
605 F.3d 1 (2010)
Artemio BORGES and Kimberly Wetherell, as Parents and Next Friends of S.M.B.W., a Minor, Plaintiffs, Appellants,
v.
Dr. Alfonso SERRANO-ISERN, et al., Defendants, Appellees.
No. 09-1699.
United States Court of Appeals, First Circuit.
Heard March 4, 2010.
Decided May 3, 2010.
*3 David Efron, with whom Law Offices David Efron, P.C. was on brief, for appellants.
Benjamin Morales Del Valle, with whom Morales-Morales Law Offices was on brief, for Serrano-Isern and related appellees.
Roberto Ruiz Comas, with whom Bufete González Villamil was on brief, for Hospital Interamericano de Medicina Avanzada and related appellees.
Before TORRUELLA, SELYA and LIPEZ, Circuit Judges.
SELYA, Circuit Judge.
This appeal grows out of a medical malpractice action brought under diversity jurisdiction. See 28 U.S.C. § 1332(a). The district court jettisoned the action at the summary judgment stage. The plaintiffs appeal. Discerning no error, we affirm.

I. BACKGROUND
We rehearse the facts limned in the summary judgment record, taking them in the light most hospitable to the plaintiffs. Alt. Sys. Concepts, Inc. v. Synopsys, Inc., 374 F.3d 23, 26 (1st Cir.2004). We add more detail in our later discussion of the plaintiffs' specific claims. To the extent that we refer to the allegations of the complaint, we caution that mere allegations are not entitled to weight in the summary judgment calculus. Id.
We start with the cast of characters. The plaintiffs are Artemio Borges and Kimberly Wetherell, husband and wife, who sue on behalf of their minor daughter, Stephanie Marie Borges-Wetherell. There are a plethora of defendants but, for present purposes, the only two who matter are Alfonso Serrano-Isern (Dr. Serrano) and Hospital Interamericano de Medicina Avanzada (the Hospital).
Dr. Serrano practices obstetrics and gynecology in Puerto Rico. Wetherell (who, like all the plaintiffs, claims Florida citizenship) became pregnant, and enlisted Dr. Serrano's services. Dr. Serrano treated her from and after February 6, 2003. Wetherell's pregnancy was unremarkable, her prenatal course uneventful, and her prognosis good.
At around 7:33 a.m. on June 2, 2003, Wetherell was admitted to the Hospital for induction of labor. Following Wetherell's admission, Dr. Serrano, together with the Hospital's nurses and other staff, took charge of her care.
Dr. Serrano decided to deliver the baby by Cesarean section (C-section). He says that he made this decision because the baseline fetal heart rate, which he characterized as low but within normal limits, indicated the wisdom of this method of delivery. The plaintiffs do not accept this explanation, suggesting that an emergency C-section was required because of the presence of fetal bradycardia (that is, a sustained, abnormally low fetal heart rate).
Whatever the reason for deciding to deliver the baby by C-section, Wetherell signed a consent form for the procedure at 8:15 a.m. She was taken to an operating room at 10:00 a.m. Anesthesia was administered at 10:18 a.m. She gave birth to Stephanie at 10:22 a.m.
In the course of performing the C-section, Dr. Serrano discovered an occult cord prolapse. The hospital records show that the C-section was well underway when that discovery occurred.
*4 At birth, Stephanie was an apparently healthy baby. She cried and suckled normally. A cranial sonogram, a neurological consultation, and a pulmonary evaluation revealed no problems.
The Hospital discharged Wetherell on June 5, 2003. It sent Stephanie home six days later.
On October 26, 2006, the plaintiffs sued for medical malpractice. The complaint alleges that Stephanie has experienced serious physical and neurological deficits, global developmental delay, and low muscle toneconditions that allegedly require, and will in the future require, continuous physical, occupational, and speech therapies. The complaint attributes these maladies to injuries sustained at birth, specifically, intrapartum anoxia secondary to umbilical cord prolapse and delay in calling for and performing the C-section.
The plaintiffs claimed that Dr. Serrano was liable for his own negligence and that the Hospital was liable both vicariously (for Dr. Serrano's carelessness) and by virtue of its independent negligence. Both the doctor and the Hospital denied these claims.
A period of pretrial discovery began, during which both sides retained experts. Following the completion of discovery, Dr. Serrano moved for summary judgment, arguing that he had provided treatment that fully comported with the applicable standard of care and that the plaintiffs had failed to show that any negligence on his part had caused harm to Stephanie. Two days later, the Hospital likewise moved for summary judgment, arguing that the plaintiffs had failed to show a basis for any liability (vicarious or direct) on its part.
The district court granted both motions. See Wetherell v. Hosp. Interamericano de Medicina Avanzada, Inc. (Wetherell II), 609 F.Supp.2d 186, 193 (D.P.R.2009) (granting the Hospital's motion); Wetherell v. Hosp. Interamericano de Medicina Avanzada, Inc. (Wetherell I), No. 06-2079, 2009 WL 921157, at *7 (D.P.R. Mar. 31, 2009) (granting Dr. Serrano's motion). In its thoughtful opinion allowing Dr. Serrano's motion, the court held that the plaintiffs had failed to show either that Dr. Serrano had transgressed his duty of care or that a causal nexus existed between Dr. Serrano's conduct and Stephanie's alleged injuries. Wetherell I, 2009 WL 921157, at *7. In a separate opinion, the court held that the plaintiffs had failed to show that the Hospital could be found either independently negligent or vicariously liable. Wetherell II, 609 F.Supp.2d at 192-93. This timely appeal ensued.

II. ANALYSIS
On appeal, the plaintiffs challenge the district court's entry of summary judgment in favor of both the Hospital and Dr. Serrano. We first delineate the summary judgment standard; then clarify a procedural point; and, finally, examine sequentially the two challenged rulings.

A. The Summary Judgment Standard.

We review orders granting summary judgment de novo, considering the facts of record and all reasonable inferences therefrom in the light most favorable to the nonmoving party. See Houlton Citizens' Coal. v. Town of Houlton, 175 F.3d 178, 183-84 (1st Cir.1999). Summary judgment is appropriate if there is no genuine issue as to any material fact and the undisputed facts show that the moving party is entitled to judgment as a matter of law. Fed.R.Civ.P. 56(c)(2).
The vocabulary of summary judgment is well-defined. An issue is "genuine" if the evidence of record permits a rational factfinder to resolve it in favor of either party. See Medina-Muñoz v. *5 R.J. Reynolds Tobacco Co., 896 F.2d 5, 8 (1st Cir.1990). A fact is "material" if its existence or nonexistence has the potential to change the outcome of the suit. See Martínez v. Colón, 54 F.3d 980, 984 (1st Cir.1995).
The moving party bears the initial burden of informing the trial court of the basis for his motion and identifying the portions of the pleadings, depositions, answers to interrogatories, admissions, and affidavits, if any, that demonstrate the absence of any genuine issue of material fact. Celotex Corp. v. Catrett, 477 U.S. 317, 323, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986). Once the moving party has accomplished this feat, the burden shifts to the nonmoving party, who must, with respect to each issue on which she would bear the burden of proof at trial, demonstrate that a trier of fact could reasonably resolve that issue in her favor. Id. at 324, 106 S.Ct. 2548; DeNovellis v. Shalala, 124 F.3d 298, 306 (1st Cir.1997). As a general rule, that requires the production of evidence that is "significant[ly] probative." Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 249, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986). If the nonmovant fails to make this showing, then summary judgment is appropriate. Celotex, 477 U.S. at 324, 106 S.Ct. 2548.

B. The Deeming Order.

The local rules of the United States District Court for the District of Puerto Rico require that parties make certain filings in connection with motions for summary judgment. The movant must support his motion with "a separate, short, and concise statement of material facts, set forth in numbered paragraphs, as to which the moving party contends there is no genuine issue of material fact to be tried." D.P.R.R. 56(b). "Each fact asserted in the statement shall be supported by a record citation...." Id.
If the target of the motion chooses to oppose it, she must file with her opposition a "separate, short, and concise" counter-statement. D.P.R.R. 56(c). "Th[is] opposing statement shall admit, deny or qualify the facts [supporting the motion for summary judgment] by reference to each numbered paragraph of the moving party's statement of material facts and unless a fact is admitted, shall support each denial or qualification by a record citation...." Id.
These statementsboth the movant's and the nonmovant'smust satisfy specific commands:
Facts contained in a supporting or opposing statement of material facts, if supported by record citations as required by this rule, shall be deemed admitted unless properly controverted. An assertion of fact set forth in a statement of material facts shall be followed by a citation to the specific page or paragraph of identified record material supporting the assertion. The court may disregard any statement of fact not supported by a specific citation to record material properly considered on summary judgment. The court shall have no independent duty to search or consider any part of the record not specifically referenced in the parties' separate statement of facts.
D.P.R.R. 56(e).
When Dr. Serrano and the Hospital filed their respective summary judgment motions, each of them filed the required statement.[1] The plaintiffs filed oppositions, *6 admitting some of the declared facts and purporting to dispute or qualify others. The plaintiffs, however, neglected to observe the strictures of the local rule and omitted appropriate citations to the record with respect to their denials and qualifications. Accordingly, the district court deemed admitted the properly supported facts set forth by the defendants in their respective statements.
The district court's deeming order is unimpugnable. See Ruiz Rivera v. Riley, 209 F.3d 24, 28 (1st Cir.2000) (explaining that "failure to present a statement of disputed facts, embroidered with specific citations to the record, justifies the court's deeming the facts presented in the movant's statement of undisputed facts admitted"). Indeed, "deeming" is precisely the remedy that the local rule envisions for failures of compliance. See D.P.R.R. 56(e). Thus, we treat the facts expressly admitted by the plaintiffs, as well as those deemed admitted by the district court, as uncontested.

C. Liability of the Hospital.

We move next to the plaintiffs' challenge to the entry of summary judgment in favor of the Hospital. We need not tarry.
The plaintiffs' brief is devoid of any developed argumentation as to the issue of the Hospital's liability. It offers only an oblique suggestion that the Hospital was vicariously liable for the acts of Dr. Serrano (ostensibly an independent contractor) and a conclusory assertion that Stephanie's injuries were the result of the Hospital's "condonation of ... negligent acts and malpractice" on the doctor's part. Appellants' Br. at 10. This sparse rhetoric falls well short of satisfying the imperative that an appellant's brief must set forth her "contentions and the reasons for them, with citations to the authorities and parts of the record on which the appellant relies." Fed. R.App. P. 28(a)(9)(A).
To say more about this assignment of error would be supererogatory. By their failure to present any developed argumentation with respect to the Hospital's liability, the plaintiffs have waived their claim that the district court erred in granting the Hospital's motion for summary judgment. See Adorno v. Crowley Towing & Transp. Co., 443 F.3d 122, 124 n. 2 (1st Cir.2006) (declining to address argument that district court erred in granting summary judgment because appellants' brief "failed to develop any ... argument sufficiently to put the correctness of the summary judgment rulings in dispute"); United States v. Zannino, 895 F.2d 1, 17 (1st Cir.1990) (explaining that "issues adverted to in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived").

D. Liability of Dr. Serrano.

We turn now to the entry of summary judgment in favor of Dr. Serrano. Because this is a diversity case, the substantive law of Puerto Rico controls. Erie R.R. Co. v. Tompkins, 304 U.S. 64, 78, 58 S.Ct. 817, 82 L.Ed. 1188 (1938); Cortés-Irizarry v. Corporación Insular De Seguros, 111 F.3d 184, 189 (1st Cir.1997). To make out a prima facie case for medical malpractice under the Civil Code, P.R. Laws Ann. tit. 31, § 5141, a plaintiff must adduce evidence sufficient to establish three elements: (i) the duty owed (i.e., the minimum standard of professional skill and knowledge required in the relevant circumstances), (ii) an act or omission transgressing that duty, and (iii) a sufficient causal nexus between the breach of duty and the harm claimed. Cortés-Irizarry, 111 F.3d *7 at 189; Lama v. Borras, 16 F.3d 473, 478 (1st Cir.1994); Rolon-Alvarado v. Mun'y of San Juan, 1 F.3d 74, 77 (1st Cir.1993).
Under this framework, breach of duty is an essential element of a cause of action for malpractice. To consider whether a breach has been shown, we first must understand the nature of the duty owed.
The general parameters of the duty of care that a physician owes to a patient under Puerto Rico law are uncontroversial. The physician must employ a level of care consistent with that set by the medical profession nationally. Cortés-Irizarry, 111 F.3d at 190. Thus, an obstetrician, like Dr. Serrano, must use the same level of care that is generally accepted as good practice in the obstetrical subspecialty, nationwide. Id.
Puerto Rico law affords a physician a presumption that he has provided an appropriate level of care. Id. It is the plaintiff's obligation to refute this presumption by adducing evidence sufficient to show both the minimum standard of care required and the physician's failure to achieve it. Id.
The plaintiffs argue that they adequately rebutted the presumption that Dr. Serrano used a reasonable degree of care and that, therefore, the district court erred in concluding that they failed to show a breach of duty. An appraisal of this argument begins with an acknowledgment that Dr. Serrano's motion and supporting statement of undisputed facts were adequate to shift to the plaintiffs the burden of providing evidence reflecting a genuine issue of material fact. See Celotex, 477 U.S. at 322-23, 106 S.Ct. 2548. In an effort to satisfy this burden, the plaintiffs asserted that Dr. Serrano breached his duty of care in two interrelated ways: (i) by inordinate delay in calling for and performing an emergency C-section; and (ii) by failing properly to diagnose and treat intrapartum anoxia secondary to cord prolapse. We evaluate these assertions in the cold light of the summary judgment record.
The charge of inordinate delay focuses on the gap of roughly one hour and forty-five minutes between the time that Wetherell signed the consent form for the C-section and the time when she was wheeled into the operating room. The claim is that Dr. Serrano, in the exercise of due care, should have performed the C-section as soon as he knew or had reason to know that Stephanie, while in utero, was suffering from fetal bradycardia. The plaintiffs say that Dr. Serrano knew or should have known of that fact when, or very shortly after, Wetherell arrived at the Hospital. The relevant facts are as follows.
During labor, the fetal heart rate is monitored and contemporaneous tracings are available to the attending obstetrician. Fetal bradycardia is a slowing of the fetal heart rate. A normal fetal heart rate ranges from 120 to 160 beats per minute. A fetal heart rate below 110 beats per minute is termed bradycardia; subject, however, to the limitation that bradycardia requires this low fetal heart rate, according to the plaintiffs' obstetrical expert, Dr. Steven Weissberg, to be "constant and for a certain period of time ... not just fractions of seconds."
Here, the plaintiffs did not adduce any evidence that Stephanie in fact had bradycardia. To establish bradycardia, the plaintiffs rely almost exclusively on Dr. Weissberg's review of the fetal heart rate tracings. Those tracings showed an occasional dip in the fetal heart rate below 110, but Dr. Weissberg did not envision this as an aposematic sign. He freely admitted that a momentary fetal heart rate under 110 beats per minute is not in itself sufficient to show bradycardia; that the presence *8 of bradycardia ordinarily would be manifested by a fetal heart rate staying below 110 beats per minute "constant[ly] and for a certain period of time"; and that the infrequent occasions when Stephanie's heart rate fell below 110 beats per minute were fleeting and not sustained. Fairly read, Dr. Weissberg's testimony undercuts, rather than supports, the proposition that Stephanie was experiencing bradycardia.
In an effort to blunt the force of this reasoning, the plaintiffs argue that an excerpt from Dr. Weissberg's report constitutes significantly probative evidence that Dr. Serrano did not act quickly enough to perform a C-section while Stephanie was experiencing bradycardia.[2] The excerpt states:
In my opinion, I feel the care rendered Kimberly Wetherell fell below the standard of care because of the failure to perform a timely Cesarean section. The patient had been informed and signed for a Cesarean section at 0815, and she alleges she was told an operating room was not available, and did not enter the operating [room] for another hour and 45 minutes, an excessive delay. During this entire period of time, the fetal heartbeat remained low.
We do not think that this passage creates a triable issue as to any material fact. Dr. Weissberg's opinion is premised on the assumption that, during Wetherell's entire waiting time, the fetal heart rate was low. But there is no evidence of this; rather, the evidence belies the assumption of a persistently low fetal heart rate. An expert opinion grounded on a nonexistent fact is not significantly probative. See, e.g., Guile v. United States, 422 F.3d 221, 227 (5th Cir.2005) (holding that expert opinion based on "incorrect factual assumptions" was insufficient to create triable issue of fact).
Indeed, Dr. Weissberg admitted in his deposition that the fetal heart rate tracings showed that the times Stephanie's heart rate went below 110 beats per minute were brief, not sustained, and did not occur in a pattern consistent with a diagnosis of bradycardia. Thus, Dr. Weissberg's deposition testimony, given after he wrote his report, conclusively shows the absence of any significantly probative evidence that Stephanie suffered from bradycardia during the relevant time frame.[3] In light of his later, more detailed deposition testimony, Dr. Weissberg's report plainly cannot be said to create a triable issue of fact. Cf. Colantuoni v. Alfred Calcagni & Sons, Inc., 44 F.3d 1, 4-5 (1st Cir.1994) (holding that nonmovant cannot avoid summary judgment by an affidavit that contradicts, without explanation for the contradiction, the witness's deposition testimony); S.W.S. Erectors, Inc. v. Infax, Inc., 72 F.3d 489, 496 (5th Cir.1996) (similar).
That ends this aspect of our inquiry. Because there is no evidence in the summary judgment record from which a reasonable factfinder could conclude that Stephanie suffered from bradycardia in the relevant time frame, the plaintiffs' first breach-of-duty theory comes to naught.
The plaintiffs' remaining breach-of-duty theory posits a failure properly to diagnose and treat intrapartum anoxia secondary to *9 cord prolapse. Dr. Serrano argued below that there was an absence of any evidence showing that he knew or should have known, prior to performing the C-section, that Stephanie was endangered by an occult cord prolapse. The plaintiffs, laboring to make out a genuine issue of material fact, once again rely on Dr. Weissberg's views. That reliance is mislaid.
We pause to lay out the medical background. A cord prolapse (sometimes called an "overt cord prolapse") occurs when the umbilical cord protrudes into the vagina, preceding the baby. The Merck Manual 2207 (18th ed.2006). It is accompanied by ruptured membranes, id., and because compression of the cord during labor may cause fetal hypoxemia,[4] requires the immediate performance of a C-section. Due to its positioning, an overt cord prolapse is visible to the obstetrician very early in the continuum of labor and delivery.
Dr. Weissberg admitted at deposition that there was no cord prolapse as such during this delivery. Rather, Stephanie's birth was complicated by a different condition: an occult cord prolapse. As we explain below, the difference is critically important.
An occult cord prolapse occurs when a prolapsed umbilical cord is confined to the uterus, not protruding into the vagina. Generally, in an occult cord prolapse the cord is compressed by the fetus's shoulder or head. Id. There are no ruptured membranes. Thus, the cord is hidden from the obstetrician's view and does not become visible until surgery is actually performed.
So it was here: there is no evidence that Dr. Serrano could have known of the occult cord prolapse in advance of actually performing the C-section. The cervix was closed and no membranes had ruptured. Indeed, even Dr. Weissberg was unable to offer any explanation as to how Dr. Serrano might have known about the occult cord prolapse prior to performing the C-section (and, thus he conceded that Dr. Serrano presumably did not know that such a condition existed prior to his actual performance of the C-section). Hence, the occult cord prolapse could not have forewarned Dr. Serrano that an immediate C-section should be undertaken.
The plaintiffs offer a weak retort. They cite a passage from the report of Dr. Allan Hausknecht, their neurological expert, and suggest that this excerpt is sufficient to create a trialworthy issue with respect to whether and when Dr. Serrano should have known of the prolapsed cord. The passage on which the plaintiffs rely reads:
The findings that this child exhibits are characteristic of hypoxic ischemic encephalopathy. Dr. Weissberg explained in his report that the prolapse of the cord which was left to exist for an inappropriate amount of time is the cause of cerebral anoxia, which is the cause of hypoxic ischemic encephalopathy. I therefore feel with reasonable medical certainty that the departures present at the time of delivery caused brain damage (hypoxic ischemic encephalopathy) to [S.M.B.W.]
The plaintiffs do not advance a specific explanation as to how this passage is evidence that Dr. Serrano breached his duty of care. Their argument is presumably that Dr. Serrano should have realized earlier that Stephanie was experiencing an occult cord prolapse and, therefore, should have performed a C-section sooner.
*10 That suggestion represents a triumph of hope over reason. The plaintiffs' obstetrical expert, Dr. Weissberg, made it pellucid that there was no way Dr. Serrano could have known about the occult cord prolapse prior to undertaking the C-section. Dr. Hausknecht's second-hand view of what he believed Dr. Weissberg meant cannot reinvent this reality. Dr. Hausknecht expressly bases his conjecture that the "prolapse of the cord ... was left to exist for an inappropriate amount of time" on Dr. Weissberg's reportand, as we have explained, Dr. Weissberg's final conclusion was to the contrary. Because the summary judgment record contains no significantly probative evidence that Dr. Serrano either could or should have known about the occult cord prolapse prior to performing the C-section, there is no trialworthy issue about the timing of the procedure.
There is one loose end. The plaintiffs tack on at the end of their brief a perfervid argumentwithout a single citation to relevant authorityto the effect that the district court's grant of summary judgment violated their due process rights.
This court, as well as many of our sister circuits, has previously rejected this type of global constitutional attack on the summary judgment mechanism. See, e.g., Calvi v. Knox County, 470 F.3d 422, 427 (1st Cir.2006) (rejecting broadside Seventh-Amendment attack on summary judgment mechanism); Koski v. Standex Int'l Corp., 307 F.3d 672, 676 (7th Cir.2002) (rejecting "frivolous" argument that district court's grant of summary judgment violated defendant's due process rights). We see no meritorious basis for the attack here.

III. CONCLUSION
We need go no further.[5] The plaintiffs' argument that Dr. Serrano breached his duty of care through delay in calling for and performing a C-section fails because the plaintiffs offered no evidence that Dr. Serrano could or should have known, at the relevant time, that Stephanie suffered from either bradycardia or a cord prolapse. A physician cannot breach a duty to call for and perform an emergency procedure when there is no evidence that the physician knew or should have known, at the relevant time, that an emergency existed. The district court did not err in entering summary judgment in favor of all defendants.
Affirmed.
NOTES
[1]  This is not to say that the defendants complied fully with the local rule. Their proffers included some factual assertions that were not accompanied by appropriate record citations. The court below accorded these assertions no weight in the summary judgment calculus, and we emulate its example.
[2]  As Dr. Weissberg testified, the terms "bradycardia" and "low heart rate" are sometimes used interchangeably.
[3]  The plaintiffs could have offered supplemental expert reports or affidavits explaining how, despite these admissions, there was still sufficient evidence of bradycardia in the record. See, e.g., Tippens v. Celotex Corp., 805 F.2d 949, 954 (11th Cir. 1986). They did not do so.
[4]  Hypoxemia is deficient oxygenation of the blood. See Merriam-Webster's Med. Desk Dict. 378 (2005).
[5]  The district court also concluded that the plaintiffs had not adduced evidence sufficient to establish a causal connection between any acts or omissions on Dr. Serrano's part and the harm alleged by the plaintiffs. In view of our disposition of the breach-of-duty issue, there is no reason for us to grapple with the causation issue.
