Are standard functions in Calc defined by the Open Document Spreadsheet definition?

For the sake of document longevity, I was wondering if the functions in Calc are defined by any standards or that they are specific to the implementation of LibreOffice (and/or OpenOffice). If they are, it should not matter with what software (version) formulas in spreadsheets are written.
If they are not standard functions, or if not all functions are standardised, how can users ensure formula output is usable across ODS implementations and durable over the longer term?

As Regina told! But there are possibly flaws in the implementation that will be fixed some day changing the behaviour of a formula depending on the “erroneous” variant. There are also some specifications I would judge unclear. And there are some standard functions specified explicitly allowing for implementation dependent behaviour. You might need to study the relevant parts of the document Regina linked to.

Almost all functions are defined in the standard ODF 1.2 part 2 OASIS Open Document Format for Office Applications (OpenDocument) Version 1.2 - Part 2: Recalculated Formula (OpenFormula) Format Only few functions, e.g. EASTERSUNDAY, are special functions of LibreOffice/OpenOffice.

For a longtime archive you should not use .ods file format but PDF/A-1a.

I’m sure no standard has anything to do with the functions. Instead, the formulas are saved in the file as is and the program executes them.

The formulas are saved together with the current values, so when opening a document ‘read-only’ you see the values of the producer. In newer versions of LibreOffice you have a special option in Tools > Options > Calc > Formula to disable the recalculating on opening.