V
plain-language theorem explainer
The definition supplies the inflaton potential on the recognition manifold by setting V(φ_inf) equal to the J-cost evaluated at one plus the field displacement. Cosmologists extending the gap-45 inflation results would cite this to obtain an explicit scalar potential for slow-roll analysis. The implementation is a direct one-line abbreviation of the Jcost function from the Cost module.
Claim. $V(φ_{inf}) = J(1 + φ_{inf})$, where $J$ is the recognition cost function and $φ_{inf}$ is the dimensionless displacement of the Z-coordinate from the canonical reference rung.
background
The module fills the gap left by prior inflation work deriving $N_e = 44$, $n_s ≈ 0.9556$, and $r ≈ 0.017$ from the gap-45 identity. It introduces the inflaton field $φ_{inf}$ as the deviation of the Z-coordinate from the consciousness-gap reference rung on the recognition manifold. The potential is defined via the same J that governs all recognition phenomena, with slow-roll parameters at $φ_{inf} = 0$ given by the quadratic Taylor coefficients of J: vacuum value zero, first derivative zero, second derivative one.
proof idea
One-line wrapper that applies the Jcost function from the Cost module (Quantity CostUnit) to the shifted argument 1 + phi_inf.
why it matters
This definition supplies the scalar potential required by the energyConservationCert and Hamiltonian structures in the Action module, including energy_conservation and hamilton_equations_from_EL. It grounds the universal slow-roll inflation profile (ε_V and η_V vanishing at the reference point) that supports the existing n_s = 1 − 2/45 and r = 2/(45 φ²) predictions. It directly implements the J-uniqueness landmark (T5) in a cosmological setting.
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