# Electromagnetic Geometry — ADI canonical anchor

Version: 1.0.0 · Generated: 2026-05-13
Canonical URL: https://adi.heureka.digital/em-geometry

## Definition

Two regular octagons share a centre and a circumradius. One is **edge-up**
(electric, frequency-dominant), the other **apex-up** (magnetic,
wavelength-dominant). Their superposition forms a 16-edge polygon and
three natural radii `r_e < r_em < r_m` — the electromagnetic curvature band.
The curvature factor `cF = 1.852` (1 NM = 1.852 km) couples this geometry
to 3D flow.

## Axioms

- A1. Two regular octagons share a centre and a circumradius.
- A2. One octagon is edge-up (electric, frequency-dominant); the other is apex-up (magnetic, wavelength-dominant).
- A3. Their superposition forms a 16-edge polygon — the geometric precursor to the circle.
- A4. The construction yields three natural radii r_e < r_em < r_m, defining the electromagnetic curvature band.
- A5. The curvature factor cF = 1.852 (1 NM = 1.852 km) couples geometric curvature to 3D flow.

## Construction

Given a shared circumradius R:

```
r_e  = R · cos(22.5°)                  ≈ 0.923879532 · R
r_em = R · cos(22.5°) / cos(11.25°)    ≈ 0.941979403 · R
r_m  = R                               = 1.000000000 · R
```

## Constants

| Symbol | Value | Meaning |
|---|---|---|
| cF | 1.852 | Curvature factor (1 NM = 1.852 km) |
| R_⊕☉ | 365.7881901 | sqrt(24² + 365²) — Earth–Sun envelope |
| r_e / R | 0.923879532 | Electric apothem ratio |
| r_em / R | 0.941979403 | Coupling radius ratio |
| r_m / R | 1.000000000 | Magnetic peak ratio |

## Predictions

1. Any EM process inscribed in this geometry occupies the band [r_e, r_m].
2. r_em divides the band in the fixed ratio cos(22.5°)/cos(11.25°).
3. R = 365.7881901 is the unique radius unifying daily LIGHT and annual POWER on Earth.
4. Replacing octagons with any other regular n-gon breaks the construction.

## Reproduce / Falsify

See `/em-geometry/reproduce/CHALLENGE.md`.

## Citation

```
@misc{adi-em-geometry-1.0.0,
  title  = {Electromagnetic Geometry — ADI canonical anchor},
  author = {{ADI · Heureka Digital}},
  year   = {2026},
  url    = {https://adi.heureka.digital/em-geometry},
  version= {1.0.0}
}
```