Quantum Worldhood as Partial Closure - Many Worlds, the Multiverse and the Emergence of Classical World Labels

This Zenodo release preserves the completed manuscript together with one additional formal development that emerged during final production: the Closure-Multiverse Existence Theorem.

The principal manuscript develops quantum worldhood through Partial Closure. Its central mathematical question is whether distinctions excluded from a retained representation can later return to affect its admissible future. Exact future closure is expressed through the discarded-to-retained block

[R_C\Phi_{t,*}D_C=0,]

while approximate operational worldhood combines future-sufficiency defect, sector support leakage, and external-autonomy response:

\left(\Delta_{C,T}^{\chi},\Sigma_{i,T},G_{i,T}^{\rm adm}\right).]

The manuscript then defines an effective world multiplicity

[N_W(T,\boldsymbol\varepsilon),]

and calls the regime

[N_W(T,\boldsymbol\varepsilon)\ge2]

a Closure Multiverse: a plurality of operationally autonomous worlds supported within a common ambient structure.

During final synthesis, a stronger question became apparent. The definition of a Closure Multiverse tells us when several operational worlds have already been identified, but it does not by itself provide structural conditions forcing such multiplicity to occur.

The supplementary theorem archived below addresses that question.

Its purpose is to establish a sufficient dynamical route

[\boxed{\text{central sector multiplicity}
+\text{future closure}+\text{sector preservation}+\text{external autonomy}\Longrightarrow\text{multiple operational worlds}.}]

This result strengthens the connection between Partial Closure and the multiverse question without changing the manuscript's ontological claim discipline.

In particular, the theorem does not establish that the physical universe is a multiverse, nor that all cosmological multiverse models reduce to Partial Closure. It establishes the narrower mathematical result that, within the stated operator-algebraic dynamical framework, multiple operational worlds can arise within one ambient quantum structure

Consequently, operational world multiplicity does not mathematically require fundamental-reality multiplicity

The theorem is archived here as a supplementary extension so that the completed manuscript can remain stable while the result is preserved for possible incorporation into a later revised version or follow-on paper.

Keywords: Partial Closure; quantum foundations; Many Worlds; future sufficiency; conditional expectations; decoherence; Quantum Darwinism; process tensors; lumpability; emergent classicality; operational worldhood; multiverse; Closure Multiverse.

Explainer video

Watch on YouTube (Roots of Reality): https://youtu.be/lTZlLTg41U8

The video, its thumbnail and description are included in this record.