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The phrase "assignment is supported by" is correct and usable in written English.
You can use it when indicating that an assignment has backing or justification from a particular source or evidence.
Example: "The assignment is supported by recent research findings that highlight the importance of sustainable practices."
Alternatives: "the assignment is backed by" or "the assignment is reinforced by".
Exact(6)
Our assignment is supported by a theoretical model based on sixth-nearest neighbour tight-binding and a force-constant approach.
This assignment is supported by the minor presence of an early pinaceous species (Pityites solmsii (Seward) Seward) within the Wealdon deposits [4].
This assignment is supported by the ν NO of 1591 cm -1 reported for 6C ferrous P450 cam-NO.
This assignment is supported by the comparable B factors of the zinc ions (13.6 Å) with the overall average B factor of 18.4 Å for protein atoms (Table 1).
This assignment is supported by H ENDOR data, presented in Figure S8, Supporting Information, which exhibits a strongly coupled doublet, exchangeable in D2O, with Amax = 12 MHz, characteristic of the hydroperoxy ligand.
This assignment is supported by several independent lines of evidence: Firstly, members of a particular subgroup show higher amino acid sequence identities to one another than to members of other subgroups (Fig. 6).
Similar(54)
This assignment was supported by H NMR analyses.
We calculated the percentage of cases in which Affymetrix gene assignment was supported by the GeneAnnot gene assignment.
This assignment was supported by subsequent Pronase digestion and ES-MS and ES-MS/MS identification of the sVSG221 glycopeptides (Supplementary Table SIV; Supplementary Figure S3A).
This assignment was supported by NOEs including C N 4 H2 → C N 4 H1, C N 4 H2 → C H5, C N 4 H1 → C H5, and C H5 → C H6.
This assignment was supported by observation of an NOE cross-peak to A H2. NOE cross-peaks for base pairs C·G, T·A, A·T, G·C, C·G, X·C, A·T, G·C, T·A, and C·G were observed.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com