Should the footnote be capitalized? [closed]

The most extensive discussion of footnote capitalization that I've found is in Words Into Type, third edition (1974):

Capitalization. Footnotes ordinarily begin with a capital and end with a period, but occasionally, in a book in which capitals are used sparingly, footnotes may begin with a lowercase letter.

[Examples:]

¹ p. 63

² op. cit.

³ ch. 9

The nature of the notes may make lowercase more logical and appropriate, as in the following from Nineteenth-Century Spanish Plays:

¹ por la posta, "in all haste"

² ab intestato, "intestate," "without having made a will"

Obviously this is only the recommendation of a single style guide, though Words Into Type is widely used in U.S. publishing houses as a style reference. The quoted advice suggests that, if a footnote consists of a phrase or sentence fragment, you need not capitalize it or end it with a period (or any other end punctuation). So in your case, the footnote could look like this:

¹ which is the case for the ambiguous queries

I get the sense that, if you preferred to open the footnote with a capital letter and to end it with a period, Words Into Type would endorse framing the footnote as a complete sentence:

¹ This is the case for the ambiguous queries.

And of course you always have the option of presenting the footnoted content as a parenthetical aside in the running text:

The proposed method is only working well with homogeneous space and it fails if the space is heterogeneous (which is the case for the ambiguous queries).

I have no sources for this, but it should either

• be capitalized, in which case the footnote is an incomplete sentence, because the subject (the word that Which refers to) is missing

  (In this case, the footnote number in the main sentence should come after the period:
  “[…] heterogeneous.¹”, because the footnote is a sentence of its own, and having a full sentence within another full sentence makes no sense.),

or,

• be left uncapitalized, in which case the footnote is a relative clause, where which is referring to the word heterogeneous in the referred-to independent clause.

  Note that in this case the trailing period in the footnote must be removed as well, since the main clause (the non-footnote one) already contains the period.