# Project context

## Research object

For each galaxy \(G\), the project studies the multichannel chamber-response fingerprint

```text
F_G(κ) = [ρ_G(κ), Aκ,G(κ), ν_G(κ)].
```

The source ladder is built from measured radial samples of the baryonic-acceleration profile. STRUC-I provides multiscale persistence/admissibility curves, while STRUC-PERC-I provides fragmentation and connectivity descriptors.

## Research progression

The programme began with two central questions:

1. Can complete chamber curves distinguish individual galaxies and organize them structurally?
2. Can those structural fingerprints transfer into prediction of gravitational discrepancy?

The completed experiments now provide a broader answer.

## Result 1 — galaxy-specific fingerprints are reproducible

Across five unchanged-ladder executions:

```
top-1 source retrieval                 1.000000
top-5 source retrieval                 1.000000
median own / nearest-wrong distance    0.117893
median ICC across ρ PC1–PC3            0.999849
minimum ICC across ρ PC1–PC3           0.999709
median top-5 neighbour Jaccard          1.000000
```

The chamber produces stable galaxy-specific response identities. Native chamber randomness is far smaller than the observed between-galaxy separation.

## Result 2 — fingerprint expression is representation-sensitive

Gate C mapped the effect of four controlled changes:

```
L — leave one radius out         top-1 0.551; median own/wrong 0.916
T — deterministic n=10 thinning top-1 0.165; median own/wrong 1.835
C — fixed-count coverage control top-1 0.050; median own/wrong 2.138
M — M/L sensitivity              top-1 0.517; median own/wrong 0.916
```

All four changes substantially moved the fingerprints. This establishes that sampling, radial coverage, and baryonic preparation are active structural coordinates of the measured response.

The result is not “no fingerprint.” It is:

> **the fingerprint has a measurable dependence on how the galaxy profile is represented.**

## Result 3 — the atlas has strong internal organization

First-three-component variance:

```
ρ                         90.8%
ν                         88.5%
Aκ                        55.9%
combined                  61.0%
```

The atlas contains:

- compact dominant response families in ρ and ν;
- a richer, more heterogeneous Aκ channel;
- galaxy-specific neighbourhoods;
- physical-property alignment;
- observation-geometry alignment;
- a pronounced Weak Persistence regime.

This is a multilayer atlas rather than a one-axis classification.

## Result 4 — persistence, fragmentation, and connectivity separate

Among 121 primary galaxies:

```
Stable Structure                       110
Weak Persistence                        11
HARD_FRAGMENTATION                     103
FULL_PERCOLATION                        17
Stable + HARD_FRAGMENTATION             94
```

All 17 full-percolation cases reached connectivity only in the adaptive extension. The project therefore demonstrates that stable persistence does not require native-range global connectivity.

## Result 5 — transfer depends on representation and scale

The compact static bridge did not improve galaxy-held-out prediction:

```
ordinary profile baseline M2 RMSE      0.188389
combined chamber M-IP RMSE             0.194554
relative change                        -3.272%
```

The complete curves retained galaxy identity but produced only a small aggregate gain in the tested global model:

```
aggregate improvement                   0.435%
positive folds                          1 / 5
```

Channel decomposition identified ρ(κ) as the leading transfer-sensitive channel:

```
ρ(κ) aggregate improvement              1.142%
positive folds                          4 / 5
```

This result redirects transfer research from one static galaxy-level coefficient toward local transitions, structural regimes, and within-galaxy alignment.

## Current research identity

The programme is now centered on **galaxy structural fingerprints and their transformation geometry**.

Its next tasks are to:

- normalize sampling and coverage dependence;
- map uncertainty-driven fingerprint motion;
- separate chamber regimes;
- test geometry-matched nulls;
- identify persistent structural analogues and outliers;
- investigate ρ through local and regime-conditioned hypotheses.
