Petitioner, 1 Irma Yolanda Aguilar-De Guillen, seeks judicial review of a Board of Immigration Appeals ("BIA") opinion affirming an Immigration Judge's ("IJ") decision denying her asylum relief, withholding of removal under the Immigration and Nationality Act ("INA"), and protection pursuant to the Convention Against Torture Act ("CAT") and ordering her removed. She claims the BIA erred in affirming the IJ's finding that: (1) she did not suffer past persecution on account of a protected ground; (2) she did not have a well-founded fear of future persecution; and (3) she was not entitled to protection under CAT. 2 Finding no merit to her arguments, we affirm.

A. BACKGROUND

1. Life in El Salvador 3

Petitioner was born in El Salvador in 1985. In 2006, she married Miguel Ángel and the pair had two children (who, as minors, are co-petitioners in this case). In El Salvador, she owned and operated a fruit and vegetable store with her husband. On several occasions, while her husband was off working as a taxi driver (his second job), gang members threatened to kill them unless their business paid monthly "rent" to the respective gang. The gang threatened to throw a grenade into her *31 home if she refused to pay. The gang members also informed Petitioner that they knew where her children went to school and she interpreted this as an additional threat. While four of the death threats were made via hand-written notes between December 2012 and January 2013, she also received several phone calls during that time with similar threats. She reported these incidents to her husband, who in turn reported them to the police. The police informed the two that they would "look into it" and advised Petitioner to turn off her telephone to avoid future threating calls. Once she reached out to a private detective about these threats and he agreed to be on the lookout at the store, the gang ceased making any threats.

While no one on Petitioner's side of the family had suffered any gang violence, both her husband's nephew and his brother were killed by a gang after they refused to join. In April 2013, her husband came to the United States, and in June 2014, Petitioner followed with their two children. She traveled to the United States through the U.S./Mexico border without inspection. 4

Upon Petitioner's entry to the United States, Petitioner was apprehended and detained. Thereafter, immigration officials filed a notice to appear alleging removability pursuant to § 212(a)(6)(A)(i) of the INA. Petitioner conceded removability and later applied for relief in the form of asylum, withholding of removal under the INA, and protection under CAT. Petitioner cited the several gang death threats she had received while living in El Salvador as the cause of her traveling to the United States and why she sought relief from removal.

2. The IJ Hearing

A hearing was held before the IJ on her application in March 2017, wherein Petitioner testified about her life in El Salvador. In support of her request for relief, in addition to her own testimony, Petitioner submitted a country condition report highlighting the violence in El Salvador relating to gangs and the police's ongoing struggle to manage the situation.

After the hearing, the IJ denied her application for relief. Although the IJ found Petitioner credible, consistent, and "extremely sympathetic," he found that she had not suffered past persecution or held a well-founded fear of future persecution on a protected ground as necessary to qualify for asylum relief. As to a well-founded fear of future persecution, the IJ noted that she had also failed to prove that any persecution was related or connected to her membership in a protected group, "as the crimes [she] suffered ... appear[ed] to be widespread according to the country conditions." The IJ found the purpose behind the death threats was extortion, and that Petitioner had failed to present any evidence that would support an inference that any future persecution would be on account of her familial relationship. 5 The IJ also found that Petitioner had failed to show government involvement-either through its inability or unwillingness to protect her from harm. Because Petitioner was unable to establish asylum, she necessarily failed to meet the requirements for withholding of removal under INA. Lastly, the IJ also denied her *32 CAT relief on the basis that she had not proved that she would likely face torture at the hands of the El Salvadoran government if she were to return. The IJ ordered Petitioner removed.

3. Appeal to BIA

Petitioner timely appealed to the BIA, which agreed with the IJ and therefore dismissed her appeal. The BIA held that "the record in this case [did] not indicate that the [petitioner's] family membership, or her familial relationship to her husband, was or will be at least one central reason for the harm she suffered or may suffer upon her return to El Salvador"-rather, the record demonstrated that the gang members were motivated by the desire to increase their wealth through extortion. The BIA also offered two reasons for rejecting Petitioner's new claim that she had a well-founded fear of future persecution on account of being a member of another particular social group: "single mothers who are living without male protection and cannot relocate elsewhere in the country." First, it did not find that this group was "cognizable as a particular social group" pursuant to asylum law because it was not defined with particularity; second, to the extent her argument regarding future persecution related to a general fear of gang violence, that too was not a recognizable ground for asylum. The BIA then quickly disposed of her withholding of removal claim before discussing her CAT claim. Like the IJ, the BIA found that because Petitioner had not met her burden for asylum, it followed she had not satisfied the higher standard of a clear probability of persecution on account of a protected ground as required for withholding of removal. As for her CAT claim, the BIA determined that Petitioner had not established "that she is more likely than not to be tortured in her country, by or at the instigation of or with the consent or acquiescence ... of a public official or other person acting in an official capacity." An order subsequently followed dismissing her appeal, and she now seeks review of that dismissal by this Court. 6

B. DISCUSSION

Before us, Petitioner assigns three errors to the BIA's decision, specifically, that it erred in affirming the IJ's finding that: (1) she did not suffer past persecution on account of being a member of a protected class; (2) she did not have a well-founded fear of future persecution (irrespective of any past persecution); and (3) she was not entitled to protection under the CAT.

1. Standard of Review

Where, as here, "the BIA adopts and affirms an IJ's decision, we review the IJ's decision to the extent of the adoption, and the BIA's decision as to any additional ground." Sunoto v. Gonzales , 504 F.3d 56 , 59-60 (1st Cir. 2007) (internal quotation marks, citation and brackets omitted). We review the IJ's findings of fact relied on by the BIA in support of its decision for substantial evidence, meaning we accept the findings "as long as they are supported by reasonable, substantial and probative evidence on the record considered as a whole." Singh v. Holder , 750 F.3d 84 , 86 (1st Cir. 2014) (internal quotation marks and citation omitted). Only where the record *33 compels a contrary outcome will we reject the IJ's findings. Thapaliya v. Holder , 750 F.3d 56 , 59 (1st Cir. 2014).

Moreover, a BIA conclusion regarding the definition and scope of the statutory term "particular social group" is a purely legal determination that we review de novo. Castañeda-Castillo v. Holder , 638 F.3d 354 , 363 (1st Cir. 2011) (citation omitted). We do, however, give deference "to the interpretation given the term 'social group' by the BIA even if we conclude that the term is susceptible to more than one permissible interpretation." Elien v. Ashcroft , 364 F.3d 392 , 397 (1st Cir. 2004) (citation omitted).

2. Asylum Relief

A petitioner may be eligible for asylum if he or she can establish persecution on account of a legally protected ground in one of two ways: (1) past persecution or (2) a well-founded fear of future persecution. Albathani v. INS , 318 F.3d 365 , 373 (1st Cir. 2003) ; 8 U.S.C. § 1158 (b)(1) ; § 1101(a)(42)(A); 8 C.F.R. § 208.13 . "[R]ace, religion, nationality, membership in a particular social group, or political opinion" are grounds specifically enumerated in asylum law. Olujoke v. Gonzáles , 411 F.3d 16 , 21 (1st Cir. 2005) (quoting 8 U.S.C. § 1101 (a)(42)(A) ). "To show that the circumstances the applicant endured constitute persecution for purposes of asylum relief, she must show 'a certain level of serious harm (whether past or anticipated), a sufficient nexus between that harm and government action or inaction, and a causal connection to one of the statutorily protected grounds.' " Martínez-Pérez v. Sessions , 897 F.3d 33 , 39 (1st Cir. 2018) (quoting Carvalho-Frois v. Holder , 667 F.3d 69 , 72 (1st Cir. 2012) ).

If a petitioner can prove she suffered past persecution while in her home country, a rebuttable presumption that her fear of future persecution is well-founded is triggered. 7 8 C.F.R. § 208.13 (b)(1) ; see Harutyunyan v. Gonzales , 421 F.3d 64 , 67 (1st Cir. 2005). "Without past persecution, an asylum applicant can still show a well-founded fear of future persecution by showing that he or 'she genuinely fears future persecution and that her fears are objectively reasonable.' " Martínez-Pérez , 897 F.3d at 39 (quoting Carvalho-Frois , 667 F.3d at 72 ) (citation omitted). In either case, however, "[a]n inability to establish any one of the three elements of persecution will result in a denial of [the] asylum application." Carvalho-Frois , 667 F.3d at 73 .

a. Past Persecution

Petitioner challenges all three grounds by which the IJ and the BIA rejected her claim of past persecution: severity, nexus, and government involvement. However, because Petitioner must establish every element of her claim to be entitled to relief, see Carvalho-Frois , 667 F.3d at 72 , we begin and end our discussion with the nexus prong. Id. (For simplicity's sake, this Court proceeds directly to petitioner's weakest argument.)

Petitioner maintains that she was persecuted because of her familial relationship to her husband and the BIA erred by not *34 concluding that it was clearly erroneous for the IJ to find that she did not establish past persecution on account of such grounds. 8 We will assume without deciding that the harm Petitioner suffered constituted past persecution and that her membership in her Husband's family constitutes a cognizable social group. See Romilus v. Ashcroft , 385 F.3d 1 , 6 (1st Cir. 2004) (because the issue was not dispositive, we assumed without deciding that the group the petitioner was a member of was a political organization).

Petitioner's protected ground needs to be "at least one central reason" for the persecution she suffered for asylum purposes. Aldana-Ramos v. Holder , 757 F.3d 9 , 18 (1st Cir. 2014) (quoting 8 U.S.C. § 1158 (b)(1)(B)(i) ). "[A]sylum is still proper in mixed-motive cases even where one motive would not be the basis for asylum, so long as one of the statutory protected grounds is 'at least one central reason' for the persecution." Id. ; accord Villalta-Martinez v. Sessions , 882 F.3d 20 , 28 (1st Cir. 2018). In other words, "the presence of a non-protected motivation does not render an applicant ineligible for refugee status." Aldana-Ramos , 757 F.3d at 19 . However, a petitioner's "speculation or conjecture, unsupported by hard evidence is insufficient to establish nexus." Ruiz-Escobar v. Sessions , 881 F.3d 252 , 259 (1st Cir. 2018) (internal quotation marks and citation omitted).

Petitioner's claim of past persecution fails because she does not point to any evidence to support an inference that her membership in her husband's family was at least one of the reasons she suffered any harm, much less does she point to record evidence compelling us to disagree with the BIA's affirmance of the IJ's findings. See Jianli Chen v. Holder , 703 F.3d 17 , 21 (1st Cir. 2012) ("[W]e will reverse only if the record is such as to compel a reasonable factfinder to reach a contrary determination.") As the BIA noted, the only reasonable inference to be made by the evidence Petitioner presented at the hearing before the IJ is that the gang members targeted Petitioner and her family to increase their wealth through extortion. Petitioner introduced no direct (or circumstantial) evidence that the gang's threats had anything to do with her membership in her husband's family. See Sosa-Perez v. Sessions , 884 F.3d 74 (1st Cir. 2018) (The petitioner "offer[ed] no direct evidence to support her assertion that the assailants knew that she was a member of the family that she alleges they were targeting, let alone that they attacked her on that basis.")

While Petitioner maintains that both the IJ and BIA failed to properly consider "mixed motive" persecution, we disagree. A review of both decisions quickly reveals that they considered the possibility of her familial relationship being only one central cause of the persecution, but both concluded Petitioner had failed to present any evidence to support her allegation. The IJ specifically acknowledged "that there often can be mixed motives and that family can serve as a cognizable particular social group." 9 Meanwhile, the BIA also acknowledged *35 that family membership can constitute a social group but that here, the evidence showed that "gang members targeted [Petitioner] for no other reason than to increase their wealth through extortion." Nothing in the IJ's or BIA's decisions indicates that either the IJ or the BIA felt that, once the IJ found the gang was motivated by increasing its own wealth, the IJ was precluded from finding that they also targeted Petitioner due to her familial relationship (or, presumably, any other reason) as she maintains. We agree with Petitioner that the gang could have had more than one motive that would have resulted in Petitioner meeting the nexus prong, but we also see nothing in the record to compel such conclusion. Accordingly, Petitioner failed to meet a necessary requirement to establish past persecution.

b. Future Persecution

Next, Petitioner argues that irrespective of her ability to establish past persecution, she has established a well-founded fear of future persecution if she were to return to El Salvador. In addition to arguing she fears persecution on the basis of her familial relationship to her husband, 10 she also adds that if she were to return to El Salvador, she would be a single mother without the protection of a male figure and unable to relocate within the country, and that this is a protected ground.

A party seeking asylum " 'based on 'membership in a particular social group' must establish that the group is: (1) composed of members who share a common immutable characteristic, (2) defined with particularity, and (3) socially distinct within the society in question.' " Paiz-Morales v. Lynch , 795 F.3d 238 , 244 (1st Cir. 2015) (quoting Matter of M-E-V-G- , 26 I&N Dec. 277 , 237 (BIA 2014) ). The BIA concluded that Petitioner failed to establish both prongs two and three in her proposed group of "single mothers who are living without male protection and cannot relocate elsewhere in the country."

While Petitioner attempts to distinguish her case from the facts and holding of Perez-Rabanales v. Sessions , 881 F.3d 61 , 66 (1st Cir. 2018), wherein we found that the proposed social grouping "Guatemalan women who try to escape systemic and severe violence but who are unable to receive official protection" failed to satisfy the particularity and social distinctiveness requirements, her discussion falls short. After outlining the facts and holding in Perez-Rabanales , she makes a boilerplate assertion that "her social group of single mothers lacking male protection and unable to relocate is socially distinct, easily perceived by society, and not defined by the persecution of its members" without telling us exactly how that is the case. Petitioner does not provide us with a meaningful discussion of how her proposed group satisfies the particularity and social distinctiveness requirements any more than the petitioner in Perez-Rabanales . Instead, she points to two things broadly to support her argument: (1) her "credible testimony", and (2) "the numerous corroborating documents submitted by [her] evidencing the pervasive and systemic violence against women, and in particular single mothers, in El Salvador." However, Petitioner's reliance on her testimony and corroborating documents is *36 misplaced because the question is whether her proposed social group generally-not her circumstances specifically-meet the requirements of a "particular social group" as a matter of law. See Elien , 364 F.3d at 397 .

In any event, our de novo review yields us to the same outcome we reached in Perez-Rabanales . Even assuming the proposed social group of "single mothers without the protection of a male figure and unable to relocate in their country" satisfies prong one, i.e., it is composed of members who share a common immutable characteristic-it nevertheless fails prong two: being defined with particularity. Like the proposed group in Perez-Rabanales , "[t]he amorphous nature of [Petitioner's] sprawling group precludes determinacy and renders the group insufficiently particular." Id. at 65. Her proffered social group is overly broad and potentially encompasses all single mothers in El Salvador who may find themselves unable to relocate in the country. See id. Moreover, exactly what constitutes "without male protection" is an "open question," and possibly a subjective determination. See Paiz-Morales , 795 F.3d at 244-45 . Accordingly, Petitioner's attempt to qualify for asylum based on her membership in a social group fails because she does not meet the particularity requirement. 11

c. Protection under the CAT

Lastly, Petitioner argues that, since the primary reason her asylum application was denied was because the BIA affirmed the IJ's finding that she did not meet the "nexus" requirement and there is no requirement that the persecution be on the basis of a protected ground under CAT, she should have been granted this form of relief. She argues that the IJ did not properly consider her claim of relief under CAT because it failed to consider the voluminous country conditions reports she submitted depicting "the rampant nationwide use of torture by ... gangs."

Pursuant to Article 3 of CAT, the United States has an obligation under international law not to "expel, return (refouler) or extradite" a person to a country where there are "substantial grounds for believing that he [or she] would be in danger of being subjected to torture." 8 C.F.R. § 208.16 (c)(4). An applicant seeking relief must show that he or she is "more likely than not" to be tortured if removed to a particular country. 8 C.F.R. § 208.16 (c)(4). The torture must be "inflicted by or at the instigation of or with the consent or acquiescence of a public official or other person acting in an official capacity." 8 C.F.R. § 208.18 (a)(1).

Contrary to Petitioner's assertion, the BIA did not reject her asylum claim because of a lack of "nexus." Rather, the BIA affirmed the IJ's finding that Petitioner had not shown that she is more likely than not to be tortured in El Salvador. As was the case in the past-persecution discussion, Petitioner wholly fails to point to any record evidence that would compel us to reach a different outcome. Instead, Petitioner takes issue with the IJ's decision because it cites 2008 and 2012 opinions 12 -which Petitioner characterizes as dated. But our review is limited to "the reasoning provided by the [BIA]." Mejia v. Holder , 756 F.3d 64 , 69 (1st Cir. 2014). The BIA noted the absence of record evidence indicating a likelihood that a Salvadoran official would acquiesce in any torture inflicted upon Petitioner *37 by gang members, and Petitioner has not articulated how the BIA got it wrong. Our review of the record before us indicates the BIA's decision is well supported, and it does not compel us to reach a different outcome.

C. CONCLUSION

For the foregoing reasons, we deny the petition for judicial review.