A connected set of manuscripts developing the Sobolev–Ozok Lattice (SOL): a discrete framework in which spacetime, gravity, and physical structure emerge from Planck-scale coherence.
These papers are not isolated uploads. They form a research program that moves from foundations and mathematical structure to emergent geometry, cosmology, black holes, galaxies, and particle-scale organization.
If you are new to SOL, these papers give the fastest path into the framework: the foundation, a core derived quantity, and the emergent-geometry connection to General Relativity.
Start with the main framework paper to understand the discrete lattice picture, coherence logic, and the overall research direction.
Open foundation paperThis paper presents a minimal axiomatic formulation of the Sobolev-Ozok Lattice (SOL)
Open axioms paperThis work presents a mathematical foundation for the Sobolev–Ozok Lattice (SOL) framework
Open mathematical foundation paperContinue with the Planck-length paper to see how a key physical scale is treated inside the lattice framework.
Open Planck-length paperThen move to the emergent-geometry paper to see how curvature and Einstein-tensor structure are connected to coherence.
Open GR paperFormal structure, stability, and internal mathematical organization of the SOL framework.
Stability analysis and how continuum-like behavior emerges from the discrete SOL model.
Open stability paperAlgebraic structure and coherence hierarchy shaping SOL internal organization.
Open quaternion paperHow curvature and Einstein-tensor structure arise as emergent coherence geometry in SOL.
Derives effective curvature/Einstein-tensor behavior from SOL coherence geometry.
Open GR paperCosmological evolution, horizon/age relations, and large-scale behavior within SOL.
Space evolution, coherence invariants, and the SOL cosmological reset mechanism.
Open K-cycle paperLinks pre-geometric coherence to horizon scale and universe age.
Open horizon/age paperCompact objects and black-hole-like structures derived within SOL.
Derivation, galaxy occupation thresholds, and quasi-black-hole signatures.
Open black holes paperExamines black-hole-type objects emerging in underdense/void-like regimes.
Open void black holes paperGalaxy-scale behavior and empirical relations derived from SOL without dark-matter tuning.
First-principles match to the baryonic Tully–Fisher relation without dark-matter tuning.
Open BTFR paperParticle-scale structure and mass relations from coherence-shell geometry in SOL.
Derivation of the Koide relation from coherence shell geometry within the SOL framework.
Open Koide paperThe SOL program progresses from foundational structure to mathematical formalization, then to emergent geometry, cosmology, compact objects, galaxy-scale behavior, and particle structure.