Can a smart radiation drug hunt down prostate cancer cells?

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Male participants aged 18 years or older. * Histologically or cytologically confirmed prostate adenocarcinoma with metastatic castration-resistant prostate cancer (mCRPC). mCRPC is defined as disease progression under continuous androgen-deprivation therapy (ADT) or after prior bilateral orchiectomy, with serum testosterone maintained at castrate level (\<50 ng/dL or \<1.7 nmol/L), meeting at least one of the Prostate Cancer Working Group 3 (PCWG3) progression criteria: PSA progression (PSA ≥1 ng/mL, ≥25 % increase compared with PSA nadir with an absolute rise ≥2 ng/mL confirmed by two consecutive measurements at least 1 week apart); or radiographic progression (≥2 new bone metastatic lesions on bone scan, or soft-tissue disease progression per Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST 1.1)). * Disease progression after treatment with at least one novel androgen-axis drug (NAAD), including abiraterone, enzalutamide, apalutamide, or darolutamide. * Prior chemotherapy, or participants who are ineligible for chemotherapy or decline chemotherapy. * PSMA-positive lesions confirmed by PSMA-PET/CT imaging; PSMA-positive is defined as tumor lesion uptake higher than liver background uptake. * At least one measurable lesion by RECIST 1.1 criteria OR at least one bone metastasis lesion by PCWG3 criteria. * Eastern Cooperative Oncology Group (ECOG) performance status score ≤ 1. * Estimated life expectancy of at least 6 months. * No transfusion of blood products, hematopoietic growth factors, or albumin within 14 days before baseline laboratory tests, and adequate organ function as follows: hematologic: absolute neutrophil count ≥ 1.5 × 10⁹/L, white blood cell count ≥ 3.0 × 10⁹/L, platelet count ≥ 100 × 10⁹/L, hemoglobin ≥ 9 g/dL; hepatic: albumin ≥ 30 g/L, total bilirubin ≤ 1.5 × upper limit of normal (ULN), alanine aminotransferase (ALT) / aspartate aminotransferase (AST) ≤ 3 × ULN (without liver metastases) or ALT/AST ≤ 5 × ULN (with liver metastases); renal: serum creatinine ≤ 1.5 × ULN; coagulation: international normalized ratio (INR) ≤ 1.5, activated partial thromboplastin time (APTT) ≤ 2 × ULN. * Willing to comply with radiation-protection instructions and scheduled study follow-up procedures. * Able to understand study procedures and voluntarily provide written informed consent, and willing to comply with all study-related assessments and follow-up requirements. Exclusion Criteria: * Participants unable to tolerate required imaging examinations. * Received systemic anti-tumor therapy (chemotherapy, radiotherapy, immunotherapy; endocrine therapy is exempt), investigational medicinal products, or investigational medical devices within 4 weeks prior to first study drug administration. * Received prior radiopharmaceutical therapy (such as strontium-89, samarium-153, rhenium-186, rhenium-188, radium-223, lutetium-177) within 6 months before first dose; or received external-beam radiation therapy (EBRT) within 2 months before first dose. * Persistent Grade 4 myelosuppression from prior anti-cancer therapy within 2 weeks before screening, or Grade 3 myelosuppression with recovery duration longer than 6 weeks. * Plan to receive cytotoxic chemotherapy, anti-tumor immunotherapy, radioligand therapy, or other similar anti-cancer treatments during study participation. * Known brain metastases identified at screening. * History of other malignant neoplasms within the past 5 years (curative-treated localized tumors such as basal-cell or squamous-cell skin cancer are permitted). * Symptomatic or impending spinal cord compression. * Prior external-beam radiation therapy covering more than 25 % of bone-marrow-containing skeletal regions. * Significant uncontrolled cardiovascular disease at screening: QTcF \> 470 ms or known long QT syndrome; myocardial infarction, angina pectoris, or coronary artery bypass graft (CABG) within 6 months before screening and judged unsuitable for study entry by investigator. * Uncontrolled bladder-outlet obstruction, urinary incontinence, claustrophobia, or radiophobia at screening. * Positive screening serology for hepatitis C virus (HCV) antibody, human immunodeficiency virus (HIV) antibody, or syphilis antibody. * Hepatitis B surface antigen (HBsAg) positive with active hepatitis B virus (HBV) replication as assessed by HBV-DNA testing and investigator judgment. * Known hypersensitivity to proteins/peptides, drug excipients, or structurally related compounds. * Documented history of drug or alcohol abuse or chronic substance dependence within 1 year prior to screening. * Unwilling to practice effective contraception during study participation and for 6 months after last study drug administration. * Severe active ongoing infection at the time of first planned study drug administration. * Any other medical condition which, in the investigator's judgment, may compromise participant safety, interfere with study result interpretation, or confer unacceptable participant risk.