68Ga-PSMA-0057 and 177Lu-PSMA-0057 in Patients With PSMA-Positive Metastatic Castration-Resistant Prostate Cancer

Inclusion Criteria: 1. Able to communicate well with investigators, understand the study purpose and requirements, voluntarily participate, and sign written informed consent. 2. Male, ≥18 years at screening. 3. Histologically or cytologically confirmed prostate cancer (excluding neuroendocrine prostate cancer and small cell prostate cancer), previously treated with at least one novel hormonal agent and 1-2 taxane-based regimens, or deemed intolerant to taxanes. 4. Serum/plasma testosterone at castrate level (\<50 ng/dL or \<1.7 nmol/L). 5. Documented progressive mCRPC based on ≥1 of the following: PSA progression (two consecutive PSA rises ≥1 week apart from a minimum value of 2.0 ng/mL); soft tissue progression per PCWG3 and RECIST v1.1; or bone progression with ≥2 new lesions. 6. PSMA-positive on imaging with 68Ga-PSMA-0057 (within 3 days before treatment start) or other investigator-accepted PSMA tracers (within 6 months before treatment start), using criteria in Section 4.8.5. 7. At least one measurable lesion per RECIST v1.1 and/or at least one bone metastasis per PCWG3. 8. Estimated life expectancy ≥12 weeks. 9. ECOG performance status 0-1 at baseline. 10. Adequate organ and bone marrow function, meeting the following lab criteria: 1)Bone Marrow: Absolute Neutrophil Count (ANC) ≥1.5×109/L, Platelets (PLT) ≥100×109/L, White Blood Cell (WBC) count ≥2.5×109/L, Hemoglobin (HGB) ≥9.0 g/dL (no transfusions/growth factors within 14 days prior to screening). 2)Liver Function: Serum Total Bilirubin (T-Bil) ≤1.5 ULN (unless Gilbert's syndrome); Alanine Aminotransferase (ALT) or Aspartate Aminotransferase (AST) ≤3 ULN for non-liver metastasis, or ≤5 ULN for liver metastasis. 3)Renal Function: Serum creatinine ≤1.5 ULN, or estimated Glomerular Filtration Rate (eGFR) ≥50 mL/min/1.73m2 (calculated using the MDRD formula). 11.Serum albumin concentration ≥30 g/L 12.Toxicities from prior therapies recovered to CTCAE v5.0 Grade 0-1 (alopecia excepted). 13.Men with reproductive potential agree to use highly effective contraception from informed consent through 6 months after last study dose and have no plans to donate sperm. Exclusion Criteria: 1. History of hypersensitivity to any study drug component or excipients, or history of specific allergic disease requiring systemic therapy, or other serious allergic reactions. 2. Prior PSMA-targeted radioligand therapy, or treatment with radionuclides such as Sr-89, Sm-153, Re-186, Re-188, Ra-223, or hemibody radiation within 6 months prior to consent. 3. Use of any investigational drug or device within 30 days before consent. 4. Systemic anticancer therapy within 28 days or 5 half-lives prior to consent (whichever is longer), including chemotherapy, radiotherapy, immunotherapy, targeted therapy, systemic immunomodulatory drugs, or antitumor traditional Chinese medicines/formulations within 2 weeks before first dose. 5. Another malignancy within the past 5 years, except for curatively treated cervical carcinoma in situ, non-melanoma skin cancers, etc. 6. Major surgery or significant traumatic injury within 4 weeks before consent. 7. Active brain metastases or CNS involvement, including untreated symptomatic lesions or those requiring radiation, surgery, or steroids within 1 month prior to screening. 8. Symptomatic spinal cord compression or clinical/imaging findings suggestive of impending cord compression. 9. Severe arterial/venous thromboembolic events within 6 months prior to screening; history of stroke; uncontrolled hypertension; decompensated heart failure (NYHA III-IV); LVEF \<50%; unstable angina; clinically significant arrhythmias requiring intervention. 10. Significant acute or chronic infections, including active TB, systemic bacterial or fungal infections requiring systemic therapy. 11. Clinically significant COPD or moderate-severe chronic respiratory disease requiring systemic therapy within 6 months before first dose. 12. Uncontrolled bladder outlet obstruction or incontinence (patients managed effectively with standard measures are allowed). 13. Active autoimmune disease requiring systemic treatment within the past 2 years or likely to recur, or active peptic ulcer disease or bleeding disorders. 14. History of solid organ transplantation or allogeneic hematopoietic stem cell transplantation (corneal transplant recipients not requiring immunosuppressants may be included). 15. Syphilis, HIV infection, HCV (HCV antibody positive with detectable HCV RNA), or active HBV infection (HBsAg positive with HBV DNA ≥ULN). 16. Contraindications to PET-CT or SPECT-CT imaging, or factors deemed by the investigator to preclude adequate imaging acquisition and interpretation. 17. Any condition judged by the investigator likely to interfere with compliance or study participation, or impair the ability to give informed consent.