SUMMARY ORDER

UPON DUE CONSIDERATION, IT IS HEREBY ORDERED, ADJUDGED, AND DECREED that the petition for review of the order of the Board of Immigration Appeals (“BIA”) is hereby DENIED in part and GRANTED in part. The BIA’s order is VACATED in part and the case is REMANDED for further proceedings consistent with this order.

Petitioner Gua Zo Lin is a Chinese citizen whose application for asylum, withholding of removal, and relief pursuant to the Convention Against Torture (“CAT”) largely derived from the alleged forcible sterilization of his wife by Chinese authorities. Gua Zo Lin now petitions for review of the BIA’s April 15, 2003 order summarily affirming the decision of an Immigration Judge (“U”) denying his request for relief for removal on a finding that he was not a credible witness. We assume the parties’ familiarity with the facts and the record of prior proceedings, which we reference only as necessary to explain our decision.

1. Asylum and Withholding of Removal

To qualify for asylum, “a refugee must demonstrate past persecution or a well-founded fear of future persecution on account of ‘race, religion, nationality, membership in a particular social group, or political opinion.’ ” Zhou Yun Zhang v. United States INS, 386 F.3d 66, 70 (2d Cir. 2004) (quoting 8 U.S.C. § 1101(a)(42)). For withholding of removal, an applicant “must demonstrate that, if returned to his country, his life or freedom would in fact be threatened on one of the protected refugee grounds.” Id. at 71 (citing 8 U.S.C. § 1231(b)(3)(A)). Where the evidence of a threat to an applicant’s freedom wholly depends upon the applicant’s credibility, a denial of asylum based upon an adverse credibility determination necessarily forecloses success on a claim for withholding of removal. See Wu Biao Chen v. INS, 344 F.3d 272, 275 (2d Cir. 2003) (per curiam).

The law recognizes forcible abortion and sterilization as forms of political persecution that can qualify an applicant for asylum. See 8 U.S.C. § 1101(a)(42); Zhou Yun Zhang v. United States INS, 386 F.3d at 71. Further, the BIA construes § 1101(a)(42) to permit derivative spousal claims. Thus, someone such as petitioner, who claims that his wife was the victim of a forcible sterilization, can base his own asylum claim on his wife’s persecution, even though she remains in them native country. Zhou Yun Zhang v. United States INS, 386 F.3d at 71-72; see In re C-Y-Z-, 21 I. & N. Dec. 915, 918, 1997 WL 353222 (BIA 1997). Moreover, this court has recently stated that a spouse’s forced abortion or sterilization establishes both past persecution and “lead[s] to an irrebuttable presumption of a well-founded fear of future persecution....” Li Yong Cao v. United States Dep’t of Justice, 421 F.3d 149, 155-156 (2d Cir. 2005) (citing In re Y-T-L-, 23 I. & N. Dec. 601, 605-08, 2003 WL 21206539 (BIA 2003)).

When, as in this case, the BIA summarily affirms an IJ’s decision to deny asylum and withholding of removal, we review the decision of the IJ directly. See Twum v. INS, 411 F.3d 54, 58 (2d Cir. 2005). The IJ’s findings of fact “are conclusive unless *550any reasonable adjudicator would be compelled to conclude to the contrary.” 8 U.S.C. § 1252(b)(4)(B). We will not disturb an IJ’s factual findings if they are “supported by ‘reasonable, substantial, and probative’ evidence in the record.” Wu Biao Chen v. INS, 344 F.3d at 275 (quoting Diallo v. INS, 232 F.3d 279, 287 (2d Cir. 2000)). Indeed, “[w]hen a factual challenge pertains to a credibility finding made by an IJ and adopted by the BIA, we afford ‘particular deference’ in applying the substantial evidence standard,” Zhou Yun Zhang v. United States INS, 386 F.3d at 73 (quoting Montero v. INS, 124 F.3d 381, 386 (2d Cir. 1997)), provided the IJ has not misstated the record and has given specific, cogent reasons for the credibility ruling, thereby demonstrating that it is not based on bald speculation or caprice, see id. at 74; see also Ramsameachire v. Ashcroft, 357 F.3d 169, 178 (2d Cir. 2004). Specific examples of an applicant’s inconsistent, contradictory, or inherently improbable testimony can provide a cogent reason for an adverse credibility ruling. See Zhou Yun Zhang v. United States INS, 386 F.3d at 74. On a challenge to such a ruling, this court will not itself “hypothesize excuses” for the inconsistencies, contradictions, or improbabilities. Id. We do, however, expect the IJ to have engaged in a “reasoned evaluation” of any explanations the applicant may have offered for flaws in his testimony. Cao He Lin v. United States Dep’t of Justice, 428 F.3d 391, 403 (2d Cir. 2005); see also Latifi v. Gonzales, 430 F.3d 103, 105 (2d Cir. 2005) (per curiam).

Applying these principles to this case, we identify several concerns that require us to remand this case for further proceedings to clarify the IJ’s decision.

First, although the IJ identified a number of inconsistencies and improbabilities in petitioner’s testimony, he summarily dismissed petitioner’s explanations as unsatisfactory without identifying the explanations or outlining his reasons for finding them unconvincing. We do not demand that an IJ address every piece of evidence offered by an applicant, but he must offer a sufficient rationale for his adverse credibility decision to demonstrate that his reasoning is sound and not arbitrary. See Cao He Lin v. United States Dep’t of Justice, 428 F.3d at 403; Zhou Yun Zhang v. United States INS, 386 F.3d at 74. The conclusory dismissal of explanations in this case does not give that assurance. While it may be obvious, even on review of a cold record, that petitioner’s professed memory lapse is an unsatisfactory explanation for inconsistent evidence about a material issue such as his wife’s incarceration in China, we cannot so easily discern the IJ’s reasoning in rejecting petitioner’s explanations for other evidentiary inconsistencies pertaining to fine amounts, an entry on petitioner’s household registry listing him as a fisherman, and the omission of his own past imprisonment on his asylum claim. Without some explication of the IJ’s reasoning, we cannot determine whether the IJ’s credibility assessment is, in fact, fairly supported by the record. See Chun Gao v. Gonzales, 424 F.3d 122, 130-31 (2d Cir. 2005).

A second concern arises from the IJ’s failure to reference In re C-Y-Z- or otherwise to acknowledge that petitioner was pursuing a derivative spousal claim of persecution and not relying only on his own alleged mistreatment by Chinese authorities. On such a derivative claim, the critical question is whether petitioner credibly established his wife’s forcible sterilization. Thus, even though the IJ found petitioner’s testimony implausible or inconsistent in other respects, he never mentioned that, as a result, he did not credit the forcible sterilization claim. Not *551insignificantly, petitioner offered medical X-rays and an affidavit from his wife to corroborate the sterilization claim. Cf. Zhou Yun Zhang v. United States INS, 386 F.3d at 78 (noting lack of any corroborating affidavit from wife of asylum applicant). While that affidavit suggests that economics also played a part in petitioner’s decision to flee China for the United States, it appears that petitioner’s wife linked their financial difficulties to her forcible sterilization. The IJ failed to discuss this affidavit or the accompanying medical evidence in assessing petitioner’s credibility.

Third, the IJ appears to have rejected petitioner’s persecution claim because petitioner failed to pursue asylum in 1993. Because petitioner’s testimony on this point was not clear, the IJ considered two alternatives. Either petitioner had not filed for asylum in 1993, or he was claiming that he had filed but that counsel had failed to pursue the matter. The IJ concluded that the former circumstance would demonstrate that petitioner’s subsequent claimed fear of persecution was not genuine. As for the latter circumstance, the IJ deemed it not credible because an immigration court would be required to address a filed application whether or not counsel withdrew from the case. There is, however, a third possibility. Petitioner’s testimony could also be construed to indicate that no asylum application was filed in 1993 because petitioner had entrusted that task to his lawyer who failed to perform it because of a fee dispute. Precisely because the facts on this point are not clear, the IJ would need to develop the record further to conclude that petitioner’s failure to file an asylum claim in 1993 supports a conclusion that he has no bona fide derivative claim of persecution based on the alleged forcible sterilization of his wife. See Cao He Lin v. United States Dep’t of Justice, 428 F.3d at 400 (noting that “an adverse credibility determination may not be based upon speculation”).

Finally, a question arises as to the IJ’s conclusion that petitioner had engaged in immigration fraud.2 The ruling was made in connection with petitioner’s charged removability pursuant to 8 U.S.C. § 1182(a)(6)(C)(i) (deeming inadmissible alien who by fraud or willful misrepresentation attempts to gain a benefit under U.S. immigration law). Because petitioner concedes that he was, in any event, removable under § 1182(a)(6)(A)(i) (pertaining to aliens not admitted or paroled into the U.S.), any error in the fraud conclusion would not affect petitioner’s removability. Such an error might be relevant, however, if it influenced the IJ’s adverse credibility determination.

For an IJ to conclude that an alien committed fraud under the immigration laws, he must find by clear and convincing evidence that, inter alia, there was knowledge of the falsity. See Matter of Hui, 15 I. & N. Dec. 288, 290, 1975 WL 31499 (BIA 1975) (referring to pre-amendment version of § 1182(a)(6)(C)(i)). Under the criminal law, where the government carries the heavier burden of proof beyond a reasonable doubt, the knowledge element of a fraud crime may be established by proof of a person’s conscious avoidance of the truth. See, e.g., United States v. Walker, 191 F.3d 326, 337 (2d Cir. 1999). It is well settled, however, that negligence or mistake are insufficient to establish knowledge of falsity. See, e.g., United States v. Bernstein, 533 F.2d 775, 801 (2d Cir. 1976) (“[Kjnolwedge could not be established by proof of mere negligence.”). Thus, on remand, the IJ should clarify his knowledge ruling to ensure compliance with these *552principles of law. He should further specify whether his fraud finding relates only to petitioner’s removability under § 1182(a)(6)(C)(i), or also influences his assessment of petitioner’s credibility on his claim for relief from removal.

2. CAT Claim

Although petitioner appeals the denial of his CAT claim, he fails to discuss this issue in his brief. Issues not sufficiently argued in a party’s brief are generally waived and not addressed on appeal. See Norton v. Sam’s Club, 145 F.3d 114, 117 (2d Cir. 1998). In any event, based on our independent review of the record, we conclude that substantial evidence supports the IJ’s finding that petitioner failed to demonstrate that it was more likely than not that if he returned to China he would be tortured, as defined by CAT. See Islami v. Gonzales, 412 F.3d 391, 395-96 (2d Cir. 2005) (discussing requirements for CAT relief).

For the reasons stated, we DENY the petition for review of the BIA’s April 15, 2003 order insofar as it denies petitioner’s CAT claim. We GRANT the petition for review insofar as the order denies petitioner’s claims for asylum and relief from removal, and to that extent we hereby VACATE the BIA order and REMAND with instructions to remand this matter to the IJ for proceedings consistent with this order.