lambdaRS_pos
plain-language theorem explainer
The theorem establishes that the RS cosmological constant is strictly positive. Cosmologists checking sign consistency of the vacuum energy prediction inside the phi-ladder framework would cite it. The proof is a direct term-mode reduction that unfolds the explicit formula and chains the standard positivity lemmas for multiplication, division, and exponentiation on the reals.
Claim. $0 < 8 phi^5 / 45$, where $phi$ denotes the golden ratio.
background
The Omega Lambda BIT Kernel Band module derives the RS cosmological constant from the phi-ladder. The definition sets lambdaRS to 8 times phi to the fifth divided by 45, using the Fibonacci identity phi^5 equals 5 phi plus 3. This positivity result sits inside the module that certifies the structural value lies in the interval (1.88, 2.03) and matches the observed Omega_Lambda band near 0.6847 times 3 H_0 squared.
proof idea
The term proof unfolds lambdaRS to expose the quotient. It applies div_pos with a positive denominator obtained by norm_num, then mul_pos on the positive constants 8 and 45, and finally pow_pos using the upstream fact that phi is positive.
why it matters
The result supplies the positivity certificate required by omegaLambdaBandCert and cosmologicalConstantCert. It closes the sign check for the RS prediction Lambda_RS equals 8 phi^5 over 45, consistent with the eight-tick octave and the phi-based constants in the Recognition Science chain. No open scaffolding remains on this point.
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