This marriage or marriage intention is listed in Elder James Wilson's Marriages, but the newspaper report says the minister was Rev. Mr. Shurtleff. There is also a discrepancy in the dates, as "Family Notes" by James N. Arnold has the date as 15 September, rather than 4 September.
The marriage intention was published on 20 & 27 Aug 1826 and also on 3 Sep 1826. At that time Edward was of Providence and Mary was of Pawtuxet.
A descendant, Martha Adams (Remington) (Davies) Bower, has the marriage date as 4 Sep 1826.
The cemetery information at usgwenwebarchives.net has the marriage date as 4 Sep 1826.
[S013398] Family notes of Martha Adams (Remington) (Davies) Bower.
[S012704] James N. Arnold, Family Notes, (unpublished manuscripts).
[S012621] James N. Arnold's Vital Record of RI, Vol. XVII, 578.
Reported in the Providence Gazette: "Edward Remington of Providence and Mary A. Smith daughter of Capt. Simeon, of and at Pawtuxet, by Rev. Mr. Shurtleff"
[S013766] Gravestone information at US genweb Archives.