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preponderance of the evidence that the child has been subjected to any of the following: (1) a parent or guardian has abandoned the child as described in AS 47.10.013, and the other parent is absent or has committed conduct or created conditions that cause the child to be a child in need of aid under this chapter; (2) a parent, guardian, or custodian is incarcerated, the other parent is absent or has committed conduct or created conditions that cause the child to be a child in need of aid under this chapter, and the incarcerated parent has not made adequate arrangements for the child; (3) a custodian with whom the child has been left is unwilling or unable to provide care, supervision, or support for the child, and the whereabouts of the parent or guardian is unknown; (4) the child is in need of medical treatment to cure, alleviate, or prevent substantial physical harm or is in need of treatment for mental injury and the child's parent, guardian, or custodian has knowingly failed to provide the treatment; (5) the child is habitually absent from home or refuses to accept available care and the child's conduct places the child at substantial risk of physical or mental injury; (6) the child has suffered substantial physical harm, or there is a substantial risk that the child will suffer substantial physical harm, as a result of conduct by or conditions created by the child's parent, guardian, or custodian or by the failure of the parent, guardian, or custodian to supervise the child adequately; (7) the child has suffered sexual abuse, or there is a substantial risk that the child will suffer sexual abuse, as a result of conduct by or conditions created by the child's parent, guardian, or custodian or by the failure of the parent, guardian, or custodian to adequately supervise the child; if a parent, guardian, or custodian has actual notice that a person has been convicted of a sex offense against a minor within the past 15 years, is registered or required to register as a sex offender under AS 12.63, or is under investigation for a sex offense against a minor, and the parent, guardian, or custodian subsequently allows a child to be left with that person, this conduct constitutes prima facie evidence that the child is at substantial risk of being sexually abused; (8) conduct by or conditions created by the parent, guardian, or custodian have (A) resulted in mental injury to the child; or (B) placed the child at substantial risk of mental injury as a result of (i) a pattern of rejecting, terrorizing, ignoring, isolating, or corrupting behavior that would, if continued, result in mental injury; or (ii) exposure to conduct by a household member, as defined in AS 18.66.990, against another household member that is a crime under AS 11.41.100 — 11.41.220, 11.41.230(a)(1) or (2), or 11.41.410 — 11.41.432, an offense under a law or ordinance of another jurisdiction having elements similar to a crime under AS 11.41.100 — 11.41.220, 11.41.230(a)(1) or (2), or 11.41.410 — 11.41.432, an attempt to commit an offense that is a crime under AS 11.41.100 — 11.41.220 or 11.41.410 — 11.41.432, or an attempt to commit an offense under a law or ordinance of another jurisdiction having elements similar to a crime under AS 11.41.100 — 11.41.220 or 11.41.410 — 11.41.432; or (iii) repeated exposure to conduct by a household member, as defined in AS 18.66.990, against another household member that is a crime under AS 11.41.230(a)(3) or 11.41.250 — 11.41.270 or an offense under a law or ordinance of another jurisdiction having elements similar to a crime under AS 11.41.230(a)(3) or 11.41.250 — 11.41.270;