IndisputableMonolith.Astrophysics.ExoplanetHabitability
The Astrophysics.ExoplanetHabitability module supplies RS-native definitions for exoplanet habitability metrics, beginning with a dimensionless year and extending to eccentricity penalties and composite scores that incorporate moon mass ratios. Exoplanet researchers working in Recognition Science units cite these for consistent scaling along the phi-ladder. The module consists of direct definitions and elementary lemmas on non-negativity and zero cases.
claimIn RS units let $Y$ denote the dimensionless year with $Y=1$. Define the RS orbital period $T_{RS}$ and eccentricity penalty $P_e$ satisfying $P_e(0)=0$ and $P_e(e)geq 0$. The habitability score combines $T_{RS}$, $P_e$, and the moon mass ratio restricted to the allowed band.
background
Recognition Science works in native units where the time quantum τ₀ equals one tick, as stated in the imported Constants module. This module adopts year units for orbital periods by defining year_dimensionless to normalize one year to unity. The Cost module supplies the J-cost framework that underlies the penalty constructions. Sibling definitions include T_RS_period for the RS-scaled orbital period and habitability_score for the composite metric.
proof idea
This is a definition module, no proofs. It consists of direct definitions for quantities such as year_dimensionless and T_RS_period, together with lemmas establishing basic properties such as positivity of T_RS_period and non-negativity of the eccentricity penalty.
why it matters in Recognition Science
The module establishes the RS-unit foundation for exoplanet habitability assessments inside the Recognition framework. It links orbital periods to the T7 eight-tick octave through T_RS_period and supports scaling consistent with D=3 and the phi-ladder. The certification object ExoplanetHabitabilityCert supplies a structured interface for downstream astrophysical modeling.
scope and limits
- Does not compute habitability for concrete exoplanet data sets.
- Does not incorporate stellar type or insolation details.
- Does not address tidal locking or atmospheric retention.
- Does not derive from the full UnifiedForcingChain T0-T8.
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