Language scratchpad/Altlangs/Alternate reconstructions/Proto-Indo-European scratchpad

This is just a compilation of some of the theories I have about Proto-Indo-European. They may not be accepted, correct, or even consistent.

One of my main sources is Miguel Carrasquer Vidal (https://independent.academia.edu/MiguelCarrasquerVidal), whose internal reconstructions of pre-PIE have interested me. However, he is a Nostraticist (i.e. a supporter of the Nostratic macrofamily comprising, among others, Indo-European, and not a generally accepted position), so a bit of scepticism is ideal (my own opinion on Nostratic is that it is plausible but unprovable, since reconstructing such a large and long-lasting family is beyond the limits of historical linguistics; at that time span there is a high signal-to-noise ratio).

Disclaimer: The entirety of this article's contents is to be considered science fiction. They are not, in any way, verified and accepted reconstructions of real-life proto-languages, even if they are largely based on accepted reconstructions.

Consonants
The general consensus is that 25 consonants can be reconstructed for Proto-Indo-European, although one (*b) is marginal. I will list them below, along with my reconstruction of their possible phonetic value:

There is considerable debate as to the actual phonetic values of many of these consonants. While the phonetic values of the resonants (and to a lesser extent, */s/) are largely uncontroversial, the stops pose a significant problem.

Dorsals
Traditionally, three series of dorsals are constructed: the "palatal", the "plain velar" and the "labiovelar" series. The satem languages exhibit a shift of the palatal series to a sibilant-like pronunciation, while the centum languages merge the palatal series with the plain velar series. Because of the shift of the palatal series and the fact that plain velars were low in frequency, the labiovelars all but merged with the plain velars in the satem languages, although remnants of a previous labiovelar series can be found. On the other hand, the merger of palatals and plain velars in the centum languages was complete and utter, and no trace of PIE palatals can be found in any attested centum language.

Personally, I do not believe that the plain velar series was, in fact, velar. Owing to its low frequency, I believe that it represents uvular consonants, which are considerably more marked than velar consonants. There may have also been a labiouvular series, but any distinction between it and the labiovelar series cannot be reconstructed for PIE, if it existed at all. As such, I reconstruct the labiovelar series as having both velar and uvular realisations.

The interpretation of the plain velars as uvular allows me to interpret the palatals as proper velar consonants. It most likely had palatal stops as allophones before */e/ and */i/, which contributed to satemisation due to the prevalence of */e/.

Sibilants
In general, one sibilant (*/s/) can be confidently reconstructed. However, an analysis of the satem languages suggests that there may be up to two more sibilants, which I tentatively reconstruct as */ɕ/ and */ʃʷ/. Existence of the latter is, from my own research, plausible, based on Armenian /kʰ/ (e.g. k'oyr, from *swesōr) and the varying reflexes of "six" in the daughter languages, but I still do not fully accept */ɕ/, and its relation to the ruki sound law.

Vowels
Proto-Indo-European is generally reconstructed as having only two or three proper vowels (*/e/, */o/, */a/), with the other vowels being vocalic allophones of the resonants and laryngeals. The reconstruction of */a/ is disputed; some scholars suggest that */a/ never existed, while others do accept the existence of a phonemic */a/.

I cannot be certain regarding the phonetic realisations of the vowels */e/, */o/ and */a/, but I can make an attempt. I posit three phonetic lengths, corresponding to two phonemic lengths.

I do not posit laryngeal colouring of long */eː/; only the short version was coloured. I suggest the following:

I reconstruct overlong vowels for *ā and *ō (which would have only arisen by Szemerényi's and Stang's laws) to account for the overlong vowels in Germanic and Balto-Slavic. In comparison, the original long vowels would have become short vowels before laryngeals, and only had their original length restored via compensatory lengthening from the loss of the laryngeal. The vowel *a may have been two vowels, differing only by length, but the distinction, if it existed, did not survive in any recorded language. I do not reconstruct long versions of *i and *u, although I suspect that the diphthong *ωw was phonetically *[uː].

Ablaut and accent shift
A prominent feature of Indo-European languages is ablaut. This involves changing the vowels of the stem to denote inflection or derived forms. Ablaut is associated with the shifting of the accent.

In the earliest forms of the protolanguage, the following accent paradigms are posited:

There is considerable debate as to whether the accusative had a different accent location than the nominative (as posited by the Leiden model). In addition, I do not know wheter static paradigms existed in Pre-PIE, due to how I reconstruct the oblique cases.

The generally accepted model is the Erlangen model, and the other major model, the Leiden model, is said to represent an earlier stage of the language. The Erlangen model is described below:

Contrary to typical reconstructions, Vidal does not reconstruct the Narten-type ablaut as ḗ ~ é (instead, he constructs it as a proterokinetic/amphikinetic paradigm rather than an acrostatic paradigm). He postulates, based on developments from Pre-PIE, the following developments from the proterodynamic paradigm:
 * *é ~ *Ø
 * *ó ~ *é
 * *ώ ~ *Ø
 * *ḗ ~ *Ø

(Note: the *ω Vidal reconstructs is supposed to represent a PIE phoneme that corresponds to /o/ in Italic (Latin nox) and Celtic (Old Irish nocht), but /u/ (→ /y/) in Greek (νῠ́ξ, núx) next to labials, as opposed to normal */o/, which is reflected as /o/ in all branches that retain it as a separate phoneme. I typically reconstruct *ω as *[o], and *o as *[ɔ], with the difference neutralised when lengthened.)

Vidal postulates that the Pre-PIE accent shifted one syllable right in the oblique cases, and that this accent shift contributed to the formation of ablaut. The ablaut grade obtained depends on the vowel of the root (Vidal assumes a three-vowel system with **/a/, **/i/ and **/u/ with vowel length) and the weight of the root and suffix. The ultimate developments of these stems is fairly complex, and I won't list them here. However, I will list the various examples he has given:

The noun *múh₂s ("mouse", feminine) is an enigma when it comes to ablaut and accent. While amphikinetic, it does not display any root ablaut, retaining an invariant */u/ (Nouns with root */a/ are expected not to show root ablaut, but */u/ is expected to form a diphthong or a glide). In most languages, it is represented as a long vowel, but the short vowel in Vedic Sanskrit and the oblique forms in Greek are unexplainable with the given reconstruction (the short vowel in Latin musculus "muscle" is expected). Vidal suggests that the differences emerged from Pre-PIE processes, giving late Pre-PIE **mū́sʷ (nominative) and **mʷsés (genitive), which would regularly give *mώs- and *m̥sés. My own Pre-PIE reconstruction is **mūws-, which would give *mus- in the oblique.

The following ablaut patterns are observed by Vidal:

For verbs, we can assume the following developments (for simplicity I leave out the dual):

In general, imperfectives are 3:3 strong to weak (strong singular, weak plural), while perfectives are 5:1 (strong singular and 1-2p, weak 3p). However, some verbs may be 3:2:1 strong to weak to strong (strong singular and 3p, weak 1-2p). Additionally, in the first and second person plural imperfective forms, the ending always attracts the accent, which may lead to shortening of the newly-unaccented vowel. However, there are exceptions (the s-aorist is 3:3, contrary to normal perfectives; this is because the ablaut of the s-aorist is not the result of accent shift but rather an analogised sound change).

Nominals
In general, I confidently reconstruct eight cases, and tentatively a ninth.

Case endings
In general, I reconstruct the athematic endings as follows:

The instrumental *-d is attested in the Anatolian languages (e.g. Hittite -at/-it); in all other attested languages, it has morphed into *-h₁ (e.g. Vedic Sanskrit -ā). The allative is only attested directly in the Anatolian languages (e.g. Hittite -a, -aḫ-), but is found in fossilisations in other languages, reflecting post-PIE *-ā or *-ō.

The above case endings preserve elements of an earlier agglutinative system. The *-bʰi- in the oblique plural forms is most likely an adverb that attached to the nominal, and there is suggestion from the Anatolian languages that there were two genitives *-os and *-om, the former becoming the singular and the latter becoming the plural in post-PIE. The dual, as is known in Indo-European historical linguistics, is an enigma, and I won't elaborate any further here.

While the ablative singular has syncretised with the genitive singular, it is possible that it was originally *-d (compare the thematic and pronominal declension), identical to the instrumental singular.

As such, I posit the following case system for pre-PIE:

I won't go into details on what I think is the morphosyntactic alignment of pre-PIE, but it's likely that whatever it had became the two-gender system found in early PIE, with neuters not distinguishing between the nominative, vocative and accusative. The general plural marker is **-sʷ, while the dual is **-xʷ.

Vidal posits, for early pre-PIE, a simple three-case distinction (zero, **-u, and **-i/**-a for the absolutive, nominative-ergative and accusative-oblique respectively). These endings were utterly lost in late pre-PIE, so additional pronominal elements of the appropriate case were added (**-t-u for the nominative, **-mw-a → -**mʷa for the accusative). These, of course, evolve into the familiar *-s and *-m endings of PIE (the former via **-tʷ → *-sʷ; the **-ts(ʷ) I posit is a possible intermediate). On the other hand, the original early pre-PIE system is partially preserved in the personal pronouns and the verbal system:

As such, the case endings would have developed as follows:

By comparison, here are the endings that would have been obtained had no remodeling occurred:

Thematic stems
Vidal (2014) suggests that thematic stems are a conflation of three different ways of forming fully inflected nominals. In general, the theme vowel, which he reconstructs as **-ā, is added to the root, and standard endings follow. However, it is instead possible that pronominal endings are added, either to the theme vowel, or directly to the root. Here are the combinations he has given (albeit modified):

The allative singular, if it existed, likely developed in the same way as the instrumental singular, except with the change **-g → *-h₂.

Interestingly, from looking at the above table, I can reconcile the differences between nominals and verbs with regards to the form of the thematic vowel. Verbs have */o/ before voiced consonants and */e/ word-finally and before voiceless consonants, but nouns have */o/ everywhere except the neuter plural (*-eh₂) and the vocative (*-e), even where */e/ would be expected due to being followed by a voiceless consonant. My observation is that the singular oblique endings, the dual endings and the nominative and genitive plural endings all began with a vowel, and this fulfils the "voiced" requirement for the thematic vowel to become */o/. The phoneme **/xʷ/ (→ *-h₃) is also considered voiced, and thus induces the formation of */o/.

eh₂-stems
The eh₂-stems are a derivative of thematic stems, basically the thematic vowel combined with the feminising marker *-ih₂. Because, unlike the o-stems, this suffix may have mobile accent, Vidal posits two separate eh₂-stem classes. One has *-eh₂- throughout the paradigm, and the other has *-oy(é)h₂- in the oblique cases and a vocative *-oi. Evidence for the latter paradigm can be found in Sanskrit (only in the singular), the Slavic languages (in the pronominal paradigm and the instrumental singular *-ojǫ ← *-oyh₂éh₁), and possibly Germanic (in the strong adjective declension in the plural).

Full declension
This is my reconstruction of the entirety of the thematic declension:

i-stems and u-stems
Vidal suggests that the i-stems and u-stems are actually a conflation of two different declensional classes each. In addition to the original vowel stems, there were also in-stems and un-stems, which survived vestigially in Sanskrit (in n-infixed inflectional forms in the i- and u-stems and in the generalised genitive plural -nām) and Armenian (nouns that end in -r in the nominative/accusative and -u(n)- in the other cases). An example in Vedic Sanskrit is dā́ru ("tree", from *dorur), whose genitive is drúṇas, which can only come from a protoform *drunós → *drunés. Another Sanskrit example is mádhu ("honey", from *médʰur, cognate with Armenian mełr), whose oblique stem is mádhun- (the expected oblique form is *adhun-, from *m̥dʰun-, but the root ablaut has been lost). The lack of word-final -r in the Sanskrit forms is expected (compare pitā́, the nominative singular of "father", which itself comes from *ph₂tḗr).

Theoretically, the i-stems and u-stems had different declensional patterns depending on the accent class of the noun (acrostatic, proterodynamic, hysterodynamic). However, analogy has largely affected the hysterodynamic paradigm, merging with the proterodynamic for the i-stems and either merging with the proterodynamic or becoming o-stems for the u-stems.

i-stems
The following is my reconstruction of Early PIE i-stems (dual omitted):

Personal pronouns
The PIE personal pronouns have posed problems with their reconstruction, owing to their variety in the daughter languages. At most, four cases can be confidently reconstructed for the personal pronouns (the nominative, accusative, genitive and dative), and in addition, up to two clitic forms per person/number combination can be reconstructed.

Here are my reconstructions of the personal pronouns (not including the dual):

As is apparent from above, the personal pronouns do not follow any "normal" declensional pattern.

Cardinal numbers
Here is my reconstruction of the cardinals:

Based on evidence from Armenian, Greek and Balto-Slavic, Vidal reconstructs the numeral "nine" as *h₁(e)dʰ-néwn̥. This follows from the following: While analogy in Slavic and East Baltic (with "ten") cannot be ruled out (compare the analogical /kʷ/ → /p/ change in *kʷetwóres in Pre-Germanic, influenced by *pénkʷe), the Armenian and Greek evidence may suggest this alternate reconstruction, along with Proto-Balto-Slavic *dnewin.
 * Pre-Armenian *enun (whence Old Armenian inn); syllabic *h₁ would have given *a-
 * Greek ἐννέα ennéa (← *ἐννέϝα *ennéwa, from Proto-Hellenic *ennéwə), where *h₁néwn̥ would have given *ἐνέα *enea ←  **ἐνέϝα **enewa ← **enéwə
 * Proto-Slavic *devętь and Lithuanian devyni, where *h₁néwn̥ would have given **nevętь and *nevyni respectively

Vidal also notes that "nine" is the only exception to the change of word-final */n/ to */r/ he can find. What should be noted is that this change does not occur after */m/, meaning that a preform could have ended in **-mn̥, and that it dissimilated into *-wn̥. The neuters in *-mn- do not undergo this change, but it is possible that the *-mn- was reinforced by inflected forms in *-mén-, reversing or preventing dissimilation.

The element *h₁dʰ- bears some explaining. Vidal states that it means "one", and may be attested in the following:
 * Armenian ez "sole, only" (from *h₁edʰ-)
 * The Hittite pronominal declension (e.g. genitive -ēd-as); compare the -sm- endings in the non-Anatolian pronominal paradigm, believed to be from *sem-
 * Proto-Slavic *edìnъ "one" (from *h₁edʰ-(H)iHnos)

As such, Vidal posits that "nine" ultimately originates from *h₁édʰ ném-n̥ ("one taken") from the roots *h₁edʰ- ("one") and *nem- ("to take").

Here are my etymologies for the numbers:
 * 1: *(H)óy(H)(n/w)os is of pronominal origin, from the anaphoric *h₁e-/*h₁i- (which Vidal believes also contributed to the thematic declension) combined with *-wos/*-nos. In general, the form with */n/ is inherited, with the form with */w/ being present only in Greek and Indo-Iranian (note that Greek also inherited the */n/ form); there is a form with */k/, but it is unique to Indo-Aryan (*Háykas). A possible Pre-PIE form is **hā́j-fun-ā-.
 * Pre-PIE ergative: **hā́jfunā-u-tu
 * Pre-PIE accusative: **hā́jfunā-a-mua
 * Pre-PIE intransitive: **hā́jfunā
 * 1: *sḗm is the root adjective of *sem- ("one"), and it is found in Armenian, Greek and Tocharian. Derivatives of the root, however are found in all branches (the English word some also comes from this root, as well as the prefixes semi-, from Latin, and hemi-, from Greek). It may also form part of the pronominal declension outside of Anatolian. Using Vidal's Pre-PIE reconstructions, I posit a preform **sum-.
 * Pre-PIE ergative: **súm-u-tu
 * Pre-PIE accusative: **súm-a-mua
 * Pre-PIE intransitive: **súm
 * 2: *dwóh₁ comes from the root *du-, which may also feature in the numeral "ten". I also reconstruct this root for Pre-PIE (**du-), and presume a thematic vowel (**du-ā-).
 * Pre-PIE ergative: **duā́-iku
 * Pre-PIE accusative: **duā́-iki
 * Pre-PIE intransitive: **duā́-iŋ
 * 3: *tréyes comes from the root *trey-. The feminine *tisres is *tri- (the zero grade) suffixed with *-sōr, with the first */r/ lost. Reconstruction of the accent of *tisres has proved problematic, as a stress on the ending (like in Vedic Sanskrit) is highly unusual for PIE, and no other language that preserves this form preserves accent information. My presumption is that it was originally a hysterodynamic **t(r)éysres, and that the first */e/ was lost before it could transition into a holokinetic paradigm. However, if Vidal is correct, then a reconstruction **tri-sár-abʰV will result in first **tri-sár-âbʰV, then shifting of the accent and pretonic vowel loss will result in **trʲsrám → *tisrém → *tisrḿ̥ (whence the standard accusative *tisrḿ̥s, by addition of the generalised plural ending *-sʷ), thus explaining both the loss of */r/ in the root (via palatalisation) and the ending accent (which may have been analogically extended to the nominative). Hypothetically, the nominative could have developed as **trí-sar-zsʷ → *tré(y)sres, but no such form is attested. For Pre-PIE, I reconstruct **tri(j)-. Other preforms I may reconstruct include **trin- (Vidal suggests that some i-stems developed from Pre-PIE in-stems), which might be evident in Sanskrit trīṇi, and maybe even **tnin-. A more radical proposal I have is that the numeral consists of a root **tir- followed by **-in or **-ī in the masculine and neuter.
 * Pre-PIE ergative: **trij-ábʰu
 * Pre-PIE accusative: **trij-ábʰi
 * Pre-PIE intransitive: **trij-ám
 * Pre-PIE collective: **tríj-x?
 * Pre-PIE feminine ergative: **tri-sár-abʰu
 * Pre-PIE feminine accusative: **tri-sár-abʰi
 * Pre-PIE feminine intransitive: **tri-sár-am
 * Regarding the **tir- followed by **-in or **-ī forms, I posit the following:
 * Combining form: **tir-ī-Cá-' → *tri-Cé-
 * Masculine nominative: **tir-ī́+tu+tu → *trḗ(y)+sʷ+sʷ → *tréyes
 * Masculine accusative: **tir-ī-ábʰi+tu → *tryém+sʷ → *tríms
 * Neuter: **tir-ī+x → *tri+x → *tríh₂
 * 4: *kʷetwóres comes from the root *kʷet- with *-wōr suffixed. The feminine instead uses the suffix *-sōr, like with the previous numeral. A peculiarity is that */e/ is preserved throughout the paradigm; this may be because an initial cluster *kʷt- may be awkward to pronounce, leading to an epenthetic */e/; however, Proto-Albanian *kátur (whence Albanian katër) may preserve the zero grade *kʷtur-. For Pre-PIE, I reconstruct **(k/q)ut- (most likely **kut-).
 * Pre-PIE ergative: **kut-wár-abʰu
 * Pre-PIE accusative: **kut-wár-abʰi
 * Pre-PIE intransitive: **kut-wár-am
 * Pre-PIE collective: **kut-wár-x
 * Pre-PIE feminine ergative: **kut-sár-abʰu
 * Pre-PIE feminine accusative: **kut-sár-abʰi
 * Pre-PIE feminine intransitive: **kut-sár-am
 * 5: *pénkʷe may be a formation from a root *penkʷ- (meaning unclear, but relates to the hand). Germanic preserves the zero grade (English fist, from Proto-Germanic *funstiz). For Pre-PIE, I tentatively reconstruct **pánkū (**púnkū is also valid).
 * 6: *(s)wéḱs is somewhat problematic. The initial may vary between *sw- and *s-, and possibly *w- (in Armenian and possibly Greek). Tentatively, I reconstruct for Pre-PIE **súks.
 * Vidal suggests that this might be a borrowing from Semitic, suggesting that an early Akkadian form *šidš (from *šidṯ-, */ʃidθ-/) yielded *sʷetsʷ → *swéḱs. I find this derivation suspect, unless one fully accepts the hypothesis that PIE *sʷ was phonetically */ʃʷ/ and that the Akkadian protoform truly had *[ʃ] (instead of [s], with which it merges in later language). A direct borrowing assuming *[s] would result in Pre-PIE **síts ~ **síks, which does not fit the attested PIE form.
 * 7: *septḿ̥ may be a loanword from Semitic *šbʿ-t- (*sabʕatum, "seven", feminine). A possible preform is **sabatúm, yielding **sptém (with **/t/ delabialised by the labial **/p/), which of course evolved into *septḿ̥.
 * 8: *(h₁)oḱtṓw is derived from a dual form. The original root may be *Heḱ-, whose thematic nominal *Hoḱtós ("breadth of four fingers", whence Avestan ašti-) gave the numeral. Some linguists reconstruct the initial as *h₃e-; I am not sure which one is correct, although the stress on the thematic vowel suggests to me that the initial laryngeal is unreconstructable. A possible preform is **fak-, with the ultimate PIE form originating from *fak-at-ā́-ikV, assuming vr̥ddhi derivation (via **fəkətā́H → **fə̄kətā́H → *h₃oḱtóH). An alternate root, also assuming vr̥ddhi derivation, is **hak-, which would yield *h₁oḱtóH
 * 9: *(h₁)néwn̥ is also problematic. Vidal suggests *h₁(e)dʰ-néwn̥, from *h₁édʰ ném-n̥. A possible Pre-PIE form is **hádʰ náman.
 * 10: *déḱm̥(t) is derived from the root *ḱemt- ("hand"). The initial */d/ represents *du-, from "two". A possible Pre-PIE form is **dú-kamt. Its dual most likely had the accent on the ending, deriving from **du-kamt-íki and becoming *-h₁km̥tih₁. The plural form *-h₁kómth₂ is a collective derived from **du-kā́mt-x (which might have been expected to become *-h₁káth₂, but changed to *-h₁kómth₂ by analogy with *déḱm̥(t) and collectives ending in *-óCCh₂; the *-h₁káth₂ form might be preserved in Indo-Iranian, with Sanskrit -śát and Avestan -sat showing no nasal, although analogy from the dual form, whose lack of a nasal is expected, cannot be ruled out).
 * 100: *ḱm̥tóm is derived from *ḱemt-. A possible Pre-PIE form is *kamt-ā-.

Agreement endings
Vidal (2015) gives a description of the possible origin of the person and number endings. In general, they are split into active, stative and middle endings.

Active
In general, the singular and the third person plural forms are easy to reconstruct:

Vidal is, so far, the only linguist I know who explains the post-PIE thematic first person singular form *-ō without reference to a laryngeal. Traditionally, this is reconstructed as *-oh₂, with the typical explanation being that the laryngeal was imported from the stative set (*-h₂e). However, Vidal suggests that a preform **-ā-mu (where **ā is the theme vowel) became **-ā-mʷ, and with the addition of the hic-et-nunc particle *-i, **-ā-mʷ-i. This would then become **-āwi → *-owi → *-owu, which becomes *-ōw in Pre-Tocharian and *-ō in the other branches. However, this does not explain the *-ō ending in Germanic (PIE *-ōw would have become *-ōu in Proto-Germanic, while *-ō would have become overlong *-ô; the only sources of Proto-Germanic *-ō are *-oH, *-aH, *-eh₂ and *-eh₃). *-ô cannot be reconstructed for Proto-Germanic as Gothic shows -a, which can only come from *-ō or *-ai (*-ô would have yielded Gothic -ō). So far, I have yet to reconcile this discrepancy (a protoform *-owo would yield Proto-Germanic *-au, as per the loss of word-final */o/, which would lead to Gothic -au; the same goes for *-owu → *-awu → -au, and *-owi would lead to *-awi → -au). It is possible that a preform *-owi became *-oi (yielding Proto-Germanic *-ai), and this is what was inherited in Gothic, although it cannot explain Old High German and Old English -u and the Old Norse zero ending (but it can explain Old English -e).

What I believed happened in Germanic is that PIE *-owi became PG *-ai, leading to syncretism between the active and passive in the first person singular (I hypothesise that the passive form was also *-ai). The different branches resolved this differently. The East Germanic languages, including Gothic, resolved this by extending the third person singular to the first person in the passive (compare the syncretism between the first and third person forms in the passive plural, which was analogically extended to the second person), while the North and West Germanic languages instead extended the active ending to *-ōi (probably from the second weak conjugational class), which regularly yielded Old High German -u, Old English -e and -u (depending on dialect), and Pre-Old Norse *-u (which appears as u-umlaut in Old Norse).

With regards to the third person plural, Vidal suggests that there would also be an ending *-(é)s ← **-(é)sʷ ← **-át-u, but it has been utterly lost in the verbal paradigm. Other alternate endings are listed below: The other forms pose problems. Here I will list expected forms:

Hittite preserves the first set, in the process merging the dual and plural (1p: -wen(i), 2p: -ten(i), 3p: -anzi). The non-Anatolian, non-Tocharian languages, on the other hand, use the second set for the first and second person (e.g. Vedic Sanskrit -masi, -mas, Ancient Greek -te), which does distiniguish between the dual and plural, and the third person dual endings are imported from the middle set (no ending **-íh₃t is attested anywhere).

Stative
Here are the stative endings:

Hittite and Tocharian seem to show a second person plural form *-s- (Hittite -steni, Tocharian -s).

Middle
The middle, according to Vidal, is even more complex. In general, the middle endings begin and end with the following:

He then gives a table showing the pre-PIE middle conjugation, assuming the endings (which become divergent tense markers in the daughter languages) denote the indirect object:

Tense, aspect, mood and voice
The traditional reconstruction of the PIE verbal system is the Cowgill-Rix system, which splits the entirety of the verbal lexicon into three different aspects: the imperfective (traditionally called present), the perfective (aorist) and the stative (perfect). Note that I said "splits the entirety of the verbal lexicon"; this is because verbal aspect is a lexical property (similarly, Slavic verbs may either be inherently imperfective or perfective), and derivation is required to obtain the other aspects. As a consequence, there may be multiple forms for the same aspect and meaning, or none for a particular aspect and meaning.

PIE does not have a particularly developed tense system. In general, tense is only marked in the imperfective verbs, and only in the indicative mood. This is a past-nonpast system, with the primary endings marking the present (the future may have been marked using the subjunctive) and the secondary endings marking the past. The perfective exclusively uses secondary endings in the indicative, due to the exceptionally narrow meaning of present perfectives (where they exist, they are typically either gnomic forms or future perfective forms, and for the latter PIE may have used the subjunctive instead of a hypothetical present), and there is no primary-secondary distinction in the stative indicative. None of the other moods are marked for tense; the subjunctive exclusively uses primary endings, while the optative exclusively uses secondary endings.

The imperfective and perfective aspects may also be marked for voice. By default, such verbs are in the active voice. However, if the middle ending set is used instead of the active, then the verb is in the middle or mediopassive voice, which encompasses many meanings, including but not limited to, passive, reflexive and reciprocal meanings. Stative verbs are not marked for voice, and are considered "voiceless", although the non-indicative moods use the active ending set. It is possible that, like the Japanese stative (-te aru), the PIE stative was inherently passive.

Origin of the aspects
Vidal suggests that the stative developed from Pre-PIE "neo-imperfectives". These were derived from a perfective stem by lengthening the root vowel and adding stative endings. In addition to agreeing with the subject, "neo-imperfectives" also agreed in number with the direct object, resulting in three different paradigms for singular, plural and no object. This agreement is reflected through reduplication if the absolutive (accusative for transitive clauses, the sole argument for intransitive clauses) is plural. The paradigms he posits for (Pre-)PIE are listed below:

The stative ultimately derives from the intransitive paradigm. This corresponds with the fact that most PIE statives were intransitive, and my hypothesis that the stative was inherently passive. The transitive singular paradigm results in molō verbs, while the transitive plural paradigm results in Narten presents.

In comparison, the "old" perfectives left the root vowel short. Here are the developments of their three paradigms: The intransitive paradigm became the reduplicated present, the transitive singular became the root aorist, and the transitive plural became the reduplicated aorist.

You may notice that the third person singular forms may feature an */s/. This is considered by Vidal to be the origin of the s-aorist.