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"absolutely binding" is correct and usable in written English.
You can use it to emphasize that an agreement or promise is very strict and must be adhered to. For example, "The terms of the contract were absolutely binding and could not be broken."
Exact(11)
"But even a previously expressed desire in a will is not absolutely binding on the court".
For a specific date to be absolutely binding, it must be stated in the contract that "time is of the essence".
on the part of the executive department, acquiesced in by the legislative department, while not absolutely binding on the judicial department, is entitled to great regard in determining the true construction of a constitutional provision the phraseology of which is in any respect of doubtful meaning.
Those cases show that the House will not treat as absolutely binding any line of reasoning in a previous case which was not necessary to the decision: but will regard itself as at liberty to depart from it if convinced that it was wrong.' Penn-Texas Corp. v. Murat Anstalt (1964) 2 Q.B. 647, 661.
It conceives of these principles as being prima facie (i.e., not absolutely) binding and lacking any a priori lexical ordering among them.
Second, pure general logic is absolutely binding on any rational human thinker and provides an unconditional logical ought: the laws of logic are the categorically normative laws of thought for all actual and possible rational animals.
Similar(49)
If a drug were absolutely selective, binding at only one receptor (e.g. salvinorin A), it would have the minimal B value of 4, regardless of the absolute affinity of the drug for its one receptor.
We instead found that amino acids 88 93 were absolutely required for binding of L22 to both EBER-1 and 28S rRNA SL7.
Determination of the IC50 using the truncated competitor peptides demonstrated that the 3-10 helis is absolutely essential for binding to PA, since any truncation of this sequence resulted in no competition (Fig. 2B).
Several studies have suggested that the presence of negatively charged phospholipids is absolutely required for binding [17] [19], but others have shown that neutral zwitterionic phospholipids are also able to bind the peptide [20], [21].
Of these, only a single basic amino acid, an arginine, was absolutely required for binding.
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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