Jump Theory: Structural Framework (v0.8) and Linear Perturbations (v0.9)

Title
Jump Theory: Structural Framework (v0.8) and Linear Perturbations (v0.9)

Author
Takehiro Furukawa

Publication Date
2025-12-25

Document Roles

Jump Theory v0.8 — definitive structural formulation of the framework.

Jump Theory v0.9  — finalized formulation focused on background evolution and linear perturbations.

Technical Notes — numerical and phenomenological consistency checks only; no new theoretical assumptions.

Abstract

Jump Theory (JT) is a unified framework in which time is not treated as an external continuous parameter, and instead emerges from the statistical density of irreversible quantum jumps.
Within this formulation, gravity, dark matter, and dark energy arise from a single scalar structure—the time-density field λ—without introducing new particles.

Version v0.9 represents the finalized pre–v1.0 formulation of Jump Theory.
This release consolidates earlier developments, clarifies the foundational quantum interpretation (Appendix Z), and explicitly defines the domain of validity as an effective theory.

In v0.9:

gravity is identified with gradients of time density,

dark-matter–like effects arise as nonlocal temporal response, and

dark-energy–like acceleration follows from global dilution of jump density.

A single nonlocal operator governs gravitational dynamics across galactic, cluster, and cosmological scales, and the cosmological Jump Sector reproduces CDM-like background evolution and linear structure growth without invoking cold dark matter particles.

Appendix Z provides a consistent quantum foundation based on open quantum systems and quantum-jump dynamics, in which λ acts as a non-propagating constraint/measure field.

No additional free parameters are introduced beyond those fixed by galactic and cluster-scale observations.
Numerical analyses serve solely as internal consistency checks.

This version is intended as a stable reference point for Jump Theory prior to v1.0.

Notes

This release consolidates the structural foundation (v0.8) and the latest perturbation analysis (v0.9).

Appendix Z constitutes the foundational quantum layer and is treated as non-modifiable in subsequent versions.

A separate Technical Notes document accompanies this release, documenting numerical implementations and phenomenological tests.

Simplified numerical solver results presented in v0.7 were used only for early consistency checks and are intentionally not retained in v0.9.

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Contact

tfk.jump.theory@gmail.com