# Structural curve atlas — foundation report

## Corpus

- Primary galaxies: **121**
- STRUC-I profile rows: **4840**
- κ points per galaxy: **40**
- Curve channels retained: **ρ(κ), Aκ(κ), ν(Vκ)(κ)**

## Structural object

Each galaxy is represented by a multiscale structural fingerprint. The atlas records:

- activation onset;
- ρ peak height and location;
- integrated ρ response across the logarithmic κ range;
- early-, middle-, and late-scale response;
- Aκ deficit burden;
- normalized vulnerability capacity;
- low-dimensional curve coordinates;
- nearest structural neighbours.

## Low-dimensionality

The first three ρ-curve components explain:

- PC1: **64.116%**
- PC1–PC2 cumulative: **81.760%**
- PC1–PC3 cumulative: **90.801%**

The corresponding first-three-component totals are **88.5%** for ν, **55.9%** for Aκ, and **61.0%** for the combined atlas.

**Finding:** complete curves form a compact structural coordinate system, especially in ρ and ν. Aκ contributes a broader heterogeneous layer.

## Atlas interpretation

The atlas contains several simultaneous forms of organization:

- galaxy-specific response identity;
- conventional physical-property alignment;
- observation-geometry alignment;
- discrete chamber-regime separation;
- persistence–connectivity structure.

These layers make the atlas richer, not invalid. The next analysis separates and normalizes them.

## Validation progression

Gate B confirmed exceptional unchanged-ladder reproducibility. Gate C then mapped how fingerprint identity moves under deletion, thinning, coverage, and M/L changes.

Together they establish both the fingerprint and its representation-response geometry.
