J_light
J_light supplies the recognition cost tied to luminosity at scale ratio r by direct reference to the underlying J-cost. Researchers deriving mass-to-light ratios from observability bounds in stellar systems cite this when assembling the total cost for minimization. The definition is a one-line alias to the cost function induced by the multiplicative recognizer.
claimThe recognition cost for a luminosity configuration at scale ratio $r$ is $J(r)$, where $J$ is the cost function induced by a multiplicative recognizer on positive ratios.
background
The module develops recognition-bounded observability for stellar systems. Observable flux must exceed the coherence energy divided by the fundamental tick, while mass assembly is limited by coherence volume of order the recognition length cubed. The J-cost for any recognition event is its J-cost, and the cost function induced by a multiplicative recognizer is the derived cost of its comparator on positive ratios.
proof idea
One-line definition that applies the J-cost function directly to the input scale ratio for the luminosity component.
why it matters in Recognition Science
This supplies the light term in the total J-cost minimized subject to observability constraints, producing M/L ratios in the set of phi powers from n=0 to 3. It feeds the parent definition of total cost and aligns with the phi-ladder and eight-tick octave of the forcing chain.
scope and limits
- Does not compute explicit numerical values for given stellar parameters.
- Does not incorporate distance-dependent attenuation or redshift effects.
- Does not address non-stellar or non-luminous configurations.
- Does not derive the optimal ratio itself.
formal statement (Lean)
85noncomputable def J_light (r : ℝ) : ℝ := Cost.Jcost r
proof body
Definition body.
86
87/-- Total J-cost for stellar configuration -/