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IndisputableMonolith.Cosmology.InflatonPotentialStructural

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The module structures the inflaton potential in Recognition Science cosmology by fixing the e-fold count at 44 on the gap-45 ladder. It supplies definitions for the inflaton regime, slow-roll parameters, and spectral index band. Cosmologists working within RS frameworks cite these for matching CMB observables. The module consists of interconnected definitions and equalities built on the imported time quantum.

claimThe module declares the e-fold count $N_e = 44$ on the gap-45 phi-ladder, the inflaton regime, slow-roll parameters $epsilon$ and $eta$, and the spectral index band derived from the J-cost function.

background

Recognition Science builds cosmology from the unified forcing chain with the fundamental time quantum $tau_0 = 1$ tick supplied by the imported Constants module. The inflaton potential is structured using the J-cost function and phi-ladder rungs, where the gap-45 case fixes the e-fold count. This module introduces the regime in which slow-roll conditions hold and organizes the associated count and parameter definitions.

proof idea

This is a definition module, no proofs. It organizes a collection of definitions for the inflaton regime, e-fold count, slow-roll parameters, and spectral index band, each built directly on the imported time quantum and phi-ladder conventions.

why it matters in Recognition Science

The module supplies the fixed e-fold count $N_e = 44$ that enters downstream calculations of the spectral index and slow-roll parameters in RS cosmology. It connects the phi-ladder structure to inflationary observables and closes the gap-45 case within the forcing chain.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (12)