N_e_rung_arithmetic
plain-language theorem explainer
The identity 44 + 11 = 55 counts the baryon rung plus passive modes to reach the tenth Fibonacci number on the phi-ladder. Inflation modelers using the J-cost potential cite this when fixing the total e-fold count for slow-roll predictions. The proof is a direct norm_num reduction on natural-number addition.
Claim. $44 + 11 = 55$, where 44 marks the baryon rung and 11 the passive mode count, yielding the tenth Fibonacci number.
background
The J-Cost as the Inflaton Potential module shows that the Recognition Composition Law forces the inflaton potential to G(t) = cosh(t) - 1 in log coordinates. Slow-roll parameters epsilon and eta are then read from the curvature of this potential, with the phi-ladder supplying discrete rung positions for mode counting. The supplied arithmetic fixes the total rung sum at 55 = F_{10}.
proof idea
The proof is a one-line term-mode wrapper that applies norm_num to evaluate the addition of the two natural numbers.
why it matters
This rung count anchors the e-fold total N in the alpha-attractor inflation derived from J-cost curvature. It supplies the denominator for the spectral index 1 - 2/N that appears in the module's master certificate InflationFromJCostCert. The result sits inside the phi-ladder structure forced by the T5-T8 chain.
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