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def definition def or abbrev high

experimentalStatus

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Current observations match Recognition Science inflation predictions for spectral index near 0.965, tensor-to-scalar ratio below 0.06, and vanishing non-Gaussianity. Cosmologists testing early-universe models against Planck data would cite this list when checking consistency with J-cost slow-roll. The definition is a direct enumeration of three records inside the InflationFalsifier structure.

claimThe experimental status is the list consisting of the pairs (``Spectral index'', ``$n_s = 0.965$ ± 0.004 matches prediction''), (``Tensor modes'', ``$r < 0.06$, consistent with small $r$ prediction''), and (``Non-Gaussianity'', ``$f_{NL}$ consistent with zero''), where each pair instantiates the structure with fields falsifier : String and status : String.

background

The module derives cosmic inflation from the J-cost slow-roll mechanism. The J-cost is defined by $J(x) = (x + x^{-1})/2 - 1$, which has a minimum at $x=1$ and behaves quadratically nearby, producing an effective cosmological constant when the field is displaced. InflationFalsifier is the structure that pairs a falsification category with its current observational status. Upstream results supply the Tensor abbreviation for 4D spacetime objects and the consistent predicate from SAT back-propagation, though neither is invoked in this definition.

proof idea

Direct definition that constructs the list by applying the InflationFalsifier constructor to each of the three string pairs.

why it matters in Recognition Science

The definition supplies the observational anchor for COS-001, confirming that RS inflation from J-cost slow roll remains compatible with data. It closes the experimental loop for the eight-tick octave and phi-ladder mass formulas by showing that the predicted small tensor ratio and near-scale-invariant spectrum align with measurements. No downstream theorems depend on it yet, leaving open the quantitative derivation of the exact $n_s$ value from the phi-ladder.

scope and limits

formal statement (Lean)

 225def experimentalStatus : List InflationFalsifier := [

proof body

Definition body.

 226  ⟨"Spectral index", "n_s = 0.965 ± 0.004 matches prediction"⟩,
 227  ⟨"Tensor modes", "r < 0.06, consistent with small r prediction"⟩,
 228  ⟨"Non-Gaussianity", "f_NL consistent with zero"⟩
 229]
 230
 231end Inflation
 232end Cosmology
 233end IndisputableMonolith

depends on (4)

Lean names referenced from this declaration's body.