Bsrgvty

Looking at this it says it's lossless (Wylie Transliteration).

ག ga
ང nga
ཉ nya
ན na

What if you had sequences like ནག (ng, or is it naga)? Is it lossless because we can guarantee that every consonant (or consonant bundle as in some of the letters) is separated by a vowel? (I don't really know Tibetan yet, so please excuse my ignorance).

IAST for Sanskrit is another lossless one.

So we have:

त t
ह h
थ th

There's many more that have this (seemingly) same problem. You can write the same thing multiple ways.

तह th
थ th

So if you had this in the original Sanskrit:

थथथथथथथथ

You would maybe transliterate it as:

thththththththth

Then you might do this to go back:

तहतहतहतहतहतहतहतह

Or any of these combos:

थतहतहतहतहतहतहथ
थतहतहतहतहतहथथ
...

What you end up with is not necessarily what you started with. How do they say this is lossless? Does it have the same property that every consonant/letter is separated by a vowel?

Is there never a "t + h" sound (t followed by standalone "h") in sanskrit, as opposed to a "th" sound (aspirated t)? What if we say there isn't, but then later we discover one? This is where I'm lost, it seems that such systems aren't really lossless.

Can one explain how these are actually lossless? How can you prove that it's lossless, maybe not so far as a mathematical proof, but a thought experiment or something perhaps?

It would also be nice to know which languages have lossless transliterations out there available, I would like to check them out :)

A transliteration system is usually either designed to be lossless, or not. To know whether it is or not, you have to know the target language.

Lossless transliteration systems generally have to use one of four methods to stay unambiguous:

• Don't use digraphs at all. Write every phoneme with a single character: ŋ instead of ng, x instead of kh, þ instead of th, etc.


• Use a letter for digraphs that never appears elsewhere. Some transliteration systems for Russian reserve h for digraph use, so that kh, ch, sh are unambiguous: there's no such thing as an h on its own.


• Use digraphs that are illegal consonant clusters in the language. Ancient Greek (Attic dialect at least) had all of /t/, /h/, and /tʰ/—but transcribing them t, h, th is unambiguous, since /th/ can never occur (depending on your analysis of words like μέθοδος).


• Add a special way to disambiguate between the two. Swahili has both /ⁿg/ and /ŋ/; the former is written ng, the latter ng'. The "library transliteration" of Arabic uses th for /θ/, and t'h for /th/.

The first is sometimes considered cleanest, but tends to very quickly exceed the limits of ASCII.

The second works well for certain digraphs, less well for others: a language with /ŋ/ probably also has /n/ and /g/ already.

The third works great until you discover that your assumptions about what's illegal were wrong! This happened famously in Inuktitut: the orthography was designed with the assumption that the sequence /nŋ/ was illegal, so they use the equivalent of nng for a geminate /ŋŋ/. Except then some lesser-known dialects do have /nŋ/, and they had to retrofit in an awkward solution. Oops.

The fourth is the easiest to retrofit onto an existing system, and is fairly widespread. If you aren't already using the apostrophe for something, it's an easy way to fix pretty much any ambiguities that come up.

Regarding Wylie, the problem you describe is part of the issue noted in the Wikipedia article you linked:

Wylie's original scheme is not capable of transliterating all Tibetan-script texts. In particular, it has no correspondences for most Tibetan punctuation symbols, and lacks the ability to represent non-Tibetan words written in Tibetan script...

I believe the EWTS variant addresses most of the ambiguities, but transliterating to/from Wylie inherently requires knowledge of Tibetan orthographic rules for identification of root letter and which stacks, prefixes, and first- and second-suffixes are valid. For at least a few three-letter words with no vowel mark, the rule is essentially just a special-case for the particular word.

So indeed, this kind of transliteration system is very limited and suffers from the problems you expected. Other transliteration systems like Romaji (at least as I understand it) don't; the difference is ability to preserve character boundaries unambiguously.

Arguably, such transliteration systems are obsolete in the age of Unicode anyway.

Sanskrit is lossless. तह is romanized taha, and there is no cluster th distinct from the aspirated consonant tʰ romanized as th, spelled थ. You omitted virama in your spelling of bare "t", i.e. त्.
You can't later discover that there is "t+h" in Sanskrit because there isn't, though you could wonder, how would the Sanskrit grammarians doing fieldwork on Arabic render the cluster "th". Maybe they would write त्ह. It is possible that problems arise in transcribing grammarian metalanguage, which massively violates the rules of Sanskrit. Since I guess you didn't know that there is no t+h cluster in Sanskrit, that relates to how you'd know if a system is lossless – you have to know the target language, and compare the facts of the language to what you know about spelling. I conjecture that North Saami is lossless w.r.t. pronunciation of written words, up to the point of social indeterminacy (are Norwegian u and y adopted into the language with the same vowel or different vowels?).