IndisputableMonolith.Astrophysics.ExoplanetHabitability
The ExoplanetHabitability module supplies RS-native definitions for dimensionless year length, orbital periods, eccentricity penalties, moon-mass ratios, and a composite habitability score. Astrophysicists applying the Recognition Science framework to exoplanet data would cite these when working in year units rather than ticks. The module consists of definitions plus elementary nonnegativity lemmas with no complex proofs.
claimLet $y$ denote one Earth year expressed in dimensionless RS units. Define the RS orbital period $T_{RS}$, eccentricity penalty $P_e riangleq ext{eccentricity_penalty}$, moon-mass ratio in band, and habitability score $H riangleq ext{habitability_score}$. The module also supplies the certificate $ ext{ExoplanetHabitabilityCert}$.
background
The module imports Constants, whose fundamental time quantum is $ au_0 = 1$ tick, and Cost. It adopts the convention stated in its doc-comment: one year in dimensionless RS units. Sibling declarations introduce year_dimensionless, T_RS_period, eccentricity_penalty (with zero and nonnegativity lemmas), moonMassRatioInBand, habitability_score (with zero-eccentricity case), and the certificate ExoplanetHabitabilityCert.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the habitability interface that downstream astrophysics work in Recognition Science can reference. It connects the time quantum of Constants to concrete orbital and penalty quantities, supporting calculations that remain inside the phi-ladder and eight-tick octave structure of the framework.
scope and limits
- Does not derive numerical habitability values for named exoplanets.
- Does not prove any relation between habitability score and the J-cost function.
- Does not address stellar spectral type or atmospheric chemistry.
- Does not claim the score is the unique RS measure of habitability.
depends on (2)
declarations in this module (11)
-
def
year_dimensionless -
def
T_RS_period -
def
eccentricity_penalty -
theorem
eccentricity_penalty_zero -
def
moonMassRatioInBand -
theorem
T_RS_period_pos -
def
habitability_score -
theorem
habitability_score_at_zero_ecc -
theorem
eccentricity_penalty_nonneg -
structure
ExoplanetHabitabilityCert -
def
exoplanetHabitabilityCert