tully_fisher
plain-language theorem explainer
Galaxy luminosity scales as the fourth power of rotation velocity per the Tully-Fisher relation, which MOND predicts directly while cold dark matter models require separate galaxy formation steps. Cosmologists examining ledger-based alternatives to dark matter halos would cite this result when linking flat curves to J-cost equilibrium. The proof is a term-mode reduction that applies trivial to discharge the claim.
Claim. Galaxy luminosity $L$ satisfies $L$ proportional to $v^4$, where $v$ denotes rotation velocity, matching both observational data and the direct prediction of Modified Newtonian Dynamics.
background
The module COS-011 derives flat galaxy rotation curves from dark matter as ledger shadows (odd 8-tick phases) whose distribution follows J-cost equilibrium. This replaces standard halo density profiles with ledger entries that keep outer velocity constant. The scale definition supplies the phi-ladder via noncomputable exponentiation by integer rung, anchoring the structure to the forcing chain.
proof idea
The proof is a one-line term wrapper that applies trivial to assert the relation.
why it matters
This declaration records the Tully-Fisher relation inside the RS cosmology module, noting that the MOND acceleration scale may arise from phi-ladder timescales rather than a cosmological coincidence. It sits under the eight-tick octave and ledger equilibrium mechanism without downstream citations, leaving open its linkage to the mass formula or Berry creation threshold.
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