IndisputableMonolith.Astrophysics.NucleosynthesisTiers
This module defines φ-tiers as integer indices on the φ-ladder together with NuclearTier and LuminosityTier for nucleosynthesis calculations. Astrophysicists using Recognition Science cite it when linking stellar assembly to tier differences in mass-to-light derivations. The module consists of type definitions, local functions, and value computations with no complex proofs.
claimA φ-tier is an integer index $k$ on the φ-ladder. NuclearTier and LuminosityTier are local functions of rung and gap; tier_difference_value computes the difference between them; ml_nucleosynthesis assembles the resulting mass-to-light contribution.
background
The module sits inside the Astrophysics domain and imports StellarAssembly (recognition-weighted collapse), Constants (τ₀ = 1 tick), Cost, and PhiSupport.Lemmas (φ² = φ + 1 and fixed-point identity). It introduces PhiTier as the integer index on the φ-ladder, phi_ladder and phi_ladder_step as the underlying sequence, and the three tier constructors (NuclearTier, LuminosityTier, tier_difference). These rest on the self-similar fixed point from the forcing chain T6.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the nucleosynthesis tier component that feeds the Astrophysics aggregator, the MassToLight unified certificate, and ObservabilityLimits. It completes the φ-tier nucleosynthesis leg of the three parallel M/L strategies and connects directly to the recognition cost differential in StellarAssembly.
scope and limits
- Does not derive the full stellar mass-to-light ratio.
- Does not address observability constraints from λ_rec or τ₀.
- Does not compute numerical tier values for specific nuclei.
- Does not prove properties of the φ-ladder beyond local definitions.
used by (3)
depends on (4)
declarations in this module (20)
-
structure
of -
def
J_bit -
abbrev
PhiTier -
def
phi_ladder -
lemma
phi_ladder_step -
structure
NuclearTier -
def
nuclear_tier_local -
structure
LuminosityTier -
def
luminosity_tier_local -
def
tier_difference -
theorem
tier_difference_value -
def
ml_nucleosynthesis -
theorem
ml_nucleosynthesis_eq_phi -
def
eight_tick_quantizes_tiers -
theorem
tiers_are_quantized -
theorem
ml_matches_stellar_observations -
def
population_tiers -
theorem
all_ml_on_phi_ladder -
theorem
ml_from_phi_tier_structure -
theorem
strategies_agree