The incoherent stress of Kuikuro

[BFK+25] [LP77] [Hay95a]

Kuikuro (Cariban; Mato Grosso, Brazil) builds iambic feet left to right, with final trochaic reversal: when an iamb would leave a phrase-final long vowel, the last two syllables parse as a trochee instead ([BFK+25] §3.1; [Hay95a] §5.3b). The last foot is the head foot of the word, and the primary stress is the head of the head foot ([BFK+25] p. 2365) — i.e. the syllable reached from the word ω by an all-head descent: the head terminal (Liberman & Prince's head terminal, Prosody.Tree.headTerminals).

The paper's title result — incoherent stress ([Gor16]) — is that the default High tone does not dock on this head terminal but surfaces displaced, on the last syllable of a tone domain that starts at the primary stress and expands rightward to (but not including) the next foot head. The metrically most prominent syllable is thereby dissociated from the high-toned salient one.

This file formalizes the default-length metrical spine the tonal analysis is anchored to: the left-to-right iambic footing (with final trochaic reversal) of words in isolation, and the certification that the primary stress is exactly the grid's head terminal. That a word has a unique head terminal (Prosody.Tree.IsHeaded) is metrical culminativity — head-terminal uniqueness ([Hym06]). The paper's Culminativity-H (§4.2) is a distinct, tonal constraint ("one violation per High tone domain with more than one foot head"), part of the deferred tone layer. Also deferred alongside tone: lexical long vowels (Max-μ, monosyllabic feet, §3.1), word minimality (FtBin, §3.5), and final shortening (§4.1). Here the head terminal is the anchor the tonal layer displaces from.

Weights: 1 = short (light) σ, 2 = a long (heavy) σ from iambic lengthening; a foot's isHead σ is its head (iamb → final, trochee → initial), and the head foot is isHead := true.

Words in isolation ([BFK+25] §3)

def BeckerEtAl2025.fell : Prosody.Tree

[(a.lá:)(ma.kí:)li] 's/he fell' ([BFK+25] Fig. 1): two iambs and a stray final σ. The rightmost foot (ma.kí:) heads the word, so the long kí: is the primary stress.

Equations

• BeckerEtAl2025.fell = Prosody.Tree.om [Prosody.Tree.ft false [Prosody.Tree.σ 1, Prosody.Tree.σ 2 true], Prosody.Tree.ft true [Prosody.Tree.σ 1, Prosody.Tree.σ 2 true], Prosody.Tree.σ 1]

def BeckerEtAl2025.weFell : Prosody.Tree

[(tsi.ha:)(la.ma:)(kí.li)] 'we (exclusive) fell' ([BFK+25] Fig. 2): even-parity, so the final two short syllables reverse to a trochee (kí.li) — the head foot — and the initial kí is the primary stress.

Equations

• One or more equations did not get rendered due to their size.

def BeckerEtAl2025.annatto : Prosody.Tree

[(u.mí:)ŋi] 'annatto' ([BFK+25] Fig. 3): one iamb and a stray final σ; the long mí: is the primary stress.

Equations

• BeckerEtAl2025.annatto = Prosody.Tree.om [Prosody.Tree.ft true [Prosody.Tree.σ 1, Prosody.Tree.σ 2 true], Prosody.Tree.σ 1]

The grid: secondary stress on every foot head, primary on the head foot's

Reading Tree.columns ∘ the footing recovers the stress profile: 1 unstressed, 2 a secondary (a non-head foot's head), 3 the primary (the head foot's head).

theorem BeckerEtAl2025.gridColumns_fell : fell.columns = [1, 2, 1, 3, 1]

theorem BeckerEtAl2025.gridColumns_weFell : weFell.columns = [1, 2, 1, 2, 3, 1]

theorem BeckerEtAl2025.gridColumns_annatto : annatto.columns = [1, 3, 1]

Primary stress is the head terminal ([BFK+25] p. 2365)

Each word has a unique head terminal (Tree.IsHeaded — metrical culminativity, Liberman & Prince's head-terminal uniqueness; cf. [Hym06]), and it is exactly the head syllable of the head foot — the long kí:/mí:, or the reversed-trochee's initial kí. The primary stress is read off the grid's live column as an element.

theorem BeckerEtAl2025.isHeaded_fell : fell.IsHeaded

theorem BeckerEtAl2025.isHeaded_weFell : weFell.IsHeaded

theorem BeckerEtAl2025.isHeaded_annatto : annatto.IsHeaded

theorem BeckerEtAl2025.headTerminals_fell : fell.headTerminals = [Prosody.Tree.σ 2 true]

's/he fell': the head terminal is the long kí: (head of the rightmost iamb).

theorem BeckerEtAl2025.headTerminals_weFell : weFell.headTerminals = [Prosody.Tree.σ 1 true]

'we fell': the head terminal is the reversed trochee's initial short kí.

theorem BeckerEtAl2025.headTerminals_annatto : annatto.headTerminals = [Prosody.Tree.σ 2 true]

'annatto': the head terminal is the long mí:.

theorem BeckerEtAl2025.isHeadTerminal_fell : fell.IsHeadTerminal (Prosody.Tree.σ 2 true)

The same fact declaratively ([LP77]): kí: is the head terminal of fell — reached from ω by an all-head descent (ω → head foot → head σ), Tree.IsHeadTerminal — lifted from the computed list by Tree.headTerminal_sound, not just by computing the list.

The trochaic reversal is OT-optimal ([BFK+25] §3.1, Table 2)

Why the final foot reverses to a trochee: an even-parity /σσσσ/ parsed as two iambs leaves a phrase-final long vowel (*V:]φ); leaving the last two σ unparsed violates Parse-σ; so they parse as a trochee, violating only the low-ranked Iamb. Ranking *V:]φ ≫ Parse-σ ≫ Iamb ([BFK+25] (1)–(3), Table 2).

inductive BeckerEtAl2025.FootingCand : Type

The three footings of /σσσσ/ weighed in [BFK+25]'s Table 2.

• twoIambs : FootingCand

  (σ́σ:)(σ́σ:) — two iambs; a final long vowel.

• iambStrays : FootingCand

  (σ́σ:)σσ — one iamb, the last two σ unparsed.

• iambTrochee : FootingCand

  (σ́σ:)(´σσ) — an iamb and a final trochee (the optimum).

@[implicit_reducible]

instance BeckerEtAl2025.instDecidableEqFootingCand : DecidableEq FootingCand

Equations

• BeckerEtAl2025.instDecidableEqFootingCand x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance BeckerEtAl2025.instReprFootingCand : Repr FootingCand

Equations

• BeckerEtAl2025.instReprFootingCand = { reprPrec := BeckerEtAl2025.instReprFootingCand.repr }

def BeckerEtAl2025.instReprFootingCand.repr : FootingCand → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def BeckerEtAl2025.FootingCand.toTree : FootingCand → Prosody.Tree

Each candidate as a footed tree (rightmost foot the head).

Equations

• One or more equations did not get rendered due to their size.
• BeckerEtAl2025.FootingCand.iambStrays.toTree = Prosody.Tree.om [Prosody.Tree.ft true [Prosody.Tree.σ 1, Prosody.Tree.σ 2 true], Prosody.Tree.σ 1, Prosody.Tree.σ 1]

def BeckerEtAl2025.cParse : Constraints.Constraint FootingCand

Parse-σ ([BFK+25] (1)): one mark per unparsed (stray) σ — a σ-leaf under ω.

Equations

• BeckerEtAl2025.cParse c = match c.toTree with | RoseTree.node value cs => (List.filter (fun (d : RoseTree Prosody.Constituent) => d.value.isSyl) cs).length

def BeckerEtAl2025.cIamb : Constraints.Constraint FootingCand

Iamb ([BFK+25] (2)): one mark per foot that is not right-headed (head σ ≠ final).

Equations

• One or more equations did not get rendered due to their size.

def BeckerEtAl2025.cStarV : Constraints.Constraint FootingCand

*V:]φ ([BFK+25] (3)): one mark for a long vowel in the phrase-final σ (for a one-word phrase, the word-final σ).

Equations

• BeckerEtAl2025.cStarV c = match c.toTree.terminals.getLast? with | some leaf => if decide ((RoseTree.value leaf).weight? = some 2) = true then 1 else 0 | none => 0

def BeckerEtAl2025.candidates : List FootingCand

Equations

• BeckerEtAl2025.candidates = [BeckerEtAl2025.FootingCand.twoIambs, BeckerEtAl2025.FootingCand.iambStrays, BeckerEtAl2025.FootingCand.iambTrochee]

theorem BeckerEtAl2025.candidates_ne : candidates ≠ []

def BeckerEtAl2025.footingRanking : List (Constraints.Constraint FootingCand)

The ranking *V:]φ ≫ Parse-σ ≫ Iamb ([BFK+25] Table 2).

Equations

• BeckerEtAl2025.footingRanking = [BeckerEtAl2025.cStarV, BeckerEtAl2025.cParse, BeckerEtAl2025.cIamb]

theorem BeckerEtAl2025.starV_violations : List.map cStarV candidates = [1, 0, 0]

The violation profiles ([BFK+25] Table 2):

candidate	*V:]φ	Parse-σ	Iamb
(σ́σ:)(σ́σ:)	1*	0	0
(σ́σ:)σσ	0	2*	0
☞ (σ́σ:)(´σσ)	0	0	1

Table 2's Max-μ (ranked *V:]φ ≫ Max-μ ≫ Parse-σ) is omitted — vacuous (0) on all three candidates; it governs lexical long vowels (Tables 4/6).

theorem BeckerEtAl2025.parse_violations : List.map cParse candidates = [0, 2, 0]

theorem BeckerEtAl2025.iamb_violations : List.map cIamb candidates = [0, 0, 1]

theorem BeckerEtAl2025.footing_optimal : (OptimalityTheory.Tableau.ofRanking candidates footingRanking candidates_ne).optimal = {FootingCand.iambTrochee}

The trochaic reversal wins ([BFK+25] Table 2): under *V:]φ ≫ Parse-σ ≫ Iamb the optimal footing of /σσσσ/ is the iamb + final trochee — no final long vowel, no unparsed σ, at the cost of one (low-ranked) non-right-headed foot.