The plumber came out to the house shortly before noon, and it turns out that our pipes did not burst. The combination of frigid weather, a splitter attached to the hose bib, and a bad seat on the bib’s frost proof led to water escaping through the bib’s vacuum breaker and subsequently freezing into the ice sculpture. The pipes didn’t go bad, just the hose bib. It still cost a chunk of money to replace, but it was a far smaller chunk of money than would have been required if the pipes themselves had failed. All in all, a fair cop in my book.
Now we can go back home.