# 80/20 — The Shape of Concentration

An original mathematical art study by the 404KIN FIELD project, 2026. No external dataset or market prices are inputs. This is a shared studio artwork, not part of the assigned V4.1 NFT imagery and not a financial product.

## Reproduce the model

1. Set alpha = ln(5) / ln(4), beta = 1 - 1/alpha. The distribution is Pareto Type I with scale 1.
2. Lorenz curve: L(p) = 1 - (1-p)^beta for 0 <= p <= 1. Explicitly set L(0)=0 and L(1)=1. A numerically stable interior calculation is -expm1(beta * log1p(-p)).
3. The highest population fraction q holds S(q) = q^beta of total modelled wealth. S(0.2)=0.8; S(0.01) is approximately 0.528087919.
4. Divide the modelled wealth into 500 equal parts. For each i from 0 through 499 take u=(i+0.5)/500. Its population destination is p=1-(1-u)^(1/beta). Exactly 400 destinations satisfy p>=0.8.
5. As an independent sum check, calculate 100 population-bin weights w[j]=L((j+1)/100)-L(j/100). Every weight is positive, all weights sum to 1, and the last 20 sum to 0.8 within 1e-12 numerical tolerance.

## Reproduce the geometry

The SVG is 1600 by 1960 units. Its field starts at (140,450) with side length 1280. For each wealth midpoint u and population destination p:

- Start: (140, 450+1280*u).
- First cubic control point: (140+1280*0.42, 450+1280*u).
- Second control point: (140+1280*p, 450+1280*0.45).
- End: (140+1280*p, 1730).
- Copper when p>=0.8, otherwise ivory; all curves have stroke width 0.8.

The central rectangle at (470,960), size 250 by 450, is an unscaled compositional void. It masks parts of the lines without changing their endpoint assignments. Background guides and type serve the composition; their areas are not financial measurements. Coordinates and some endpoints can coincide at rendering precision near the concentrated tail.

## Read the claim accurately

80/20 is a deliberate model calibration, not an empirical discovery or a rule about this collection's sales. Fractions refer to an ideal population, not individual people, wallets or NFT holders. At this alpha the theoretical mean is finite and variance infinite. This does not estimate market risk or promise any investment outcome.

Parameters, bin weights and the SVG SHA-256 are in model.json. A hash detects byte changes; it does not establish token ownership. This study is free to view and download, carries no token assignment and changes no existing NFT rights. Public availability is not a transfer of copyright or a commercial-use/AI-training licence.