58 torture in the Criminal Code of the state of Guerrero, they concluded that the State had failed to comply with the obligations established in Articles 1, 6, and 8 of the Convention Against Torture, in relation with Articles 1(1) and 2 of the American Convention. 172. In the answer to the application, the State, based on different arguments, denied that it had violated Mrs. Rosendo Cantú’s rights to judicial guarantees and judicial protection. Subsequently, the State made a partial acknowledgement of its international responsibility concerning the right to judicial guarantees and to judicial protection (supra paras. 14 and 18), even though it asked the Court to rule on certain specific points, “in its analysis of the scope of the obligations of the State in the context of Articles 8(1) and 25 of the American Convention.” (infra paras. 187 to 192). 173. On the other hand, Mexico denied the violation of the Convention of Belém do Pará regarding the investigation of the facts and presented information regarding “the actions progressively carried out to guarantee the promotion and respect of the human rights of women,” so as to “corroborate […] the compliance of its conventional obligations enshrined in Articles 1(1) and 2 of the [American Convention], in relation with Article 7 of the [Convention of Belem do Para].” The State referred to various public policy initiatives implemented in order to “reach a level of [progressive] protection, prevention, and punishment of [all] the acts […] of discrimination and violence against women in all of its forms.” Regarding the alleged violation of the Inter-American Convention to Prevent and Punish Torture, the State of Mexico observed that, “the constituent objective and subjective elements of torture have not been gathered to be able to condemn the State for its omission,” and requested the Court to determine “the inexistence of violations of Articles 1, 6, and 8 of the Convention [against Torture].” * * * 174. The Court notes that Mexico acknowledged its international responsibility in relation to Articles 8 and 25 of the American Convention for the following facts: the lack of timely and specialized medical care at the time she filed her criminal complaint, the lack of specialized attention given her status as a female minor of age at the time the criminal complaint was filed, and the delay in the integration of the investigations and the impacts to her mental integrity because of said delay in the investigation. Nevertheless, it affirmed that it had not violated other rights established in the American Convention, or in any other Inter-American legal instrument (supra para. 17). Consequently, the Court still needs to determine certain facts and to decide the dispute with regard to whether the criminal investigation failed to comply with unacknowledged aspects of the guarantees arising from Articles 8(1) and 25(1) of the American Convention, in relation to Articles 1(1) and 2 thereof, and also Article 7 of the Convention of Belém do Pará and Articles 1, 6, and 8 of the Inter-American Convention to Prevent and Punish Torture. 175. The Court recalls that the obligation to investigate human rights violations is one of the positive measures that States must adopt to guarantee the rights established in the Convention.234 The obligation to investigate is an obligation of means rather than results. However, it must be undertaken by the State as an inherent legal obligation and not as a mere formality preordained to be ineffective, or as a step taken by private interests that depends upon the procedural initiative of the victims or their next of kin, or upon their offer of proof.235 In light of this obligation, once State authorities are aware of an incident, they should initiate ex officio and without delay, a serious, impartial, and 234 Cf. Cf. Case of Velásquez Rodríguez. Merits, supra note 33, paras. 166 and 176; Case of Valle Jaramillo et al., v. Colombia. Merits, Reparations and Costs. Judgment of November 27, 2008. Series C No. 192, para. 98, and Case of Garibaldi, supra note 211, para. 112. 235 Cf. Case of Velásquez Rodríguez. para, supra note 33, para. 177; Case of Radilla Pacheco, supra note 36, paras. 192 and 233, and Case of Chitay Nech et al., supra note 25, para. 192