I have came across your point and claim that ‘proof’ is exclusively for mathematics or syllogisms but I have never taken that seriously.
I don’t think it is necessary to be that pedantic about it.
In any case I qualified my ‘proof’ to within the Scientific Framework to provide context and to avoid confusion.
I notice ‘proof’ is not exclusively for only mathematics & syllogism.
There are contexts below where ‘proof’ is related to evidence, i.e. Science, Law, theology, philosophy [non-logic situations] and in general.
One of the most common use of ‘prove’ and ‘proof’ is with reference to the existence of God and this is ‘evidence’ [absence of] related.
Here is a list of related context where ‘proof’ is acceptable.
(note not all are relevant to our point but many [bolded] are]
en.wikipedia.org/wiki/Proof
Proof may refer to:
Proof (truth), argument or sufficient evidence for the truth of a proposition
Formal proof
Mathematical proof, a convincing demonstration that some mathematical statement is necessarily true
Proof theory, a branch of mathematical logic that represents proofs as formal mathematical objects
Alcohol proof, a measure of an alcoholic drink’s strength
Artist’s proof, a single print taken during the printmaking process
Galley proof, a preliminary version of a publication
Prepress proof, a facsimile of press artwork for job verification
Proof coinage, coins once made as a test, but now specially struck for collectors
Proofreading, reviewing a manuscript or artwork for errors or improvements
Proofing (baking technique), the process by which a yeast-leavened dough rises, also called “proving”
Law[edit]
Evidence, information which tends to determine or demonstrate the truth of a proposition
Evidence (law), tested evidence or a legal proof
Legal burden of proof
dictionary.com/browse/proof?s=t
noun
- evidence sufficient to establish a thing as true, or to produce belief in its truth.
2.anything serving as such evidence:
What proof do you have?
3.the act of testing or making trial of anything; test; trial:
to put a thing to the proof.
4.the establishment of the truth of anything; demonstration.
5.Law. (in judicial proceedings) evidence having probative weight.
6.the effect of evidence in convincing the mind.
7.an arithmetical operation serving to check the correctness of a calculation.
adjective
18.able to withstand; successful in not being overcome:
proof against temptation.
19.impenetrable, impervious, or invulnerable:
proof against outside temperature changes.
20.used for testing or proving; serving as proof.
21.of standard strength, as an alcoholic liquor.
22.of tested or proven strength or quality:
proof armor.
23.noting pieces of pure gold and silver that the U.S. assay and mint offices use as standards.
verb (used with object)
24.to test; examine for flaws, errors, etc.; check against a standard or standards.
25.Printing. prove (def 7).
26.to proofread.
27.to treat or coat for the purpose of rendering resistant to deterioration, damage, etc. (often used in combination):
to proof a house against termites; to shrink-proof a shirt.
28.Cookery.
to test the effectiveness of (yeast), as by combining with warm water so that a bubbling action occurs.
to cause (especially bread dough) to rise due to the addition of baker’s yeast or other leavening.