IndisputableMonolith.Gravity.RotationILG
This module defines the ILG-enhanced galactic rotation velocity satisfying the fixed-point equation v squared equals w_t of r and v times G M_b over r. Galaxy modelers working in Recognition Science gravity cite it to replace Newtonian rotation curves with the ILG correction. The module supplies the velocity function together with existence and mismatch predicates built on the imported Rotation and ILG modules.
claimThe module introduces the ILG rotation velocity $v(r)$ obeying the fixed-point relation $v^2 = w_t(r,v) · G M_b / r$, where $w_t$ is the ILG weight drawn from the ILG module and $M_b$ is the baryonic enclosed mass from the Rotation module.
background
The module sits inside the Gravity domain and imports the RS time quantum τ₀ from Constants, the ILG weight function from Gravity.ILG, and the standard rotation setup (G and Menc) from Gravity.Rotation. These pieces combine to replace the Newtonian balance v² = G M / r with an ILG-modified fixed point that incorporates the Recognition Composition Law through the weight w_t. The setting assumes a thin-disk geometry and uses the phi-ladder mass scaling only indirectly via the imported constants.
proof idea
This is a definition module. It declares the velocity function, the predicate is_ilg_vrot that checks the fixed-point equation, the existence theorem solution_exists, and the SPARC_mismatch_falsifier predicate. No tactic scripts or algebraic reductions appear at the module level; all content is supplied by the three imported modules.
why it matters in Recognition Science
The module supplies the velocity object used by the sibling declarations is_ilg_vrot, solution_exists, and SPARC_mismatch_falsifier. It therefore bridges the Rotation and ILG modules to enable direct comparison of predicted rotation curves against SPARC data, closing one link in the T8 spatial-dimension chain for galactic dynamics.
scope and limits
- Does not derive the weight function w_t from the J-cost or RCL.
- Does not perform numerical integration of rotation curves.
- Does not treat non-axisymmetric or three-dimensional mass distributions.
- Does not address time-dependent or relativistic corrections.