IndisputableMonolith.Physics.StellarEvolution
Module collecting Recognition-Science scalings for main-sequence stars: nuclear mass-to-energy efficiency of hydrogen fusion, Gamow barrier energy, virial temperature, radius and luminosity power laws, and solar calibration. A physicist deriving stellar structure from the J-cost and phi-ladder would cite these constants and monotonicity lemmas. Most statements are definitional equalities or elementary inequalities over positive reals.
claimNuclear efficiency $\eta_{\mathrm{nuc}} \approx 0.007$ for $4p\to{}^{4}\mathrm{He}$; Gamow energy $E_G(T)$ increasing in temperature; virial temperature $T_{\mathrm{vir}}(M)$ increasing in mass; main-sequence radius $R\propto M^{\alpha}$ with $\alpha<1$; luminosity $L$ strictly increasing in mass, calibrated so the solar point matches.
background
Recognition Science fixes the cost functional $J(x)=(x+x^{-1})/2-1$ (T5) and the golden ratio $\varphi$ as the self-similar fixed point (T6). Stellar structure is treated here as a thin physics layer on top of that cost: rest-mass conversion, Coulomb barrier penetration, and hydrostatic equilibrium are written as explicit real-valued functions of mass and temperature.
The only external import beyond Mathlib is the J-cost compatibility surface, which re-exports the canonical $J$ without redefinition. No eight-tick or dimension-forcing material is used; the module stays inside classical stellar-structure scalings expressed in RS-native constants where convenient.
Sibling declarations introduce nuclear efficiency ($\Delta E/mc^2\approx0.007$ for hydrogen fusion), Gamow energy, virial temperature, sub-linear radius scaling, luminosity scaling, and a solar calibration point that anchors the mass-luminosity relation.
proof idea
The module is largely definitional. Nuclear efficiency is a numerical constant with a validity lemma checking the accepted 0.007-range. Gamow energy, virial temperature, main-sequence radius and luminosity are closed-form expressions in mass and temperature; monotonicity (energy rises with $T$, temperature and luminosity rise with mass, radius exponent sub-linear) is proved by elementary calculus or algebraic comparison on $\mathbb{R}_+$. Solar calibration is an equality fixing the solar mass-luminosity point. No deep forcing-chain argument appears.
why it matters in Recognition Science
Places classical main-sequence scalings inside the Recognition monolith so later mass-ladder or luminosity arguments can cite a single physics module rather than ad-hoc constants. Downstream use is not yet wired (no used_by edges), but the declarations are the natural feed for any stellar or nucleosynthesis layer that needs $\eta_{\mathrm{nuc}}$, Gamow penetration, or $L(M)$. Ties to the broader framework only through the shared $J$-cost import; it does not itself advance T0-T8 or the fine-structure band.
scope and limits
- Does not derive nuclear efficiency from the J-cost or phi-ladder; the value is inserted by hand.
- Does not treat post-main-sequence evolution, degeneracy pressure, or supernovae.
- Does not prove existence of hydrostatic equilibrium from Recognition axioms.
- Does not connect luminosity scalings to the eight-tick octave or D=3 forcing.
- Does not supply observational error bars or metallicity dependence.
depends on (1)
declarations in this module (21)
-
def
nuclear_efficiency -
theorem
nuclear_efficiency_valid -
def
gamow_energy -
theorem
gamow_energy_increases_with_T -
def
virial_temperature -
theorem
temp_increases_with_mass -
def
main_sequence_radius -
theorem
radius_sublinear -
def
luminosity_scaling -
theorem
luminosity_increases -
theorem
solar_calibration -
theorem
massive_star_more_luminous -
def
ms_lifetime -
theorem
lifetime_decreases -
theorem
solar_lifetime_approx -
def
chandrasekhar_limit -
theorem
endpoint_classification -
structure
MainSequenceStar -
def
ms_luminosity -
def
ms_temperature -
theorem
hr_diagram_direction