public were defined in the cache-control, e.g.
What is the expected behavior?
It seem it tells browser that the cache expires after 1 year, 31461276 seconds means 1 year.
More details in this post: EXPIRES VS. MAX-AGE
It's conceivable (likely?) that there are proxies in the wild which break this but since the only failure mode could be treating a public resource as private the consequences should be minimal beyond a modest performance hit. You'll have far more problems with proxies which do things like cache resources far beyond your specified