Explanation of habitability_score

(1) In plain English, the declaration defines a function that accepts a real number e (representing orbital eccentricity) and returns the value 1 / (1 + eccentricity_penalty e). The penalty itself is Jcost(1 + e), where Jcost is the recognition cost function. The result is a real-valued score that is maximized at 1 when e = 0 and decreases as eccentricity increases.

(2) In Recognition Science this matters because the score quantifies orbital stability via minimization of the J-cost of recognition events. It forms one component of the exoplanet habitability model that ties planetary parameters to the forced arithmetic structure (phi-derived resonances and cost symmetry) downstream of the Law of Logic.

(3) The formal statement is read as a noncomputable definition def habitability_score (e : ℝ) : ℝ := 1 / (1 + eccentricity_penalty e). In standard mathematical notation this is the function h(e) = 1 / (1 + J(1 + e)). The surrounding theorems establish that h(0) = 1 and that the penalty is nonnegative for e > -1.

(4) Visible dependencies include the definition of eccentricity_penalty (which calls Jcost) and the theorem habitability_score_at_zero_ecc. The master structure ExoplanetHabitabilityCert bundles the zero-eccentricity case together with positivity and nonnegativity certificates; the concrete witness is exoplanetHabitabilityCert.

(5) The declaration does not prove any composite formula that incorporates T_RS_period or moonMassRatioInBand, nor does it establish empirical agreement with observed exoplanets or derive the score from the full forcing chain.