Observation Plan: Mapping the Topological Merger Spike

Objective: To extract spatial $\alpha$ maps from galaxy cluster mergers and verify the predicted $+2$ unit boost in topological bridge regions.

1. Primary Targets

1. Abell 520 (“The Train Wreck”): Unique due to the central “dark core” which sits in a bridge region between stellar concentrations.
2. 1E 0657-56 (Bullet Cluster): Clean separation of gas and stars.

2. Required Data Channels

* Weak Lensing (WL): Convergence maps ( $\kappa$ ) from HST/Subaru to provide the “Total Gravitating Mass” $\Sigma_{total}$ .
* X-Ray (Chandra): Gas mass distribution $\Sigma_{gas}$ .
* Photometry (HST): Stellar mass distribution $\Sigma_{stars}$ .

3. The Alpha Mapping Formula

We define the spatial $\alpha$ map as:

$\alpha(\mathbf{x}, \mathbf{y}) = \frac{\Sigma_{total}(\mathbf{x}, \mathbf{y})}{\Sigma_{baryon}(\mathbf{x}, \mathbf{y})} - 1$

Where $\Sigma_{baryon} = \Sigma_{gas} + \Sigma_{stars}$ .

4. Extraction Zones

* Core Zone ( $\chi=2$ ): Centered on the main baryon peaks. Prediction: $\alpha \approx 6, 14, 30$ .
* Bridge Zone ( $\chi=0$ ): The region of minimum baryon density between merging cores where gravitational connectivity is established.
* Prediction: $\alpha_{bridge} = \alpha_{core} + 2$ .

5. Statistical Signature: The “Hinge”

We are looking for a Bimodal/Discrete Distribution in the spatial map.
Traditional Dark Matter expects a smooth distribution following the collisionless centers.
Digital Gravity expects the map to “snap” to a higher integer in the topological bridge, regardless of the local baryon density.

6. Success/Failure Criteria

* Success: Observation of a discrete, integer-stepped increase in $\alpha$ in the bridge region.
* Failure: $\alpha$ remains constant or decreases in the bridge, or varies continuously without integer steps.

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Status: Ready for Data Ingestion.