What is the authenticity of the two reported traditions (athar): "I saw a dog with Malik bin Dinar, so I said: 'What are you doing with this, O Abu Yahya?' He replied: 'This is better than an evil companion,'" and "That Umm Al-Mu'minin Maymunah had a dog named Mismar," and can they be used as evidence for the permissibility of keeping a dog for purposes other than guarding and hunting?

Conclusion:

The first narration attributed to Malik bin Dinar, stating that a dog is better than a bad companion, was transmitted through three channels, all of which are weak due to the presence of unknown, weak, or denier-of-hadith (definition) narrators in their chains of transmission.

As for the second narration concerning Maymuna (may Allah be pleased with her) regarding naming a dog "Mismar," it was narrated by Ibrahim al-Harbi with an extremely weak chain of transmission, which is unacceptable because it contains a narrator whose weakness is agreed upon and whose narrations are reversed (Abdullah bin Shabeeb), and another narrator whose singular narrations of unusual reports are not accepted (Ibn Abi Owais).