Title Jump Theory v0.6: The Complete Open Specification — Unified Time–Gravity Framework, Full Lagrangian, and Observational Validation Authors TFK (Takehiro Furukawa) Publication Date 2025-11-17 Abstract Jump Theory v0.6 presents the first fully open, technically complete specification of a unified time–gravity framework in which time density—the quantum jump rate λ(x)—plays the central physical role. Gravity emerges as the spatial gradient of λ, while the flow of proper time is determined by dτ = λ dt. This redefinition provides a single mechanism for gravitational dynamics, cosmic acceleration, and black-hole structure without invoking dark matter or dark energy as physical substances.The theory is formulated within the scalar–tensor Horndeski class, ensuring second-order covariance, ghost freedom, and luminal tensor modes. In the quasistatic limit, Jump Theory reduces to a fourth-order Poisson equation, introducing two universal scale parameters: ℓ_gal (galaxies) and ℓ_cl (clusters).Using these two fixed scales and no dark-sector components, v0.6 reproduces:• galaxy rotation curves (SPARC 165) at MOND-level accuracy,• strong + weak lensing mass profiles of massive clusters including A1689,• stability and structure of black holes without singularities,• FRW cosmic expansion driven by temporal-density dilution,• scale-dependent large-scale structure growth compatible with observations.This release includes the full Lagrangian, complete derivations, numerical solvers, observational pipelines, and appendices A–Z covering mathematical foundations, causality, error propagation, and comparative analysis against GR and MOND. Jump Theory v0.6 is designed as a reproducible, falsifiable, and publicly accessible foundation for next-generation gravitational physics. Keywords Jump Theory; Modified Gravity; Dark Matter Alternatives; Dark Energy Alternatives; Scalar-Tensor Gravity; Horndeski; Galaxy Rotation Curves; A1689; Cosmology; Unified Gravity Model; Time Density Subjects Astrophysics; Cosmology and Nongalactic Astrophysics; General Relativity and Quantum Cosmology; High Energy Physics – Theory License CC-BY 4.0 Version v0.6 — First Complete Public Release Notes Upload the unified Word/PDF file containing Sec1–9 and Appendices A–Z. Zenodo will automatically assign a DOI.