CORDY, J.

This case concerns the constitutionality of the criminal harassment statute, G. L. c. 265, § 43A (a), and its application to acts of cyberharassment among others. Specifically, we consider whether a pattern of harassing conduct that includes both communications made directly to the targets of the harassment and false communications made to third parties through Internet postings solely for the purpose of encouraging those parties also to engage in harassing conduct toward the targets can be constitutionally proscribed by the statute. We also consider whether, to the extent that this pattern of conduct includes speech, that speech is protected by the First Amendment to the United States Constitution or is unprotected speech integral to the commission of the crime.

The defendants, William and Gail Johnson, were both convicted of criminal harassment. William2 was also convicted of making a false, or "frivolous," report of child abuse, G. L. c. 119, § 51A (c). Among other things, the defendants' conduct included posting information about the victims online along with false statements about items that the victims allegedly either had for sale or were giving away, with the object of encouraging unwitting third parties to repeatedly contact and harass the victims at their home and on their telephone. The defendants also anonymously sent hostile and ominous communications directly to the victims.

William claims that the criminal harassment statute is facially unconstitutional, arguing that it regulates protected speech and does not provide sufficient notice of the type of conduct that is proscribed. Additionally, both defendants argue that the statute is unconstitutional as applied to their conduct because they did not engage in "fighting words," an unprotected category of speech that we held could be constitutionally proscribed under the statute in Commonwealth v. Welch, 444 Mass. 80 (2005), abrogated on another ground by O'Brien v. Borowski, 461 Mass. 415 (2012).3 Further, both defendants contend that their conduct did not meet the statutory requirements because their actions were not actually directed at the victims and there was inadequate evidence that their conduct caused any serious alarm to the victims. We conclude that the Legislature drafted a sufficiently specific statute that is not unconstitutional on its face; that the defendants' conduct included speech that was not protected by the First Amendment, but rather was integral to criminal conduct; and, accordingly, that the statute is not unconstitutional as applied to the defendants. We also conclude that the defendants' conduct as established at trial met all of the statutory requirements for a guilty verdict.

Background. We summarize the facts that the jury could have found, reserving certain details for our analysis of the issues raised on appeal. The victims, James "Jim" J. Lyons, Jr., and his wife, Bernadette, have lived on the same street as the defendants in Andover since around 2000. In 2003, the defendants acquired a tract of land abutting the Lyonses' property and intended to subdivide and develop it. The Lyonses, along with other neighbors, objected to the proposed development and years of litigation ensued between the parties. By 2008, the relationship between the families had become strained and communication between them was infrequent.

Gerald Colton, a childhood friend of the Johnsons, did not know the Lyons family prior to 2008. Throughout the 1990s and early 2000s, William hired Colton to work as a handyman on an hourly basis and to identify lots for potential real estate development. If William later developed a lot Colton had identified, Colton would collect a finder's fee.4

In either late February or early March, 2008, William telephoned Colton and enlisted him to play a series of "pranks" on Jim. The ideas for these "pranks" were generated in several ways: (1) William would directly instruct Colton or convey ideas through Gail; (2) the Johnsons would provide information about the Lyons family to Colton so that he could use this information to harass them; or (3) the Johnsons would prompt Colton to think of ideas.

Over the course of thirty-five days in late March and early April, 2008, the defendants, directly and through Colton, engaged in a series of acts directed at the Lyons family. The Commonwealth alleged four separate acts of harassment in addition to the false report of child abuse, and Colton was called as its key witness at the trial.

The first alleged act occurred on March 18, 2008, when Colton posted from his computer an advertisement that appeared on the Internet site "Craigslist." The advertisement provided the Lyonses' home telephone number and address and stated that there were free golf carts available at this location on a "first come, first serve" basis. The Lyonses did not own any golf carts and had never used Craigslist. When Bernadette arrived home at 2:30 P.M. that same day, there were strangers in both her driveway and on the street near her home. These individuals informed her about the advertisement and explained that they were looking for golf carts. In total, about thirty to forty people arrived at the Lyonses' house that afternoon, causing Bernadette to be "scared" and "fearful."

When Jim arrived home later that evening, he telephoned the police, as Bernadette was in a state of "uneasiness" and Jim felt the incident was "really unusual" and "bizarre." Andover police Sergeant Chad Cooper responded and advised Jim to contact Craigslist to remove the advertisement and get the Internet protocol address for the computer that posted it. In Sergeant Cooper's presence, Jim received numerous telephone calls from people inquiring about the golf carts. When William learned that the Craigslist advertisement had been removed, he asked Colton to "put it back up" and Colton complied. After reposting, Colton testified that he and William "laughed" about it and Colton said that he would post another advertisement.

The second alleged act occurred on March 19, when Colton posted a different Craigslist advertisement, selling "my late son's" motorcycle and directing interested parties to call Jim on his cellular telephone after 10 P.M.5 Colton then told William about the posting. That night, Jim received "non-stop" telephone calls regarding the advertisement, approximately twenty every ten minutes. Sergeant Cooper responded again. These late night calls continued for months after the posting.

The third alleged act occurred one week later on March 26, when Colton sent an electronic mail (e-mail) message to the Lyonses from a fictitious account. The subject of the message read, "It's just a game for me," and the text stated, "Let The Games Begin!" The message contained Jim and Bernadette's personal identifying information, including names, home telephone number and address, Social Security numbers, e-mail address, bank name and location, and Jim's date of birth and cellular telephone number. At the bottom, the message stated: "Remember, if you aren't miserable, I aint happy! Let's Play." Colton testified that Gail had sent him an e-mail message with the Lyonses' personal information.

The following evening, William arrived at Colton's home and told Colton that he wanted to call and "turn [Jim] in." William had a piece of paper with a hotline telephone number written on it and proceeded to use Colton's home telephone to call the Department of Children and Families (DCF) to file a false report alleging child abuse by Jim. William later telephoned Colton to report that a police cruiser and another vehicle were at the Lyonses' home.6

Investigator Carrie Riley of the DCF testified that an after-hours "child abuse hotline" had received a call from someone using fictitious information and reporting that Jim was physically abusing his son. Riley and another investigator arrived at the Lyonses' home at 10:30 P.M. and said they had to examine their son. Jim testified that he and Bernadette were "panicked" and "frightened," but that, acting on the advice of their attorney, he awakened their son and permitted Riley to inspect him. Riley examined his body for marks and bruises. The DCF case was closed as the son denied any abuse and the investigators found no signs of it.

The fourth alleged act occurred on April 3, 2008, when Colton sent another anonymous e-mail message to the Lyonses from another fictitious e-mail account. The subject line was "Brian," and the text read, "What have you done James? ... or ... Why James? You stole the innocence of a young man." Shortly thereafter, Jim received a letter by postal mail purportedly sent from an individual named "Brian." Brian claimed to have worked for Jim when he was fifteen years of age, accused Jim of sexually molesting him as a teenager, and threatened to press charges against him. Colton testified that William told Colton that he had sent the letter.7 Even though the allegations were false, reading the letter was "very tough" and "absolutely alarmed [Jim]."

Throughout this entire time period, Colton consistently kept in contact with both defendants, letting them know what he was doing or had done to the Lyons family. William and Gail acquiesced to Colton's conduct and encouraged him to do more.

Procedural history. Police traced the relevant Internet activity back to Colton, who was charged on June 5, 2008, with stalking and identity fraud. Colton spent seventeen days in jail before posting bail. On August 14, 2008, Colton made a statement taking responsibility for the Internet postings and e-mail messages and implicating the defendants in the scheme.

The Johnsons were charged on October 16, 2008, in Lawrence District Court with making a false report of child abuse (G. L. c. 119, § 51A [c]); identity fraud (G. L. c. 266, § 37E); conspiracy (G. L. c. 274, § 7); and criminal harassment (G. L. c. 265, § 43A [a]). Colton entered into a written plea agreement with the Commonwealth in exchange for his testimony against the Johnsons.

During pretrial proceedings, the defendants filed motions to dismiss, asserting that (1) the Commonwealth failed to provide discovery; (2) there was no probable cause that the defendants had committed any crime; (3) the destruction of evidence caused by the Commonwealth warranted dismissal; (4) the defendants' right to a speedy trial was violated; (5) venue for the charge of making a false report was improper; and (6) there was prosecutorial misconduct. All of these motions were denied.

At the close of the Commonwealth's case, the Johnsons moved for required findings of not guilty on all of the charges. The judge entered a finding of not guilty on the charge of identity fraud, but denied the defendants' motion in all other respects. The judge also denied the defendants' motion at the close of all of the evidence. The charge of conspiracy was dismissed at the Commonwealth's request.

On December 1, 2011, a jury convicted the defendants of criminal harassment and convicted William of making a false report of child abuse. On the harassment charge, William was sentenced to two and one-half years in the house of correction, eighteen months to be served with the balance suspended until December 1, 2014, with probation conditions; on the charge of making a false report of child abuse, he was fined $1,000. Gail was sentenced to two years in the house of correction, six months to be served with the balance suspended until December 1, 2014, with probation conditions, and fined $1,000. We transferred the defendants' appeal to this court on our own motion.

Discussion. On appeal, the defendants make multiple claims of error regarding the Commonwealth's compliance with discovery rules, alleged prosecutorial misconduct, choice of venue, evidentiary rulings at trial, the sufficiency of the evidence, statements made in closing argument, and the right to a speedy trial. We conclude that the judge's rulings were correct and these claims are without merit.

We begin, however, with a discussion of the defendants' challenges to the constitutionality of G. L. c. 265, § 43A (a) (§ 43A [a]), both facial8 and as applied to them. Such constitutional challenges are questions of law that we review de novo. Commonwealth v. Martin, 467 Mass. 291, 301 (2014).

A criminal conviction under § 43A (a) requires proof that "(1) the defendant engaged in a knowing pattern of conduct or speech, or series of acts, on at least three separate occasions; (2) the defendant intended to target the victim with the harassing conduct or speech, or series of acts, on each occasion; (3) the conduct or speech, or series of acts, were of such a nature that they seriously alarmed the victim; (4) the conduct or speech, or series of acts, were of such a nature that they would cause a reasonable person to suffer substantial emotional distress; and (5) the defendant committed the conduct or speech, or series of acts, `willfully and maliciously'" (citations omitted). Commonwealth v. McDonald, 462 Mass. 236, 240 (2012).

Although this court has previously construed the criminal harassment statute, it has not yet considered its application to the type of conduct at issue here. An analysis of whether the defendants' actions amounted to criminal harassment necessarily includes the consideration whether their conduct satisfied the statutory requirements and whether they engaged in constitutionally protected speech.

1. Facial challenge. William argues that § 43A (a) is both unconstitutionally overbroad and vague. He contends that the statute is dangerously susceptible of application to constitutionally protected speech and is so vague that it leaves the public uncertain as to the conduct it prohibits. His challenge fails on two accounts.

First, the claim is raised for the first time on appeal, and consequently is waived. See Commonwealth v. Dockham, 405 Mass. 618, 632-633 (1989). Although, as the defendant notes in his reply brief, we are nevertheless not prevented from considering his claim, we "rarely exercise[]" this power and only do so in instances where a "serious and obvious" mistake poses a "substantial risk of a miscarriage of justice." Commonwealth v. Oakes, 407 Mass. 92, 94-95 (1990).

Second, the challenge fails because the statute is neither overbroad nor vague. William bears the burden of showing "`from the text of [the law] and from actual fact' ... that substantial overbreadth exists" (citation omitted). Virginia v. Hicks, 539 U.S. 113, 122 (2003). As an initial matter, § 43A (a) is a statute directed at a course of conduct, rather than speech, "and the conduct it proscribes is `not necessarily associated with speech'" (citation omitted). United States v. Petrovic, 701 F.3d 849, 856 (8th Cir. 2012) (considering similar statute). In particular, § 43A (a) specifically criminalizes "a knowing pattern of conduct or series of acts ... directed at a specific person, which seriously alarms that person and would cause a reasonable person to suffer substantial emotional distress" (emphases added). As the United States Court of Appeals for the Ninth Circuit held in United States v. Osinger, 753 F.3d 939, 944 (9th Cir. 2014), when considering a similar statute, because § 43A (a) "proscribes harassing and intimidating conduct, the statute is not facially invalid under the First Amendment."

Further, as the statute requires both malicious intent on behalf of the perpetrator and substantial harm to the victim, "it is difficult to imagine what constitutionally-protected speech would fall under these statutory prohibitions." Id., citing Petrovic, 701 F.3d at 856. Contrary to William's claim, the statutory elements such as "seriously alarms" "are not esoteric or complicated terms devoid of common understanding." Osinger, supra at 945. Rather, these elements are similar to those that have led courts in other jurisdictions to uphold their criminal harassment statutes as constitutionally permissible. See, e.g., State v. Brown, 207 Ariz. 231 (Ct. App. 2004); Bouters v. State, 659 So.2d 235 (Fla.), cert. denied, 516 U.S. 894 (1995).

Together the component parts of the statute provide adequate notice and safeguards to prevent its application to protected speech. Contrary to William's claim that the statute leaves it to the hearer of the speech to determine what conduct is criminal, the Commonwealth must prove that a defendant knew he or she was engaged in a pattern of conduct that intentionally targeted a victim for the purpose of harassment with acts of such a nature that they would cause a reasonable person to suffer substantial emotional distress. This scienter requirement undermines William's claim that he could be liable under § 43A (a) if his actions were accidental and that putative harassers are at the mercy of a hearer's sensitivities. Moreover, William has offered no meaningful evidence to show that the statute has a real and substantial deterrent on protected speech or that it actually denies fair notice of what conduct is proscribed. The required elements are clearly delineated such that § 43A (a) leaves no putative harassers wondering what is prohibited. Accordingly, William's facial challenge to § 43A (a) fails.

2. As-applied challenge. The defendants' as-applied constitutional challenge also fails because the conduct in question was not protected speech, but rather a hybrid of conduct and speech integral to the commission of a crime. Accordingly, § 43A (a), as applied to the defendants, does not implicate constitutionally protected speech rights.

"[I]t has never been deemed an abridgment of freedom of speech or press to make a course of conduct illegal merely because the conduct was in part initiated, evidenced, or carried out by means of language, either spoken, written, or printed." United States v. Sayer, 748 F.3d 425, 433 (1st Cir. 2014), quoting Giboney v. Empire Storage & Ice Co., 336 U.S. 490, 502 (1949). The defendants do not claim that creating fictitious Internet postings and sending a letter falsely accusing someone of a crime constitute legal conduct. Their conduct served solely to harass the Lyonses by luring numerous strangers and prompting incessant late-night telephone calls to their home by way of false representations, by overtly and aggressively threatening to misuse their personal identifying information, and by falsely accusing Jim of a serious crime. Where the sole purpose of the defendants' speech was to further their endeavor to intentionally harass the Lyonses, such speech is not protected by the First Amendment. "The [F]irst [A]mendment does not provide a defense to a criminal charge simply because the actor uses words to carry out his illegal purpose." United States v. Barnett, 667 F.2d 835, 842 (9th Cir. 1982).

In this respect, we are guided by the reasoning of the United States Supreme Court and several circuit courts of the United States Court of Appeals. In Giboney, 336 U.S. at 498, cited with approval in United States v. Stevens, 559 U.S. 460, 468-469 (2010), the United States Supreme Court held that speech or writing used as an integral part of conduct in violation of a valid criminal statute is not protected by the First Amendment. Following the holding in Giboney, in Sayer, the United States Court of Appeals for the First Circuit held that the defendant's posting of fictitious Craigslist advertisements to induce anonymous third parties seeking casual sexual encounters to harass the victim amounted to unprotected speech integral to the criminal conduct proscribed by the Federal cyberstalking statute, 18 U.S.C. § 2261A (2012 & Supp. I 2013).9 748 F.3d at 433-434.

Similarly, in Petrovic, 701 F.3d at 854-856, the United States Court of Appeals for the Eighth Circuit concluded that § 2261A was properly applied to a defendant who created a Web site with links to images of the victim nude or engaged in sex acts with him, where the sole purpose of the communications was to carry out the defendant's threats to harass and humiliate the victim if she ended their sexual relationship. As integral to the commission of the crime of cyberstalking, the defendant's communication, although speech, fell outside the purview of the First Amendment.

The speech here, much as the speech at issue in Giboney, Sayer, and Petrovic, was also "integral to criminal conduct," serving only to implement the defendants' purpose to harass and cause substantial emotional distress to the Lyonses in violation of § 43A (a).10 The defendants point to no lawful purpose of their "communications" that would take them outside of the exception delineated in Giboney. To the extent that any of the harassing contacts were composed of words, they were used "so close in time and purpose to a substantive evil as to become part of the ultimate crime itself." United States v. Freeman, 761 F.2d 549, 552 (9th Cir. 1985), cert. denied, 476 U.S. 1120 (1986). In such instances, "where speech becomes an integral part of the crime, a First Amendment defense is foreclosed." Id. While the content of the speech in question certainly affected the Lyonses, much of the alarming impact was the product of the frightening number, frequency, and type of harassing contacts with which the defendants bombarded the Lyonses. In these circumstances, the application of § 43A (a) to the defendants fully withstands constitutional scrutiny.11

Nonetheless, the defendants attempt to argue that they are entitled to a required finding of not guilty on the criminal harassment charge because none of their speech constituted "fighting words," which they contend was the only form of speech punishable at the time of the offense under our interpretation of the statute in Welch. See generally 444 Mass. at 93-100. This argument is meritless. While the focus of our decision in Welch was centered on the "fighting words" doctrine, we expressly noted that "[a]ny attempt to punish an individual for speech not encompassed within the `fighting words' doctrine (or within any other constitutionally unprotected category of speech) would of course offend our Federal and State Constitutions" (emphasis added). Id. at 99. These well-defined and limited categories of speech "are not protected because they are `no essential part of any exposition of ideas, and are of such slight social value as a step to truth' that whatever meager benefit that may be derived from them is `clearly outweighed' by the dangers they pose." Borowski, 461 Mass. at 422, quoting Chaplinsky v. New Hampshire, 315 U.S. 568, 572 (1942). Speech integral to criminal conduct is one such long-standing category that is constitutionally unprotected, directly applicable to the defendants' conduct here, and permissibly proscribed by § 43A (a).12 Accordingly, the denial of the defendants' motion for a required finding of not guilty on the basis that they engaged in protected First Amendment activity was not error.

3. Sufficiency of evidence. The defendants contend that there was insufficient evidence of their joint venture to criminally harass the victims, arguing that both the "directed at" and "seriously alarms" prongs of the statute were not met. In reviewing the sufficiency of the evidence, we consider the facts in the light most favorable to the Commonwealth, see Commonwealth v. Latimore, 378 Mass. 671, 676-677 (1979), and determine whether any rational trier of fact could have found beyond a reasonable doubt all of the statutory elements.

a. "Directed at" prong. Section 43A (a) requires that the Commonwealth prove three or more predicate acts of harassment that were "directed at a specific person." See McDonald, 462 Mass. at 240. The defendants argue that the Craigslist postings (two of the four acts supporting the harassment charge) were not directed at the victims, but were merely directed at the general public.

This argument is without merit. As a factual matter, the jury clearly could have concluded that the "directed at" prong was met. While the defendants' methods were indirect, the false information in the Craigslist postings was intended solely to ensure that the victims were harassed as a consequence by unwitting third parties contacting them at all hours of the night by telephone and showing up at their home. Essentially, the "sole immediate object" of the false advertisements was to create a marketplace for the guaranteed harassment of the victims. See Giboney, 336 U.S. at 498.

The defendants cite to Welch for the contention that statements made to a third party are not speech directed at a specific person. 444 Mass. at 92-93 (shouting abusive epithets in one's apartment and speaking in normal tone of voice to third party outside does not satisfy requirements of § 43A [a]). The defendants' acts in the instant case are appreciably different from those at issue in Welch. The Craigslist postings were the equivalent of the defendants recruiting others to harass the victims and the victims alone. The causation link is satisfied. The defendants cannot launder their harassment of the Lyons family through the Internet to escape liability.

b. "Seriously alarms" prong. Section 43A (a) also requires the Commonwealth to prove that the acts of alleged harassment "seriously alarm[ed]" the victims. The serious alarm required under § 43A (a) is a "demanding, subjective element of harm" that must be satisfied by a victim's testimony rather than conjecture. Commonwealth v. Braica, 68 Mass.App.Ct. 244, 247 (2007). The defendants argue that (1) the Commonwealth offered insufficient proof that the victims were seriously alarmed, and (2) the victims did not experience serious alarm separately for each act, as required, rather than cumulatively as the result of the pattern of harassing acts. We disagree with both contentions.

First, the Lyonses' subjective feelings of fear and anxiety were actual (not hypothetical), significant, and well documented at trial. As a general matter, Jim and Bernadette testified that they felt "bombarded," "attacked," and "very frightened" throughout the ordeal. Jim described the thirty-five-day "odyssey" in which the defendants would "torture [them]," stating that he was concerned about the safety of his family and himself: "The[y] attacked my business. They attacked my family. And they tried to take my kids away from me." Bernadette described the situation as "very traumatic," stating that her family was in a "siege mentality where [e]very day something was happening so [they] got afraid." The Lyonses were sufficiently alarmed to call the police "right away" after the very first harassing act. Jim testified that the second act "stepped it up a notch" and made him feel "[t]errible," and that the correspondence that he received alleging sexual molestation was "very tough" and "absolutely alarmed" him. The police took notice of and corroborated Jim's testimony that the defendants' conduct took a substantial emotional toll on him.

The Lyonses' testimony of feeling frightened, tortured, and attacked more than meets the "seriously alarms" standard. The victims testified to an abundance of distressing and alarming conduct that amounted to a serious invasion of their emotional tranquility. Unlike the victims in Commonwealth v. Kessler, 442 Mass. 770, 773-774 (2004), who offered no proof that they were "actually `alarmed or shocked,'" but rather just "offended" by the defendant's indecent exposure, the Lyonses testified to having a level of fear and anxiety similar to the victims in Commonwealth v. Robinson, 444 Mass. 102, 105, 108 (2005) (serious alarm requirement met where, as result of harassment, victim felt vulnerable, son's grades dropped due to nervousness, and family felt constantly under surveillance). See Commonwealth v. O'Neil, 67 Mass.App.Ct. 284, 294 (2006) (defendant's letters and telephone calls seriously alarmed victim who felt "concern[ed]" and "very scared," and asked State officials for assistance). Here, the Lyons family did not merely experience uneasiness associated with day-to-day living, but rather, as the ominous and hostile acts perpetrated by the defendants continued to escalate, the totality of the situation evoked the type of "serious negative emotional experience" required under the statute. Kessler, supra at 774.

As for whether serious alarm must be shown for each individual act or may be measured cumulatively, we conclude that the statute's wording ties the requirement to the over-all pattern of conduct. The statutory language of § 43A (a) requires that the "pattern of conduct" or "series of acts" "seriously alarms." As a general rule of statutory construction, "words importing the plural number may include the singular." G. L. c. 4, § 6, Fourth. Accordingly, "acts" might refer to a single act as well as multiple acts. However, the rules of grammar and proper subject-verb agreement instruct a reading of "alarms" to modify the singular noun of one "pattern" or one "series," rather than the noun "acts."13 The evidence at trial was sufficient to support the verdict rendered by the jury.

4. Pretrial motions. In three joint motions before the trial court, the defendants unsuccessfully asked for the case to be dismissed, alleging prosecutorial errors that caused undue delay and prejudice. Specifically, they contended that dismissal was appropriate based on the Commonwealth's "loss" of Colton's telephone records and the Commonwealth's delayed disclosure of (1) promises, rewards, and inducements made to Colton in exchange for his cooperation; (2) Colton's statements regarding the location of the DCF call; and (3) a diary that Colton kept.

While the Commonwealth has a duty to disclose all material, exculpatory evidence in its possession, see Brady v. Maryland, 373 U.S. 83, 87 (1963); Commonwealth v. Tucceri, 412 Mass. 401, 404-405 (1992), we agree with the motion judge that the Commonwealth did not withhold any such evidence here and that delays in disclosure did not result in prejudice.

Colton's telephone records were potentially significant to the case because they could corroborate (or not) that a call was made from his telephone to the DCF hotline falsely reporting child abuse, and was not made from William's telephone. In November, 2009, the Commonwealth subpoenaed these records from Verizon and was notified that Colton's correct telephone service provider was Comcast. However, it was not until June of 2010 that the prosecutor attempted to obtain Colton's records from Comcast. By then, the subpoenaed records were no longer available as they were outside the company's retention period. The defendants argue that this "loss" of records was prejudicial to their defense strategy. We agree that the Commonwealth could have and should have attempted to obtain Colton's telephone records earlier, but, ultimately, these records would not have provided any exculpatory information and their "loss" was not prejudicial. The Commonwealth had already disclosed the DCF hotline records to the defendants, which identified the telephone number of the caller as Colton's, thus establishing that a call was made to DCF from Colton's telephone number, not William's, precisely what Colton's telephone records would have established. Further, the defendants had considerable opportunity and bases for cross-examining Colton even without his telephone records, "`effectively' remov[ing]" any prejudice (citation omitted). Commonwealth v. Molina, 454 Mass. 232, 236-237 (2009).

Regarding promises, rewards; and inducements, well before trial, the prosecutor acknowledged Colton's preliminary discussions with the government. Once an agreement was formalized on September 22, 2010, the prosecutor properly disclosed its terms and filed a discovery packet including all of the Commonwealth's documents. See Commonwealth v. Burgos, 462 Mass. 53, 62-63, cert. denied, 133 S.Ct. 796 (2012) (prosecutor informed defendant before trial of formalized cooperation agreements). Until the agreement was formalized, Colton received no promises, rewards, or inducements that the Commonwealth was obligated to disclose.

With respect to the Commonwealth's delayed disclosure of a later statement Colton made about the DCF call, we disagree with the defendants that this statement was a critical change in his story. In his initial statement to the police, Colton did not provide specific information about the location from which the DCF telephone call was made, and, later, Colton asserted that William had made the call from Colton's home telephone. The defendants had adequate notice of this assertion in the Commonwealth's bill of particulars, a supplemental police report, and Colton's follow-up interview report. The information was provided long before trial, permitting ample time for the defense to weave it into its over-all strategy and counsel's cross-examination of Colton. See Commonwealth v. Baldwin, 385 Mass. 165, 175 (1982) ("disclosure was sufficiently timely to allow the defendant `to make effective use of the evidence in preparing and presenting his case'" [citation omitted]).

Regarding the alleged delay in disclosing Colton's diary, the prosecutor promptly disclosed it to the defendants on learning of its existence in May, 2011, again, well before trial. This provided the defendants with a sufficient opportunity to investigate its contents and conduct a meaningful cross-examination of Colton.

Finally, the defendants' due process rights were adequately protected given the defendants' unhampered ability to extensively cross-examine Colton and the jury's instruction to carefully weigh his testimony. The defendants have not demonstrated that any delays in receiving information legitimately prejudiced their opportunity to effectively prepare their defense.

5. Venue. During pretrial proceedings and prior to jury empanelment, William moved for dismissal of the charge of making a false report of child abuse, asserting lack of jurisdiction and improper venue under G. L. c. 277 § 57A.14 He argued that since the telephone call to DCF (located in Suffolk County) was made from Colton's home (in Middlesex County), the charge should have been tried in either Suffolk or Middlesex County. The motion was denied.

Article 13 of the Massachusetts Declaration of Rights grants the Legislature "discretion ... to establish venue requirements for criminal trials," Opinion of the Justices, 372 Mass. 883, 897 (1977), but acknowledges "that fairness to a defendant normally requires that the defendant not be transported far away for trial but rather be tried where there is access to witnesses and evidence for the defense." Commonwealth v. Brogan, 415 Mass. 169, 174 (1993). Since the statute at issue, G. L. c. 119, § 51A (c), does not include a venue provision, the question of venue here "is one of common law within any limitation that art. 13 may impose." Brogan, supra at 173.

The defendant has made no showing that the trial in Essex County "was in any way prejudicial to [his] defences on the merits, or otherwise disadvantageous to [him]." Commonwealth v. Libby, 358 Mass. 617, 620 n.2 (1971). It is not as though the crime is unrelated to Essex County: William lived in Essex County, as did the victims, and the child abuse investigation became fully manifested there. William has not demonstrated that he was "unduly hampered by being required to appear" in Essex County. Commonwealth v. Adelson, 40 Mass.App.Ct. 585, 589 (1996).15

6. E-mail authentication. The defendants moved in limine on the first day of trial to exclude e-mail correspondence between Gail and Colton, arguing that the circumstances were insufficient to permit authentication or confirm Gail's identity as the sender. During voir dire on the issue, Colton testified that the defendants shared a joint e-mail account with which he had exchanged many friendly messages for nearly a decade. Regarding the proposed evidence, Colton testified that he understood these messages to be from Gail, on William's behalf, as they were sent after William had enlisted Colton in the scheme, were signed using Gail's typical signature, and referenced Colton's responses to inquiries about the harassment scheme.16 The judge ruled that the preponderance of the evidence authenticated the messages and laid a foundation for their admissibility. We agree.

"Evidence may be authenticated by direct or circumstantial evidence, including its `[a]ppearance, contents, substance, internal patterns, or other distinctive characteristics.'" Commonwealth v. Purdy, 459 Mass. 442, 447-448 (2011), quoting Mass. G. Evid. § 901(b)(4) (2013). The voir dire of Colton presented sufficient evidence that some of the messages sent to Colton were authored by Gail given the long-standing relationship between Colton and the defendants, the defendants' prior use of the e-mail address at the time of the scheme, and the referencing of the harassing acts in the messages.17

7. Closing argument. In summarizing the evidence for the jury, the prosecutor stated: "Now, how in the world can the Johnsons explain to you why...." William argues on appeal that this statement could be interpreted as a comment on the defendants' failure to take the stand. Viewed in context, the prosecutor's rhetorical question was merely an attempt to illustrate the point that the defendants' conduct could not be reconciled with their defense. It was a "fair, unemotional response to defense counsel's argument," grounded in both the evidence and its reasonable inferences. See Commonwealth v. Duguay, 430 Mass. 397, 404 (1999). There was no improper burden shifting.

Additionally, William contends that the prosecutor argued facts not in evidence in two instances, amounting to reversible error. Specifically, the prosecutor mistakenly stated that people came to the Lyonses' home in response to the motorcycle advertisement (they only had telephoned), and that the Lyonses received the letter alleging sexual molestation before rather than following the e-mail message sent by "Brian."18 The prosecutor's two misstatements of fact did not result in a substantial risk of a miscarriage of justice. The facts were many and varied, and none of the misstatements "went to the heart of the case." Commonwealth v. Coren, 437 Mass. 723, 731 (2002). Further, the judge properly instructed the jury that closing arguments are not evidence. Consequently, reversal is not required.

8. Speedy trial claim. Approximately two years after the defendants were charged, they moved for a dismissal pursuant to Mass. R. Crim. P. 36, as amended, 422 Mass. 1503 (1996), due to speedy trial violations. The motion judge acted well within his discretion in declining to accept defense counsels' unsworn representations regarding various continuances, and in denying the motion. We agree with the motion judge that the defendants did not undertake a proper rule 36 calculus or sufficiently develop their argument, leaving the judge unable to adequately assess their claim. Accordingly, it is waived.

Judgments affirmed.