The Haller-Obidi Structural Reduction Theorem of the Theory of Entropicity (ToE)

Theorem 5.1 (Haller-Obidi Structural Theorem). (Structural Reduction).

The Obidi Action of the Theory of Entropicity (ToE) reduces to the Haller-Obidi Action upon localization of the entropic field to a single timelike worldline.

This expresses the formal reduction — the mathematical statement that the Obidi Action reduces to the Haller–Obidi Action under worldline localization. It’s a structural theorem, not a correspondence. It provides the explicit reduction chain:

S_Obidi→S_ent→S_action,

and the conversion H=(2/ℏ)S_HO.

Note:

Theorem 5.1 formalizes the reduction underlying Proposition 5.1, establishing the structural basis of the Obidi–Haller Correspondence.

References 

1)

https://app.clickup.com/9011914914/docs/8cjdu52-591/8cjdu52-611

2)

https://app.clickup.com/9011914914/docs/8cjdu52-591/8cjdu52-611

3)

https://app.clickup.com/9011914914/docs/8cjdu52-591

4)

GitHub/Cloudflare: 

1) https://entropicity.github.io/Theory-of-Entropicity-ToE/papers/

2) https://entropicity.github.io/Theory-of-Entropicity-ToE/docs/The-Theory-of-Entropicity-(ToE)-Living-Review-Letters-Series-Letter-IB-On-the-Haller-Obidi-Action-and-Lagrangian-U1.pdf

Zenodo: 

1) https://doi.org/10.5281/zenodo.19660059

OSF:

1) https://osf.io/5p74x/wiki?wiki=

ORCID Identifier: https://orcid.org/0009-0004-3606-3182