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Would it be helpful to collect "corroborating" support from third parties, such as our paediatrician, to lend credibility to my claims? I try to catch videos of some of the more "outlandish" activities on my iPhone, but I'm not much of a cinematographer! Plus, these talents reveal themselves unannounced.

I am going to say No. Because say you are looking for early entry to school for example. If you pull out a letter from your pediatrician about what he was doing when he was 14 months, it does not add anything to the case AND it makes you look a bit mad, and over invested. And when they head off to college or whatever it does not matter in the end what they did when they were a baby. It's kind of nice to keep some records for yourself if you want to. You think you won't' forget... but you do!