What is the test for establishing that a crime actually occurred?

"To convict an accused of a criminal offense, the prosecution must prove that ... a crime actually occurred." ( People v. Alvarez (2002) 27 Cal.4th 1161, 1164, 119 Cal.Rptr.2d 903, 46 P.3d 372.) "[T]he corpus delicti or body of the crime ... cannot be proved by exclusive reliance on the defendants extrajudicial statements." ( Id ., p. 1165, 119 Cal.Rptr.2d 903, 46 P.3d 372.) "The independent proof may be circumstantial and need not be beyond a reasonable doubt, but is sufficient if it permits an inference of criminal conduct, even if a noncriminal explanation is also plausible. [Citations.] There is no requirement of independent evidence of every physical act constituting an element of an offense, so long as there is some slight or prima facie showing of injury, loss, or harm by a criminal agency. [Citation.] In every case, once the necessary quantum of independent evidence is present, the defendants extrajudicial statements may then be considered for their full value to strengthen the case on all issues." ( Id ., p. 1171, 119 Cal.Rptr.2d 903, 46 P.3d 372.)

[7 Cal.5th 219]