappropriate when pleading a defamation claim. Our defamation jurisprudence has emphasized that “the complaint [must] afford defendant sufficient notice of the communications complained of to enable him to defend himself.” Kelly v. Schmidberger, 806 F.2d 44, 46 (2d Cir. 1986) (internal quotation marks omitted). As a practical matter, this rule requires the plaintiff to identify not only the publication, but also the respect in which it was allegedly false. A publication of even brief length often includes thousands of direct statements and implied messages whose veracity could be questioned by a defamation plaintiff. Some specificity is necessary so defendants and courts may address themselves to the parts of a communication alleged to be false and defamatory instead of those not objected to.10
Tannerite’s complaint failed to identify NBC’s statements regarding terrorism or explain why those statements were false. Instead, the complaint referred generally to an article that presented a scattershot collection of nearly a dozen objections to NBC’s publications. From that reference, a defendant and the court could not reasonably have understood that Tannerite wished to allege, in particular, that NBC’s discussion of the product’s links to terrorism were defamatory. The theory was thus not pled properly.
Tannerite is not saved by the brief remark in its memorandum opposing dis*252missal. The statement did not .point to any facts in the complaint showing that NBC’s claims regarding connections to “overseas terrorists” were false. Additionally, Exhibit E to the complaint, the article on which Tannerite relies for the factual basis of its terrorism argument, included, no specific factual statement bearing on whether Tan-nerite was “in cahoots with overseas terrorists.” Its arguments regarding NBC’s references to terrorism largely considered statements about domestic terrorism, and made general comments about the use of ammonium nitrate for non-explosive, non-terroristic purposes. App’x at 43-45. Although the article briefly opined that Tan-nerite would not be “useful” as a component of IEDs, because “easier and more reliable options” existed for “even the dumbest and most desperate terrorist,” App’x at 47, these comments do not sufficiently explain why any particular statement in NBC’s publications was false.
Neither the complaint nor the memorandum suffices to show that Tannerite pled this theory of liability below. The district court’s decision not to address it was thus appropriate.
III. Tannerite’s Motion to Amend
Tannerite also complains that the district court improperly denied its motion to amend, and that granting the motion would have allowed Tannerite to plead additional theories of defamation;
A. Tannerite’s Motion Below
Tannerite’s motion appeared in the last sentence of its brief in opposition to defendant’s motion to dismiss. It reads, in its entirety, as follows:
If the Court is inclined to grant NBC’s motion, then Tannerite Sports respectfully seeks leave to file an amended complaint to correct any defects identified by the Court[.]
App’x at 193. The motion thus identified no particular facts that would be introduced into an amended complaint. The district court denied this request, ruling that, “[b]ased on Tannerite’s failure to ... present-proof of falsity with respect to [NBC’s] statements ..., it would be futile to permit Tannerite to further amend its Complaint.” Tannerite Sports, 135 F.Supp.3d at 236.
“Proposed amendments are futile,” and thus must be denied, “if they would fail to cure prior deficiencies or to state a claim under Rule 12(b)(6) of the Federal Rules of Civil Procedure.” Thea v. Kleinhandler, 807 F.3d 492, 496-97 (2d Cir. 2015) (internal quotation marks and citation omitted). Here, Tannerite simply stated that an amendment would “correct any defects identified by the Court.” App’x at 193. That request made no specific argument as to how an amended complaint would “cure prior deficiencies” or pass muster under Rule 12(b)(6). It was properly denied as futile,'
B. Tannerite’s Proposals for Amendment
Tannerite argues that it could have amended its complaint to allege that NBC made false claims regarding its connections to terrorists, to allege that NBC falsely claimed that its targets were “flammable,” to add a product disparagement claim, and to include “further emphasis on certain aspects of the video to create a more rigorous showing of defamation by implication,” Appellant’s Br. at 41; Appellant’s Reply Br. at 29-31. In Tannerite’s view, these amendments would have cured the legal deficiencies identified by the district court.
We reject Tannerite’s proposed amendments, all of which are newly raised on appeal. “It is a, well-established general rule that an appellate court will *253not consider an issue raised for the first time on appeal.” Bogle-Assegai v. Connecticut, 470 F.3d 498, 504 (2d Cir. 2006) (brackets omitted) (quoting Greene v. United States, 13 F.3d 577, 586 (2d Cir. 1994)). Although “we have discretion to consider [such] arguments ... the circumstances normally do not militate in favor of an exercise of discretion” to do so “where those arguments were available to the parties bélow and they proffer no reason for their failure to raise the arguments below.” Id. (internal quotation marks, citations, arid brackets omitted). None of Tan-nerite’s new theories of liability were put before the district court in the brief motion to amend. Nor did Tannerite offer the district court a full account of its plans to amend by moving to alter or amend the judgment under Federal Rule of Civil Procedure 59, which would have allowed the district court to “take into account the nature of the proposed amendment in deciding whether to vacate the previously entered judgment.” Nat'l Petrochem. Co. of Iran v. M/T Stolt Sheaf, 930 F.2d 240, 245 (2d Cir. 1991). Tannerite provides no good reason for its failure to have requested below the relief it now seeks here, particularly given that the new arguments rely only on facts that Tannerite knew when the operative complaint was filed.
CONCLUSION
We have reviewed Tannerite’s other arguments and have determined that they are meritless. Accordingly, the district court’s judgment is AFFIRMED.
. "IED” stands for "improvised explosive device." IED, Webster’s Third New International Dictionary, Unabridged (2017).
. Tannerite also sued one of NBC’s affiliates, but that party’s dismissal from the suit is not appealed, and the allegations against the affiliate are not relevant to the case against NBC,
. Traditional New York law appears to have applied a similar, but not identical, rule. There was no requirement that falsity be alleged in the complaint. See Ernest P. Seelman, The Law of Libel and Slander in the State of New York § 392 (1964 ed.); see also Gutkes v. N.Y. Produce Exch., 46 Misc. 133, 93 N.Y.S. 254, 256 (Sup. Ct. 1905); Hunt v. Bennett, 19 N.Y. 173, 176 (1859). Although truth was an absolute defense to defamation, see Stuart v. Press Pub. Co., 83 A.D. 467, 82 N.Y.S. 401, 409 (1st Dep’t 1903), a statement claimed to be defamatory would be "presume[d] ... to be false,” Hunt, 19 N.Y. at 176, and it was the defendant's burden to rebut the presumption of falsity. See Rinaldi v. Holt, Rinehart & Winston, Inc., 42 N.Y.2d 369, 379-80, 397 N.Y.S.2d 943, 366 N.E.2d 1299 (1977) (“At common law, the libelous statement was presumed to be false and the defendant carried the burden of pleading and proving, in defense, that the statement was true.”). Additionally, malice—an element of defamation—was often supported by the presumption that a statement was false; a defendant’s proof of a statement’s truth could thus also defeat a defamation claim by showing that malice was lacking. See Root v. King, 7 Cow. 613, 625 (N.Y. 1827) ("It is the settled law of this state, that, to support an action [for defamation], malice is essential; and whether there is malice in the publication, belongs to the jury to decide as matter of fact.... But how is malice to be proved? In few cases will it be declared. It must be inferred from the libellous nature of the publication, and (unless in certain excepted cases) falsehood, added to the character of the publication, must be considered, prima facie, evidence of malice.”).
. Even if falsity were not an element of a New York defamation claim, Tannerite would likely be required to plead it in this case. In Philadelphia Newspapers, Inc. v. Hepps, the United States Supreme Court held, based on First Amendment principles, that “where a newspaper publishes speech of public concern, a private-figure plaintiff cannot recover damages without also showing that the statements at issue are false." 475 U.S. 767, 768-69, 106 S.Ct. 1558, 89 L.Ed.2d 783 (1986). NBC’s report, appears to have discussed a matter of public concern inasmuch as it profiled a product it viewed as dangerous to the public and considered the government’s efforts to regulate the product. The broadcast featured an interview with a sitting United States Senator and discussion of actions taken by federal agencies, It also provided Tan-nerite an opportunity to weigh in on the debate, which it did by asserting that "only girly-men” would seek to increase regulation of the product.
Although the Supreme Court has not explicitly ruled that falsity must be alleged in a defamation complaint to comport with Hepps, it is difficult to see how the rule could be otherwise. A complaint must "contain sufficient factual matter, accepted as true, to state a claim to relief that is plausible on its face,” Ashcroft v. Iqbal, 556 U.S. 662, 678, 129 S.Ct. 1937, 173 L.Ed.2d 868 (2009) (internal quotation marks omitted). If a plaintiff must ultimately show falsity to win, a defamation claim described in the plaintiff’s complaint would not be "plausible” absent an allegation that the defendant’s statements were false. In other words, “[a] defamation case does not •putter along as a state law case in its earliest stages, only to suddenly acquire First Amendment implications upon the tender of an affirmative defense.” Hatfill v. New York Times Co., 427 F.3d 253, 254-55 (4th Cir. 2005) (Wilkinson, J., dissenting from denial of rehearing en banc).
Indeed, it appears that New York courts have recognized falsity as a necessary element in all defamation actions at least partly in response to First Amendment cases such as Hepps and New York Times Co. v. Sullivan, 376 U.S. 254, 84 S.Ct. 710, 11 L.Ed.2d 686 (1964), See Rinaldi, 42 N.Y.2d at 380, 397 N.Y.S.2d 943, 366 N.E.2d 1299 ("Although there has been doubt, the burden is now on the libel plaintiff to establish the falsity of the libel. This requirement follows naturally from the actual malice standard [articulated in Sullivan for cases brought by public-figure plaintiffs].”); Immuno AG. v. Moor-Jankowski, 77 N.Y.2d 235, 245, 566 N.Y.S.2d 906, 567 N.E.2d 1270 (1991) (citing Hepps, among other sources, for the proposition that "a libel plaintiff has the burden of showing .,. falsity”). Evidently, such an evolution in state law has not been atypical, although it is unclear at this stage that Supreme Court precedent requires falsity as an element in all cases. See Dan B. Dobbs, Paul T. Hayden & Ellen M. Bublick, The Law of Torts § 519 (2d ed. 2016) (“These added elements[, including falsity,] came about as courts attempted to integrate federal Constitutional rules of free-speech into the common law of libel.... A later Supreme Court decision, however, suggests that the Constitution does not require these added elements where the defendant defames a purely private person on. an issue that is not of public concern. Nevertheless, states apparently continue to state these added elements of proof for all cases, not merely those involving public figures or issues of public concern.”) (citations omitted).
. It is also noteworthy that the court in Garcia cited no authority suggesting that truth or substantial truth must always be presented as an affirmative defense. The court did, however, cite significant authority demonstrating that privilege, another argument raised by the defendants in that case, must be a defense. See Garcia, 793 N.Y.S.2d at 384.
. The test is one of legal sufficiency, not journalistic competence.
. Certain items on Tannerite’s list, including firecrackers,’ could perhaps qualify as "bombs,” given that they are created with explosion (or at least ignition) in mind. As for Champagne, the pop is incidental rather than intentional, .
. New York state law requires that, “[i]n an action for libel or slander, the particular words complained of shall be set forth in the complaint,” Nowak v. EGW Home Care, Inc., 82 F.Supp.2d 101, 113 (W.D.N.Y. 2000) (emphasis added) (quoting N.Y. C.P.L.R. § 3016(a)). Although federal pleading standards, not state standards, govern this matter, see Kelly, 806 F.2d at 46, the strictness of New York’s law reflects the importance of giving defendants notice of why any alleged statements were defamatory. Similarly, we note that stricter rules for defamation pleading prevailed under earlier pleading regimes, see, e.g., Foltz v. Moore McCormack Lines, Inc., 189 F.2d 537, 539 (2d Cir. 1951), and although we do not suggest a return to those standards, they underline the importance of receiving proper notice of a defamation claim.