HARTZ, Circuit Judge.

Daniel R. Cahill was injured in a car accident on January 14, 1998. He received benefits from his insurer, American Family Mutual Insurance Company, until March 23, 1998, when American Family said that he had exhausted the maximum benefits available. On August 14, 2007, Mr. Cahill sued American Family in Colorado state court on several state-law causes of action arising out of American Family's failure to comply with Colorado insurance law. American Family removed the case to the United States District Court for the District of Colorado, based on diversity of citizenship. See 28 U.S.C. §§ 1332 (diversity jurisdiction) 1441 (right of removal). It then moved for summary judgment on the ground that all of Mr. Cahill's claims were time-barred. The district court granted the motion.

Mr. Cahill appeals. Exercising jurisdiction under 28 U.S.C. § 1291, we affirm. Although Mr. Cahill's brief appears to raise six challenges on appeal, we consider only one. We need not consider the others, because they were either inadequately preserved or presented, or the result would not be altered even if they were successful. The one challenge we address on the merits is Mr. Cahill's claim that he is entitled to equitable tolling; but we reject the argument that the limitations periods should have been tolled until American Family informed him that it had not paid benefits required by law.

I. BACKGROUND

The relevant facts are largely undisputed. To the extent that they are, we view the evidence in the light most favorable to Mr. Cahill because we are reviewing a summary judgment against him. See Milne v. USA Cycling Inc., 575 F.3d 1120, 1122 n. 1 (10th Cir. 2009).

On January 14, 1998, Mr. Cahill was driving a car that was struck by a vehicle driven by a drunk, uninsured motorist. Mr. Cahill, who was 20 years old, suffered severe injuries, including a brain injury that left him in a coma. He was hospitalized for about five months.

After Mr. Cahill's release from the hospital, he moved back in with his parents, where he remained until 2005. While living at home, Mr. Cahill continued to receive speech, physical, occupational, recreational, and language therapy as an outpatient.

At the time of his accident, Mr. Cahill was insured under his father's automobile policy issued by American Family. The policy provided no-fault personal-injury-protection (PIP) coverage. Because of the extent of Mr. Cahill's injuries, his PIP coverage was quickly depleted, and on March 23, 1998, American Family informed his father that Mr. Cahill's PIP benefits had been exhausted.

Mr. Cahill's PIP coverage was the minimum required under Colorado law. Under the Colorado Auto Accident Reparations Act (CAARA), Colo.Rev. Stat. § 10-4-701 et seq., which governed automobile insurance at the time of Mr. Cahill's accident, insurers were required to offer, for an increased premium, enhanced PIP coverage in addition to the minimum coverage. See Colo.Rev. Stat. § 10-4-710(2) (2002); see generally Clark v. State Farm Mut. Auto. Ins. Co., 319 F.3d 1234, 1237-38 (10th Cir. 2003) (describing the PIP requirements of CAARA). But many American Family policyholders, including Mr. Cahill's father, had not been offered such enhanced PIP benefits.

Several American Family policyholders filed separate putative class-action and single-plaintiff lawsuits against American Family based on its CAARA violations. Each sought, among other things, reformation of the policy so that the policyholders would be entitled to the enhanced PIP benefits. Three putative class-action suits are noted by the parties. The first was French v. American Family, filed in Colorado state court in November 2000. The French plaintiffs alleged breach-of-contract and deceptive-trade-practice claims on behalf of a putative class consisting of all holders of defective American Family policies. Class certification in French was denied on December 4, 2002. The next putative class action was Marshall v. American Family, which was filed in Colorado state court in April 2003. Its claims were similar to those in French. Class certification was denied on November 13, 2003. The third, Hicks v. American Family, was filed in June 2004 in Colorado state court. Hicks sought reformation of insurance policies on behalf of a class of insureds that included Mr. Cahill. The Hicks class was certified and reformation was granted on November 2, 2005.

Meanwhile, American Family began reviewing its policies in late 2000 and ultimately concluded that it had not complied with Colorado law. In May 2004 American Family voluntarily notified some policyholders that they might be eligible for policy reformation. Although American Family contends that it notified Mr. Cahill, he has denied receiving the notification.

In the spring of 2007, American Family, acting under a court order in Hicks, notified Mr. Cahill that he was entitled to enhanced PIP benefits. Mr. Cahill acknowledges receiving this notification. On August 9, 2007, American Family determined that it owed Mr. Cahill $37,489 in additional PIP benefits for his 1998 injury, and it paid him that amount. On August 14 Mr. Cahill commenced this action in Colorado state court.

After American Family removed the case to federal district court, Mr. Cahill filed an amended complaint alleging five state-law causes of action: (1) fraudulent misrepresentation, because in 1998 American Family falsely represented to him that his PIP benefits had been exhausted; (2) concealment, because American Family had failed to disclose that its policy did not comply with Colorado law, even though it had known of the noncompliance since 2000; (3) bad-faith breach of insurance contract, because American Family had knowingly failed to provide him with the enhanced PIP benefits to which he was entitled; (4) outrageous conduct, because American Family had failed to provide enhanced PIP benefits and had not investigated whether this failure would cause him harm, thereby intentionally inflicting emotional distress on him; and (5) violation of the Colorado Consumer Protection Act (CCPA), Colo.Rev. Stat. § 6-1-101 et seq., because American Family had misrepresented the qualities and benefits of its insurance coverage.

American Family moved for summary judgment, arguing that all of Mr. Cahill's claims were barred by the applicable statutes of limitations. The district court granted the motion and dismissed Mr. Cahill's claims. According to the district court, a two-year limitations period applied to the outrageous-conduct claim, and a three-year period applied to the other claims. It ruled (1) that the fraudulent-misrepresentation, bad-faith-breach-of-contract, and CCPA claims had accrued by March 23, 1998, when American Family sent notification that Mr. Cahill's PIP benefits had expired, and (2) that his concealment and outrageous-conduct claims had accrued no later than November 2000, when American Family knew that it had violated CAARA. It rejected Mr. Cahill's contention that the limitations periods were tolled by American Family's failure to inform him that he was entitled to additional PIP benefits, reasoning that Mr. Cahill could have ascertained that his policy failed to comply with Colorado law even without such notification. The court assumed that the limitations periods for the bad-faith and CCPA claims had been tolled during the pendency of the French litigation, which raised both claims; but it calculated that the limitations periods for both claims would still have expired well before this litigation commenced. And even though Mr. Cahill had "recite[d] some facts that arguably could support a toll based on his incapacity," the court declined to consider such tolling because he had failed to "put forth any meaningful argument regarding such a toll." Cahill v. Am. Family Mut. Ins. Co., No. 07-cv1910-MSK-MJW, 2009 WL 973565, at *4 n. 3 (D.Colo. April 9, 2009)

II. DISCUSSION

A. Standard of Review

We review de novo the district court's grant of summary judgment. See Evers v. Regents of Univ. of Colo., 509 F.3d 1304, 1308 (10th Cir. 2007). Summary judgment is appropriate "if the pleadings, the discovery and disclosure materials on file, and any affidavits show that there is no genuine issue as to any material fact and that the movant is entitled to judgment as a matter of law." Fed.R.Civ.P. 56(c)(2). Because the basis for the district court's jurisdiction was diversity of citizenship, the accrual, limitations periods, and tolling determinations are governed by Colorado substantive law. See State Farm Mut. Auto. Ins. Co. v. Boellstorff, 540 F.3d 1223, 1228 (10th Cir. 2008). Mr. Cahill bears the burden of establishing the factual foundation for tolling. See Overheiser v. Safeway Stores, Inc., 814 P.2d 12, 13 (Colo.Ct.App. 1991).

B. Issues on Appeal

In deciding what issues to address on appeal, we have no interest in denying relief to Mr. Cahill on technical grounds. But it is not our role to serve as his lawyer. We will not construct arguments for him out of isolated sentences in his briefs. Nor will we fill the gaps in undeveloped arguments unsupported by citations to relevant authority. See Gross v. Burggraf Constr. Co., 53 F.3d 1531, 1547 (10th Cir. 1995). Moreover, we must not be unfair to the opposing party, who should not be required to guess at what issues are being raised and must be addressed or, alternatively, to devote its brief to every argument that is possibly being raised. And it will be an unusual case in which we consider on appeal an argument not raised by an appellant in the district court, both because of the inefficiencies caused by parties' holding arguments in reserve and because the appellee would have been deprived of the opportunity to present evidence either to rebut the newly raised argument or to support an alternative ground that moots that argument. See Tele-Commc'ns, Inc. v. Comm'r, 104 F.3d 1229, 1232-33 (10th Cir. 1997).

With these considerations in mind, we turn to Mr. Cahill's arguments in his opening brief on appeal. (We do not address arguments first raised in his reply brief. See Hill v. Kemp, 478 F.3d 1236, 1250-51 (10th Cir. 2007) (arguments first raised in a reply brief come too late).) As previously stated, the district court ruled (a) that a two-year limitations period applied to Mr. Cahill's outrageous-conduct claim and a three-year period applied to the other claims; and (b) that the fraudulent-misrepresentation, bad-faith-breach-of-contract, and CCPA claims accrued by March 23, 1998, and the concealment and outrageous-conduct claims accrued by November 2000. In opposition to those rulings, Mr. Cahill raises the following contentions: (1) that his claims were equitably tolled until American Family disclosed to him that it had violated CAARA; (2) that his causes of action could not have accrued before December 2003, when American Family began voluntarily reforming its policies and informing insureds; (3) that the court erred in saying that despite his disabilities he could reasonably have known the essential elements of his claims before he moved out of his parents' home in 2005; (4) that the limitations periods were extended by class-action tolling; (5) that each of his causes of action is subject to a three-year statute of limitations; and (6) that his causes of action could not have accrued before November 2000, when American Family learned of its failure to comply with CAARA.

We believe that contention 1 is properly before us, but, as explained below, we are not persuaded by Mr. Cahill's arguments. As for the other five contentions, we need not resolve their merits.

Two of the contentions have not been properly presented. We decline to address contention 2 because Mr. Cahill's opening brief provides no argument why the date of voluntary reformation or notice to other insureds is relevant to the accrual date, and he failed to raise this contention in district court. Similarly, we decline to address contention 3 because Mr. Cahill's opening brief provides no legal authority regarding why his mental condition extended his time to bring suit and, more importantly, because he did not adequately raise such an argument below, so American Family had no occasion to seek or offer evidence regarding the extent of his impairment. We are not unsympathetic to the view that limitations periods are tolled while the prospective plaintiff is mentally disabled. But the alleged period during which Mr. Cahill was in a coma was too brief to affect the result in this case. And in the absence of facts developed below and legal theories advanced in this court, we cannot determine whether Mr. Cahill's mental condition was such that tolling would be appropriate during the period that he lived at home after recovering consciousness.

In light of our disposition of contentions 1, 2, and 3, Mr. Cahill's remaining contentions cannot affect the result. With respect to contention 4 — class-action tolling — his opening brief argues only that the limitations periods were tolled by the Hicks class-action litigation. But that suit was not brought until June 2004, after the limitations periods had already expired. Likewise, even if we adopted his views that the applicable limitations period for all claims is three years (contention 5), and that no claim accrued before November 2000 (contention 6), the limitations periods would still have expired in November 2003, several years before he filed suit.

Accordingly, we confine the remainder of this opinion to one issue — whether the limitations periods were tolled until American Family informed Mr. Cahill of its violation of CAARA.

C. American Family's Failure to Disclose Mr. Cahill's Entitlement to Enhanced PIP Benefits

Mr. Cahill argues that the limitations periods on his claims were tolled by American Family's failure to disclose to him that he was entitled to enhanced PIP benefits. He appears to contend that because American Family did not make the disclosure until June 2007, the limitations periods governing his claims should not have begun to run until that date.

We disagree. To begin our analysis, it is important to explain precisely what American Family allegedly failed to disclose. Mr. Cahill does not argue that American Family concealed the terms of its policy, the communications between American Family and the Cahill family regarding PIP coverage, the amount it had paid in benefits, or any other historical fact. The only matter not disclosed to Mr. Cahill was legal: the statutory mandate that American Family offer the opportunity to purchase additional coverage and the availability of reformation of the policy if the statutory mandate was violated.

But it is knowledge of facts, not of the law, that controls the application of a statute of limitations. Under Colorado law a claim accrues when "the plaintiff knows, or should know, in the exercise of reasonable diligence, all material facts essential to show the elements of that cause of action." Miller v. Armstrong World Indus., 817 P.2d 111, 113 (Colo. 1991) (internal quotation marks omitted). A plaintiff's "knowledge of the legal theory supporting a claim does not determine the date of accrual for that claim." Murry v. GuideOne Specialty Mut. Ins. Co., 194 P.3d 489, 494 (Colo.Ct.App. 2008); see Olson v. State Farm Mut. Auto. Ins. Co., 174 P.3d 849, 855 (Colo.Ct.App. 2007) ("[T]he relevant issue is when a plaintiff discovers facts essential to the cause of action, not the legal theory upon which the cause of action would be based." (internal quotation marks omitted)). If a plaintiff need not know the law for a cause of action to accrue, then the defendant's failure to disclose the law should not delay the start of the limitations period. Tolling should arise only when the defendant conceals something that the plaintiff needed to know for his cause of action to accrue. We might also point out that the days of Caligula are long past. Today, the law is not concealed by inscribing it in small letters on tablets hung high, out of sight of the populus. The law, including Colorado law, is public and accessible to all "in the exercise of reasonable diligence." Miller, 817 P.2d at 113 (internal quotation marks omitted).

The authority cited by Mr. Cahill does not contradict what we have said. He relies on Colorado statutes and two Colorado Supreme Court decisions. In his view, the statutes required American Family to disclose to him its violation of CAARA and his entitlement to enhanced PIP benefits. And he reads the two court decisions as requiring equitable tolling whenever a defendant fails to disclose information that it was required by law to disclose to the plaintiff. See Garrett v. Arrowhead Improvement Ass'n, 826 P.2d 850 (Colo. 1992); Shell W. E P, Inc. v. Dolores County Bd. of Comm'rs, 948 P.2d 1002 (Colo. 1997). But we reject his statutory arguments, and the cases that he cites are readily distinguishable.

Mr. Cahill's briefs on appeal assert that three Colorado statutory provisions required American Family to disclose its CAARA violation. His opening brief cites Colo.Rev. Stat. §§ 10-3-1104(1)(h)(I) and 10-4-706(4)(a). His reply brief cites Colo.Rev. Stat. § 10-3-1104(1)(a)(I), but not the provisions cited in his opening brief. We address only § 10-3-1104(1)(h)(I). He did not preserve for appeal any argument predicated on § 10-4-706(4)(a), because he did not cite or otherwise rely on it in the district court. See Tele-Commc'ns, 104 F.3d at 1232-33. And his reliance on § 10-3-1104(1)(a)(I) in his reply brief on appeal was too late. See Hill, 478 F.3d at 1250-51.

Not that Mr. Cahill's opening brief makes much of an argument regarding § 10-3-1104(1)(h)(I). He merely asserts, without explanation, that the disclosure was required by that section, which he describes as "prohibiting an insurer from misrepresenting pertinent facts or insurance policy provisions relating to coverages at issue." Aplt. Br. at 13. His description of the provision is perfectly accurate. See Colo.Rev. Stat. § 10-3-1104(1)(h)(I) ("Misrepresenting pertinent facts or insurance policy provisions relating to coverages at issue"). But we are at a loss to see what fact (as opposed to a law) or policy provision was misrepresented by American Family. See Olson, 174 P.3d at 857 (§ 10-3-1104(1)(h)(I) does not impose duty on insurer to inform insured when limitations period would run).

As for the case law relied upon by Mr. Cahill, it does not support equitable tolling for failure to disclose the law. In both Shell and Garrett what was undisclosed (and required to be disclosed) was a fact. Shell owned an oil-and-gas production unit that encompassed leaseholds in both Montezuma and Dolores Counties. See Shell, 948 P.2d at 1005. Although it was required to file gas-production information with each county for assessment of its ad-valorem-tax obligations, it filed its unit-production-value information with only Montezuma County from 1985 until 1990. See id. In 1992, after Shell began filing with both counties, the Dolores County Treasurer issued Shell a tax notice for tax years 1985 through 1990 based on Shell's unreported gas assets during that period. See id. Shell paid the taxes for 1986 through 1990, but it contested the 1985 assessment. It argued that the six-year limitations period for assessing unpaid taxes precluded Dolores County from assessing taxes for that year. See id. at 1006-07. The Colorado Supreme Court disagreed. The limitations period, it held, was equitably tolled because Shell's statutory violation in failing to inform the county of its assets prevented a timely assessment by the county. See id. at 1008. According to the court, it would have been "manifestly unjust" for Shell to assert a statute-of-limitations defense when its failure to file precluded the county from obtaining notice of Shell's gas production. Id. (internal quotation marks omitted).

Garrett is similar. Garrett was injured while working for Arrowhead. See Garrett, 826 P.2d at 851. He filed a workers' compensation disability claim and received benefits until September 10, 1986. His injury worsened and he petitioned to reopen his claim so that he could seek additional disability benefits. The right to reopen a workers' compensation claim, however, was subject to a two-year limitations period that ran from the date of the last disability payment, and he did not file his petition until November 25, 1988, two months after the deadline. See id. at 851-52. But he had an excuse: He had been awaiting a medical report from his physician — a necessary component of a petition to reopen. See id. at 852. Arrowhead and its disability insurer had received this report on August 12, 1988, before the limitations period expired, but they had failed to share this report with Garrett, as required by regulation. See id. The Colorado Supreme Court held that the petition to reopen may have been timely because of equitable tolling. It recognized that "[e]quity will toll a statute of limitations if a party fails to disclose information that he is legally required to reveal and the other party is prejudiced thereby." Id. at 855. The court remanded for further factual development.

Here, in contrast, Mr. Cahill is not seeking equitable tolling based on a failure to disclose facts. And there would have been no sound reason for him to refrain from checking what the law was. We therefore reject his equitable-tolling argument.

III. CONCLUSION

We AFFIRM the district court's dismissal of Mr. Cahill's claims.