OPINION OF THE COURT
Appellants USX Corporation (USX) and U.S. Steel Mining Company, Inc; (USSM),1 plaintiffs below, challenge several decisions by the District Court granting summary judgment for the Commissioner on the majority of appellants’ claims. We will affirm.
I
In 1970, USX purchased the assets of the Grapevine No. 8 Mine, the last significant coal mine owned by Crystal Block, which ceased to operate coal mines after that sale. In 1981, USX in turn sold those same assets to Old Ben Coal Company, which was still operating when appellants filed their complaint. Pursuant to the Coal Industry Retiree Health Benefit Act of 1992, 26 U.S.C. §§ 9701-9722 (the “Coal Act”),2 on September 28 and October 7 and 8, 1993, the Social Security Administration (SSA) assigned USX health benefit premium responsibility for sixty-seven retired miners (and their dependents) who had been employed by Crystal Block. In the letters notifying appellants of the assignments, SSA informed them that they had the right to request the miners’ earning records and bases for the assignments within thirty days, and then to seek admin*164istrative review within thirty days of receipt of that information.
On June 30, 1995, the Commissioner assigned additional miners employed by Crystal Block to USX on the ground that USX was related to the signatory operator. By letter dated August 1, 1995, USX requested the earnings records of those miners, as well as the bases for the assignments. On September 5, 1995, SSA denied USX’s request for information on the ground that the request was untimely. Despite denying this request, SSA nevertheless provided USX with the Crystal Block miners’ earnings records. On May 14, 1996, USX requested additional information and a ninety-day extension of time to appeal the assignments.
By letter dated June 10, 1996, SSA supplied USX with the names of the originally assigned coal operators. In a separate letter on that same day, however, it informed USX that it had erroneously provided the information regarding the beneficiaries assigned on June 30, 1995 and that it could not review those assignments because USX’s request had been untimely. On August 12, 1996, USX requested that SSA revoke the Crystal Block beneficiary assignments because they were improper. SSA denied review of the June 30, 1995 assignments on September 4, 1997, informing USX on September 23, 1997 that its decision was final.
Appellants commenced this action on July 2, 1999, alleging that the Commissioner had improperly assigned to appellants the health benefit premium responsibilities for a significant number of coal miners. Appellants also claimed that the Commissioner had refused to provide the earnings records upon request, as required by the Coal Act, and that the Commissioner had improperly refused to review many of the allegedly erroneous assignments. Appellants’ Second Amended Complaint contained thirteen counts, which the District Court disposed of on summary judgment in a series of opinions and orders. The District Court entered a final judgment on November 5, 2003. The court then denied appellants’ motion to amend the judgment on January 6, 2004 and appellants timely appealed.
II
Our review of a District Court’s grant of summary judgment is plenary. See Fed. Home Loan Mortgage Corp. v. Scottsdale Ins. Co., 316 F.3d 431, 443 (3d Cir.2003). We assess the record using the same summary judgment standard that guides district courts. See Farrell v. Planters Lifesavers Co., 206 F.3d 271, 278 (3d Cir.2000). To prevail on a motion for summary judgment, the moving party must demonstrate “that there is no genuine issue as to any material fact and that the moving party is entitled to a judgment as a matter of law.” Fed.R.Civ.P. 56(c).
A
The Coal Act directs the Commissioner to assign health benefit premium responsibilities to a “related person” where the beneficiary’s pertinent signatory operator is no longer in business. 26 U.S.C. §§ 9701(c)(2), 9706(a). The Commissioner initially construed this provision as authorizing assignments to the direct successor-in-interest of the employing, signatory operator when the signatory operator was no longer in business. Appellants claimed below that the Commissioner lacked statutory authority to make assignments under this successorship theory.
The District Court initially rejected this contention and granted partial summary judgment to the Commissioner. Appellants moved for reconsideration and, while that motion was pending, the Supreme *165Court held in Barnhart v. Sigmon Coal Co., 534 U.S. 438, 122 S.Ct. 941, 151 L.Ed.2d 908 (2002), that the Commissioner lacked statutory authority to assign miners to the direct successor of a signatory operator. Appellants in this case then argued that Sigmon Coal compelled the court to grant their pending motion for reconsideration and grant them judgment on their challenges to the successorship theory in Counts I and II of their Second Amended Complaint. Appellants also argued that they should be permitted to amend their complaint for the third time so as to challenge additional miner assignments that, though not identified in any of the prior complaints, were also allegedly based on the successorship theory rejected by Sigmon Coal.
The District Court reversed its holding and granted summary judgment for appellants with respect to the successorship-based miner assignments identified in the Second Amended Complaint. However, it denied appellants leave to file a third amended complaint insofar as the amendment would add a challenge to successor-ship-based miner assignments appellants had not previously identified.
1
Appellants first argue that the District Court violated Federal Rule of Civil Procedure 54(c) when it refused to order the Commissioner to rescind all of the assignments she had made under the successor-ship theory invalidated in Sigmon Coal, including those assignments not identified in Counts I and II of the Second Amended Complaint. The argument is meritless.
Rule 54(c) provides, in pertinent part, that “every final judgment shall grant the relief to which the party in whose favor it is rendered is entitled, even if the party has not demanded such relief in the party’s pleadings.” Fed.R.Civ.P. 54(c). This rule “requires that a court ascertain whether the plaintiffs are entitled to any remedy. As long as the plaintiffs have stated a claim for relief, it is the court’s obligation to grant the relief to which the prevailing party is entitled whether it has been specifically demanded or not.” Kirby v. United States Gov’t, 745 F.2d 204, 207 (3d Cir.1984) (emphasis omitted).
Appellants misconstrue the benefit afforded plaintiffs by Rule 54(c). The rule was meant to protect a plaintiff from clumsy pleading, which, through technical oversight, might deprive it of a deserved recovery. “The [rule’s] most common usage is when the amount of the award varies from the demand for relief.” 10 Charles Alan Wright, Arthur R. Miller & Mary Kay Kane, Federal Practice and Procedure § 2664, at 183 (3d ed.1998). The rule has also been used to allow for the award of attorney’s fees and costs even though none was demanded, or for recovering interest on a claim as damages. Id. at 185-86. As the Advisory Committee explains, it “makes clear that a judgment should give the relief to which a party is entitled, regardless of whether it is legal or equitable or both.” Fed.R.Civ.P. 54 advisory committee’s note to 1937 adoption. In other words, Rule 54(c) addresses and cures a limited formal problem. It is not designed to allow plaintiffs to recover for claims they never alleged.
Here, by contrast, appellants are not seeking to vary relief but to add judgments based on new claims of additional improper beneficiary assignments. By trying to invoke Rule 54(c), appellants confuse the demand for relief with the claims on which that demand is based. While “[ijnasmuch as the demand for relief does not constitute part of the pleader’s claim for relief, a failure to demand the appro*166priate relief will not result in a dismissal,” the converse is not true. Wright et al., supra, § 2664, at 180. That is, “the court cannot provide a remedy, even if one is demanded, when plaintiff has failed to set out a claim for relief.” Id. at 179; see also 10 James Wm. Moore et al., Moore’s Federal Practice § 54.72(2), at 54-137 (3d ed. 2004) (“The Rule permits relief not demanded only when the party affirmatively shows an entitlement to the relief and is inapplicable when the pleader fails to demonstrate the proper substantive grounds for relief.”). That is precisely what appellants seek here.
Moreover, simply entering judgment against the Commissioner on numerous additional assignments of unidentified miners would prejudice the SSA. There may be other issues that need to be litigated to determine whether an assignment was improper. Had the District Court simply granted judgment for appellants on the unspecified assignments, the Commissioner would be foreclosed from litigating those issues. Under any reading of Rule 54(c), it cannot be deployed to pretermit the Commissioner from raising additional defenses to hitherto unlitigated claims. Wright et al., supra, § 2664, at 173-79 (noting that relief should not be amended under Rule 54(c) if failure to include in the demand has prejudiced adversary). For these reasons, the District Court did not err.
2
As an alternative, appellants also moved in the District Court to file a third amended complaint listing the additional miners that had allegedly been improperly assigned in light of Sigmon Coal. The District Court denied leave on two grounds: (1) that amendment would be futile as the new claims were barred by the statute of limitations, and (2) unreasonable delay. We will uphold the District Court’s decision on the ground of unreasonable delay.
Federal Rule of Civil Procedure 15(a) provides, in pertinent part, that after a responsive pleading, a party may amend its pleading “only by leave of court or by written consent of the adverse party; and leave shall be freely given when justice so requires.” In the absence of substantial or undue prejudice to the nonmoving party-which “is the touchstone for the denial of an amendment”-“denial instead must be based on bad faith or dilatory motives, truly undue or unexplained delay, repeated failures to cure the deficiency by amendments previously allowed, or futility of amendment.” Lorenz v. CSX Corp., 1 F.3d 1406, 1413-14 (3d Cir.1993) (quotation marks omitted) (citing Foman v. Davis, 371 U.S. 178, 182, 83 S.Ct. 227, 9 L.Ed.2d 222 (1962)).
Turning first to futility of amendment, a six-year statute of limitations applies to civil actions brought against the United States for review of decisions by administrative agencies. 28 U.S.C. § 2401(a). Appellants concede that the proposed amendment would be outside this limitations period. However, they argue that the amendment would not be futile because it would relate back to the date of the original complaint, which was within the limitations period.
Federal Rule of Civil Procedure 15(c)(2) provides, in relevant part, “An amendment of a pleading relates back to the date of the original pleading when ... the claim or defense asserted in the amended pleading arose out of the conduct, transaction, or occurrence set forth or attempted to be set forth in the original pleading....”
[AJmendments that restate the original claim with greater particularity or amplify the factual circumstances surrounding the pertinent conduct, transaction or occurrence in the preceding pleading fall *167within Rule 15(c). In essence, application of Rule 15(c) involves a search for a common core of operative facts in the two pleadings. As such, the court looks to whether the opposing party has had fair notice of the general fact situation and legal theory upon which the amending party proceeds.
Bensel v. Allied Pilots Ass’n, 387 F.3d 298, 310 (3d Cir.2004) (citations omitted).
Appellants argue that the language of the original eomplaint-speeifically, that “[t]he Commissioner cannot, as a matter of law, assign miners to successors under Section 9706(a) of the Coal Act” (App. 162; see also App. 165 (same))-is broad enough for Rule 15(c) purposes to capture the listing of additional miners. Appellants cite FDIC v. Conner, 20 F.3d 1376 (5th Cir.1994). There, the FDIC filed suit against the directors of a failed bank, alleging that they had acted negligently in approving twenty-one specified loans to specified borrowers. Id. at 1378. The FDIC later sought leave to amend its complaint to add several more loans that had not been identified in the original complaint. Id. at 1385. The Fifth Circuit held that the amendment related back to the date of the original complaint because it simply identified “additional sources of damages that were caused by the same pattern of conduct identified in the original complaint.” Id. at 1386.
The Commissioner responds that appellants fail to account for factual and procedural issues that may bear on the validity of each individual assignment, such as whether the successorship theory was actually the basis for the assignment, whether appellants exhausted administrative remedies, and whether a miner’s work history affords a basis for sustaining the assignment on other grounds. These arguments-while meritorious in rebuffing appellants’ effort to invoke Rule 54(c)-are misplaced in the context of a request to amend a pleading. The Commissioner is not foreclosed from defending the assignments once the complaint is amended.
While the assignment of each miner was itself a separate transaction or occurrence, the conduct of the Commissioner in relying on the (now-invalidated) successorship doctrine was common to all of the assignments. In this way, the Commissioner had notice of the problem in its assignments and had notice that any assignments based on that theory were in jeopardy. Furthermore, the Commissioner could still argue that some or all of the added assignments were not based on the successorship doctrine and that those specific assignments should not relate back. She would also have various substantive and procedural arguments at her disposal to defend the assignments that do relate back. Allowing relation back under Rule 15(c) also comports with “the general presumption in favor of allowing a party to amend pleadings.” Boileau v. Bethlehem Steel Corp., 730 F.2d 929, 938 (3d Cir.1984) (per curiam) (citing Foman, 371 U.S. at 182, 83 S.Ct. 227).
That being said, however, we conclude that the District Court did not abuse its discretion in denying leave to amend based on appellants’ “undue delay.” Foman, 371 U.S. at 182, 83 S.Ct. 227. We have held that “[t]he mere passage of time does not require that a motion to amend a complaint be denied on grounds of delay”; “delay alone is an insufficient ground to deny leave to amend.” Cureton v. NCAA, 252 F.3d 267, 273 (3d Cir.2001). At some point, however, “delay will become ‘undue,’ placing an unwarranted burden on the court, or will become ‘prejudicial,’ placing an unfair burden on the opposing party.” Id. (quotation marks omitted). Significantly, “[djelay may become undue when a movant has had previous opportunities to *168amend a complaint.” Id. Interests in judicial economy and finality of litigation become “particularly compelling” when “a party delays making a motion to amend until after summary judgment has been granted to the adverse party.” Id. We must therefore “focus on the movant’s reasons for not amending sooner” in analyzing the question of undue delay. Id.
Appellants originally explained their delay in seeking an amendment (or challenging the additional assignments at all) on the ground that they did not have notice of these assignments when they filed their original complaint. In support of that explanation, they submitted the affidavit of a vice president of USSM stating that when he assumed responsibility for the Coal Act assignments in December 1995, he did not have personal knowledge of the assignments now sought to be included because the letters were not in the files he received when he took charge. He first learned of these assignments when he reviewed the administrative record sometime after May 15, 2001.
As that administrative record reflects, SSA sent assignment letters to appellants on September 28, 1993 and June 30, 1995. The District Court correctly concluded that, based on these letters to appellant corporations, the vice president’s personal knowledge was irrelevant. Appellants had notice and in fact belatedly challenged the June 30, 1995 assignments on August 21, 1995. Appellants’ plea that one official-out of a large organization~did not have personal notice is therefore no justification.
Appellants offer no other excuse for failing to include these assignments in their original complaint. Rather, the thrust of their argument is as follows: The District Court originally denied their successorship argument. Until the Supreme Court decided Sigmon Coal, they had no reason to believe that amending their complaint to include the additional assignments would have been worthwhile. Therefore, that delay, and the failure to list the additional assignments in their first and second amendments, should not be held against them. Cf. Boileau, 730 F.2d at 938 (not charging plaintiff with delay where district court proceedings had been stayed).
Even accepting the legal premise, appellants’ argument is belied by the facts. The Magistrate Judge issued her report recommending summary judgment for the Commissioner on Counts I and Il-on the later-rejected successorship ground-on August 30, 2000. The District Court adopted that report on September 29, 2000. Appellants first amended complaint, however, was filed on November 3, 1999.3 Therefore, at the time of them first amendmenb-and for almost a year thereafter-appellants had no reason to believe that listing the additional assignments would be futile.
Finally, appellants assert that “between September 29, 2000 and February 2002, [they] did not have any reason to believe that the Court would permit [them] to amend the dismissed Counts to expand [their] claim for relief.” (Appellants Br. at 27.) This excuse is strikingly similar to that rejected in Cureton, where “the only real reason advanced by plaintiffs for the substantial lapse in time was plaintiffs’ misplaced confidence in their original disparate impact theory.” 252 F.3d at 274.
In Cureton, denial of leave was not an abuse of discretion where the motion was filed three years after the complaint was filed, the facts underlying the amendment were known almost two-and-one-half years before plaintiffs sought leave to amend, judicial efficiency would be damaged, and *169the interest in finality would be compromised. Id. Similarly, in Lorenz, despite no finding of prejudice to defendants, leave to amend was properly denied where it was requested three years after the action was filed and nearly two years after the complaint was amended for the second time, all of the facts were available to plaintiff before she amended her complaint (and most were known before she filed her original complaint), and she had numerous opportunities to correct any deficiencies. 1 F.3d at 1414. The facts in this case fit comfortably within Cureton and Lorenz. Appellants waited over three years to amend to contest these assignments and had notice of the assignments prior to filing both the original complaint and the first amended complaint. It was not an abuse of discretion for the District Court to deny leave to amend.
B
The District Court granted summary judgment for the Commissioner on appellants’ claim that the Commissioner improperly refused to review the June 30, 1995 assignments on timeliness grounds. Conceding that they requested the miners’ earning records “a few days late” (Appellants Br. at 28), appellants argue that SSA nonetheless provided those records and appellants, in turn, requested review within thirty days of receiving those records. Appellants conclude that their request was therefore timely. Alternatively, appellants contend that the Commissioner violated a number of regulations and internal operating procedures, rendering her refusal arbitrary and capricious. These arguments are meritless.
1
The Coal Act provides as follows, in pertinent part:
(f) Reconsideration by Commissioner.-
(1) In general.-Any assigned operator receiving a notice under subsection (e)(2) with respect to an eligible beneficiary may, within 30 days of receipt of such notice, request from the Commissioner ... detailed information as to the work history of the beneficiary and the basis of the assignment.
(2) Review.-An assigned operator may, within 30 days of receipt of the information under paragraph (1), request review of the assignment. The Commissioner ... shall conduct such review if the Commissioner finds the operator provided evidence with the request constituting a prima facie case of error.
26 U.S.C. § 9706.
Though appellants argue that § 9706(f)(2) provides an independent right to review within thirty days of receiving additional information, the structure of the section precludes such a reading. Specifically, subsection (2) provides that an operator may request review within thirty days of receipt of the information “under paragraph (1).” A proper request under subsection (1), however, is made within thirty days of notice of the assignments. As appellants’ request for information was untimely under subsection (1), they cannot benefit from the additional thirty days provided for by subsection (2).4
2
Appellants next contend that the Commissioner violated her own internal operating procedures, specifically the Supplemental Coal Act Instruction No. 3, issued *170December 1994, which provided, in pertinent part:
Use the following guidelines to process a request for review received after the timeframe for requesting the review has expired.
Review the assignment (regardless of whether the assignee submitted evidence).
1. If your review decision concludes that the assignment(s) should be reversed:
Then revise the assignments, and send the assignee the appropriate review response.
2. If your review decision affirms the assignment(s);
Then notify the assignee that the request for review has been denied because it was not timely filed.
(App.482.)
Appellants’ argument fails for two reasons. First, we held in Lindsey Coal Mining Co. v. Chafer that the Commissioner’s internal Coal Act guidelines “lack the force of law,” and “[therefore, the agency is not bound to follow them and [coal operators are] not entitled to rely on them.” 90 F.3d 688, 693 (3d Cir.1996). The cases cited by appellants are not to the contrary, as they hold only that an agency must provide an explanation when failing to follow its prior, established precedent. See Borough of Columbia v. Surface Transp. Bd., 342 F.3d 222, 229 (3d Cir.2003); Fertilizer Inst. v. Browner, 163 F.3d 774, 778 (3d Cir.1998); Stardyne, Inc. v. NLRB, 41 F.3d 141, 153 (3d Cir.1994).
Second, the procedure quoted above was not in effect when, in 1997, the Commissioner denied appellants’ appeals. Rather, the procedures in force in 1997 state that “[i]f the request is not timely filed ... [d]o not review the request.” (App.490.) Therefore, the Commissioner’s decision was consistent with the internal procedures in effect at the time of the disputed decision.5
C
In making assignments, the Commissioner employs a rebuttable presumption in which she assumes that, absent evidence to the contrary, a miner who otherwise qualified for benefits under the Coal Act was “employed in the coal industry” for purposes of 26 U.S.C. § 9706(a) if (1) his employer was a coal mine operator that signed a national coal wage agreement and (2) his employment occurred during the employer’s participation in the national coal wage agreement. Appellants claim that they employed some of their assigned beneficiaries in the steel industry, not the coal industry. They argue that the Commissioner’s use of this rebuttable presumption is arbitrary and capricious. Their argument is both time-barred and merit-less.
1
The District Court held that appellants’ claims were barred as they had failed to seek administrative review within the required thirty-day period. Appellants concede this but argue that the thirty days should be tolled because of false and misleading statements made by the Commissioner. This argument is meritless.
*171We will equitably toll a statute of limitations where a plaintiff shows “active misleading by the defendant and ... that he exercised reasonable diligence in attempting to uncover the relevant facts.” Forbes v. Eagleson, 228 F.3d 471, 487 (3d Cir.2000) (citation omitted).
Appellants point to various language in letters sent by SSA that they claim rises to the level of active misleading. Under a header reading “How We Assign Responsibility,” SSA states, “We assign responsibility to an operator who our records show employed the miner in the coal industry under an UMWA agreement.” (App.773.) Also, in a “List of Assigned Miners and Other Beneficiaries,” the SSA states, “Our records show that you employed the miner in the coal industry under an UMWA agreement and you are still in business.” (App.775.) Appellants contend that, in fact, the records SSA reviewed did not contain the information that SSA said they did, and that SSA concealed its use of the presumption by not mentioning it in its notices of assignment.
However, in the same notices, SSA explicitly states that it reviewed its “earnings records of retired coal miners identified by the UMWA benefit plans.” (App.772.) SSA does not purport to have reviewed records documenting the industry in which the miner worked. Furthermore, the agency’s internal guidelines, which are available to the public, expressly state that “[e]arnings from a signatory operator posted to SSA’s earnings records for a miner are assumed to be ‘work in the coal industry.’ ” (App. 431 (emphasis added).) Finally, appellants-large and sophisticated businesses-had easy access to information describing the industries in which their employees worked. Had appellants exercised elementary due diligence, they could easily have dispelled any confusion. For these reasons, appellants’ claims are time-barred.
2
In any event, the Commissioner’s use of the rebuttable presumption is not arbitrary or capricious. “Presumptions may, of course, be established both by legislative bodies and by administrative agencies, but their validity depends as a general rule upon a rational nexus between the proven facts and the presumed facts.” United Scenic Artists, Local 829 v. NLRB, 762 F.2d 1027, 1034 (D.C.Cir.1985); accord NLRB v. Baptist Hosp., Inc., 442 U.S. 773, 787, 99 S.Ct. 2598, 61 L.Ed.2d 251 (1979) (“It is, of course, settled law that a presumption adopted and applied by the Board must rest on a sound factual connection between the proved and inferred facts.”). We review the Commissioner’s presumption both, for consistency with the Coal Act and for rationality, id., but we “may not simply substitute a different judgment that we might consider preferable,” Inland Steel Indus., Inc. v. United States, 188 F.3d 1349, 1361 (Fed.Cir.1999). Appellants bear “the heavy burden of demonstrating that there is no rational connection between the fact proved and the ultimate fact to be presumed.” Cole v. United States Dep’t of Agric., 33 F.3d 1263, 1267 (11th Cir.1994).
Presumptions are permissible
if there is a sound and rational connection between the proved and inferred facts and when proof of one fact renders the existence of another fact so probable that it is sensible and timesaving to assume the truth of the inferred fact until the adversary disproves it.... [But i]f there is an alternate explanation for the evidence that is also reasonably likely, then the presumption is irrational.
Sec’y of Labor v. Keystone Coal Mining Corp., 151 F.3d 1096, 1100-01 (D.C.Cir.*1721998) (quotation marks, alteration, and ellipsis omitted).
In support of their challenge to the presumption, appellants point to 26 U.S.C. § 9706, which provides, in pertinent part:
(c) Identification of eligible beneficiaries.-The 1950 UMWA Benefit Plan and the 1974 UMWA Benefit Plan shall ... provide to the Commissioner ... a list of the names and social security account numbers of each eligible beneficiary.... In addition, the plans shall provide, where ascertainable from plan records, the names of all persons described in subsection (a) [i.e., signatory operators to whom the miners should be assigned] with respect to an eligible beneficiary....
(d) Cooperation by other agencies and persons-
(1) Cooperation.-The head of any department, agency, or instrumentality of the United States shall cooperate fully and promptly with the Commissioner ... in providing information which will enable the Commissioner to carry out his responsibilities under this section.
Appellants read this provision as a “Congressional mandate” and “statutory obligation” that the Commissioner “use the UMWA Benefit Plans’ employment records” and not make the rebuttable presumption at issue here. (Appellant Br. at 46-47.) The statute, however, merely imposes an obligation on the benefit plans and the heads of other federal agencies to assist the Commissioner in matching beneficiaries with the appropriate signatory operators. The quoted provisions require nothing of the Commissioner and they certainly do not prohibit her from employing the rebuttable presumption at issue.
The Commissioner’s rebuttable presumption is entirely reasonable. As appellants note, beneficiaries’ personnel files can date back fifty to sixty years, and even a miner’s own employer can have difficulty retrieving them. The Commissioner’s re-buttable presumption is a sensible response to this problem. See Panduit Corp. v. All States Plastic Mfg. Co., 744 F.2d 1564, 1581 (Fed.Cir.1984) (“Presumptions of fact have been created to assist in certain circumstances where direct proof of a matter is. for one reason or another rendered difficult.”). As the District Court observed, “SSA’s presumption that earnings from a signatory operator (of coal mines), posted to SSA’s earnings records for the (coal) miner, were for ‘work in the coal industry’ constitutes a ‘reasonable inference’ as contemplated by Congress.” (App.58.) Furthermore, though appellants may do business in other industries, they are (or are related to) signatory operators, i.e., businesses that signed collective bargaining agreements governing the wages to be paid UMWA workers by employers in the coal industry. See 26 U.S.C. § 9701(b)(1) & (c). They are therefore in a position to correct any misapprehensions. The presumption is rebuttable and therefore avoids problematic mechanical operation. For these reasons, the Commissioner’s rebuttable presumption is not arbitrary or capricious.6
*173III
For the foregoing reasons, we will affirm the judgment of the District Court.