In this context, "affirmation de la qualité héréditaire" translates as "affirmation of hereditary quality" because it refers to the acknowledgement of the hereditary rights or status of an individual, as stated in an act of notoriety.

Example sentences:
1. The act of notoriety included an affirmation of hereditary quality, recognizing the individual's rights as an heir.
2. The court requested additional documentation to support the affirmation of hereditary quality in the probate case.
3. In accordance with the law, the act of notoriety confirmed the hereditary quality of the individual, securing their rightful inheritance.

First off, I have always been given to understand that in English legal documents titles such as this have no legal standing, being there just to guide the reader through the document. They simply evoke what is to follow.

In such cases, one must be careful to introduce into the following body text the missing words that might be necessary for the full meaning to slot into place. At this point, therefore, you needn't worry about attestation which may, or may not, come later.

Now, the actual text in question ... I have always seen this as preuve de la qualité d'héritier. I imagine someone has at some time, probably later rather than sooner, seen fit to call this into question, for there are two points that might cause problems.

Héritier ould wonce have been deemed to have covered the female, if I may speak animalistically. Not so today, so instead of qualité d'héritièr.e we have qualité hériditaire, which to my mind at least makes a mockery of French grammar, but be that as it may be.

Secondly, I think it entirely possible that preuve had to be done away with since it suggests something definitive, absolutely certain, unquestionable. Affirmation is less certain, I think.

There is no shortage on the Ouèbbhe of examples of 'status of heir', very many of them being on EU and, strangely, German embassy sites across the world, but I give below a triple of examples in ze muzzer tong.

However, this doctrine does not grant individuals full rights of inheritance and does “not change [an individual’s] status as heir;
https://law-hawaii.libguides.com/c.php?g=939506&p=6771015

Upon the death of an ancestor, one just “becomes” an heir. Hence, for example, without a “slayer’s statute,” a murder victim’s property may pass by will or intestacy to his murderer, so separate is the killer’s status as heir or devisee from the circumstances that caused that expectancy to vest
https://law.lclark.edu/live/files/3455

The Green Paper also considered ways of removing certain administrative and practical obstacles facing individuals wishing to have their status as “heir” recognised across Europe. The idea of establishing a “European Certificate of Inheritance” was mooted.
https://publications.parliament.uk/pa/ld200708/ldselect/ldeu...




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Note added at 12 hrs (2023-12-26 23:22:11 GMT)
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Sorry, slip of the fingers. Read first above not 'status of heir' but 'status as heir'.

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Note added at 1 day 5 hrs (2023-12-27 16:28:32 GMT)
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While the ngram below does not show that qualité d'héritierhas been superseded by qualité héréditaire, it does show that usage of the former has declined while use of the latter has remained stable (and hence risen proportionally against the former).

Given that it is the heading of a paragraph, this seems appropriate.