402 F.3d 489
Jerry KRIM; et al., Plaintiffs,David Petrick, Lead Plaintiff; Bret Beebe, Lead Plaintiff; Gene Burke, Lead Plaintiff, Plaintiffs-Appellants,Dawn Rusing-Bell; Kishore Mehta; Dierdre Humphrey, Appellants,v.PCORDER.COM, INC.; Ross A. Cooley; Trilogy Software, Inc.; Peter J. Barris; Joseph A. Liemandt; Robert W. Stearns; Linwood A. Lacy, Jr., Defendants-Appellees.Jean Schwartz Burke, On Behalf of Herself and All Others Similarly Situated; Plaintiff-Appellant,Dawn Rusing-Bell; Kishore Mehta; Dierdre Humphrey, Appellants,v.PcOrder.com, Inc.; Ross A. Cooley; Cristina C. Jones; James J. Luttenbacher; Joseph A. Liemandt; Peter J. Barris; Linwood A. Lacy, Jr.; Robert W. Stearns; Trilogy Software, Inc.; Goldman, Sachs & Co.; Credit Suisse First Boston; SG Cowen & Co., Defendants-Appellees.Barry J. Pinkowitz, On Behalf of Himself and All Others Similarly Situated, Plaintiff,Dawn Rusing-Bell; Kishore Mehta; Dierdre Humphrey, Appellants,v.PcOrder.com, Inc.; Ross A. Cooley; Cristina C. Jones; James J. Luttenbacher; Joseph A. Liemandt; Peter J. Barris; Linwood A. Lacy, Jr.; RobertW. Stearns; Trilogy Software, Inc.; Goldman, Sachs & Co.; Credit Suisse First Boston; SG Cowen & Co., Defendants-Appellees.
No. 03-50737.
United States Court of Appeals, Fifth Circuit.
March 1, 2005.

James D. Baskin, III (argued), The Baskin Law Firm, Austin, TX, Joe R. Whatley, Jr., Whatley Drake, Birmingham, AL, for Plaintiffs-Appellants and Appellants.
James Edward Maloney, Baker Botts, Houston, TX, for pcOrder.com, Inc., Ross A. Cooley, Christina C. Jones and James J. Luttenbacher.
Noel M.B. Hensley (argued), P. Nicholas Even, Richard Thaddeus Behrens, Haynes & Boone, Dallas, TX, for Trilogy Software, Inc., Peter J. Barris and Joseph A. Liemandt.
Robert W. Brownlie, Gray, Cary, Ware & Freidenrich, San Diego, CA, Alan D. Albright, Geoffrey Robert Unger, Gray, Cary, Ware & Freidenrich, Austin, TX, for Robert W. Stearns and Linwood A. Lacy, Jr.
Harry M. Reasoner, Karl S. Stern, Gary Ewell, Vinson & Elkins, Houston, TX, for Goldman Sachs & Co., Credit Suisse First Boston and SG Cowen & Co.
Appeal from the United States District Court for the Western District of Texas.
Before HIGGINBOTHAM, DAVIS and GARZA, Circuit Judges.
PATRICK E. HIGGINBOTHAM, Circuit Judge:


1
Investors who purchased stock in pcOrder.com brought this consolidated securities action under Sections 11 and 15 of the Securities Act of 1933 against defendants pcOrder.com, its directors, its controlling shareholder Trilogy Software, and its investment bankers (collectively "PCOrder"), alleging that the registration statements filed with the Securities and Exchange Commission were false and misleading. The district court concluded that, with one exception, the investors lacked Section 11 standing because they could not trace their stock to the registration statements in question. Finding the remaining investor's claims moot, the court dismissed all of the claims and denied a third-party motion to intervene. We affirm.


2
* PCOrder conducted an initial public offering of pcOrder.com stock on February 26, 1999, and a secondary public offering on December 7, 1999. In connection with each offering PCOrder filed a registration statement with the SEC.


3
Several holders of pcOrder.com stock filed multiple lawsuits against PCOrder under Section 11 of the Securities Act of 1933, which provides a right of action to "any person acquiring" shares issued pursuant to an untrue registration statement.1 The plaintiffs alleged that the registration statements were false and misleading by indicating that pcOrder.com had a viable business plan, had an ability to generate and report accurate operating and financial information, and was not competing with Trilogy Software for revenue. The district court consolidated the actions and appointed Lead Plaintiffs.2 The Lead Plaintiffs sought to have a class action certified and have themselves designated as class representatives.


4
In its October 21, 2002, order denying class certification,3 the district court first found that none of the Lead Plaintiffs purchased their stock during the public offerings — that is, they were "aftermarket" purchasers.4 However, it held that Section 11 is available not only to those who purchased their stock during the relevant public offerings, but also to aftermarket purchasers as long as the stock is "traceable" back to the relevant public offering.5


5
The district court then considered whether Lead Plaintiffs Beebe, Dr. Burke, and Petrick could trace their stock back to either of the two public offerings. The district court found that the approximately 2.5 million shares issued in the pcOrder.com IPO were registered in a stock certificate in the name of Cede & Co., the nominee of the Depository Trust Company. The court found that, on April 19, 1999, when Beebe purchased 1000 of these "street name" shares, the pool of street name stock still contained only the IPO stock. Therefore, because all of his stock was necessarily IPO stock, Beebe was able to satisfy the traceability requirement and establish standing.


6
In contrast, the court concluded that standing was lacking for Dr. Burke and Petrick. By the end of June 1999 when Dr. Burke purchased 3000 shares, the court found that non-IPO shares — specifically, insider shares — had entered the street name certificate and intermingled with the IPO shares, but that IPO shares still comprised 99.85% of the pool. Subsequent to the December 7, 1999, secondary public offering, Dr. Burke made additional purchases and Petrick also purchased a number of shares at a time when IPO and SPO shares (collectively "PO stock") constituted 91% of the market. Appellants' expert acknowledged that there is no way to track individual shares within a pool once it becomes contaminated with outside shares.


7
In light of the intermingling of PO and non-PO stock in the market at the time of their purchases — even though PO stock was the overwhelming majority — the district court held that Dr. Burke and Petrick could not demonstrate that their shares were traceable to the public offering registration statements. In reaching this conclusion, the court considered expert testimony indicating that, given the number of shares owned by each Lead Plaintiff and the percentage of PO stock in the market, the probability that each Lead Plaintiff owned at least one share of PO stock was very nearly 100%.6 However, the court held that this did not satisfy the traceability requirement because the "Lead Plaintiffs must demonstrate all stock for which they claim damages was actually issued pursuant to a defective statement, not just that it might have been, probably was, or most likely was, issued pursuant to a defective statement."7 The district court noted that, "[o]therwise, `all persons who held stock in street name on and after the offering date could claim a proportional interest in the shares.'"8


8
Having found that Dr. Burke and Petrick lacked Section 11 standing, the court concluded that they could not serve as class representatives and denied class certification.9 We rejected a request for an interlocutory appeal.10


9
On May 5, 2003, the district court granted PCOrder's motion to dismiss for lack of subject matter jurisdiction under Federal Rule of Civil Procedure 12(b)(1).11 The district court reiterated its conclusion that Beebe had standing to sue under Section 11, but that Dr. Burke and Petrick did not. It concluded that the other plaintiffs, Barry Pinkowitz, Jerry Krim, and Jean Schwartz Burke, also lacked standing because they too could not trace their stock back to the public offerings.12 The court dismissed all of these claims without prejudice. The court then dismissed Beebe's claim as moot because PCOrder had offered Beebe a settlement equal to his full recovery under the statute. Having disposed of the suits, the district court denied a motion to intervene by three individuals ("Intervenors")13 and entered final judgment in favor of PCOrder. Appellants14 challenge the district court's rulings regarding standing and the motion to intervene. The denial of class certification is not before us.

II

10
In general, we review a dismissal for lack of subject matter jurisdiction pursuant to Rule 12(b)(1) de novo.15 "A case is properly dismissed for lack of subject matter jurisdiction when the court lacks the statutory or constitutional power to adjudicate the case."16 In considering a challenge to subject matter jurisdiction, the district court is "free to weigh the evidence and resolve factual disputes in order to satisfy itself that it has the power to hear the case."17 We review the district court's jurisdictional findings of fact for clear error.18 The denial of a motion to intervene as of right is reviewed de novo.19 The denial of a permissive motion to intervene is reviewed for abuse of discretion.20

III

11
* Appellants argue that Dr. Burke, Mrs. Burke, and Petrick can establish Section 11 standing by proffering nothing more than statistics indicating a high mathematical probability, based on the number of shares purchased by each individual and the number of PO shares in the market, that at least some of their shares were issued pursuant to the challenged registration statement. We disagree.21


12
* We turn first to the language of the statute.22 In general, the Securities Act of 1933 ("Securities Act")23 "is concerned with the initial distribution of securities."24 Section 11 of the Securities Act, imposing civil liability for public offering of securities pursuant to a false registration statement, permits "any person acquiring such security" to sue.25 While Section 11's liability provisions are expansive — creating "virtually absolute" liability for corporate issuers for even innocent material misstatements26 — its standing provisions limit putative plaintiffs to the "narrow class of persons" consisting of "those who purchase securities that are the direct subject of the prospectus and registration statement."27


13
In Rosenzweig v. Azurix Corp., we recently held that aftermarket purchasers do not inevitably lack standing.28 The district court here foreshadowed this in holding that Section 11's "language suggests a much broader class of potential plaintiffs than those who literally purchased their shares in the challenged offering."29 Indeed, the plain language of the statute confers standing on "any person acquiring such security,"30 and there is no reason to categorically exclude aftermarket purchasers, "`so long as the security was indeed issued under that registration statement and not another.'"31 As such, aftermarket purchasers seeking standing must demonstrate the ability to "trace" their shares to the faulty registration.32 As one court explained:


14
[T]o be able to take advantage of the lower burden of proof and almost strict liability available under § 11, a plaintiff must meet higher procedural standards. The most significant of the procedural standards is the requirement that a plaintiff be able to trace the security for which damages are claimed to the specific registration statement at issue.33


15
In Rosenzweig, we further held that this traceability requirement is satisfied, as a matter of logic, when stock has only entered the market via a single offering.34 We did not speculate on what other methods might be available to satisfy the traceability requirement for aftermarket purchases, but we were careful to note the Supreme Court's concern "that the Securities Act remain anchored to its original purpose of regulating only public offerings."35


16
Appellants, as aftermarket purchasers, assert that they can also demonstrate standing by showing a very high probability that they each have at least one PO share. Appellants argue that their statistical determinations, being over 50%, demonstrate by a preponderance of the evidence, that it is "more likely than not," that their shares are traceable to the public offerings in question.


17
We are persuaded that accepting such "statistical tracing" would impermissibly expand the statute's standing requirement. Because any share of pcOrder.com stock chosen at random in the aftermarket has at least a 90% chance of being tainted, its holder, according to Appellants' view, would have Section 11 standing.36 In other words, every aftermarket purchaser would have standing for every share, despite the language of Section 11, limiting suit to "any person acquiring such security."37 As the district court found, it is "likely that any street name shareholder can make a similar claim with regard to one share."38 This cannot be squared with the statutory language — that is, with what Congress intended. We decline the invitation to reach further than the statute.


18
The fallacy of Appellants position is demonstrated with the following analogy. Taking a United States resident at random, there is a 99.83% chance that she will be from somewhere other than Wyoming.39 Does this high statistical likelihood alone, assuming for whatever reason there is no other information available, mean that she can avail herself of diversity jurisdiction in a suit against a Wyoming resident? Surely not.40


19
In limiting those who can sue to "any person acquiring such security," Congress specifically conferred standing on a subset of security owners (unless of course, as in Rosenzweig, all shares in the market are PO shares). To allow Appellants to satisfy the tracing requirement for aftermarket standing in this case with the proffered statistical methodology would contravene the language and intent of Section 11.

2

20
Appellants urge this Court to not hew the statutory line, contending that to do so, in light of current market conditions, effectively precludes recovery under Section 11; that there is no reason to "express a preference for" the interests of defendants over plaintiffs. Appellants point out that, given the fungible nature of stocks within a street name certificate, it is virtually impossible to differentiate PO shares from non-PO shares.


21
However, as we have explained, Section 11 is available for anyone who purchased directly in the offering and any aftermarket purchasers who can demonstrate that their shares are traceable to the registration statement in question — e.g. when, as with Beebe, there had only been one offering at the time of purchase.41 When Congress enacted the Securities Act of 1933 it was not confronted with the widespread practice of holding stock in street name that Appellants describe as an impediment, absent our acceptance of statistical tracing, to invoking Section 11.42 That present market realities, given the fungibility of stock held in street name, may render Section 11 ineffective as a practical matter in some aftermarket scenarios is an issue properly addressed by Congress. It is not within our purview to rewrite the statute to take account of changed conditions. In the words of one court, Appellants' arguments may "have the sound ring of economic reality but unfortunately they merely point up the problems involved in the present scheme of statutory regulation."43


22
It is, therefore, perhaps not surprising that we failed to locate any court, nor did Appellants point to any, that found Section 11 standing based solely on the statistical tracing theory espoused today. Given that the statute has been in existence for over 70 years and such elementary statistical calculations have been around for centuries, it is difficult to conclude that this is a coincidence. We note that a handful of lower courts have rebuffed similar attempts by plaintiffs.44 In one case, Kirkwood v. Taylor, the district court — later summarily affirmed by the Eighth Circuit — rejected the "fungible mass" method whereby every purchaser is deemed to own a pro rata portion of PO shares for the purpose of determining Section 11 standing.45 Because "all persons who held stock in street name on and after the offering date could claim a proportional interest in the shares," the court held that "the logical extension of plaintiffs' fungible mass theory would ... effectively circumvent the tracing requirement."46 Similar concerns persuade us to reject today's attempt at statistical tracing.


23
In Barnes v. Osofsky,47 the Second Circuit confronted an intermingled stock pool not unlike the one we face today. In that case, two individuals challenged the settlement of a class action alleging Section 11 violations in a secondary public offering. The challengers, who purchased stock after the SPO, were unable to trace a portion of their shares to the SPO as opposed to the preexisting shares on the market. They objected to a provision of the settlement "limiting the benefits of the settlement to persons who could establish that they purchased securities issued" in the SPO.48 The court was not deterred by the reality that this "eliminated those who purchased after the issuance of the allegedly incomplete prospectus but could not so trace their purchases," because Section 11 "extends only to purchases of the newly registered shares."49 While not addressing the question before us today, Barnes is nonetheless instructive. Plaintiffs in that case urged a broad reading of Section 11 to cover anyone purchasing stock after the SPO — whether or not it was traceable to the SPO. Not unlike the concerns expressed by Appellants in the instant case, the plaintiffs in Barnes argued as follows:


24
[O]nce it is agreed that § 11 is not limited to the original purchasers, to read that section as applying only to purchasers who can trace the lineage of their shares to the new offering makes the result turn on mere accident since most trading is done through brokers who neither know nor care whether they are getting [tainted] or [clean] shares.... [I]t is often impossible to determine whether previously traded shares are [clean] or [tainted], and that tracing is further complicated when stock is held in margin accounts in street names since many brokerage houses do not identify specific shares with particular accounts but instead treat the account as having an undivided interest in the house's position.50


25
The court rejected these arguments and rejected the plaintiffs' broad reading of Section 11's standing requirement as "inconsistent with the over-all statutory scheme" and "contrary to the legislative history."51 The same is true of Appellants' view today.

3

26
Appellants' reliance upon the Fourth Circuit's opinion in Friends of the Earth v. Gaston52 is misplaced. Rather, this case offers support to PCOrder. In Gaston, the Clean Water Act53 specifically provided standing for persons "having an interest which is or may be adversely affected."54 This language, chosen by Congress, "confers standing on a `broad category of potential plaintiffs' who `can claim some sort of injury,' be it actual or threatened, economic or noneconomic."55 In fact, "Congress has indicated that this provision confers standing to enforce the Clean Water Act to the full extent allowed by the Constitution."56 As such, Gaston illustrates Congress's ability to provide for standing based on risk, confined only by the strictures of Article III:


27
While Article III sets the minimum requirements for standing, Congress is entitled to impose more exacting standing requirements for the vindication of federal statutory rights if it wishes. Here the legislature chose to go to the full extent of Article III in conferring standing on any person with "an interest which is or may be adversely affected."57


28
Here, by contrast, Congress conferred standing on those who actually purchased the tainted stock, not on the whole class of those who possibly purchased tainted shares — or, to put it another way, are at risk of having purchased tainted shares. Unlike the standing conferred by Congress in the Clean Water Act, Appellants here cannot meet the statutory standing requirement of Section 11 merely by showing that they jumped into a potentially polluted "pool" of stock.58

4

29
Appellants are surely correct in pointing out that, at some level, all evidence is "probabilistic."59 As we have explained, however, this does not answer the question before us today. In concluding that Appellants' attempt to "statistically trace" is incompatible with the standing requirement of Section 11, we cast no shadow on the use of statistical evidence in general. We recognize, for example, the widely accepted use of DNA evidence in criminal matters — even in capital murder trials — where proof must be beyond a reasonable doubt.60 While both are rooted in statistical calculations, at least two distinctions between DNA evidence and the statistics presented by Appellants come to mind. First, in most trials, DNA evidence does not stand alone.61 Here, Appellants have relied exclusively on a presentation of background statistics. Second, in any case, DNA evidence is more particularistic than the statistics here. DNA analysis seeks to establish a match between the DNA of a particular individual (e.g. a suspect) and a "mystery" sample (e.g. from a crime scene), essentially by quantifying and narrowing the universe of possible sources of the DNA.62 In contrast, Appellants' evidence merely demonstrates the probability that anyone with x number of shares will possess some tainted shares. It says nothing about the shares that one particular individual actually owns. The more particularized nature of DNA is further evident from the fact that "a nonmatch between any band of the suspect's DNA and the corresponding band of the questioned sample conclusively eliminates the suspect as the source of that sample."63 There is no such analog in the general statistics before us today.


30
Unquestionably, principles of probability are powerful tools, when deployed in appropriate tasks. Unquestionably, the statistics in this case indicate a high probability that a person purchasing a given number of shares will obtain at least one tainted share. However, these general statistics say nothing about the shares that a specific person actually owns and have no ability to separate those shares upon which standing can be based from those for which standing is improper. The task before the district court was to determine, by a preponderance of the evidence, whether and in what amount a plaintiff's shares are tainted, not whether the same number of shares drawn at random would likely include at least one tainted share. Understood in this light, statistical tracing is not up to the task at hand.

5

31
In sum, aftermarket purchasers seeking Section 11 standing must demonstrate that their shares are traceable to the challenged registration statement. We are not persuaded that the statistical tracing method advanced today is sufficient to satisfy this traceability requirement.

B

32
Appellants argue that the district court erred in denying the motion to intervene. We disagree.


33
As a preliminary matter, we note that this is not a case where intervention is sought for the purpose of appealing the denial of class certification.64 Indeed, Appellants have chosen in this appeal not to challenge the class certification denial.65 Thus, the "prerequisite of an intervention" that there be "an existing suit within the Court's jurisdiction" depends here on the individual claims.66 That none of the individual claims remained viable on February 14, 2003, when the motion to intervene was filed, disposes of the attempt at intervention.


34
As we have explained, by October 21, 2002, the district court had correctly made clear that only Beebe had standing. Furthermore, the district court held that, as of January 15, 2003, Beebe's individual claims were rendered moot because PCOrder offered Beebe a settlement equal to the statutory limit on his damages.67 Appellants do not dispute that a full settlement offer, even if refused, would dispose of Beebe's individual claims.68 Instead, Appellants contend that Beebe's claims were not fully satisfied because the involuntary settlement imposed by the district court did not include prejudgment interest. The statute, however, does not require prejudgment interest, and such an award of interest is up to the district court's discretion.69 The district court concluded that it would deny any request from Beebe for prejudgment interest because the delay in the payment of his award was due to his "meritless motion for class certification."70 We are not persuaded that the district court abused its discretion in denying prejudgment interest. Therefore, as we are not faced on appeal with a challenge to the denial of class certification, in the absence of viable individual claims, we are not persuaded that the district court erred in denying intervention.71

IV

35
For the foregoing reasons the judgment of the district court is AFFIRMED.



Notes:


1
 15 U.S.C. § 77k(a)


2
 Bret Beebe, Dr. Gene Burke, and David Petrick were appointed Lead Plaintiffs, along with two other individuals who subsequently dropped out of the suit and are not part of this appeal


3
 Krim v. pcOrder.com, Inc., 210 F.R.D. 581 (W.D.Tex.2002).


4
 The "aftermarket," also termed the "secondary market," is the "securities market in which previously issued securities are traded among investors." BLACK'S LAW DICTIONARY 990 (8th ed.2004)


5
 Krim, 210 F.R.D. at 585. We have since adopted the traceability test and allowed such aftermarket purchasers to establish standing in Section 11 cases. See Rosenzweig v. Azurix Corp., 332 F.3d 854, 873 (5th Cir.2003).


6
 Appellants' expert arrived at the odds of getting at least one PO (or "tainted") share using elementary principles of binomial probabilitySee generally PAUL G. HOEL, INTRODUCTION TO MATHEMATICAL STATISTICS (4th ed.1971), cited in Castaneda v. Partida, 430 U.S. 482, 496 n. 17, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977); see also Vuyanich v. Republic Nat'l Bank of Dallas, 505 F.Supp. 224, 345-46 (N.D.Tex.1980), vacated, 723 F.2d 1195 (5th Cir.1984).
The expert treated the purchase of shares as a series of independent random draws from the stock pool (similar to flipping a weighted coin once for each share), and calculated the probability that at least one of the shares would be tainted according to the following formula: 1-(1-PO%)# shares, where PO% is the percentage of PO stock in the market and # shares is the number of shares owned. For example, at the end of June, when Dr. Burke had purchased 3000 shares, PO shares (specifically IPO shares) constituted 99.85% of the street name certificate. Therefore, the probability that he owned at least one PO share was 1-(1-0.9985)3000, or very nearly 100%.


7
 Krim, 210 F.R.D. at 586.


8
 Id. at 587 (quoting Kirkwood v. Taylor, 590 F.Supp. 1375, 1380 (D.Minn.1984), aff'd 760 F.2d 272 (8th Cir.1985) (table)).


9
 The district court further concluded as an independent ground for not certifying the class or appointing the representatives that even if each of the Lead Plaintiffs had standing to sue under Section 11, they were each, including Beebe, unqualified to be class representatives because they were, for other reasons, not able to "fairly and adequately protect the interests of the class."Id. at 587-89.


10
 Krim v. pcOrder.com Inc., No. 03-00001 (5th Cir. Mar. 18, 2003) (order denying petition for leave to appeal under FED.R.CIV.P. 23(f)).


11
 Krim v. pcOrder.com, Inc., No. A-00-CA-776-SS, 2003 WL 21076787 (W.D.Tex. May 5, 2003) (order dismissing for lack of subject matter jurisdiction and denying intervention).


12
 PCOrder's motion to dismiss for lack of standing was unopposed with respect to the claims of Pinkowitz and KrimId. at *2 n. 1. Jean Burke purchased 200 shares at the end of June 1999 around the same time that her husband, Dr. Gene Burke, made his initial purchases.


13
 The Intervenors were Dawn Rusing-Bell, Kishore Mehta, and Dierdre Humphrey


14
 Appellants include Beebe, Dr. Burke, Mrs. Burke, Petrick and the Intervenors. No argument is advanced on appeal on behalf of either Krim or Pinkowitz


15
 John Corp. v. City of Houston, 214 F.3d 573, 576 (5th Cir.2000); Robinson v. TCI/US W. Communications Inc., 117 F.3d 900, 904 (5th Cir.1997).
We note that the motion before the district court was styled as a "Motion to Dismiss for Lack of Subject Matter Jurisdiction, or Alternatively, for Summary Judgment," but the district court chose to dispose of it as the former. Neither party has objected on appeal to that choice. In Montez v. Department of Navy we noted:
[W]here issues of fact are central both to subject matter jurisdiction and the claim on the merits, we have held that the trial court must assume jurisdiction and proceed to the merits. In circumstances where "the defendant's challenge to the court's jurisdiction is also a challenge to the existence of a federal cause of action, the proper course of action for the district court... is to find that jurisdiction exists and deal with the objection as a direct attack on the merits of the plaintiff's case' under either Rule 12(b)(6) or Rule 56."
392 F.3d 147, 150 (5th Cir.2004) (quoting Williamson v. Tucker, 645 F.2d 404, 415 (5th Cir.1981)).


16
 Home Builders Ass'n of Miss., Inc. v. City of Madison, 143 F.3d 1006, 1010 (5th Cir.1998) (quoting Nowak v. Ironworkers Local 6 Pension Fund, 81 F.3d 1182, 1187 (2d Cir.1996)) (internal quotation marks omitted).


17
 Montez, 392 F.3d at 149 (citing Land v. Dollar, 330 U.S. 731, 735 & n. 4, 67 S.Ct. 1009, 91 L.Ed. 1209 (1947)); see Robinson, 117 F.3d at 904 ("A court may base its disposition of a motion to dismiss for lack of subject matter jurisdiction on (1) the complaint alone; (2) the complaint supplemented by undisputed facts; or (3) the complaint supplemented by undisputed facts plus the court's resolution of disputed facts.").


18
 Robinson, 117 F.3d at 904; see also Kelly v. Syria Shell Petroleum Dev. B.V., 213 F.3d 841, 845 (5th Cir.2000).


19
 Doe v. Duncanville Indep. Sch. Dist., 994 F.2d 160, 167 (5th Cir.1993).


20
 Bush v. Viterna, 740 F.2d 350, 359 (5th Cir.1984).


21
 Appellants' related argument that the district court applied an inappropriately high burden of proof to the standing issue misses the mark. Appellants correctly point out that the correct burden of proof is a preponderance of the evidenceSee Lujan v. Defenders of Wildlife, 504 U.S. 555, 560-61, 112 S.Ct. 2130, 119 L.Ed.2d 351 (1992) (plaintiff's burden of proof on standing issue is same as for other elements of the claim); Herman & MacLean v. Huddleston, 459 U.S. 375, 390, 103 S.Ct. 683, 74 L.Ed.2d 548 (1983) (burden of proof in securities cases, in absence of contrary congressional expression, is preponderance of the evidence). While the district court did not make explicit the standard that it was applying, it is clear that it found Appellants could not, based solely on general mathematical probabilities, and in light of admissions about the nature of securities markets, demonstrate the ability to satisfy the tracing requirement under any of the proffered standards.


22
 See, e.g., Blue Chip Stamps v. Manor Drug Stores, 421 U.S. 723, 756, 95 S.Ct. 1917, 44 L.Ed.2d 539 (1975) (Powell, J., concurring).


23
 15 U.S.C. § 77aet seq.


24
 Rosenzweig, 332 F.3d at 861.


25
 15 U.S.C. § 77k(a). Section 11 provides, in relevant part:
In case any part of the registration statement, when such part became effective, contained an untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary to make the statements therein not misleading, any person acquiring such security (unless it is proved that at the time of such acquisition he knew of such untruth or omission) may, either at law or in equity, in any court of competent jurisdiction, sue [various individuals].
Id. (emphasis added).


26
 Herman & MacLean, 459 U.S. at 382, 103 S.Ct. 683 ("If a plaintiff purchased a security issued pursuant to a registration statement, he need only show a material misstatement or omission to establish his prima facie case. Liability against the issuer of a security is virtually absolute, even for innocent misstatements." (footnote omitted)); Lone Star Ladies Inv. Club v. Schlotzsky's Inc., 238 F.3d 363, 369 (5th Cir.2001).


27
 Fischman v. Raytheon Mfg. Co., 188 F.2d 783, 786-87 (2d Cir.1951), quoted in Barnes v. Osofsky, 373 F.2d 269, 273 (2d Cir.1967).


28
 332 F.3d at 872;accord DeMaria v. Andersen, 318 F.3d 170, 175-78 (2d Cir.2003); Lee v. Ernst & Young, LLP, 294 F.3d 969, 974-78 (8th Cir.2002); Joseph v. Wiles, 223 F.3d 1155, 1158-61 (10th Cir.2000); Hertzberg v. Dignity Partners, Inc., 191 F.3d 1076, 1079-82 (9th Cir.1999).


29
 Krim, 210 F.R.D. at 585.


30
 15 U.S.C. § 77k(a)


31
 DeMaria, 318 F.3d at 176 (quoting Lee, 294 F.3d at 976-77).


32
 Rosenzweig, 332 F.3d at 873.


33
 Harden v. Raffensperger, Hughes & Co., 933 F.Supp. 763, 766 (S.D.Ind.1996) (citing Kirkwood, 590 F.Supp. at 1378).


34
 Rosenzweig, 332 F.3d at 873 ("[B]ecause there was only one offering of Azurix stock, all the plaintiffs' stock is traceable to the challenged registration statement."); accord Hertzberg, 191 F.3d at 1080 (finding standing for aftermarket purchaser because "the only Dignity stock ever sold to the public was pursuant to the allegedly misleading registration statement at issue in this case"); Joseph, 223 F.3d at 1160 ("[B]ecause [the defendant] made only one debenture offering, the debentures [the plaintiff] purchased are directly traceable to the May offering and registration statement.").
In Hertzberg v. Dignity Partners, Inc., the Ninth Circuit noted that "[i]f there is a mixture of pre-registration stock and stock sold under the misleading registration statement, a plaintiff must either show that he purchased his stock in the initial offering or trace his later-purchased stock back to the initial offering" but that "it might present a problem of proof in a case in which stock was issued under more than one registration statement." 191 F.3d at 1080 & n. 4.


35
 332 F.3d at 873 (citingGustafson v. Alloyd Co., 513 U.S. 561, 115 S.Ct. 1061, 131 L.Ed.2d 1 (1995)).


36
 Indeed, under Appellants' view, in any case where more than 50% of the available shares are issued pursuant to an allegedly false registration statement, all shareholders would have standing. Furthermore, even when the PO% is less than that, applying the "coin flip" methodology,see supra note 6, it would take relatively few shares to confer standing. For example, even if only 30% of the available shares are PO, or "tainted," shares, two shares will suffice to confer standing because there would be a 51% chance that at least one of the two shares is a PO share, i.e. 1-(1-0.30) 2 = 51%. (Put another way, the chance that both shares will be "clean" is (0.70) 2, or 49%. Therefore, the likelihood of this not being the case — i.e. that at least one share is tainted — is 51%.) When PO shares are 10% of the market, still only 7 shares are needed: 1-(1-0.10) 7 = 52%. Even when PO shares are only 2% of the pool, 35 shares would confer standing: 1-(1-0.02) 35 = 51%.


37
 15 U.S.C. § 77k(a) (emphasis added)


38
 Krim v. PcOrder.com Inc., 212 F.R.D. 329, 332 n. 2 (W.D.Tex.2002) (order denying motion for reconsideration of refusal to certify class).


39
 U.S. CENSUS BUREAU, U.S. DEP'T OF COMMERCE, STATISTICAL ABSTRACT OF THE UNITED STATES: 2004-2005, at 23 tbl.20 (124th ed.2004),available at http://www.census.gov/prod/www/statistical-abstract-04.html (last visited Mar. 1, 2005).


40
 This is not unlike the well-known blue bus hypothetical to which Appellants refer in their Reply Brief. One commentator offers the following account of this hypothetical:
While driving late at night on a dark, two-lane road, a person confronts an oncoming bus speeding down the center line of the road in the opposite direction. In the glare of the headlights, the person sees that the vehicle is a bus, but he cannot otherwise identify it. He swerves to avoid a collision, and his car hits a tree. The bus speeds past without stopping. The injured person later sues the Blue Bus Company. He proves, in addition to the facts stated above, that the Blue Bus Company owns and operates 80% of the buses that run on the road where the accident occurred. Can he win?
In this case and others like it, the plaintiff will lose; in fact, the case is unlikely even to reach the jury. Although the defendant probably caused the plaintiff's injury ... [t]he factfinder can only conclude from the plaintiff's evidence that there was an 80% chance that he was injured by the Blue Bus Company and a 20% chance that he was not.... [T]he factfinder cannot, and the public knows it cannot, make anything other than a bet on the evidence. Because the judicial system strives to project an acceptable account about what happened, then, the plaintiff's evidence is insufficient, notwithstanding the high probability of its accuracy.
Charles Nesson, The Evidence or the Event? On Judicial Proof and the Acceptability of Verdicts, 98 HARV. L.REV. 1357, 1378-79 (1985) (footnotes omitted); see also Laurence H. Tribe, Trial by Mathematics: Precision and Ritual in the Legal Process, 84 HARV. L.REV. 1329, 1349 (1971) ("[E]ven assuming a [preponderance of the evidence] standard of proof ..., the plaintiff does not discharge that burden by showing simply that four-fifths, or indeed ninety-nine percent, of all blue buses belong to the defendant.").
This hypothetical is based on Smith v. Rapid Transit, Inc., 317 Mass. 469, 58 N.E.2d 754 (1945) (affirming directed verdict for defendant bus company). In Smith, the court further noted that "`the fact that colored automobiles made in the current year outnumber black ones would not warrant a finding that an undescribed automobile of the current year is colored and not black, nor would the fact that only a minority of men die of cancer warrant a finding that a particular man did not die of cancer.'" Id. at 755 (quoting Sargent v. Mass. Accident Co., 307 Mass. 246, 29 N.E.2d 825, 827 (1940)); cf. Howard v. Wal-Mart Stores, Inc., 160 F.3d 358, 359-60 (7th Cir.1998) (Posner, C.J.).


41
 There might well be other acceptable methods of aftermarket tracing even where non-PO stock has entered the market. For example, if a putative plaintiff possesses more shares than the number of non-PO shares on the market, our reasoning inRosenzweig suggests that she must have standing for at least some of the shares. If, for example, there are 100 non-PO shares and 900 PO shares, a plaintiff with 101 shares would seem to have at least 1 PO share. In any case, because Appellants have not suggested that these conditions apply here, we need not resolve this issue. Nor need we consider at this time what effect, if any, the practice of "short selling" would have in such a situation.


42
 See J. Robert Brown, The Shareholder Communication Rules and the Securities and Exchange Commission: An Exercise in Regulatory Utility or Futility?, 13 J. CORP. L. 683, 693 (1988) (noting relatively infrequent use of street name and nominee accounts in 1930s) (citing LOUIS LOSS, SECURITIES REGULATION 42 n. 226 (1951)); see also Silber v. Mabon, 957 F.2d 697, 700 (9th Cir.1992) ("The widespread practice of holding securities in street names grew out of a perceived `paperwork crisis' in the securities industry in the 1960s. Using street names facilitated the prompt handling of a huge volume of transactions on the various exchanges in the buying and selling of securities by investors and speculators." (internal quotation marks and citation omitted)).


43
 Colonial Realty Corp. v. Brunswick Corp., 257 F.Supp. 875, 881 (S.D.N.Y.1966), cited approvingly, Barnes, 373 F.2d at 273.


44
 See, e.g., In re Elscint, Ltd. Sec. Litig., 674 F.Supp. 374 (D.Mass.1987); Abbey v. Computer Memories, Inc., 634 F.Supp. 870 (N.D.Cal.1986); Kirkwood, 590 F.Supp. at 1378-83 (discussing various tracing techniques and rejecting all but the "direct trace" method); see also In re Quarterdeck Office Sys., Inc. Sec. Litig., No. CV 92-3970, 1993 WL 623310 (C.D.Cal. Sept.30, 1993).


45
 590 F.Supp. 1375, 1381 (D.Minn.1984),aff'd 760 F.2d 272 (8th Cir.1985) (table).


46
 Id. at 1380-81.


47
 373 F.2d 269 (2d Cir.1967) (Friendly, J.)


48
 Id. at 271.


49
 Id.


50
 Id. at 271-72 (emphasis added) (footnote omitted).


51
 Id. at 272. Judge Friendly went on to note:
Without depreciating the force of appellants' criticisms that this construction gives § 11 a rather accidental impact as between one open-market purchaser of a stock already being traded and another, we are unpersuaded that, by departing from the more natural meaning of the words, a court could come up with anything better. What appellants' arguments does suggest is that the time may have come for Congress to reexamine these two remarkable pioneering statutes in the light of thirty years' experience....
Id. at 273.


52
 204 F.3d 149 (4th Cir.2000) (en banc)


53
 33 U.S.C. § 1251et seq.


54
 33 U.S.C. § 1365(g) (emphasis added)


55
 Gaston, 204 F.3d at 155 (quoting Middlesex County Sewerage Auth. v. Nat'l Sea Clammers Ass'n, 453 U.S. 1, 16-17, 101 S.Ct. 2615, 69 L.Ed.2d 435 (1981)). In another CWA case, we held that "the Constitution does not require Sierra Club to produce an affiant who claims that Cedar Point's discharge in particular injured him in some way." Sierra Club, Lone Star Chapter v. Cedar Point Oil Co., 73 F.3d 546, 558 (5th Cir.1996) (emphases added). Indeed, "[t]he Supreme Court has expressly held that a `threatened injury' will satisfy the `injury in fact' requirement for [constitutional] standing." Id. at 556 (quoting Valley Forge Christian Coll. v. Ams. United for Separation of Church & State, Inc., 454 U.S. 464, 472, 102 S.Ct. 752, 70 L.Ed.2d 700 (1982)).


56
 Gaston, 204 F.3d at 152.


57
 Id. at 162 (quoting 33 U.S.C. § 1365(g)).


58
 Cf. In re Ames Dep't Stores Inc. Stock Litig., 991 F.2d 953, 964 (2d Cir.1993) ("[I]t is not a bar to a 10b-5 action that the false and misleading statements in a Registration Statement are pertaining to an issue of a security ... which is not the security purchased.").


59
 See, e.g., Victor v. Nebraska, 511 U.S. 1, 14, 114 S.Ct. 1239, 127 L.Ed.2d 583 (1994) ("The beyond a reasonable doubt standard is itself probabilistic."); Riordan v. Kempiners, 831 F.2d 690, 698 (7th Cir.1987) (Posner, J.) ("All evidence is probabilistic — statistical evidence merely explicitly so."); see also Richard A. Posner, An Economic Approach to the Law of Evidence, 51 STAN. L. REV. 1477, 1508 (1999) ("It is now generally recognized, even by the judiciary, that since all evidence is probabilistic — there are no metaphysical certainties — evidence should not be excluded merely because its accuracy can be expressed in explicitly probabilistic terms....").


60
 See, e.g., Prible v. State, ___ S.W.3d ___, No. AP-74487, 2005 WL 156555 (Tex.Crim.App. Jan.26, 2005) (affirming conviction in capital murder case, rejecting argument that evidence was insufficient, where evidence included DNA and several other factors).


61
 See, e.g., People v. Soto, 21 Cal.4th 512, 88 Cal.Rptr.2d 34, 981 P.2d 958, 965 (1999) ("[The] probability that the suspect was indeed the source of the sample ... will usually depend, not on the DNA findings alone, but on a combination of those findings together with other, non-DNA incriminating evidence.").


62
 See 3 DAVID L. FAIGMAN ET AL., MODERN SCIENTIFIC EVIDENCE: THE LAW AND SCIENCE OF EXPERT TESTIMONY § 24-9.2 (2d ed. 2002) ("DNA typing is capable of exceedingly high discrimination, and in favorable circumstances it can be shown that only one person in several billion could have been the source of the evidence bloodstain."); see also Commonwealth v. Gaynor, 443 Mass. 245, 820 N.E.2d 233, 240 (2005) (noting that "one in 64 quadrillion (64 x 10 15) African-Americans would be expected to have the same DNA profile as the sperm fraction"); Rayford v. State, 125 S.W.3d 521, 526 (Tex.Crim.App.2003) ("The DNA expert testified that the probability of the DNA belonging to someone other than Hall was one in 116 billion."); cf. Miller v. Albright, 523 U.S. 420, 484-85, 118 S.Ct. 1428, 140 L.Ed.2d 575 (1998) (Breyer, J., dissenting) (citing E. Donald Shapiro et al., The DNA Paternity Test: Legislating the Future Paternity Action, 7 J.L. & HEALTH 1, 29 (1992-1993), for the proposition that "current testing methods can determine probability of paternity to 99.999999% accuracy").


63
 Soto, 88 Cal.Rptr.2d 34, 981 P.2d at 965.


64
 Cf. Deposit Guar. Nat'l Bank v. Roper, 445 U.S. 326, 332 n. 5, 100 S.Ct. 1166, 63 L.Ed.2d 427 (1980) (noting that the district court may have "a responsibility, prior to approval of a settlement and ... dismissal of the class action, to provide an opportunity for intervention by a member of the putative class for the purpose of appealing the denial of class certification" (emphasis added)); Nichols v. Mobile Bd. of Realtors, Inc., 675 F.2d 671, 675 (5th Cir.1982) (permitting putative class members to intervene "solely for the purpose of appealing the district court's decertification of the class action" even after settlement of named plaintiffs' claims); see also United Airlines, Inc. v. McDonald, 432 U.S. 385, 392, 97 S.Ct. 2464, 53 L.Ed.2d 423 (1977).


65
 Cf. Roper, 445 U.S. at 331-40, 100 S.Ct. 1166, 63 L.Ed.2d 427 (1980) (holding that plaintiffs can appeal denial of class certification despite a tender to named plaintiffs in a class action of the amounts claimed in their individual capacities, followed by the entry of judgment in their favor on the basis of that tender, over their objection); United States Parole Comm'n v. Geraghty, 445 U.S. 388, 404, 100 S.Ct. 1202, 63 L.Ed.2d 479 (1980) (where denial of class certification is challenged on appeal, "an action brought on behalf of a class does not become moot upon expiration of the named plaintiff's substantive claim, even though class certification has been denied").


66
 Non Commissioned Officers Ass'n of the United States v. Army Times Publ'g Co., 637 F.2d 372, 373 (5th Cir.1981).


67
 See Krim, 2003 WL 21076787, at *3 (citing 15 U.S.C. § 77k(e)).


68
 See Zeidman v. J. Ray McDermott & Co., 651 F.2d 1030, 1045 (5th Cir.1981) ("[A] suit brought as a class action must as a general rule be dismissed for mootness when the personal claims of the named plaintiffs are satisfied and no class has properly been certified."). This, as the district court acknowledged, does not foreclose the right to appeal the denial of class certification. See Krim, 2003 WL 21076787, at *4 (citing Roper, 445 U.S. at 332-36, 100 S.Ct. 1166).


69
 See Whitfield v. Lindemann, 853 F.2d 1298, 1306 (5th Cir.1988) ("Absent statutory mandate, the award of prejudgment interest generally is discretionary with the trial court.").


70
 Krim, 2003 WL 21076787, at *3.


71
 Appellants' argument that the defendants'"maneuver" (i.e. defeating class certification and then "picking off" the only remaining plaintiff with standing) deprived absent class members their day in court is without merit. It was the Appellants who chose not to pursue an appeal of the denial of class certification. In any case, the district court afforded the plaintiffs the opportunity to return in the event that they can establish standing and suggested that Intervenors are free to initiate a suit of their own.


