The Emergent Frame: A Minimal Framework for Spacetime Rollout, Interaction, and Excitation

Research Context

Paper VII brings the geometric and matter-closure branches of TEF into a minimal working framework. It connects the inherited helix of Paper I, the relative-framing construction of Paper IV, the closure energetics of Paper V, and the closure obstruction and interface ansatz of Paper VI.

The organizing distinction is between persistent closed matter topology, the spacetime structure associated with its ongoing rollout, and excitations supported by that structure. This consolidates the research program’s assumptions and next tests; it does not supply a completed dynamics or derive the interactions of the Standard Model.

Matter, Rollout, and Excitation

Globally complete matter closures are provisionally assigned an independent rollout-source identity. Rollout denotes an ongoing update of associated spacetime structure, not dilution into an already existing volume. Excitations have no independent rollout-source identity in this proposal, but their energy, momentum, and stress must still contribute to gravitational backreaction. The source label is therefore not a substitute for gravitational energy–momentum accounting.

The local helical picture retains transverse phase closure alongside axial advance:

$$\mathbf{r}(\theta )=(a\theta ,R\cos \theta ,R\sin \theta ),q=\frac{a}{R}.$$

A full turn advances by $\Delta x=2\pi a$. This is a geometric construction: a periodic spatial projection does not itself establish a propagating wave, a wave equation, or Lorentz covariance. Excitation phase remains state-dependent and distinct from a possible rollout phase reference.

Interaction as a Research Direction

The framework assigns different structural questions to the interaction sectors: closure energetics for strong-sector phenomena, interface reconfiguration for matter-changing weak processes, covariant phase transport for electromagnetism, and compatibility between matter-associated rollouts for gravity.

For phase transport, the proposed comparison takes the form

$$\Delta {\phi }_{\mathrm{phys}}={\phi }_B-{\phi }_A-{\int }_{\gamma }A.$$

A connection constructed only as a smooth local phase gradient has zero local curvature. A physical electromagnetic construction would therefore require additional connection structure. Likewise, compatibility with a spin lift does not yet derive spin or statistics. Each sector still needs explicit dynamical laws and observable tests.

A Separate Calibration Conjecture

The paper retains an empirical energy relation

$$E_C^2=\frac{\pi }{2}{E}_e{E}_I,E_I=(\sqrt{2}{G}_F{)}^{-1/2},$$

where $E_e$ is the electron rest energy and $G_F$ is the Fermi constant in natural units. It gives $E_C\approx 444.56\mathrm{MeV}$, retrospectively close to a reported lattice-QCD flux-tube scale.

This is a replaceable calibration conjecture, not an independent prediction or a consequence derived from the helix. The lattice comparison is tied to a specified flux-tube observable and is not a continuum-limit determination. Subsequent tests must retain that target rather than select whichever reported value lies closest.

Publication Status

Version 2.5 is publicly archived on Zenodo as a preprint under the Creative Commons Attribution 4.0 International license. Its version-specific DOI is 10.5281/zenodo.22723329; the concept DOI for the complete version history is 10.5281/zenodo.22723328. The manuscript has not undergone peer review.

The authoritative PDF, LaTeX source, citation metadata, checksums, and numerical verification code are preserved in the frozen GitHub release. The code checks reported numerical relations; it does not validate the physical framework. Manuscript, source, and metadata use CC BY 4.0; verification code uses the MIT license.

Citation

Wu, X. (2026). The Emergent Frame: A Minimal Framework for Spacetime Rollout, Interaction, and Excitation (Version 2.5). Zenodo. https://doi.org/10.5281/zenodo.22723329

@misc{wu2026minimalframework,
  author = {Wu, Xiaodan},
  title = {The Emergent Frame: A Minimal Framework for Spacetime Rollout, Interaction, and Excitation},
  year = {2026},
  publisher = {Zenodo},
  version = {2.5},
  doi = {10.5281/zenodo.22723329},
  url = {https://doi.org/10.5281/zenodo.22723329}
}

Version History

v2.5 - September 12, 2026

Public preprint release on Zenodo, with companion GitHub release TEF-2026-007-v2.5.

@unpublished{wu2026minimal,
  author = {Xiaodan Wu},
  title = {The Emergent Frame: A Minimal Framework for Spacetime Rollout, Interaction, and Excitation},
  year = {2026},
  note = {TEF-2026-007, version v2.5},
  url = {https://theemergentframe.org/papers/minimal-framework-spacetime-rollout/},
  doi = {10.5281/zenodo.22723329},
}