Vrachy/macron versions of ancient Greek words?

[spiros]

Where/How can these be found or decided? LSJ appears to use them erratically.

For example:

ᾰ̓ντᾰ́λλᾰγος
ᾰ̓ντᾰλλᾰγή
ἡγεμονῐ́ᾱ
ᾰ̓ποκᾰ́λῠψῐς

ἀνταλλαγή - Wiktionary

[billberg23]

Users of the lexicon often want to know (e.g. for metrical analysis) whether a vowel is long or short. With epsilon, eta, omicron, and omega, the vowels are clearly long or short by nature, so there's no need to label them with a vrachy or a macron.  Alpha, iota, and ypsilon, however, are ambiguous, so LSJ takes the trouble  to label them wherever their quantity in any given word is known.

[spiros]

Well, not all are labeled and the way the diacritics are used is non-standard. For example in Wiktionary you get symbols combining vrachy/macron with accents and breathings. So how can one know the values of ambiguous vowels?

[billberg23]

Not all vowels are labeled because some vowels are clearly long or short by nature.  The ambiguous vowels (α, ι, υ), however, should be labeled. If they're not, it's a mistake or misprint, or the quantity is just unknown. And if an ambiguous vowel is rough or smooth breathing, or accented, then that label should also be affixed above the vowel.  It can get crowded up there, but it's necessary information.
I can't find an instance of failure to label the value (quantity) of an ambiguous vowel. What am I missing?
 Oops, I'm forgetting about "long by position."  When an ambiguous vowel comes before two consonants, it is automatically considered long.  However, if one of the consonants is a liquid, the vowel remains ambiguous, and therefore requires labeling in lexical entries.

[spiros]

Well, the idea behind it is to create an algorithm that would add the necessary values automatically. I.e. the user enters a word without such diacritics and it comes out with vrachy/macron on ambiguous vowels. For this  to happen, all rules and possible exceptions should be accounted for. So, do we know all the rules?

[billberg23]

Rules exist and I think we know those that don't depend on an individual context.  Of course, to determine the quantity of any ambiguous vowel, the researcher has to see the word in a poetic context in an original text; that's the only way to determine ambiguous vowel length.  If we can't find the word in poetry, and the vowel is ambiguous, we're pretty much up a creek.  But those indeterminate words are fortunately few and far between (e.g. neologisms appearing in prose papyri).
So in default of any non-contextual basis for an easy algorithm, we at least have the results of efforts of hundreds of generations of scholars who have been able to derive vowel-quantities from authentic ancient texts.  For 99% of instances, we have certainty, but getting that information requires laborious hand digging for each appearance of an indeterminate value.  You could probably tell me if this has anything to do with the fact that machine translations of ancient Latin and Greek are apparently impossible. Or is vowel length just an extra complication on top of the morphological complexity and arbitrary word order?