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Cohesion Dynamics (CD)

R-PRED-DM1 — Prediction Interface for P-DM1

Purpose

This document defines the prediction interface for P-DM1.

It specifies:

  • What quantities must be extracted from data
  • How they map onto the prediction
  • What constitutes agreement or failure

This document introduces no new predictions and no new theory.

Normativity

R-PRED-DM1 is non-normative.

  • It does not add constraints to P-DM1
  • It may be revised without changing the prediction
  • It exists to ensure disciplined and reproducible testing

1. Required Observables

To test P-DM1, an empirical study must determine:

  1. Total halo mass ( M_{\text{halo}} )
  2. Core radius ( r_{\text{core}} )
  3. Enclosed mass profile within ( r_{\text{core}} )

These may be inferred via rotation curves, mass models, or equivalent methods.

2. Definition of Core Radius

For the purposes of P-DM1 testing:

  • ( r_{\text{core}} ) is defined as the radius over which the density profile flattens to an approximately constant central value
  • Any reasonable, published core definition may be used provided it is applied uniformly

The interface does not mandate a specific halo model (e.g. Burkert, ISO), but consistency must be demonstrated.

3. Mapping to the Prediction

Empirical results should be compared against:

rcore∝Mhalo1/2r_{\text{core}} \propto M_{\text{halo}}^{1/2}

Testing must include:

  • Power-law fit to extracted ( (M_{\text{halo}}, r_{\text{core}}) )
  • Estimated exponent with uncertainty
  • Scatter analysis

4. Surface Density Test

Compute the boundary-limited surface density:

Σ0=M(<rcore)rcore2\Sigma_0 = \frac{M(<r_{\text{core}})}{r_{\text{core}}^2}

This follows P-DM1’s boundary-limited saturation definition (without π\pi), reflecting that reconciliation is an interface process rather than a volume process.

Test whether:

  • ( \Sigma_0 ) is approximately constant
  • Scatter is consistent with observational uncertainty
  • No systematic trend with ( M_{\text{halo}} )

Note: The absence of π\pi is not a notational choice—it reflects the substrate-level claim that closure saturation is boundary-limited, not volume-limited.

5. Statistical Expectations

The interface does not prescribe:

  • Specific fitting algorithms
  • Bayesian vs frequentist approaches
  • Error models

However:

  • The same method must be applied across the dataset
  • Sensitivity tests should be reported
  • Model selection freedom must be declared

6. Reporting Requirements

Any empirical paper testing P-DM1 must clearly state:

  • Dataset used
  • Core definition employed
  • Halo mass inference method
  • Deviations from this interface (if any)

7. What This Interface Does Not Do

This document does not:

  • Judge empirical success or failure
  • Compare against alternative theories
  • Recommend datasets
  • Provide software or code

Those belong to application papers.

Status

Epistemic Role: Reference specification
Normativity: None
Primary Value: Preventing analytic degrees of freedom from obscuring falsification

This interface exists to make failure as clear as success.