OPH
07 · The Output Universe

Why does the output look like our Universe?

-21.255.6132209286v_f = (G M_b a₀)^¼ = 140 km/sradius (kpc)circular speed (km/s)
law

derivation map

1
Overlap collars carry unrecovered record

Repair leaves a bounded anomalous modular energy on the collars between observer caps. Under the supplied coupling it gravitates like any other modular charge.

2
Two premises fix the whole profile

Scale covariance in the deep regime and quadrature composition of independent sources force M_A(r) = r √(M_b a₀/G), with one constant.

3
Flat curves and the Tully-Fisher slope

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.

4
The value of a₀ is measured, not derived

A replay of the SPARC catalogue gives a₀ = 1.1613e-10 m/s² with 0.1327 dex scatter. The source fixes the shape only.

flat speed
140 km/s
matching radius
5.5 kpc
fitted a₀
1.1613 ± 0.0802 e-10
a₀ / a_dS
0.214

what the replay covers

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.

data pointers
    verified payloads

      package shared-physics-2026-09-10 · manifest sha256 ec364cad65eede46c7367badf480632e8e39899eedb3abfc883a651789149ff4