This case concerns a complex, long-running cocaine conspiracy operating in and near Atlanta, Georgia. Eight appellants1 were convicted in various combinations of conspiracy to distribute and to possess with intent to distribute, possession within 1,000 feet of a school, maintaining a place for manufacture, distribution, or use and maintaining such a place within 1,000 feet of a school, weapons violations, immigrations violations, and false statements.
I. The conspiracy
Without doubt there was a massive conspiracy with many actors. Its existence and the details of its operation were established by a host of witnesses. Several defendants, however, contest the sufficiency of the evidence tending to show them as participants in the conspiracy. Evidence of participation in the conspiracy is important not only with respect to the convictions under the conspiracy count but also, as to some defendants, to responsibility for offenses committed by one or more co-conspirators in furtherance of the conspiracy, pursuant to Pinkerton v. U.S., 328 U.S. 640, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946). The thread of Pinkerton runs through the case.
Evidence showed the following. The operation centered on distribution of cocaine in a low-income area of Atlanta — ironically, near the walls of the Atlanta Federal Penitentiary — at and around a square or court known as The Trap. The Trap was a known location for drug dealing. The entire neighborhood was dangerous, and gunfire was commonplace. The leader of the conspiracy was Ronald Druses, who was apprehended but fled before trial. In mid-May 1988 the conspiracy rented 760 Ann Avenue, one of a series of small houses rented to low-income residents. This house was the original point for temporary warehousing and distribution to street sellers, who in turn distributed to the streets nearby. Various defendants were housed at 760 Ann, or at least slept there. Others *1084came back and forth to the house. Some were street sellers who picked up their contraband there.
Much of the evidence came from Larry Brooks, a government informer, who managed the Ann Avenue houses and other houses in the area. Druses told Brooks that he intended to use 760 Ann as a place for “his people” to sleep. After 760 Ann was rented Brooks became concerned about the volume of traffic to that site, overparking, and complaints by other tenants about traffic and noise. Druses told Brooks that if he had any problem to contact him and he would see that things were quiet in the community. Brooks did complain that “Druses’ people” were getting out of control and that there was too much gunfire. Tenants were complaining about traffic and their children being unable to come out of doors. Druses would “take care of” these complaints, and things would quiet down for a day or two.
Brooks reported to police that he suspected drug activity. Police put the house under surveillance for several weeks beginning in early June. During the period of approximately a month that 760 Ann was in operation, but at a date not established by the evidence, Brooks saw in the house a large quantity of material that “appeared to be cocaine” and large amounts of money being counted. He saw persons going back and forth between 760 Ann and The Trap, carrying packages from the house to The Trap. He described exchanges of packages for money at the fence in back of the house and similar exchanges at The Trap. Sur-veilling police officers identified various of the defendants. Videotapes were taken, and various defendants depicted on them were identified. Kathy Brooks, wife of Larry Brooks, testified to her observations of the area and identified at least one of the defendants.
On June 22, 760 Ann was raided. Officers found large quantities of plastic bags, manila envelopes, and glassine bags containing cocaine residue. A convicted conspirator who has not appealed was arrested. On the day of the raid occupants presumably received a tip that the raid was to occur. Several of them left the premises, carrying suitcases and parcels.
Soon after the raid the house was closed down. The enterprise rented another house close by at 740 Ann Avenue, and distribution continued from there to the streets until it was raided in January 1989. Surveillance was conducted off and on from June until the raid. At this house Brooks saw powdered cocaine, rock cocaine, cocaine packaged in small tubes, and marijuana. Some of the appellants were identified as persons involved in activities in and around the house. Ultimately Brooks penetrated the organization and, around Thanksgiving, was employed to transport shipments to Ann Avenue. Shipments were brought by others to a parking area near Ann Avenue, where they were delivered to Brooks. In turn, he would deliver them to 740 Ann and would store all or part of some of these shipments in a locked tool shed. Many of Brooks’ pickups were surveilled, and the persons delivering to him were identified as well as the automobiles they used. Members of the conspiracy would withdraw cocaine from these shipments to 740 Ann for distribution to street sellers, who operated in three shifts 24 hours a day.
The operation established two houses elsewhere, in Stone Mountain and Decatur, Georgia. In June 1988, 3002 Summerview Drive, in Stone Mountain, was rented. In mid-September 1601 Weatherly Drive, in Decatur, was rented. There was evidence that some of the conspirators lived at these houses.
On January 13, 1989, 740 Ann was raided. Cocaine was found in parcels on the premises and was seized. Large amounts of currency were found in a bedroom and in a handbag belonging to Clavis, who was arrested at the scene. Also arrested was Ronald Phillips. Distribution paraphernalia was found, including coin envelopes often used for drugs (ten boxes of 1,000 each) and a pistol. That same day Grant and Edwards, the transporters to the parking lot, were arrested in the car they had been using.
*1085Also, on January 13, 1601 Weatherly Drive was raided. Agents found drugs, paraphernalia, $5,000 in cash, and records of the operation kept in the handwriting of Grant.
The house at 3002 Summerview Drive was raided January 18. Raiding agents found cocaine packaged for distribution, packaging materials, heat sealers, and identifying documents. John Doe # 1 (Greene) and an unindicted conspirator were arrested. The same day the home of Druses was raided. Officers seized from there a document with the name “Kirkland” on it and an envelope addressed to John Fluker, 740 Ann Avenue.
Documentary evidence found at some of the houses connected various of the defendants to the operation.
Summarizing relevant dates:
May 18, 1988: 760 Ann Avenue rented by the enterprise.
Late May (approx.) 1988: According to testimony of Brooks, he saw a substantial amount of what appeared to be cocaine at 760 Ann.
Early June 1988: Surveillance of Ann Avenue area began.
June 22, 1988: 760 Ann Avenue raided.
June 1988: Summerview Drive rented.
July 5, 1988: 740 Ann Avenue rented.
Sept. 13, 1988: 1601 Weatherly Drive rented.
January 13, 1989: 740 Ann Avenue raided. 1601 Weatherly Drive raided.
January 18, 1989: 3002 Summerview Drive raided.
Over the life of the conspiracy Druses regularly purchased with cash airline tickets for several persons to and from Atlanta and the Caribbean Basin area in what the jury could find was a courier operation. Couriers were intercepted bringing cocaine to Atlanta by air and by automobile on behalf of the conspiracy.
II. Count One, the conspiracy count2
We review the sufficiency of the evidence in the light favorable to the government, drawing reasonable inferences in favor of the government, seeking to determine if a reasonable trier of fact could find the defendant guilty beyond reasonable doubt. U.S. v. Delgado, 903 F.2d 1495, 1500 (11th Cir.1990).
There is no need to discuss in detail the sufficiency of the evidence of conspiracy with respect to Clavis, Edwards, Grant, Ronald Phillips and John Doe #2 (a/k/a Kirkland or Fluker).3 With respect to each of them the evidence was more than sufficient. Once the existence of a conspiracy is established, only slight evidence is necessary to connect a particular defendant to the conspiracy. U.S. v. Orr, 825 F.2d 1537, 1543 (11th Cir.1987).
We discuss sufficiency with respect to John Doe # 1 (a/k/a Greene).
With respect to John Doe # 1 (Greene), when Summerview Drive was raided on January 18, 1989, he and an unindicted conspirator, Rudolph Hines, were present. This house had been rented by Druses’ wife. Hines was named as a passenger on an air ticket purchased by Druses. In one bedroom officers found 161 grams of crack cocaine hidden in the bedsprings of a mattress, a heat sealer, and documents bearing Edwards’ name and address. In another bedroom they found sandwich bags and another heat sealer. A photograph, showing two persons, was seized in one of the bedrooms. When shown the photograph at trial Brooks identified one of the persons depicted as Greene and stated that “maybe one time” that person had picked up a *1086package of cocaine from 740 Ann Avenue and departed.
When Greene was arrested in the Sum-merview Drive raid he identified himself as Orin Greene, nickname “Terry,” a citizen of Guyana, a country on the northeast tip of South America, and identified his mother as “Yvonne Greene.” He gave two different birth dates, May 20 and May 28, 1961. He claimed to be a resident alien, which would entitle him to an alien registration “green card” showing entitlement to be in the United States. He had no green card and said that he had left it at the home of his girlfriend in Brooklyn. He was asked to give her telephone number and address in order that his story could be checked, but he could give neither. A possessor of a green card would have had to be admitted to the United States. Records of INS showed no evidence of lawful admission to the United States of an immigrant known as Orin Greene or Terry Greene, born in Guyana on May 20 or 28, 1961.
At trial the government produced as witness Orin Greene, a resident of Brooklyn. He testified that he entered the United States on May 10, 1986. He gave a birth date of August 21, 1966. He testified that he had lost his green card and a few days later had applied for a new one. His application was dated November 28. He advised that his mother was named Yvonne, the same name that Doe had given as his mother’s name. The witness testified that he had a brother named Terrence. But he denied recognizing the defendant Doe in the courtroom.
The totality of the evidence against John Doe # 1 (Greene) was sufficient to meet the standard of slight evidence necessary to connect a particular defendant to a conspiracy. U.S. v. Orr, supra.
III. The possession counts
Count Four
This count charged possession by Clavis and Ronald Phillips on or about May 1988 of more than 500 grams of a substance containing cocaine with intent to distribute, within 1,000 feet of a school. 21 U.S.C. §§ 841(a)(1) and 845a(a) and 18 U.S.C. § 21. Both were convicted. Each has properly raised the sufficiency of the evidence under this count. The government bases these convictions upon testimony by Brooks that at 760 Ann Avenue he saw a substantial quantity of material that appeared to be cocaine. Brooks testified that he entered the premises to check the air conditioning because occupants were complaining of the heat. As he entered he saw on a table large amounts of money — fives, tens, twenties, fifties, hundreds — being counted into stacks of thousands. Persons present sought to cover the money. He also saw, on a counter between kitchen and living room, approximately five loaves of white material in plastic bags that “seemed to appear cocaine.” The bags were not the type one would get at the grocery. Each was about the size of a loaf of bread. Brooks could see through the bags. As he entered the house someone put the materials under the counter.
Clavis correctly contends that the evidence is insufficient to support an inference that he possessed the material seen by Brooks. There is no evidence that he had actual possession. He was not identified as one of the persons present when Brooks saw the material. Brooks identified only one person, who is not a party to this appeal. With respect to possible vicarious possession arising from membership in the conspiracy, there is no evidence that Clavis was a member of the conspiracy at the time Brooks’ observation occurred. The evidence does not fix the date of Brooks’ observation. 760 Ann was rented on May 18. At one point in his testimony Brooks stated that persons moved into 760 the following weekend, which he described as “the weekend of the 20th.” Then he said that he was not sure of the 20th. He stated that he first went to the police after 760 Ann was rented. He was asked whether he was in 760 during the three or four weeks from the time he went to see the police until the time of the search of 760 Ann (unquestionably June 22). He responded, “Oh, about a week after I was in there they was complaining about the heat,” which caused him to go into the *1087house to check the air conditioning. He did not explain what event “a week after” referred to, or clarify his confusing reference to two entries. At another point Brooks stated that he saw the material before he went to the police. It is not possible to fix, from this testimony, the date of Brooks’ observation or even an intelligible sequence of events.
There is evidence that Clavis arrived in Atlanta, and became part of the conspiracy, in June. In the search of 760 Ann on June 22 a receipt from an Atlanta physician was found, bearing Clavis’ name and dated June 7. Clavis’ mother testified that he arrived in Atlanta “between June and July.”
The government points us to no substantial evidence tending to show that Clavis had become a participant in the conspiracy when Brooks saw the material — whenever that was. Rather it has tried to finesse the issue by asserting that a jury reasonably could have found that Clavis was part of the conspiracy from the beginning — whenever that was — but it points to no evidence that supports this assertion.4
We review the evidence in the light most favorable to the government, accepting credibility judgments and reasonable inferences in the government’s favor, to determine if it is sufficient that a reasonably minded jury could find that it establishes guilt beyond reasonable doubt. U.S. v. Sarro, 742 F.2d 1286, 1297 (11th Cir.1984). Applying this test, no evidence connects Clavis to the material as an actual or constructive possessor. The evidence does not support a conviction on vicarious grounds because Clavis is not vicariously responsible for substantive acts done by a co-conspirator before he joined the conspiracy. U.S. v. Blackmon, 839 F.2d 900 (2d Cir.1988). Clavis’ conviction under this count must be reversed.5
With respect to Ronald Phillips we reach a different conclusion. As with Clav-is, there is no direct evidence that he was an actual or constructive possessor of the material Brooks stated that he saw. There was, however, sufficient evidence to support a finding of his guilt beyond reasonable doubt under Pinkerton. That case requires that there be proof of a conspiracy of which the defendant charged is a member, that the substantive offense committed by another of the conspirators was in furtherance or expectation of the conspiracy and fell within its scope, and that the substantive offense could be reasonably foreseen as a natural and probable consequence of the unlawful agreement. Pinkerton, 328 U.S. at 647-48, 66 S.Ct. at 1184.
We have already noted the sufficiency of the evidence to support a conclusion that a conspiracy existed when Brooks saw the material. The evidence was also adequate to support a conclusion that the cocaine was in the house in furtherance of the conspiracy and that possessing cocaine in the house could be foreseen. The evidence justified an inference that beyond reasonable doubt Phillips was serving as a courier for the conspiracy at the time Brooks saw the material. Druses purchased with cash air tickets in the names of several persons, some of whom served as couriers. On May 6, 1988 Druses paid in cash for an air ticket in the name of Ronald Phillips for travel from Atlanta to New *1088York. Though Brooks’ observation of the material may have occurred before May 23 (see discussion above), events of May 23 are relevant to substantiate Phillips’ status as courier as of the May 6 ticketing. On May 23 Druses purchased airplane tickets in the name of Karen Smith and Steven Zellous. That same day at the Atlanta airport agents stopped Phillips, boarding for Miami. He gave the name of “Zellous” and produced a driver’s license in that name. He was found to have more than $10,000 in his possession. He was arrested on a state charge for giving a false name to a police officer, to which he later pleaded guilty. Karen Smith was stopped later on May 23 as her flight reached Miami and was found to have more than $50,000 in her possession. From this evidence of a pattern of ticketing by Druses for members of the conspiracy, and the May 6 and May 23 ticketing for Phillips, the jury could infer that Phillips became a member of the conspiracy as early as May 6. This was well before Brooks saw the apparent cocaine.
The evidence is sufficient to support an inference that beyond reasonable doubt the material Brooks testified that he saw was in fact cocaine. The identity of a narcotic can be established by circumstantial evidence. U.S. v. Sanchez, 722 F.2d 1501, 1506 (11th Cir.1984); U.S. v. Harrell, 737 F.2d 971, 978 (11th Cir.1984). Shortly before Brooks’ observation he had complained to police of apparent drug activities centered on 760 Ann. Soon after Brooks’ observation he or his wife, or both, saw movements of packages from 760 Ann to The Trap and the exchanges of packages for money at the back fence. Contemporaneously with observing the loaves of material in the house Brooks saw in the same area of the house a person counting and stacking large sums of money. When he entered there was an effort to hide the material, which was in transparent bags. On June 22, when 760 Ann was raided, agents seized glassine bags containing cocaine residue. The totality of this circumstantial evidence was sufficient to permit a jury to infer that what Brooks saw and described as appearing to be cocaine was in fact cocaine. The evidence was also sufficient to permit the jury to infer that the amount was at least 500 grams. Brooks described the five loaves as looking like loaves of bread, each in “like a pound bag.” Normally a loaf of bread weighs at least one pound, which is about 454 grams. While a jury may not know the exact weight of a loaf of bread it can infer from its own experience that five loaves of material of the size described would total more than 500 grams.
This brings us to the issue of the correct way to measure the distance from a drug site to a school to determine if the distance is less than 1,000 feet. There was evidence, not contested by defendants, that measured along direct point-to-point lines, the distance from 760 Ann to the school was less than 1,000 feet. The district court did not err in rejecting proffered testimony of an engineer that, measured along traveled pedestrian routes, or footpaths, the distance was more than 1,000 feet. We agree with the Second Circuit, U.S. v. Ofarril, 779 F.2d 791 (2d Cir.1985), that the statutory distance must be measured by a straight line method rather than a pedestrian travel route. Using pedestrian routes “would violate the plain meaning of the statute. Moreover, it would generate needless and time-consuming debate, and ultimately hamper the statute’s enforcement.” Id. at 792. A trafficker could operate free of the statute by placing his operation within tossing distance of the schoolyard fence if he could find — or create — a long enough footpath leading to it. And where there is more than one path, as in this case, one path might traverse 1,100 feet and the other 950 feet. These uncertainties created by the way a child meanders, or a drug dealer or buyer walks, is antithetical to the expressed intention of Congress to create a drug-free zone around each school. The way to create a definite and identifiable zone is by extending radii outward around the property on which the school is located.6
*1089Summarizing, the evidence under Count Four was sufficient as to Ronald Phillips but not sufficient as to Clavis.
Count Twelve
This count involved possession with intent to distribute cocaine base found at 740 Ann and 1601 Weatherly Drive when those houses were searched on January 13, 1989. 21 U.S.C. § 841(a)(1) and 18 U.S.C. § 2. Those convicted were Clavis, Ronald Phillips, Edwards, and Grant.7 All were convicted as Count One conspirators. The evidence supported that all were conspirators before January 13. With respect to each of these locations, evidence of possession was sufficient as to one or more of those convicted. Under the standards of Pinkerton, set out above, the evidence permitted the jury to find that each of those convicted was a possessor as alleged.8
Count Nineteen
This charged possession with intent to distribute more than 50 grams of cocaine base on or about January 18, 1989. It relates to the raid and the seizure at 3002 Summerview Drive. Those convicted were Edwards and John Doe # 1 (a/k/a Greene). Both were Count One conspirators.
Edwards was not present when the premises were searched. Greene was present. In one bedroom agents found cocaine base hidden in the bedsprings. In the same room they found a small book containing bible verses and names and addresses. It was labeled “The Little White Bible” and bore Edwards’ name. In the second bedroom they found sandwich bags and a heat sealer. Also, in that room, they found a Western Union money receipt bearing Edwards’ name and the address 3002 Summerview, an application for a social security number dated 12/22/88 bearing Edwards’ name and showing his address as 3002 Summerview. This evidence was sufficient to support an inference that Edwards had been living at 3002 Summer-view.
However, Edwards had been arrested on January 13, together with Grant, in the car used to transport cocaine to the parking lot. He had been jailed and was still incarcerated at the time of the January 18 search. The evidence does not support a conclusion that Edwards was in actual possession of the cocaine found at Summer-view five days after he was jailed. The government suggests that the evidence permitted the jury to find that he was in constructive possession, based upon his right to exercise dominion and control over the contraband hidden in the bedsprings. But the evidence will not support an inference that five days after being jailed Edwards continued to have dominion and control over the premises. As a second fallback position the government suggests that Edwards could be found in constructive possession because his co-conspirator Greene was present on January 18 and had possession. But, as discussed below, the evidence is not sufficient to support an inference of actual or constructive possession by Greene.
We turn to whether Greene possessed the cocaine base found in the bedsprings. He was present at 3002 Sum-merview Drive when it was raided. Drug paraphernalia was openly visible. There is no substantial evidence that Greene resided at this site. At trial the government contended that he was guilty under Pinkerton. But, absent sufficient evidence to show possession by Edwards (or some other conspirator), that theory must fall. The sweep of Pinkerton extends no further than legal responsibility of the charged defendant for substantive offenses committed by a co-conspirator, done in furtherance of *1090the conspiracy and falling within its scope, and reasonably foreseeable as a natural consequence of the unlawful agreement. It is not enough for Pinkerton vicarious liability of Greene that the evidence tends to show that 3002 Summerview is a “conspiracy site” and that “conspiracy” contraband is found hidden at that site. Pinkerton liability is predicated on proof of a substantive offense by a co-conspirator from which vicarious liability of another conspirator is drawn. The record is silent on who brought the material to the site, who hid it, and for what purpose. As to the specific cocaine found at Summerview Drive no substantive offense by a co-conspirator was established.
The government suggests that the jury could infer that Greene was a possessor because he made a false statement to arresting officers when he told them his name was Greene. Evidence at trial permitted the jury to find that Greene’s statement was false. Under some circumstances a false explanatory statement is so unbelievable that it gives rise to positive evidence. U.S. v. Morales, 868 F.2d 1562 (11th Cir.1989); U.S. v. Eley, 723 F.2d 1522, 1525 (11th Cir.1984). In Morales the false explanatory statement that the court held could be viewed as substantive evidence consisted of the defendant’s testimony in which he gave an incredulous account for his presence at a drug transaction and of his involvement in driving a co-defendant from one drug transaction to another. In the case before us Greene did not take the stand. There is no substantial nexus between the elements of possession and Greene’s statement made to arresting officers, if found to be false, that his name was Greene when in fact it was not.
The evidence was not sufficient to find either Edwards or Greene guilty under this count.
IV. The “knowingly maintaining a place” counts
Four counts, one for each of the four houses, charged violation of 21 U.S.C. § 856(a)(1), which makes it unlawful to “knowingly maintain or open any place for the purpose of manufacturing, distributing, or using any controlled substance.”
Manufacturing, distributing or using any controlled substance are not themselves punishable under § 856(a)(1). Rather they are elements that must be proved under the purpose provision of § 856(a)(1). As predicates for liability to convict under this section a jury must find that the defendant (1) knowingly, (2) operated or maintained a place, (3) for the purpose of manufacturing, distributing, or using any controlled substance. The offense requires two mental elements, knowledge and purpose. The purpose element applies to the person who is charged with maintaining the place for the illegal activity. It is not sufficient that others possess the requisite purpose. U.S. v. Chen, 913 F.2d 183 (5th Cir.1990).
The district court charged the jury on knowingly maintaining as follows:
Now, I instruct you in that regard that the term “maintain” is not defined by law. In other words, it has no legal or technically legal definition under the statute. Thus, it should receive its common and everyday meaning. However, the term does contemplate that a defendant exercise some degree of control over the premises and knowingly made such place available for the use alleged in the indictment.
The purpose for which the place is alleged to have been maintained as alleged by the indictment contemplates continuity in pursuit of the alleged objectives; that is, the manufacture, distribution or use of controlled substances. That is, cocaine some form of cocaine. Thus, an isolated instance of drug use or distribution or manufacture is not sufficient to constitute a violation of this statute.
Under this instruction, the critical elements are: (1) knowingly exercising some degree of control over the premises; (2) knowingly making the place available for the use alleged in the indictment; and (3) continuity in pursuing the manufacture, distribution, or use of controlled substances. An isolated instance of use, distribution, or manu*1091facture is not a violation pursuant to this instruction.
We turn next to consideration of acts that might constitute knowingly maintaining. Necessarily these are acts other than, and distinguished from, the “statutory purpose” acts, considered by themselves, of manufacturing, distributing, or using. The government mistakenly contends that evidence that a defendant regularly used premises as a site from which to distribute cocaine is, by itself, sufficient to sustain a conviction of that defendant for knowingly maintaining those premises. Such acts of distribution would be evidence of purpose, but, by themselves, they are not sufficient proof of knowingly maintaining the premises for that purpose. Acts evidencing such matters as control, duration, acquisition of the site, renting or furnishing the site, repairing the site, supervising, protecting, supplying food to those at the site, and continuity are, of course, evidence of knowingly maintaining the place considered alone or in combination with evidence of distributing from that place.
Count Three
This charged knowingly maintaining 760 Ann, a dwelling within 1,000 feet of a school for the purpose of manufacturing, distributing and using cocaine. Defendants convicted under this count were Ronald Phillips and Clavis. Both raise the sufficiency of the evidence. We affirm as to both.9
The government has not briefed the sufficiency of the evidence under Count Three as to Ronald Phillips.10 Phillips was identified on the videotape made in early June. He was seen taking packages from 760 Ann to The Trap and selling them. Larry Brooks saw him making specific exchanges of bags for money. Also, Brooks saw Phillips at 760 Ann on four or five occasions when he went there to fix something. When Brooks complained to Druses of gunfire and traffic, Druses would try to take care of the matter by talking to “his people” living at 760 Ann, including Ronald Phillips. Brooks specifically saw Druses talking to Ronald Phillips.
Kathy Brooks testified that Phillips lived at 760 Ann, based upon the fact that he would leave every morning, come back every night, and was back and forth all day long. He would carry paper bags to the fence and at times left the house with a duffle bag.
Vena Culliver, a courier, would bring suitcases and bags to 760 Ann by automobile. At least twice Kathy Brooks saw Phillips with Culliver, with one or both of them carrying suitcases that were placed in the trunk of the car, and the two of them then left together in the car.
Kathy saw Phillips carrying a pistol in the back of his pants. When Larry Brooks visited 760 Ann he saw firearms there and discussed them with Phillips.
On June 22, just before the raid, Phillips and others left 760 Ann with bags, parcels and suitcases.
This evidence relating to Phillips goes far beyond single or isolated acts. It has day-to-day continuity. The quality and nature of the acts go beyond mere distribution by Phillips. They include his participation in the chain of supply to 760 Ann and in moving the inventory when a raid was impending. His possession of a firearm, plus presence of firearms in the house and his discussion of firearms with Brooks, permitted the jury to infer that he was protecting the stash house and its inventory.
The totality of this evidence was sufficient to submit to the jury the issue of whether Phillips was knowingly maintaining 760 Ann.
The conviction of Ronald Phillips under Count Three must be affirmed. Applying Pinkerton, the conviction of Clavis also must be affirmed.
*1092Count Ten
This count charged knowingly maintaining 740 Ann Avenue within 1,000 feet of a school for the purpose of manufacturing, distributing and using cocaine base. Those convicted were Clavis, Ronald Phillips, Grant, and John Doe #2 (Kirkland/Fluker).
With respect to Kirkland: Shortly after the June 22 raid on 760 Ann, Kirkland approached Brooks and told him “They didn’t want to go back into that unit [760 Ann].” He requested that Brooks get him another house so “those guys could have somewhere to sleep.” A couple of days later 740 Ann became vacant. Brooks got it ready for occupancy and got in touch with Kirkland. Kirkland brought a woman by the name of Coleman to sign the lease, but her application was not cleared because it showed insufficient income. Kirkland then produced a statement that tended to show Coleman’s income was greater than shown, and the application was approved. Kirkland signed Coleman’s name to the lease. Kirkland paid the first month’s rent. Brooks delivered the keys to Kirkland. On a later occasion Kirkland had a confrontation with Coleman in Brooks’ house, and chased her through Brooks’ house because he (Kirkland) had given her the money to pay the rent and she had spent it.
Additionally, the telephone at 760 was in the name of Fluker, a name that Kirkland used. After his arrest in April 1989 Kirkland told the FBI that he was introduced to Druses in March 1988. Druses told him that he was distributing drugs in the Ann Avenue area. Druses asked Kirkland to get beepers for him, and Kirkland did so. Kirkland flew to Guyana on tickets supplied by Druses. From time to time Drus-es paid money to Kirkland.
With respect to Kirkland, the evidence of knowingly maintaining 740 Ann was sufficient. All others convicted under this count were Count One conspirators. We perceive no reason why Pinkerton should not be applied to the substantive offense of knowingly maintaining. Applying Pinkerton, the conviction of each of these others must be affirmed.
Count Eleven
Grant and Edwards were convicted under Count Eleven, which charged knowingly maintaining 1601 Weatherly Drive for the purpose of manufacturing, using and distributing cocaine base. This house was leased in the name of Derrick Anderson, an alias of Grant. When the house was searched agents found substantial quantities of cocaine and crack and numerous items of drug paraphernalia. They found in a locked closet records in Grant’s handwriting showing inventories, sales, shifts, shift leaders, and other data identified as records of a drug operation.
Grant was a transporter who, together with Edwards, delivered shipments from Weatherly Drive and Summerview Drive to Brooks at the shopping center.
This evidence was sufficient to submit to the jury the issue of whether Grant knowingly maintained 1601 Weatherly.11 Edwards was a Count One conspirator and either had knowledge or could foresee the use of 1601 Weatherly as a source away from Ann Avenue for such purposes as processing, originating shipments, storage, and maintenance of records. Under Pinkerton, the evidence was sufficient as to Edwards.
Count Eighteen
Edwards and John Doe # 1 (Greene) were convicted under this count of knowingly maintaining 3002 Summerview. We have set out above, in discussion of Count Nineteen (possession at 3002 Summerview), the evidence that tended to connect Edwards with this site. In a bedroom officers found a book bearing Edwards’ name. In a second bedroom they found a Western Union money receipt and an application for a *1093social security number, both bearing Edwards’ name and showing his address as 3002 Summerview, and a heat sealer and sandwich bags.
In the discussion of Count Nineteen, we held that the evidence was not sufficient to support conviction of Edwards of possessing the cocaine found hidden in the bedspr-ings at 3002 Summerview. The evidence connecting Edwards with 3002 Summer-view was sufficient to support a conclusion that he had been living there. A heat sealer and sandwich bags were found there, but there is no evidence that they were there while he lived there. As we have pointed out, the search of this site occurred five days after Edwards had been arrested elsewhere and jailed. Greene was present at the search and was arrested, but there was not substantial evidence that he lived there.
The government says that it is sufficient, by itself, that it introduced evidence that Edwards had lived at the premises. For this it relies upon a single sentence statement by the Fifth Circuit in U.S. v. Onick, 889 F.2d 1425 (5th Cir.1989): “The jury could infer that Tolliver maintained the house because he lived there.” Onick is not so sweeping, and the content of the word “living” is not sufficiently certain, to permit a facile conclusion that living equates to maintaining. In Onick officers found illegal drugs and drug paraphernalia concealed throughout the house. They found numerous guns and $80,000 in cash hidden in clothing and a safe. Tolliver was present and was arrested. The court held:
The police found numerous receipts made out to Tolliver at the house address. They also found papers belonging to Tol-liver, clothes labeled with his nickname, and prescription bottles in his name. In addition, Tolliver selected clothing from one of the closets to wear to the police station. Based on this evidence, the jury could conclude that Tolliver lived in the house and exercised dominion and control over the premises and the drugs.
Id. at 1430. Applying these facts to the issue of maintaining, the court went on to say:
A reasonable jury could find that Tolliver knowingly maintained a place to manufacture, distribute, or use drugs. Beginning with the premise that Tolliver lived in the house, the jury first could infer that Tolliver came across and therefore knew about the drugs and drug paraphernalia scattered throughout the house. Second, the jury could infer that Tolliver maintained the house because he lived there. Third, based on the large quantify of drug paraphernalia used to measure and package drugs (particularly the 4,063 gelcaps), the jury could infer that Tolliver intended to use the property to distribute drugs. Therefore, a reasonable jury could convict Tolliver for knowingly maintaining a place to manufacture, distribute, or use drugs.
Id. at 1431. (Footnote omitted.) The court had said just previously, however, in its footnote 2:
We do not mean to suggest that living on the premises is either necessary or sufficient for conviction under this statute.
Id. Read in light of the facts, the decision in Onick appears to be that living on the premises in the manner that Tolliver did — papers, clothing, prescription bottles, selection of clothing from the closet, knowledge of drugs and paraphernalia hidden throughout the house which the jury could infer that he came across, plus his presence when these items were found — permitted a conclusion that he “lived in the house and exercised dominion and control over the premises and the drugs.” As the court noted in its footnote 2, it did not decide that “living on the premises” is alone sufficient for conviction under the statute. The facts of “living” relating to Edwards are far removed from those relating to Tolliver. Whether he had dominion and control over the heat sealer and sandwich bags is speculative.
There is evidence that Edwards and Grant transported shipments to the parking lot. The government has not referred us to evidence that specifically links these shipments to 3002 Summerview or that connects any activities by Edwards at Sum-*1094merview relating to shipments that could be said to establish that Edwards was knowingly maintaining that site within the meaning of the statute.
The totality of the evidence as to Edwards does not support his conviction.
The evidence was also not sufficient to submit to the jury on knowingly maintaining by Greene. He was identified as having “maybe” picked up a single package of cocaine from 740 Ann. He was present at 3002 Summerview Drive on the single occasion when it was raided. Drugs were hidden in bedsprings, and drug paraphernalia was visible. There was no substantial evidence that he “lived” at this site. The evidence was not sufficient.
Y. Constitutionality of the knowingly “maintaining a place” statute
Several defendants contend that § 856(a)(1) is void for vagueness. They cite to us differing dictionary definitions as support for the proposition that the statute does not give adequate notice of the conduct that is proscribed. We have already discussed, at the beginning of part IV, our reading of § 856(a)(1). Additionally, we construe the statute, as did the district court in its jury instruction, to exclude a single, isolated act as a violation and to embrace some degree of continuity. We examine the statute in the light of our narrowing construction.
In addressing a vagueness challenge to a statute, the court must answer two questions: (1) does the statute give a “person of ordinary intelligence a reasonable opportunity to know what is prohibited?” and (2) does the statute provide explicit standards to those who enforce the law to prevent arbitrary and capricious enforcement? Grayned v. Rockford, 408 U.S. 104, 108, 92 S.Ct. 2294, 2298, 33 L.Ed.2d 222 (1972).
In determining the sufficiency of the notice that a statute must give, the statute must of necessity be examined in the light of the conduct with which the defendant is charged. U.S. v. National Dairy Products Corp., 372 U.S. 29, 34, 83 S.Ct. 594, 598, 9 L.Ed.2d 561 (1963). The statute is not evaluated in the abstract, id. at 32, 83 S.Ct. at 597, but in the light of the facts at hand, U.S. v. Mazurie, 419 U.S. 544, 550, 95 S.Ct. 710, 714, 42 L.Ed.2d 706 (1975), and without focus on marginal offenses. The presence of the two intent elements, “knowingly” and “for the purpose” does much to eliminate the contention of vagueness or unfairness in application. Village of Hoffman Estates v. The Flipside, 455 U.S. 489, 499, 102 S.Ct. 1186, 1193, 71 L.Ed.2d 362 (1982); Boyce Motor Lines, Inc. v. United States, 342 U.S. 337, 342, 72 S.Ct. 329, 331, 96 L.Ed. 367 (1952).
We have affirmed on sufficiency of evidence grounds the convictions of certain of the defendants for knowingly maintaining a place based upon their own actions and, for each of these defendants, have described his actions: Phillips (Count Three), Kirkland (Count Ten) and Grant (Count Eleven). The “facts at hand” of acts done by each of these defendants are so clearly within the concept of “knowingly maintaining a place” that as to each of them the statute meets constitutional scrutiny.
Phillips and Clavis were convicted under one or more of these counts. Because they were convicted by application of Pinkerton, their challenges of the statute on vagueness grounds fail.
VI. Firearms counts
Count Five
Count Five charged possession of a .38 cal. Taurus revolver and a nine millimeter pistol by Ronald Phillips in relation to possession with intent to distribute on or about May 1988. 18 U.S.C. §§ 2 and 924(c). Brooks testified that every time he visited 760 Ann Avenue there were firearms inside. He talked to Phillips about the firearms. He recalled handling “one 357, a nine millimeter.” He thought he saw a .22. Later he said that one of the weapons was a 357 or .38 Smith & Wesson. He was certain that one of the weapons was a nine-millimeter. He saw a .38 Taurus underneath a couch on which one of the conspira*1095tors was lying. Kathy Brooks testified that she often observed Phillips carrying a firearm in the back of his pants as he made deliveries from 760 Ann to The Trap.
The connection of Phillips with 760 Ann was adequately established. The presence of weapons in a location that the defendant used to distribute a significant quantity of illegal drugs is sufficient to submit to the jury the issue of whether the defendant used the firearm in connection with a drug trafficking crime. U.S. v. Poole, 878 F.2d 1389, 1393 (11th Cir.1989). The evidence against Phillips was sufficient.
Count Sixteen
Grant contests the sufficiency of the evidence of his possession and use of a firearm in relation to the crime of possession with intent to distribute cocaine on or about January 13. 18 U.S.C. § 924(c). On that day he and Edwards were arrested while in the Honda automobile that they had been using to transport cocaine to the parking lot where it would be delivered to Brooks. The weapon was found in the glove box. Grant had bought the weapon on August 26, 1988, using an alias. This evidence was sufficient to submit this count to the jury. It was not necessary to prove that Grant had the weapon on his person.
VII. Interrogation of Grant
When Grant was arrested he was cuffed and placed in a police car. Over a substantial period of time immigration officers and other law enforcement officers came to the scene and were in contact with Grant. It is clear that he was given a Miranda warning by an INS agent who then asked his name and his citizenship. Grant gave a false name and stated that he was a citizen of the United States. He does not contest the validity of this questioning.
The sequence of events thereafter is confusing, and testimony concerning it is in conflict. Grant had conversations with Alcohol, Tobacco and Firearms agents. Somebody gave him a Miranda warning again, and Grant responded that he would not answer any questions. An agent noted on a waiver form “Grant refused to be interviewed.” There is an implication that the warning was given a third time. At some point Grant was questioned about drug-related activities and made incriminating statements.
Grant asserts that these incriminating statements violated Michigan v. Mosley, 423 U.S. 96, 96 S.Ct. 321, 46 L.Ed.2d 313 (1975), because they were made in response to interrogation carried on after he had said he would not answer questions. After a full hearing the district court held that the statements were freely and voluntarily given and therefore admissible. Evidence showed that Grant hired Brooks into the organization. His role in delivering packages to the parking area was clearly established. Some of the deliveries to Brooks at the parking area were surveilled. Shipments were traced from the parking area to Ann Avenue. On some occasions Brooks would notify police when he received telephone instructions to make a pickup at the parking area and they would supply “cover” to him as he transported the material to Ann Avenue (thus protecting Brooks from arrest by officers who would not know of his undercover work). On at least one occasion Brooks interrupted delivery to Ann Avenue and took the shipment to a neutral site where it was opened by police, found to contain drugs, and photographed.
Grant was arrested in the transport car with Edwards, his co-transporter. Previously we have described Grant’s activities as a record-keeper for the organization and his residence in one of the organization’s houses.
In view of the compelling weight of this evidence against Grant, if it was error to admit the incriminating statements, it was error without injury beyond reasonable doubt, Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967).
VIII. Search of Claris’ purse
The search of 740 Ann was conducted pursuant to a warrant that autho*1096rized search of the premises and of Clavis’ person. A purse or handbag was found at the house, and Clavis was arrested there. Officers opened the purse and found a substantial amount of currency, which was admitted into evidence over the objection of Clavis, who suggests that the purse could not be opened without a separate warrant. Pretermitting whether a separate warrant was required, if the admission of this currency was error, it was error without injury beyond reasonable doubt, considering the other evidence against Clavis.
IX. Jury instruction — Ronald Phillips
At trial Phillips testified that he neither told officers his name was Zellous nor gave them a driver’s license bearing that name. He further testified to an alibi for which there was no evidence except his testimony, and that was contradicted by direct evidence from other witnesses.
The court charged the jury:
When a Defendant voluntarily and intentionally offers an explanation or makes some statement tending to how his innocence and this explanation or statement is later shown to be false if the jury so finds, then the jury may consider whether this circumstantial evidence points to a consciousness of guilt. Ordinarily, it is reasonable to infer that an innocent person does not usually find it necessary to invent or fabricate an explanation or statement tending to establish his innocence.
Phillips contends that the second sentence in this charge was an improper comment upon his credibility. His argument focuses on his false statement of identity to investigating officers at the Atlanta airport and does not mention his testimony about an alibi.
It is arguable whether this point was raised by Phillips at trial, but in any event it has no merit. A defendant subjects himself to a determination by the jury of his credibility when he takes the stand in a criminal case. The jury is free to reject a defendant’s explanation as complete fabrication. U.S. v. Cotton, 770 F.2d 940, 945 (11th Cir.1985). If the jury determines that defendant’s testimony is false this may be used as circumstantial substantive evidence of guilt. “Moreover, wholly incredible explanations may also form a sufficient basis to allow the jury to find that the defendant had the requisite guilty knowledge.” U.S. v. Morales, 868 F.2d 1562, 1574 (11th Cir.1989) (quoting U.S. v. Eley, 723 F.2d 1522, 1525 (11th Cir.1984)).
The jury instruction was not error.
X. Sentencing issues
Grant: The district court imposed a three-level increase on Grant on the ground he was a supervisor or manager. He was the bookkeeper who kept books and records of the operation that we have described above, found at 1601 Weatherly. Grant approached Brooks and hired him to become a member of the organization and to receive cocaine shipments in the parking lot and deliver them to Ann Avenue. Grant delivered shipments to Brooks at the parking lot, and Brooks in turn delivered them to others. The court did not err.
Phillips: The PSI referred to § 3Bl.l(c), which allows only a two-point increase, rather than 3Bl.l(b) which allows a three-point increase. This did not cause his sentence to be erroneously calculated. More than five persons were involved, which falls under (c). The reference to (b) was an obvious typographical error.
Phillips’ receipt of deliveries of cocaine to 740 Ann, his distribution of it to distributors, and his supervisory role over 740 Ann adequately support the finding that he was a supervisor. A two-point increase for obstruction of justice was fully supported by Phillips’ false testimony at trial.
Clavis: The court included in the quantity of cocaine attributable to Clavis 36.8 grams of cocaine and 115.6 grams of cocaine base found at 1601 Weatherly Drive on January 13, 1989. Count Twelve charged possession of more than 50 grams on January 13. The proof of January 13 possession embraced both the drugs seized at 1601 Weatherly and those seized the same day at 740 Ann Avenue. Clavis was *1097convicted under Count Twelve. He contends, however, that the Weatherly Drive drugs could not be attributed to him because he was acquitted under Count Eleven, which charged knowingly maintaining 1601 Weatherly. This argument overlooks the conviction of possession under Count Twelve. Moreover, we have explained above the contours of knowingly maintaining, which sweep more broadly than possessing. An acquittal of knowingly maintaining does not preclude responsibility for the narrower offense of possession of drugs at the same site.
Clavis contends also that the court could not attribute to him 161.5 grams of cocaine seized at 3002 Summerview on January 18. Count Nineteen charged possession of this cocaine, Count Eighteen charged knowingly maintaining this house, and Clavis was not charged under either count. The standards embodied in § 3B1.1 “roughly approximate” but do not codify Pinkerton. U.S. v. LaFraugh, 893 F.2d 314, 317-18 (11th Cir.1990). “Relevant conduct” by Clavis includes conduct in furtherance of the conspiracy that was known to or reasonably foreseeable by him. Activities at 3002 Summerview were activities attributable to the conspiracy. Clavis, as a member of the conspiracy, could foresee that cocaine distributed at Ann Avenue was being brought from elsewhere and being processed and packaged elsewhere. The cocaine was properly attributed to him.
Both Phillips and Clavis contest the attribution to them of 369 grams of cocaine base seized from courier Lamar Hampton on January 19,1989, on the interstate highway south of Atlanta, because they, and most of the other conspirators, had been arrested five days before on January 13. At least as to them, they say, the conspiracy was over on January 13. There was evidence, however, that the cocaine had been ordered by Druses in December. It is sufficient that it was reasonably foreseeable that the conspiracy would continue unabated after their arrest to the extent of continued movement of cocaine previously ordered. U.S. v. Vinson, 886 F.2d 740 (4th Cir.1989). This cocaine base was properly attributed to both Phillips and Clavis.
XI. Miscellaneous issues
Some defendants raise a Batson argument. Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986). We agree with the district court that they did not make out even a prima facie case.
The court did not abuse its discretion in refusing to permit a defendant to call as a witness a government agent who had been in the courtroom as an observer during part of the proceedings.
John Doe #2 (Kirkland/Fluker) urges that the court erred in denying his motion for a new trial. The motion was based in large part on the theory that Brooks was not a credible witness. There was no error.
Various of the defendants objected to this statement by the prosecutor in oral argument:
The point of the matter is this: That the government — and you’ve seen the government in this case. We’re just human beings, too. We can’t lick the drug problem by ourselves. It takes people like Larry Brooks who are willing to stand up and say no to the drug dealers. You’ve got to say to the Larry Brookses of this country and this community that we’re not going to stand to have you villified [sic] and condemned when you come into court and you testify to what you lived and what you saw and what you did. When you take that oath and swear to tell the truth, and you do so and you work to make this a better community, we’re not going to let you down.
The district judge responded:
I’ll overrule the objection. He has proper opportunity to comment upon the witness who has been attacked by every lawyer who’s argued for the defense.
And you may have additional time to respond to the argument just made by the defendants if you need it.
The major thrust of the prosecutor’s comment was a plea to the jury that it protect Brooks, as a truthful witness to *1098activities of a drug conspiracy, from vilification and condemnation by defense counsel. Defense counsel had indeed attacked Brooks with full force. They had suggested, or in some instances directly stated, that he was involved in the drug business, that he was using the police to cover his own operations, and that he was testifying to protect his own drug business. It was even suggested that he was in charge of drug distribution in the area, and that he had distributed drugs for Druses as early as 1988. These comments or suggestions had no support in the record.
Considering the nature and the contents of the remarks of defense counsel the ruling of the district court was not error.
Edwards was acquitted under Count Ten (maintaining 740 Ann Avenue). He contends, on collateral estoppel and double jeopardy grounds, that, because of this acquittal, testimony that might inferentially link him to maintaining 740 Ann Avenue could not be considered in connection with any other charges against him. This is frivolous.
AFFIRMED in part, REVERSED in part.
. Henry Louis Ismond and Winston Daniel Frazer also appealed from their convictions in this case. Their appeals have been bifurcated and will be submitted and decided separately.
. 21 U.S.C. §§ 841(a)(1) and 846.
. Grant did not move for judgment of acquittal on Count One so as to him the question of sufficiency of evidence is not reviewable. Had Grant properly raised sufficiency, however, it would be summarily rejected.
. The government has not addressed this issue with the candor to which this court is entitled. As evidence of the beginning of Clavis’ participation its brief points to events that under the evidence occurred after Brooks’ observation (such as June 9 and June 22). At another point it avoids assigning a date to the observation by saying that it occurred "Once, when Brooks was inside the house [760 Ann].’’ At oral argument the government addressed relevant events with the cryptic description "May-June.” We are entitled to more responsible advocacy than the government’s obfuscation of this issue, which Clavis had raised head-on.
. Since proof of the exact date alleged (May 1988) is not required, an argument could be made that the sufficiency of the evidence under this count might be sustained by proof of shipments of cocaine that came to 760 Ann at times after Clavis was shown to have become a conspirator. But the stream of shipments that came later were not the subject of testimony as to quantity. Moreover, this alternative possibility was not the government’s theory of Count Four, either at trial or on appeal. The government has stood on Brooks’ observation and so must fall on it.
. Other appellants raise this issue by incorporation as to Counts Three and Ten: (Grant *1089(Ten); Clavis (Three, Ten), Kirkland (Ten)). Our holding applies to Counts Three and Ten as well as Count Four.
. Grant did not move for judgment of acquittal on this count so sufficiency as to him is not reviewable. Were this question properly before us, however, we would summarily reject it.
. We need not set out other grounds (for example, actual or constructive possession and aiding and abetting) on which, as to some of the defendants, the jury could have reached the same conclusion. The jury was charged on aiding and abetting.
. We have addressed evidence of distance from the school under Part III, Count Four, above.
. Nor has Phillips, but the issue is before us because he moved for judgment of acquittal, and on appeal he adopted the arguments of all other appellants.
. Grant did not move for judgment of acquittal on Count Eleven. We must, however, consider sufficiency of the evidence with respect to him. We affirm Edwards' Count Eleven conviction on Pinkerton grounds, derived from Grant’s offense, and Edwards did move for judgment of acquittal and presented-the sufficiency issue on appeal.