5. Conjugation Matrix

Continuity

The complete structure of any Kifuliiru verb. This matrix defines how verbs are built from modular pieces, allowing generation of thousands of verb forms from a single root.

V_{t o t} = [(S P + T M + O P) + R] + (E x t + F V)

Data & measurement

Continuity metrics emphasize intergenerational transmission, corpus completeness, and structural stability. Keep cohort definitions fixed across measurement waves. Symbols: V_tot (Total verb form (complete conjugated word)); SP (Subject prefix (who does the action)); TM (Tense marker (when it happens)); OP (Object prefix (who receives the action)); R (Root (the core meaning)); Ext (Extensions (modifications like causative, passive)); FV (Final vowel (mood indicator)). Log instrument versions, sample frames, and cleaning rules whenever estimates are refreshed so longitudinal comparisons stay valid.

Solution & proof

Conceptual summary: The complete structure of any Kifuliiru verb. This matrix defines how verbs are built from modular pieces, allowing generation of thousands of verb forms from a single root. Treat this as a measurement recipe: map each symbol to an empirical quantity, substitute estimates, and simplify with ordinary algebra (including logarithms, min/max caps, or piecewise branches where shown). Where limits or integrals appear, approximate with discrete sums on cohorts or time steps when closed forms are impractical. Interpret the result against thresholds in the cited source and report uncertainty on inputs.

Examples

1. Word problem — field log

Word problem

A measurement round produced the table below. Each symbol matches the Variables section for “Conjugation Matrix”. Find the computed value using the formula above.

Illustrative inputs—replace with your field numbers

Quantity	Symbol	Value
Total verb form (complete conjugated word)	V_tot	0.52
Subject prefix (who does the action)	SP	0.54
Tense marker (when it happens)	TM	0.63
Object prefix (who receives the action)	OP	0.72
Root (the core meaning)	R	0.81
Extensions (modifications like causative, passive)	Ext	0.9
Final vowel (mood indicator)	FV	0.54

Solution

Step 1 — From the table, assign V_tot = 0.52; SP = 0.54; TM = 0.63; OP = 0.72; R = 0.81; Ext = 0.9; FV = 0.54.

Step 2 — Substitute into the definition of “Conjugation Matrix” at the top of the page (same structure as the source formula).

Step 3 — Finish any remaining algebra (sums, caps, logs, or limits) by hand or in a CAS when the expression still contains Σ, integrals, or non-numeric parameters. Tie final numbers back to your corpus or community records.

Given: V_{t} o t = 0.52, S P = 0.54, T M = 0.63, O P = 0.72, R = 0.81, E x t = 0.9, F V = 0.54 V_{t o t} = [(S P + T M + O P) + R] + (E x t + F V)

2. Second scenario — adjusted inputs

Word problem

The same measure applies with corrected inputs for the next report (see table). Recompute using the same formula.

Revised values for the next report (illustrative)

Quantity	Symbol	Value
Total verb form (complete conjugated word)	V_tot	0.47
Subject prefix (who does the action)	SP	0.54
Tense marker (when it happens)	TM	0.63
Object prefix (who receives the action)	OP	0.72
Root (the core meaning)	R	0.81
Extensions (modifications like causative, passive)	Ext	0.9
Final vowel (mood indicator)	FV	0.54

Solution

Step 1 — From the table, assign V_tot = 0.47; SP = 0.54; TM = 0.63; OP = 0.72; R = 0.81; Ext = 0.9; FV = 0.54.

Step 2 — Substitute into the definition of “Conjugation Matrix” at the top of the page (same structure as the source formula).

Given: V_{t} o t = 0.47, S P = 0.54, T M = 0.63, O P = 0.72, R = 0.81, E x t = 0.9, F V = 0.54 V_{t o t} = [(S P + T M + O P) + R] + (E x t + F V)

Variables

Symbol	Description
`V_tot`	Total verb form (complete conjugated word)
`SP`	Subject prefix (who does the action)
`TM`	Tense marker (when it happens)
`OP`	Object prefix (who receives the action)
`R`	Root (the core meaning)
`Ext`	Extensions (modifications like causative, passive)
`FV`	Final vowel (mood indicator)

Source

ALL_FORMULAS.md — Continuity