Time-Density / Time-Gradient Model: Research Declaration

# Heading 1Research DeclarationTime-Density / Time-Gradient ModelResearch by Kaji This record presents an ongoing independent research project conducted by Kaji.The study is based on the original theoretical framework called theTime-Density / Time-Gradient Model, which treats time density and its spatial gradientas primary physical quantities. The research explores new descriptions of cosmic structure,gravity, observation, and the internal structure of black holes. # Heading 11. Research Ownership 1.1 This research is independently led by Kaji.1.2 External studies are referenced when necessary and used to support understanding.1.3 Adoption of external studies is determined by confirming mutual consistency with this theoretical framework.1.4 This maintains the independence of the model while preserving a cooperative relationship with external research. # Heading 12. Scope of Research (Depth 3 + Depth 2) 2.1 The project formally includes both Depth 3 (new foundational theories) and Depth 2 (theoretical candidates) as research targets.2.2 Depth 2 items are already suitable for basic investigation and are managed as a dynamic list, subject to addition, integration, or reclassification as the research progresses. # Heading 13. Depth 3 — Foundational Theories (Numbered List) 3.1 Gravity as Time-Gradient (Gravity = −c² ∇T) Gravity is defined not as curvature of space but as the spatial gradient of time density. 3.2 Time as a Density Field (Time = pt) Time is treated as a density field, not as a flow. 3.3 Time-Stopping Boundary (pt = 0) A boundary where time fully stops, forming the basis of black hole interior structure. 3.4 Information Fixation Layer A layer at pt = 0 where information becomes fixed. 3.5 Cosmic Structure from Time-Density Landscape Filaments correspond to valleys of pt, voids to highlands—a new model of cosmic structure. 3.6 Redshift from Time-Density Gradient (Redshift = ∇pt) Redshift is interpreted as an optical effect caused by gradients in time density, not cosmic expansion. 3.7 Optical Displacement of the Observer The observer’s apparent position changes optically according to the time-density landscape. Total Depth 3 theories: 7. # Heading 14. Depth 2 — Theoretical Candidates (Full List) 4.1 Black hole growth (outer time-density shell expansion)4.2 Neutron accumulation and internal instability4.3 Formation of time-density fractures4.4 Time phase transition (Δt revival)4.5 Black hole collapse explosions4.6 Big Bang traces as black hole collapse afterglow4.7 Supernova energy deviation explained by BH formation/collapse4.8 Non-alignment of black hole age and cosmic age4.9 Unobserved supernovae (observer optical displacement)4.10 Local rupture of outer universe by neutrons (pt=0 wall breach)4.11 Independent phenomena in the outer universe4.12 Multiple phase-transition collapse events4.13 Absence of neutron accumulation in galaxy outskirts4.14 Time-density flow field4.15 Non-fixed observer position (pt landscape dependence)4.16 Local reconstruction of time density4.17 Role of the outer universe in hierarchical cosmic models4.18 Causal isolation between inner universes4.19 Phase-transition potential in the outer universe4.20 Stability and fluctuation of time-density boundaries4.21 Variability of the information fixation layer4.22 Synchronized nuclear reactions during Δt revival4.23 Directional dependence of observables from pt landscape4.24 Curvature of light paths due to time density4.25 Local destruction conditions of time-stopping boundaries4.26 Critical points of time density and phase transitions4.27 Layered time-density structures4.28 Boundary structure between outer and inner universes4.29 Nonlinear evolution equation of time density (candidate) # Heading 15. Research Objective The aim of this research is to construct a new physical description based ontime density and time gradients, expanding the understanding of cosmic structure,gravity, and observation. # Heading 16. Publication Policy Research content is released progressively and updated as theoretical structure,mathematical formulation, and observational consistency advance. # Heading 1Summary This project is an independent theoretical study by Kaji.All Depth 3 theories and Depth 2 candidates are included as research targets.Depth 2 items are managed as a dynamic list, and external studies are evaluatedbased on mutual consistency with the Time-Density / Time-Gradient Model.