**Core Concept**
Ovarian carcinoma staging is based on the FIGO (International Federation of Gynecology and Obstetrics) system, which takes into account the extent of tumor spread and involvement of surrounding tissues. The correct staging of ovarian carcinoma is crucial for determining prognosis and guiding treatment.

**Why the Correct Answer is Right**
Given the presence of bilateral ovarian carcinoma with capsular wall involvement, ascites, and peritoneal metastasis, the correct stage is FIGO stage IIIc. This is because the tumor has spread beyond the ovaries, involving the peritoneum and causing ascites, which is a characteristic feature of advanced ovarian cancer. The positive cytology further supports the diagnosis of metastatic disease.

**Why Each Wrong Option is Incorrect**
**Option A:** Stage I is incorrect because it represents early-stage disease confined to one ovary or fallopian tube, without capsular wall involvement or metastasis.
**Option B:** Stage II is incorrect because it represents disease spread to the pelvis, but not beyond, which is not the case here.
**Option C:** Stage IV is incorrect because it represents distant metastasis, such as to the liver, lungs, or distant lymph nodes, which is not specified in the given scenario.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the FIGO staging system for ovarian carcinoma is based on clinical evaluation and imaging studies, rather than surgical findings. This is because the goal is to accurately predict the extent of disease and guide treatment decisions.

**Correct Answer: C. Stage IIIc ovarian carcinoma.**