
    UNITED STATES of America, Appellee v. Sherman MITCHELL, Appellant.
    Nos. 14-3039, 14-3040.
    United States Court of Appeals, District of Columbia Circuit.
    Argued Dec. 8, 2015.
    Decided March 8, 2016.
    
      Douglas J. Behr, appointed by the court, argued the cause and filed the briefs for the appellant.
    Elizabeth H. Danello, Assistant United States Attorney, argued the cause for the appellee. Vincent ,H. Cohen Jr., Acting United States Attorney, Elizabeth Tros-man, John K Han and Stratton C. Strand, Assistant United States Attorneys,' were with her on brief.
    Before: HENDERSON and GRIFFITH, Circuit Judges, and RANDOLPH, Senior Circuit Judge.
   'Opinion for the Court filed by Circuit Judge HENDERSON.

KAREN LECRAFT HENDERSON, Circuit Judge:

Sherman Mitchell (Mitchell) was convicted by jury of multiple counts of drug crimes resulting from his role in a .phency-clidine (PCP) distribution ring. Mitchell challenges his convictions on several grounds, including, inter alia, the. government’s purported failure to properly authenticate and demonstrate chain of custody for PCP samples used to establish his guilt and the district court’s alleged error in admitting summary witness evidence. We reject his challenges and affirm his convictions.

I. Background

A.

In February 2012, the U.S. Drug Enforcement .Agency (DEA), led by Special Agent Jamey Tarrh (Tarrh), opened an investigation into drug trafficking between California and the District of Columbia focused on Mitchell and his associate, Harvey Couser (Couser). In early May 2012, Mitchell moved into an apartment at the Onyx on First (Onyx) in the District of Columbia, which was leased by Mitchell’s half-brother, Stephon. Although the apartment was leased in Stephon’s name, either Mitchell or Couser paid the rent on the apartment from June through November 2012 and Couser had apartment keys Stephon had given him.

Between May and August 2012, Mitchell took seven roundtrip flights to Los Ange-les, remaining there for short periods each time. During every trip, one or more packages were shipped via UPS to Mitchell’s apartment at the Onyx from Los An-geles, with multiple packages addressed to “Jane Mitchell”—“Jane” matching Mitchell’s mother’s given name. The government did not seize any of the packages but DEA agents observed Couser retrieving the packages addressed to Jane Mitchell at the Onyx several times. Specifically, on August 10, 2012, Tarrh’s team identified Couser entering the Onyx and retrieving a package shipped from Los Angeles by “James Campbell”—“James” matching Mitchell’s father’s given name and “Campbell” matching Mitchell’s mother’s surname—to Jane Mitchell at the Onyx. The August 10, 2012 package was labelled with a contact number corresponding to a cell phone later seized from Couser.

B.

Mitchell eventually moved to Los Ange-les in late August 2012, where he resided in various hotels until his arrest in February 2013. The shipments to the Onyx apartment from Los Angeles continued, with Couser retrieving multiplé packages at the Onyx in September, October and November 2012. On November 24, two packages were shipped from Los Angeles to the Onyx apartment for delivery on November 26. The two concierges at the Onyx, who cooperated with the ongoing investigation, notified Tarrh of the delivery of the packages. Tarrh asked the concierges not to deliver the packages to Couser until he, Tarrh,,gave them permission. When Couser arrived at the Onyx to retrieve them, the concierge on duty told Couser that no package addressed to Mitchell’s apartment had been delivered that day. Couser returned to the concierge desk a few hours later and again requested the packages. The concierge again reported that no packages had been delivered and, at that point, Couser handed the concierge a cell phone to speak with Mitchell. Mitchell identified himself and excitedly explained the importance of the packages and asked her to contact Couser immediately . when the packages arrived.

While the delivery of the packages to Couser was delayed, Tarrh obtained a warrant, picked up the two packages from the Onyx and searched them. Inside the boxes, Tarrh found a total of four 64-ounce apple juice bottles filled with amber liquid. The bottles were delivered to Metropolitan Police Department (MPD) Detective Joseph Abdalla (Abdalla), who weighed the bottles, removed samples of the amber liquid from each and prepared the bottles for controlléd delivery by refilling three of the bottles with tea' and the remaining bottle with a mixture of tea and a small amount of the amber liquid. Following protocol, Abdalla then sent the remaining amber liquid to the MPD property division for destrüction. Tarrh repacked the two boxes and returned the boxes to the Onyx for delivery. The next day, Mitchell telephoned the Onyx manager hourly about the packages until they were picked up by Couser once Tarrh had given permission to release them.

When Couser returned to the Onyx to make the pick-up, Tarrh arrested him as he left the building. Two cell phones were recovered from Couser at that time. A subsequent search of the Onyx apartment led to the seizure of a money-counting machine, starter fluid, an oral syringe, a funnel and empty half-ounce glass vials— all tools of the PCP distribution trade.

C.

Based on information obtained at Couser’s arrest, Tarrh and his team executed an arrest warrant for Mitchell at a Gardena, California hotel on February 6, 2013. During Mitchell’s arrest, DEA agents seized a scrap of paper from his pocket with the name “Eric Gates” written on it. The agents found four cell phones in Mitchell’s hotel room," one of which- displayed a text message with a UPS tracking number that was open and visible to the agents, and another scrap of paper with addresses for an “Eric Gates” in Gardena and a “Lisa Carter” in the District of Columbia. Based on this information, Corporal Dennis Reighard (Reighard) of the Prince George’s County Police Department intercepted two packages from the Prince George’s County UPS facility before the packages could be delivered to the Ijistrict addresses. Reighard seized the first package—corresponding to the tracking number displayed on Mitchell’s phone at the time of his arrest—on Fébrü-ary 8, 2013. The package contained three 64-ounce bottles filled with amber liquid. As he had done with the November 2012 package, Abdalla took samples from the bottles and the DEA laboratory determined that the amber liquid in one of the bottles, weighing. 1,148 grams, contained 15.7 per cent PCP. Reighard seized the second package—addressed to “Lisa Carter” and shipped by “Eric Gates”—on February 12.' This package contained a 32-ounce bottle filled with- amber liquid. After Abdalla again removed a sample from the bottle, the DEA laboratory determined that the bottle’s amber liquid, weighing 776.7 grams, contained 15.9 per cent PCP.

D.

Reighard had also been involved with the seizure of a package before the start of the DEA investigation. On July 1, 2011, Reighard took custody from the UPS facility in Burtonsville, Maryland of a package that was addressed to the mother of one of Mitchell’s children. The UPS security team had opened the package and contacted Reighard because it was leaking a' substance with a strong odor the security team believed to be PCP. The package contained two - one-gallon and four 64-ounce plastic bottles filled with amber liquid. Reighard stored the unopened bottles at the Prince George’s County Police Department until May 7, 2013, when the DEA connected the tracking number for the July 1, 2011 package to Mitchell. At that point, Abdalla removed a sample from each of the-six bottles arid the DEA laboratory, after testing one sample, found that the amber liquid from-that bottle, weighing 482.8 grams, contained 13.9 per cent PCP.

E.

On April 4, -2013, Mitchell and Couser were indicted on one count (Count I) of conspiracy to possess with intent to distribute one kilogram or more of a mixture or substance containing PCP between February 2011 and February 2013 in violation of 21 U.S.C. § 841(a)(1), (b)(1)(A)(iv) and 21 U.S.C. § 846 and one count (Count II) of possession with intent to distribute, or aiding and . abetting possession with intent to distribute, one kilogram or more of a mixture or substance containing PCP on November 27, 2012 in violation of 18 U.S.C. § 2(a) and 21 U.S.C. § 841(a)(1), (b)(1)(A)(iv). Mitchell was further indicted on two counts of attempted unlawful possession with intent to distribute, aiding and abetting unlawful possession with intent to distribute or attempting to cause unlawful possession with - intent to distribute one kilogram or more on February 8, 2013 (Count III) and one hundred grams or more on. February 12, 2013. (Count IV) of-a mixture or substance containing-PCP in violation of 18 U.S.C. § 2 and 21 U.S.C. § 841(a)(1), (b)(l)(A)(iv), (b)(1)(B)(iv). His jury trial lasted, from October 1, 2013 through October 15, 2013. On October 21, 2013, the jury found Couser not guilty on Counts I and II and found Mitchell guilty on-Counts I-IV.- After denying Mitchell’s motions for - acquittal and for a new trial, the district-court sentenced Mitchell to life imprisonment and 120 months’ supervised release, on Counts I—III and 360 months’ imprisonment and 96 months’ supervised release, to run concurrently, on Count IV. Mitchell timely appealed. Our jurisdiction arises under 28 U.S.C. § 1291.

II. Analysis

Mitchell raises multiple challenges to his conviction, almost all of which are without merit and require no further discussion. See, e.g., United States v. Hoover-Hanker-son, 511 F.3d 164, 168 (D.C.Cir.2007) (“[The defendants] present a large number of issues on appeal, not all of which deserve discussion.”); United States. v. Thomas, 97 F.3d 1499, 1503 (D.C.Cir.1996) (“Thomas’s remaining contentions do not warrant discussion. These have been considered and rejected.”). We address only two arguments in full: the government’s alleged failure to authenticate and prove chain, of custody for the samples of amber liquid the DEA tested for PCP and the government’s use of a summary witness at the end of its case-in-chief.

A. Chain, of Custody

Mitchell claims that the government failed to adequately authenticate and prove chain of custody for the samples tested at the DEA laboratory and used to show Mitchell’s constructive possession of the PCP. Mitchell specifically points to two related evidentiary gaps: (1) the government allegedly failed to track, with specificity, the evidence from its seizure by Tarrh or Reighard to Abdalla.and thence to the DEA laboratory; and (2) the government allegedly failed to authenticate that the vials the DEA. tested matched the samples Abdalla collected. Because of these gaps, Mitchell argues, the DEA laboratory evidence should have been excluded. We disagree.

1.

We review the trial court’s admissibility rulings for abuse of discretion if the defendant made a timely ..objection and plain error, if the defendant did not. See United States v. Coumaris, 399 F.3d 343, 347 (D.C.Cir.2005); see also Fed.R.Crim.P. 52(b). Mitchell claims that he objected to chain of custody before DEA forensic chemist John Liu (Liu) , testified and again in his motion for acquittal. The first colloquy Mitchell relies on involved an objection under the Confrontation Clause. Sherri Tupik (Tupik), a DEA chemist, initially tested the 2012 and 2013 samples. Tupik was unavailable to testify at trial and, consequently, the government enlisted Liu to retest the samples, produce new reports and be available to testify regarding his reports at trial, Mitchell claimed that he should have had the opportunity to confront Tupik because Liu allegedly relied on her reports in generating his reports and his reports were the only ones introduced into evidence at trial. Mitchell also claimed that there was inadequate chain of custody evidence for the period between Tupik’s and Liu’s reports. See, e.g., Oct. 9, 2013 Trial Tr. at 76 (“There is no chain of custody for [Liu’s] reports, and so there is no way to establish-what drugs these were seized from.”); id. at 85 (“Because they have to prove chain of custody; otherwise, there is no evidence whatsoever that these are the drugs that were recovered on -November 27th or sent to the DEA lab on the 30th other than Agent Tupik’s report that we can’t confront,”). Later, when the government moved to introduce the reports into evidence during Liu’s direct testimony, Mitchell objected to the reports relating to the 2012 and 2013 samples Liu retested. In arguing Couser’s motion for acquittal, Couser’s, counsel claimed that “[t]here is absolutely no chain of custody in connection with the” 2012 samples taken by Abdalla and with Liu’s retesting reports. Oct. 10, 2013 Trial Tr: at 163-64. Mitchell’s counsel adopted Couser’s “argument with respect to chain of.custody.” Id. at 167.

The government assumes without conceding that Mitchell preserved a challenge to the chain of custody for the samples Liu retested—the 2012 and 2013 samples—but claims that we should review the chain-of-custody evidence of the 2011 samples for plain error. We need not determine the applicable standard of review as we conclude that the district court did not err— whether under an abuse of discretion standard or plain error standard—in.admitting Liu’s reports.

2.

“It is generally-recognized that tangible objects become admissible in evidence only when proof of their original acquisition and subsequent custody forges their connection with the accused and the criminal offense.” United States v. Mejia, 607 F.3d 1329, 1335 (D.C.Cir.2010) (quoting Gass v. United States, 416 F.2d 767, 770 n. 8 (D.C.Cir.1969)). The government has the burden to demonstrate that the “item still is what the [government] claims it to be.” Id. at 1336 (quoting 2 McCormick on Evid. § 213 (6th ed.2009)). “In order for evidence to be admissible, however, a complete chain of custody need not always be proved.” United States v. Garcia, 757 F.3d 315, 319 (D.C.Cir.2014) .(internal quotation mark omitted). The proponent of the evidence need only “demonstrate that, as a matter of reasonable probability, possibilities of misidentification and adulteration have been eliminated.” Mejia, 597 F.3d at 1336 (internal quotation marks omitted). Once the evidence is admitted, a gap in the chain of custody goes only to the weight given to the evidence by the trier of fact. Garcia, 757 F.3d at 319; see also Melendez-Diaz v. Massachusetts, 557 U.S. 305, 311 n. 1, 129 S.Ct. 2527, 174 L.Ed.2d 314 (2009) (“[G]aps in the chain ... normally go to the weight of the evidence rather than its admissibility.”). “A break in the chain of custody,” however, “can be serious enough that the district court may abuse its discretion in admitting the evidence.” Mejia, 597 F.3d at 1336. To assess an allegedly faulty chain of custody, we look for “ample corroborative evidence as to [the evidence’s] acquisition and subsequent custody.” Id.

The information necessary for the government to prove chain of custody is fairly clear. The government must demonstrate that the jury could have “reasonably believe[d]” that the amber liquid contained in the various packages seized by Tarrh or Reighard was the same as the samples Liu tested: Garcia, 757 F.3d at 319. The government must have therefore traced the liquid from its seizure to its transfer to Abdalla for sampling and then to the DEA laboratory for testing.

For the sample taken from the July 2011 package, Reighard testified, that he seized the package from the UPS facility on July 1, 2011, and placed the contents (six bottles) in a labelled storage bin at the Prince George’s County Police Department. The bottles remained in storage there until May 7, 2013, when, Abdalla testified, he picked them up for sampling. Abdalla stated’ that on that date he took samples from all six bottles, gave each sample a separate exhibit' number and placed the samples into evidence bags la-belled by DEA Special Agent Andy Harris (Harris). Liu testified that the DEA laboratory received the samples from Abdalla for testing on May 9, 20Í3, he tested one of the samplés and he then created the report introduced at trial. For the four bottles contained in the two packages seized in November 2012, Tarrh testified that he retrieved them from the Onyx on November 26-27, 2012. Abdalla testified that either Tarrh or DEA.Agent Brian Mulcahy (Mulcahy), another member of the DEA investigative team, delivered the packages to him for sampling on November 27. Abdalla further testified that he took five samples from the four bottles and put the samples in evidence bags that Mul-cahy then sealed and signed. Liu explained that the laboratory received the samples on November 30, 2012, that Tupik originally tested them in May 2013 and that he retested them in October 2013 and prepared the reports introduced into evidence. And finally, for the two February 2013 packages containing four bottles in toto, Reighard testified that he seized one package from the UPS facility on February 8 and 12, 2013, respectively. Again, Abdalla testified that either Tarrh or Mul-cahy then delivered the packages to him, he sampled the four bottles, placed the samples in evidence bags and gave the bags to Mulcahy to seal and sign. Liu testified that the DEA laboratory received the samples on February 13, 2013, and that he eventually retested the samples and generated the reports introduced into evidence. Liu explained that he generally used the same procedures and analytical methods to test all samples.

There are three gaps in the chain of custody for the samples Liu either tested or retested. The government concedes one of the gaps, Appellee’s Br. 51-52, namely, that it presented no evidence to explain precisely how the sealed evidence bags went from Abdalla to the DEA laboratory for testing. Id. It argues, however, that the gap is “minor” and goes to the weight, not admissibility, of the testing reports. Id. at 52. We agree that this is a relatively minor gap in the chain of custody. For all four sets of samples, the time lag between Abdalla’s or Mulcahy’s sending the evidence bags to the DEA laboratory and the laboratory’s receipt thereof was fairly short—a few days at most. Further, the evidence bags were signed and sealed and' Liu testified that he checked evidence bag seals for tampering before opening and retesting them.- Liu also explained that an evidence technician put information about the evidence bags, including their date of delivery, into an internal tracking system at the time of receipt and that Liu checked the bags against the tracking system information before performing his analysis. We are thus convinced that the government met its burden to show that “as a matter of reasonable probability, possibilities of misidentifícation and adulteration have been eliminated” for the evidence bags from the time of their creation to their receipt by the DEA laboratory for testing. Mejia, 597 F.3d at 1336 (quoting United States v. Stewart, 104 F.3d 1377, 1383 (D.C.Cir. 1997)) (internal quotation marks omitted).

The other breaks in' the chain of custody—the break caused by Abdalla’s apparent failure to label his samples and the lack of evidence regarding the creation of the evidence bags—present closer questions. During the sampling process, Abdalla removed a one-ounce sample of amber liquid from each seized bottle and placed it into a separate vial for each sample. Abdalla then photographed the vial next to a typewritten placard with identifying information; he did not, however, label the vials themselves. Abdalla testified that either he gave the one-ounce samples to Mulcahy to place into the labeled evidence bags or, for the 2011 samples, he and Harris prepared and .sealed the evidence bags themselves. - Abdalla did not identify or authenticate the evidence bags at trial. And although Mulcahy testified at trial, he also was not asked about his preparation of the evidence bags. Liu, however, identified the evidence bags that contained the samples-he tested. The government therefore failed to introduce testimony establishing that the evidence bags prepared by Abdalla or Mulcahy were the ones that contained the samples tested by Liu—instead, .Abdalla testified that he matched the samples with the case numbers given to him by Tarrh and with the exhibit numbers Abdalla himself generated. Liu then explained that generally he checked the evidence bags against the DEA’s internal system to make sure he was testing the sample with the correct case and exhibit numbers. Thus, the only evidence linking the vials photographed by Abdalla to the vials tested by Liu are the evidence bags themselves. Mulcahy and Harris should have testified that the evidence bags Liu authenticated were -the same evidence bags they prepared using the samples obtained from- Abdalla. The government thus failed to close this evi-dentiary gap.

Nevertheless, we' do not think these gaps mean that the district court abused its discretion in admitting Liu’s reports into evidence. The government had the burden to demonstrate that the jury could have “reasonably believe[d]” that the samples tested by Liu were the samples prepared by Abdalla. Garcia, 757 F.3d at 319. We believe the government met its burden, albeit not with flying colors. Ab-dalla testified that he matched each sample with its ease number and the specific bottle seized, as demonstrated by the photographs showing the unlabeled sample next to an identifying placard. Abdalla further stated that he transferred the samples to Mulcahy to place into the evidence bags and the evidence bags—which were themselves authenticated by Liu and introduced into evidence—display identifying information, including the case number, exhibit number, date and location of acquisition of the sample and either Mulcahy’s or Harris’s signature.. And Liu explained that he checked the evidence bags against the DEA’s internal tracking system for congruity and that the case and evidence numbers on the reports matched those on the evidence bags and the placards. This testimony and the use of identical case and exhibit numbers provide “ample corroborative evidence as to [the sample’s] acquisition and subsequent custody.” Mejia, 597 F.3d at 1336. The jury could have reasonably concluded that the samples tested by Liu were the samples prepared by Abdalla and packaged by Mulcahy—thus confirming a low probability that the samples were misidentified or adulterated. See generally id. at 1335-36. Although Mul-cahy and Harris should have presented testimony about their role in preparing the evidence bags and Abdalla should have labelled the vials themselves, we conclude that the gaps in the chain of custody were not so substantial that the district court committed reversible error in admitting Liu’s reports into evidence.

B. Summary Witness

Mitchell also argues that the district court erred in admitting portions of DEA Investigator Lisa Amoroso’s (Amoroso) testimony as a summary witness. Mitchell claims that Amoroso exceeded the proper scope of summary witness testimony by improperly drawing conclusions and .inferences from earlier—introduced evidence based on her independent investigation or personal opinion. Mitchell also claims the district court’s failure to give a limiting instruction regarding Amoroso’s testimony compounded the error. We find that'any such error was harmless.

1.

To prove conspiracy, the prosecution relied on a series of telephone calls allegedly made by Couser or Mitchell from eight different phone numbers. Two numbers were tied to the phones seized from Couser on his arrest and one was registered in Mitchell’s name. Three numbers belonged to various persons named “Michael” at addresses connected to Mitchell. And two phone numbers were linked to default addresses under the name “Michael Smith” or “Del Ta.” Amoroso’s testimony focused on the introduction and explanation of an exhibit—Exhibit 30—that summarized voluminous records of all eight phone numbers. Exhibit 30 listed, in table form, the owner and number of the phone initiating the call; the date, time and duration of the call; and the number of the recipient phone and that phone’s owner and address.

Before Amoroso testified, the prosecution and defense disputed the admissibility of a preliminary version of Exhibit 30. That version included parentheticals next to the owner’s name that connected certain phone numbers to Couser and Mitchell even though those phones were registered either to different names or to no name at all. The prosecution asserted that it planned to establish links between the numbers and Couser'or Mitchell based on Amoroso’s analysis. The defense objected to the introduction of a version of Exhibit 30 that included the- parentheti-cals, particularly because the parenthetical comments were derived from Amoroso’s own interpretation and investigation. The defense agreed to Exhibit 30 with the par-entheticals removed and only the registered owners .listed—counsel for both defendants stated that such a chart would be “consistent with what* the records show.” Oct. 9, 2013 Trial Tr; at 239; see also id. at. 239-40 (Couser’s counsel stating “I would have no objection to the column that contains-[the] target name and the dialed name..... ”); id. at 241 (Mitchell’s counsel agreeing with Couser’s “position with respect to the parentheticals”). The government prepared a version of the table without the parentheticals,- producing the version of Exhibit 30 introduced .at trial.

Amoroso then testified,' connecting the relevant phone numbers to Couser or Mitchell through a series of inferences. Amoroso took the jury through each phone number at issue, detailing how, based on the phone records and subscriber information, it could be tied to Couser or Mitchell. For example, Amoroso testified that the eight phone, numbers could be linked to Couser or Mitchell because: (1) phones associated with certain numbers were taken. from Couser at the time of his arrest; or (2) the number belonged to a person who lived at Couser’s home address; or (3), the number listed one of Mitchell’s previous addresses or the Onyx apartment complex; or (4) there was an unusually large number of calls between the listed number and a number directly associated with Couser or Mitchell at the time packages were being shipped to the Onyx from Los Angeles.' Amoroso also explained that she had learned during her investigation that, for the numbers registered to various Michaels, no one with that name lived at the registered address at the relevant time.

During cross-examination, Amoroso conceded that her conclusions were not based on information about the persons who in fact made the calls listed in Exhibit 80 but on the phone records themselves and the registered names and addresses. Amoro-so also admitted that her information did not specify which apartments in the relevant complexes were connected to certain phone numbers.

2.

At no point during Amoroso’s testimony did the defense object to the scope of her testimony. When the government moved to introduce Exhibit 30, the defense simply repeated its earlier objections, one of which unnecessarily challenged the content of the preliminary (and excluded) version of Exhibit 30—and was granted—and one involved hearsay statements regarding the phones seized from Couser. Because Mitchell failed to object to the scope of Amoroso’s testimony, we review for plain error. See United States v. Kayode, 254 F.3d 204, 212 (D.C.Cir.2001); see also Fed. R.Crim.P. 52(b).

Federal Rule of Evidence 1006 permits the use of a “summary, chart, or calculation to prove the content of voluminous writings, recordings, or photographs that cannot be conveniently examined in court.” Fed.R.Evid. 1006. A summary “can help the jury organize and evaluate evidence which is factually complex and fragmentally revealed in the testimony of a multitude of witnesses throughout the trial.” United States v. Lemire, 720 F.2d 1327, 1348 (D.C.Cir.1983). To be admissible, the summary must be “accurate and nonprejudicial; and the 'witness who prepared the summary should introduce it.” United States v. Fahnbulleh, 752 F.3d 470, 479 (D.C.Cir.2Ó14). The witness who prepared the summary may testify about how he prepared it. See Lemire, 720 F.2d at 1347 (admitting “one witness’s summary of evidence already presented by prior witnesses”).

We have previously limited the government’s use of summary evidence in particular situations. Id. at 1346-50 (permitting summary evidence but detailing problems such \evidence can raise). The government must first lay a sufficient foundation for any summary evidence. See id. at 1349. The trial judge can issue a limiting instruction regarding its use and cross-examination can expose inaccuracies or unfair characterizations. See id. at 1348. The summary “should not draw controversial inferences, or pronounce[] judgment,” id. at 1350, and we have found overview testimony given at the beginning of the government’s case-in-chief prejudicial in contexts inapplicable here. United States v. Moore, 651 F.3d 30, 51-52 (D.C.Cir.2011) (per curiam).

We conclude that even if the trial judge committed plain error in admitting Amoroso’s summary testimony or by failing to give a limiting instruction, any error was harmless. Although the portion of Amoroso’s testimony that was based on her personal investigations was detailed, 'Mitchell’s cross-examination of Amoroso helps to allay any concern. See Lemire, 720 F.2d at 1348 (“[A] full opportunity to cross-examine ... alleviat[es] any danger of inaccuracy or unfair characterization.”). Amoroso inferred that certain phone numbers were connected to Couser or Mitchell for several reasons, including the frequency of calls to phones registered to Mitchell or taken from Couser on his arrest and the fact that phones were registered to addresses connected to Couser or Mitchell but under different names. Amoroso admitted that she did independent research in concluding that no one living at those residences matched the name listed on the registration information. The use of a summary witness’s independent judgment, however, should be limited. See id. at 1349 (such testimony could allow “the subtle introduction of otherwise inadmissible evidence” and could permit government extra opportunity to summarize its -case-in-chief before closing argument “from the witness stand rather than the counsel’s lect[e]rn”).

Here, Amoroso’s independent investigation was fairly minor—she simply confirmed that no 'one living at the address to which the-phone-nufnber was registered had the registered name. ’ And Mitchell’s cross-examination made clear that Amoro-so’s conclusions were based on her own inferences. Amoroso admitted that the phone records showed only that someone at one phone number called someone at another at a'specific time. Mitchell also elicited from Amoroso ‘ a concession- that her conclusions about the connection between certain addresses and Mitchell or Couser were not as clear as the prosecution implied on direct. Oct. 10, 2013 Trial Tr. at 151-53. Thus, even if Amoroso’s limited testimony about her independent investigation was erroneously admitted, any error was harmless given the scope of cross examination.

Mitchell also argues that the trial judge plainly erred in failing to give a limiting instruction after Amoroso’s summary testimony. Appellant’s Br. 49-51 (citing United States v. Smith, 601 F.3d 530, 541 (6th Cir.2010), United States v. Fullwood, 342 F.3d 409, 413 (5th Cir.2003) and United States v. Johnson, 54 F.3d 1150, 1160-61 (4th Cir.1995)). Whatever the merits of Mitchell’s plain error argument, any error was again harmless. We have recognized that “[o]ne danger” of summary testimony is that .the “jury will treat the summary as additional evidence or as corroborative of the truth of the underlying testimony” and, to meet the danger, have characterized limiting instructions as “requisite.” Lemire, 720 F.2d at 1348. Objections to summary evidence and voir dire examination of a summary witness help protect against the risk that “the jury might treat the summary [witness] as substantive evidence.” Id. Here, the district court did exactly that—it allowed Mitchell to challenge and limit Exhibit 30 before its introduction into evidence and to conduct vigorous cross-examination of Amoroso. Mitchell pannot show that any inference Amoroso made “affected [Mitchell’s] substantial rights” or “seriously a£fect[ed] 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), as her testimony allowed the jury to conclude, at most,, that Mitchell attempted to hide his identity by- using multiple phones and aliases. But even this conclusion does not supply the showing of prejudice o.r of a miscarriage pf justice required for reversal. Nguyen v. United States, 539 U.S. 69, 84-85, 123 S.Ct. 2130, 156 L.Ed.2d 64 (2003) (Rehnquist, C.J., dissenting) (“[W]e exercise our power under Rule 52(b) sparingly ... and only in those circumstances in which a miscarriage of justice would otherwise result.” (citations and internal quotation marks omitted)).

For the foregoing reasons, the judgment of the district court is affirmed.

So ordered. 
      
      . The DEA laboratory subsequently tested the unmixed sample of amber liquid removed from one of the bottles, weighing 1,470 grams, and determined that it contained 9.9 per cent PCP. This amount sufficed to support Count II of the indictment. See infra at 869-70; see also 21 U.S.C. § 841 (b)(1)(A)(iv) (unlawful to possess with intent to distribute 1 kilogram or more of a mixture or substance containing a detectable amount of phencycli-dine”).
     
      
      . The record does not explain the gap between Couser’s arrest in November 2012 and Mitchell’s arrest in February 2013.
     
      
      
        , Mitchell and Couser were also indicted on • two money laundering counts that were dismissed pre-trial.
     
      
      . Mitchell does not raise a Confrontation Clause challenge to the admissibility of the PCP testing reports on appeal.
     
      
      . Mitchell did not object to the introduction of Liu’s report on the 2011 samples because Liu was the only DEA chemist who tested those samples,
     
      
      . Mitchell claims that there are both authentication and chain-of-custody problems with the samples taken by Abdalla and tested by Liu. Here, the authentication and chain-of-custody concerns are one and the same— whether the samples tested by Liu were the same as the amber 'liquid in the containers seized by Tarrh and Reighard. ‘ We therefore proceed with a single chain-of-custody analysis instead of separate chain-of-custody and authentifcation analyses. Cf. Fed.R.Evid. 901(a) ("To satisfy the requirement of authenticating or identifying ¡an item of evidence, the proponent must produce evidence sufficient to support a finding that the item is what the proponent claims it is.”).
     
      
      .The evidence bags Abdalla and Mulcahy prepared held the sample vials. The record is unclear whether the evidence bags also held the bottles used to ship the liquid, except for the four bottles used for the November 2012 controlled delivery to Couser.
     
      
      . The DEA assigns a case number to a particular investigation and an exhibit number to a specific piece of evidence collected in the course of that investigation.
     
      
      . Apart from the samples taken directly from the bottles in 2011, 2012 and 2013, there was a potential evidentiary problem with a sample sent to the DEA laboratory that was purportedly removed from the amber liquid/tea mixture created for the November 2012 controlled delivery. Abdalla failed to testify that he in fact removed a sample from the mixture before the controlled delivery. The government asks us to rely on a series of inferences based on the timing of the DEA laboratory’s testing of the samples to confirm that the specific report at issue corresponds to the mixed sample taken from the 2012 package. We need not resolve this question because the government met its chain-of-custody burden for the unmixed 2012 sample, see supra n. 1, and therefore any error related to the mixed sample would be harmless. See Garcia, 757 F.3d at 319 (“Like other evidentiary rulings, a district court’s decision to admit evidence over a chain-of-custody objection is subject to harmless error review.”); see also United States v. Johnson, 216 F.3d 1162, 1166 n. 4 (D.C.Cir.2000) (“[N]onconstitutional error, is harmless if it did not have 'substantial and injurious effect or influence in determining the jury's verdict.’ ” (quoting Kotteakos v. United States, 328 U.S. 750, 776, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946))).
     
      
      . Mitchell argues that the government forfeited any reliance on the evidence bag labels as proof of chain of custody by failing to discuss the labels during trial. But during a colloquy with the district judge, the prosecution asserted that it relied on the case number as it appeared throughout the evidence—including on the placard in Abdalla’s photograph and on the evidence bags—to connect the samples Abdalla prepared to the samples Liu tested. Thus, even though the government did not explicitly .use the labels as proof of chain of custody, it did rely on the case number to establish chain of custody.
     
      
      . The table listed the owner as "NONE NONE” if there was no registered owner.
     
      
      . The number was registered to someone living at the same street address as Couser but in an adjacent town where no such address existed.
     
      
      . While testifying, Amoroso used the excluded version óf Exhibit 30 with parentheticals to refresh her recollection. That version was not introduced into evidence. The defendants objected to its use to refresh her recollection but the court denied the objection because Mitchell had the opportunity to cross-examine Amoroso on the basis of her knowledge. The defense also objected to Amoroso testifying that certain phones were seized from Couser during his arrest, claiming it was impermissible hearsay—the district court also denied the objection. Mitchell does not challenge the hearsay objection on appeal.
     
      
      . In his reply brief, Mitchell highlights statements made during the Exhibit 30 colloquy purportedly sufficient to avoid plain error review. See Reply Br. 20. Those statements were made in the context of his challenge to the parentheticals used in the first version of Exhibit 30. Mitchell did not raise a similar objection to the version of Exhibit 30 admitted into evidence and did not object to the scope of Amoroso's testimony based on Exhibit 30.
     
      
      .Our discussion is limited to a summary witness testifying about charts prepared and introduced under Rule 1006 and does not address summary witness testimony standing alone.
     
      
      . We appear to treat summary testimony and summary exhibits differently regarding the necessity of limiting instructions. See United States v. Weaver, 281 F.3d 228, 233 (D.C.Cir,2002).
     