Final answer:
Oedipus' proclamation regarding the murderer of Laius in Sophocles' tragedy entails harsh punishment, including exile and social ostracism, which ironically leads to Oedipus' own tragic downfall when he discovers that he is the murderer.
Step-by-step explanation:
The proclamation or curse of Oedipus regarding the murderer of Laius is a pivotal moment in Sophocles' tragedy. In his determination to rid Thebes of the plague, Oedipus declares that the murderer, once identified, will be exiled or executed, and no one in the city shall give him shelter or speak to him, effectively cutting off the perpetrator from all social and religious comforts of the community.
This proclamation not only sets the tone for the king's pursuit of justice but also, ironically, seals his tragic fate once he learns that he himself is the murderer he seeks. Oedipus's proclamation reflects his strong sense of justice and his quick judgement, which ultimately leads to his downfall as he unravels the truth of his own identity and his unwitting fulfillment of the horrific prophecy that he would kill his father and marry his mother.