Final answer:
The most likely diagnosis is Sudden Infant Death Syndrome (SIDS), considering the age of the infant, the sudden death during sleep, and the absence of other informative physical signs.
Step-by-step explanation:
The most likely diagnosis for a 4-month-old that arrives cold and stiff with an uninformative physical examination is Sudden Infant Death Syndrome (SIDS). Since the case involves an otherwise healthy infant who suddenly died during sleep, and given that no other physical signs point towards conditions such as abuse, scurvy, congenital syphilis, or osteogenesis imperfecta, SIDS is the most fitting diagnosis. SIDS is a condition where an infant unexpectedly stops breathing during sleep and dies without an obvious reason. It is one of the leading causes of death in infants under one year old and can be associated with factors like immaturity of the brain's arousal and breathing control centers.