Why does the output look like our Universe?
derivation map
Repair leaves a bounded anomalous modular energy on the collars between observer caps. Under the supplied coupling it gravitates like any other modular charge.
Scale covariance in the deep regime and quadrature composition of independent sources force M_A(r) = r √(M_b a₀/G), with one constant.
a_A = √(a_b a₀) gives v² = √(G M_b a₀), independent of radius, so v⁴ = G M_b a₀. The exponents ½ and 4 carry no free parameter.
A replay of the SPARC catalogue gives a₀ = 1.1613e-10 m/s² with 0.1327 dex scatter. The source fixes the shape only.
what the replay covers
| quantity | value |
|---|---|
| points retained | 2,696 in 147 galaxies |
| parent selection | 153 galaxies |
| log residual scatter | 0.1327 dex |
| fitted anomalous exponents | 0.454, 0.461, 0.239 |
| weighting sensitivity | -9.58% and +15.49% |
| de Sitter scale | a_dS = c²√(Λ/3) = 5.42e-10 m/s² |
The curve you move is the paper law evaluated for a point baryonic mass. The catalogue fit and the de Sitter comparison are quoted values from Dark sector and rotation curves (r2042). The magnitude of a₀, the transition inside the matching radius, and a lensing law are open.
Follow the complete readout from finite causal records into a smooth spacetime image, effective gravity, microscopic interactions, a black-hole lens and an observer-centred sky diagnostic.
The shape and exponents follow from two named premises. The value of a₀ is fitted to public rotation-curve data, and lensing plus abundance are open.
source and scope
What is drawn: Closed-form laws M_A(r) = r√(M_b a₀/G), a_A = √(a_b a₀) and v⁴ = G M_b a₀, with the catalogue replay values.
package shared-physics-2026-09-10 · manifest sha256 ec364cad65eede46c7367badf480632e8e39899eedb3abfc883a651789149ff4