c_RS
plain-language theorem explainer
Recognition Science defines its leading-log coefficient for black-hole entropy corrections as c_RS = -log φ / 2. Researchers comparing discrete ledger models to semiclassical gravity would cite this value when distinguishing the φ-rational term from LQG or string-theory predictions. The definition is a direct algebraic expression drawn from the J-cost and eight-tick ledger structure.
Claim. The Recognition Science leading-log coefficient for black-hole entropy is given by $c_{RS} = - (ln φ)/2$, where φ is the golden ratio fixed point of the Recognition Composition Law.
background
The Black-Hole Entropy from the Ledger module recovers the Bekenstein-Hawking entropy from the discrete RS ledger as the count of admissible horizon states modulo σ-equivalence. The leading-order term is S_lead(A) = A/4 in RS-native units with ℓ_P = 1. The logarithmic correction carries the coefficient defined here. Upstream results supply Constants.phi from the Law of Existence structure and the propagation speed set to 1 in Gravity.PropagationSpeed. The module doc-comment states that this φ-rational coefficient is structurally distinct from the LQG value -1/2 and the string-theory value -3/2.
proof idea
The declaration is a direct definition that sets the coefficient to the negative of the natural logarithm of Constants.phi divided by two. No lemmas or tactics are applied; the expression is the explicit algebraic form of the leading-log term.
why it matters
This supplies the numerical coefficient that enters the combined entropy formula S_RS(A) = A/4 + c_RS log A. It feeds downstream derivations in Cosmology.EtaBPrefactorDerivation for washout prefactors. The value distinguishes the RS prediction from LQG and string-theory coefficients, closing the algebraic structure part of the leading-log coefficient theorem in the F6 track. It aligns with T5 J-uniqueness and T7 eight-tick octave landmarks.
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