The 4-month-old infant a Bloomfield man was arrested for beating into “grave condition” has died, authorities confirmed Sunday.

The Allegheny County Medical Examiner’s Office has identified the child as Micaiah Williams.

Pittsburgh police were dispatched around 8:45 a.m. Tuesday to West Penn Hospital, where Micaiah was being treated for multiple traumatic head injuries, according to court papers. He was taken to UPMC Children’s Hospital of Pittsburgh in grave condition.

Micaiah had suffered four skull fractures that, a Child Advocacy Center doctor told police, appear to have come from three or more blows to the head, a criminal complaint said. CT scans revealed areas of dead brain tissue, brain damage and herniation of the brain down into the spinal cord.

There was external bruising on the child’s right eye and scalp and fractures to both shoulders, police said.

Doctors pronounced Micaiah dead at 2:35 p.m. on Saturday, nearly five days after the injuries, the medical examiner said.

Seth F. Williams, 28, of Pittsburgh’s Bloomfield neighborhood, was arrested Sept. 11 on aggravated assault and other charges.

The charges were modified Tuesday after Micaiah’s death, and prosecutors added a count of criminal homicide.

Williams waived a preliminary hearing Wednesday and now faces trial in Allegheny County Common Pleas Court.

The child’s mother, who court documents do not name, told police Williams called her while she was at work Monday. She and Williams have three children — the 4-month-old and 4-year-old twins.

Williams told her during the phone call that one of the twins knocked over the bassinet where the 4-month-old was sleeping, a criminal complaint said.

The children’s mother told police she came home to find the house in disarray. Her 4-month-old baby had bruises on his head.

Williams told a family member that the children had been acting up, the criminal complaint said. He had asked his father to take them.

When Williams’ father arrived at their apartment on Monday, he found broken glass on the floor, the complaint said. An interior door had been pulled off its hinges.

According to police, Williams’ father spoke to the twins, one of whom told him that Williams had punched them in the head and threw the other across the room. He returned the twins to his house and left the sleeping 4-month-old at Williams’ apartment.

The children’s mother awakened Tuesday morning to find the 4-month-old’s lips blue and eyes rolling back into their head. She carried the child to West Penn Hospital. Police said the child stopped breathing and was unresponsive en route.

One of the twins told investigators their father threw the 4-month-old onto the floor, the complaint said.

A Child Advocacy Center doctor told police the baby’s severe injuries could not have come from a fallen bassinet.

Police executing a search warrant later found Williams hiding in the basement.

He remained in the Allegheny County Jail on Sunday, court records show. A judge on Thursday denied him bail.

Williams’ preliminary hearing is scheduled for Wednesday.

Police said the mother has not been charged.