The phrase "with a rigor" is correct and can be used in written English.
It is typically used to indicate something is done with strictness or precision. Example: The students were expected to approach their research papers with a rigor, ensuring that all sources were properly cited and the arguments were logically sound.
Ratzinger had earned derision in his nearly 25-year role as Prefect, during which he'd enforced Church doctrine with a rigor that many Catholic theologians found chilling.
She described Dr. Beck as a voracious reader of scientific studies and agency reports, diving deep into footnotes and scientific data with a rigor matched by few colleagues.
"In the common fashion, he'd set out believing cows were big and dumb when, it turned out, they were dumb first and with a rigor he'd not expected".
The film could have been the merest mush, yet it is cut and spliced with a rigor that fights the sentimental.
Her precedents include Matisse, Miró, Stuart Davis and Alexander Calder, but she explores her chosen terrain with a rigor that is very much her own.
When not searching for loved ones or batteries, a group of survivors commit "Cape Feare" to memory with a rigor that would do the manuscript-copying monks of Ireland proud.
It has always replicated, in its own way, the dynamic of America itself, a nation where some came to make a fresh start with a new rigor and others came to free themselves from rigor.
Lockstep suburban conformism enforced with a fascist rigor is the ugly (but admittedly sometimes funny) joke driving this family comedy.
The scholars engaged black death in the digital with a deliberate rigor and care for black life.
The Nikisch Beethoven Fifth - one of three Beethoven Fifths in the collection - is a justifiably famous performance, balancing a freedom of pulse with a fine rigor of dramatic exposition.
The two young architects quickly made a name for themselves with designs that treated regional motifs boldly with a modernist rigor.
