What is the test for denying an affidavit of probable cause?

"Under Franks v. Delaware, supra, 438 U.S. 154,..., a defendant has a limited right to challenge the veracity of statements contained in an affidavit of probable cause made in support of the issuance of a search warrant. When presented with such a challenge, the lower court must conduct an evidentiary hearing if a defendant makes a substantial showing that (1) the affidavit contains statements that are deliberately false or were made in reckless disregard of the truth, and (2) the affidavit's remaining contents, after the false statements are excised, are insufficient to support a finding of probable cause. The defendant must establish the statements are false or reckless by a preponderance of the evidence. [Citation.] Innocent or negligent misrepresentations will not defeat a warrant. [Citation.] 'Moreover, "there is a presumption of validity with respect to the affidavit. To merit an evidentiary hearing[,] the defendant's] attack on the affidavit must be more than conclusory and must be supported by more than a mere desire to cross-examine.... The motion for an evidentiary hearing must be 'accompanied by an offer of proof... [and] should be accompanied by a statement of supporting reasons. Affidavits or otherwise reliable statements of witnesses should be furnished, ' or an explanation of their absence given."' [Citations.] Finally, '[a] defendant who challenges a search warrant based upon an affidavit containing omissions bears the burden of showing that the omissions were material to the determination of probable cause.' [Citation.]" (People v. Panah (2005) 35 Cal.4th 395, 456.) We review the denial of a Franks hearing de novo.(Ibid.)