Phaistos Disc decipherment claims

Many people have claimed to have deciphered the Phaistos Disc.
The claims may be categorized into linguistic decipherments, identifying the language of the inscription, and non-linguistic decipherments. A purely ideographical reading is semantic but not linguistic in the strict sense: while it may reveal the meaning of the inscription, it would not allow us to identify the underlying language.
A large part of the claims are clearly pseudoscientific, if not bordering on the esoteric. Linguists are doubtful whether the inscription is sufficiently long to be unambiguously interpreted. It is possible that one of these decipherments is correct, and that, without further material in the same script, we will never know which. Mainstream consensus tends towards the assumption of a syllabic script, possibly mixed with ideogram, like the known scripts of the epoch (Egyptian hieroglyphs, Anatolian hieroglyphs, Linear B).
Some approaches attempt to establish a connection with known scripts, either the roughly contemporary Cretan hieroglyphs or Linear A native to Crete, or Egyptian or Anatolian hieroglyphics. Solutions postulating an independent Aegean script have also been proposed.
Linguistic.
Greek.
Hempls readings of side A: A-po-su-la-r
ke-si-po e-pe-t e-e-se a-po-le-is-tu te-pe-ta-po. (Lo, Xipho the
prophetess dedicates spoils from a spoiler of the prophetess.) Te-u-s,
a-po-ku-ra. (Zeus guard us.) Vi-ka-na a-po-ri-pi-na la-ri-si-ta
a-po-ko-me-nu so-to. (In silence put aside the most dainty portions of
the still unroasted animal.) A-te-ne-Mi-me-ra pu-l. (Athene Minerva,
be gracious.) A-po-vi-k. (Silence!) A-po-te-te-na-ni-si tu-me. (The
victims have been put to death.) A-po-vi-k. (Silence!)
"Proto-Ionic".
Jean Faucounau, 1975 considers the script as the original invention of a Cycladic and maritime Aegean people, the proto-Ionians, who had picked up the idea of a syllabic acrophonic script from Egypt at the time of the VIth Dynasty. He interprets the text as "proto-Ionic" Greek in syllabic writing.
Reading A-side first, inwards, he deciphers a (funerary) hymn to one Arion, child of Argos, destroyer of Iasos. The language is a Greek dialect, written with considerable phonological ambiguities, comparable to the writing of Mycenean Greek in Linear B, hand-crafted by Faucounau to suit his reading, among other things postulating change of digamma to "y" and loss of labiovelars, but retention of Indo-European "-sy-" (in the genitive singular "-osyo", Homeric "-oio").
Faucounau has gathered evidence, which he asserts shows the existence of proto-Ionians as early as the Early Bronze Age and of a proto-Ionic language with the required characteristics during the Late Bronze Age. He has presented this evidence in several papers and summarized it in his two books, of 1999 and 2001.
The text begins
Faucounau's solution was critically reviewed by Duhoux (2000), who in particular was sceptical about the consonantal sign "s" (D12) in the otherwise syllabic script, which appears word-finally in the sentence particle "kas", but not in nominatives like "ahamos". Most syllabaries would either omit "s" in both places, or use a syllable beginning with "s" in both places.
Luwian.
Achterberg et al., 2004 interpreted the text as Anatolian hieroglyphic, reading inwards, A-side first. The research group proposes a 14th-century date, based on a dating of PH 1, the associated Linear A tablet. The resulting text is a Luwian document of land ownership, addressed to one "na-sa-tu" ("Nestor"; Dative "na-sa-ti") of "hi-ya-wa" (Ahhiyawa). Toponyms read are "pa-ya-tu" (Phaistos), "ra-su-ta" (Lasithi), "mi-SARU" (Mesara), "ku-na-sa" (Knossos), "sa3-har-wa" (Scheria), "ri-ti-na" (Rhytion). Another personal name read is "i-du-ma-na" ("Idomeneus"), governor of Mesara.
The strokes are read as a 46th glyph, expressing word-final "ti". The text begins