A Discrete Informational Framework for Classical Gravity: Ledger Foundations and Galaxy Rotation Curve Constraints.

Area of Science:

• Theoretical Physics
• Cosmology
• Gravitational Physics

Background:

• The Newton-Poisson equation describes gravity in the weak-field, quasi-static regime.
• Existing models often require extensive parameter tuning for galactic dynamics.
• A need exists for fundamental, constraint-based models of gravitational response.

Purpose of the Study:

• To construct the weak-field, quasi-static gravitational response from first principles using a discrete variational framework.
• To investigate the implications of finite equilibration and scale-free properties on gravitational response.
• To test the derived model against observational data of galaxy rotation curves.

Main Methods:

• Development of a cost-first discrete variational framework incorporating Recognition Composition Law (RCL) and discrete ledger axioms.
• Derivation of a scale-free modification to the source-potential relation with a power-law kernel in Fourier space.
• Evaluation against SPARC galaxy rotation curves using a multiplicative surrogate for the nonlocal disk operator under strict global-only constraints.

Main Results:

• The Newton-Poisson baseline is recovered in the instantaneous-closure limit.
• Finite equilibration introduces fractional memory, resulting in a scale-free modification characterized by a power-law kernel.
• The model achieved a median(χ²/N)=3.06 for 147 galaxies, outperforming the NFW benchmark under identical constraints.

Conclusions:

• The derived quasi-static kernel provides a scale-free modification of gravitational response motivated by fundamental principles.
• The model's performance against galaxy rotation curves suggests consistency within the tested non-relativistic, quasi-static sector.
• Further research is needed for relativistic completion and Solar System viability, requiring UV regularization and screening.