These names - Arthur Livermore True and Louisa Kimball are a match, but the dates and names of children don't match.
My line is -
Arthur Livermore True born about 1804 Grafton County, New Hampshire - died after 1870 (I've discovered him in the Belknap County census).
Louisa Kimball could be the daughter of Jesses Kimball and Abigail Varney, she was born about 1804 Grafton County, New Hampshire and also died after 1870 as I found her with Arthur in the 1870 census.
The True family seems to have used the same names over and over and also within cousin groups, but the catch is Louisa Kimball?
Arthur and Louisa had a son Cyrus B. True who moved his family to California, some of his children settled in South Dakota and Washington state. Cyrus and wife Margaret Cretsinger had a son Arthur Livermore True who married Lydia Brownlow.
Could your book have incorrect death dates for Arthur Livermore True and Louisa Kimball - if so this could be a match, but where is Cyrus in your reference for this family group?