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module module high

IndisputableMonolith.Cosmology.InflatonPotentialFromJCost

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This module defines the inflaton potential on the recognition manifold as V(φ_inf) = J(1 + φ_inf), with φ_inf the dimensionless displacement from the canonical reference rung. Cosmologists modeling inflation within Recognition Science cite it to link the J-cost to early-universe dynamics. The module consists of definitions and basic properties built directly from the imported J-cost and time quantum.

claim$V(\phi_{\inf}) = J(1 + \phi_{\inf})$, where $\phi_{\inf}$ denotes the dimensionless displacement from the canonical reference rung on the recognition manifold.

background

The module imports the J-cost from IndisputableMonolith.Cost and the RS time quantum τ₀ = 1 tick from IndisputableMonolith.Constants. Recognition Science constructs all physics from the functional equation whose solution yields the J function satisfying the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). The inflaton potential is obtained by evaluating this J-cost at the shifted argument 1 + φ_inf.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the inflaton potential for cosmological models in the Recognition framework. It realizes the J-cost in the context of inflation and connects to the phi-ladder and mass formulas. No direct downstream theorems are listed in the used_by edges.

scope and limits

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (9)