I ran through your example locally. If you use git cat-file
to examine the commit objects...
After the first commit:
$ git cat-file -p f9afca7508e2d97ca4babfb897fa5acefe67af54
tree 56e3dd6f60494c9bbe56ea178b9a86c91d3139c6
author Lars Kellogg-Stedman <lars@example.com> 1376499716 -0400
committer Lars Kellogg-Stedman <lars@example.com> 1376499716 -0400
Commit 1
After amending:
$ git cat-file -p 976778e7f58c4b2f89b4f652e89c420e1266d297
tree 56e3dd6f60494c9bbe56ea178b9a86c91d3139c6
author Lars Kellogg-Stedman <lars@example.com> 1376499716 -0400
committer Lars Kellogg-Stedman <lars@example.com> 1376499733 -0400
Commit 1
Note that these two commits have different timestamps for the "commiter" metadata. Since the data is different, the commit ID is different. If you change the data, you change the SHA1 of the object.