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It began like a typical 911 call. The operator instructed a woman how to perform chest compressions on her husband, who was unconscious on the floor of their Manhattan apartment.

But six minutes into the call, Shelley Gilbert revealed the uniquely heart-wrenching circumstances she found herself in on the afternoon of Jan. 4, 2015.

“He has been shot,” Ms. Gilbert said, trying to keep her voice calm.

When the operator asked her who had done it, she quickly added: “My son, who is nuts. But I had no idea he was this nuts. He shot him in the head.”

Moments earlier she had greeted her son, Thomas Gilbert Jr., and had left him alone with his father, Thomas Gilbert Sr., a fixture on Wall Street who had founded a successful hedge fund.