2. Language Vitality Index (LVI)

Continuity

A comprehensive "health score" for Kifuliiru that combines how many people speak it, where they use it, and how many generations are actively speaking it.

L V I = \frac{( P _{f} \cdot U _{d} ) + D _{g e n}}{P _{t o t}}

Data & measurement

For Kifuliiru vitality, P_f should come from a defined speaker census or sample; P_tot is the community denominator you are scoring (state it explicitly). U_d is a bounded usage-domain score for Kifuliiru in daily life—keep the 0–10 rubric stable across waves. D_gen counts active generations on the same rule (often 1–5). Avoid double-counting passive recognition as full fluency unless the handbook allows it.

Solution & proof

LVI aggregates (P_f · U_d) + D_gen in the numerator and scales by P_tot for a Kifuliiru-speaking community. The product P_f · U_d rewards both speaker mass and domain breadth; adding D_gen rewards multi-generational use of Kifuliiru. If P_tot grows but numerator is fixed, LVI falls—so pair population estimates with Kifuliiru speaker estimates from the same frame.

Examples

1. Rural community headcount
Word problem
A Kifuliiru-speaking village of 5,000 registered members has 300 fluent Kifuliiru speakers. Usage of Kifuliiru across domains scores 6 on the 0–10 rubric, and three generations actively use the language in daily life (D_gen = 3). Compute LVI.
Kifuliiru vitality inputs
Quantity Symbol Value
Fluent speakers P_f 300
Usage domains score U_d 6
Generational depth D_gen 3
Total community P_tot 5000
Solution
Step 1 — Write LVI = ((P_f · U_d) + D_gen) / P_tot.
Step 2 — Multiply P_f and U_d: 300 × 6 = 1800.
Step 3 — Add D_gen: 1800 + 3 = 1803.
Step 4 — Divide by P_tot: 1803 / 5000 = 0.3606. Round for reporting as needed.
$LVI = \frac{( P _{f} \cdot U _{d} ) + D _{g e n}}{P _{t o t}} LVI = \frac{( 300 \cdot 6 ) + 3}{5000} = \frac{1803}{5000} = 0.3606$
2. More speakers, same domains
Word problem
One year later, fluent Kifuliiru speakers rise to 420; U_d stays 6, D_gen stays 3, and P_tot stays 5,000. What is the new LVI?
Updated Kifuliiru inputs
Quantity Symbol Value
Fluent speakers P_f 420
Usage domains score U_d 6
Generational depth D_gen 3
Total community P_tot 5000
Solution
Step 1 — Numerator becomes (420 × 6) + 3 = 2520 + 3 = 2523.
Step 2 — LVI = 2523 / 5000 = 0.5046. The index rose because P_f increased while other terms were fixed.
$LVI = \frac{( 420 \cdot 6 ) + 3}{5000} = \frac{2523}{5000} = 0.5046$

Quantity	Symbol	Value
Fluent speakers	P_f	300
Usage domains score	U_d	6
Generational depth	D_gen	3
Total community	P_tot	5000

Quantity	Symbol	Value
Fluent speakers	P_f	420
Usage domains score	U_d	6
Generational depth	D_gen	3
Total community	P_tot	5000

Variables

Symbol	Description
`LVI`	Language Vitality Index (0 to 1)
`P_f`	Fluent population count
`U_d`	Usage domains score (0-10)
`D_gen`	Generational depth (1-5)
`P_tot`	Total population of the community

Source

ALL_FORMULAS.md — Continuity

Data & measurement

Solution & proof

Examples

1. Rural community headcount

2. More speakers, same domains

Variables

Source

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