Last month, Aguirre was found guilty of first-degree murder in the death of his girlfriend's 8-year-old son, Gabriel Fernandez.
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The jury found him guilty of first-degree murder and also guilty in the special circumstance allegation of murder involving the infliction of torture.
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Jurors then had a choice between recommending life in prison or the death penalty.
Deliberations in the penalty phase began Monday and jurors gave notice they had reached a recommendation by Wednesday afternoon.
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The official sentencing by the judge is scheduled for March.
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During trial, prosecutors presented a long history of abuse against the boy committed by Aguirre and allegedly by the boy's mother, Pearl Fernandez.
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That included shooting him with a BB gun, feeding him cat feces and forcing him to sleep while gagged and bound inside a small cabinet.
Gabriel died in May 2013.
Pearl Fernandez is to be tried separately.
CORRECTION: This story has been updated to reflect that the jury has recommended the death penalty, while the actual sentencing will take place in March.