IndisputableMonolith.Astrophysics.NucleosynthesisTiers
This module defines φ-tiers as integer indices on the φ-ladder and introduces NuclearTier and LuminosityTier for nucleosynthesis organization. Astrophysicists deriving stellar mass-to-light ratios cite it when eliminating external calibration in M/L calculations. The module supplies supporting definitions that rest on golden-ratio identities and stellar-assembly cost differentials.
claimA $\phi$-tier is an integer index $n$ on the $\phi$-ladder. NuclearTier and LuminosityTier are local tier assignments derived from the ladder step function.
background
The module operates in the astrophysics domain and imports the RS time quantum $\tau_0 = 1$ tick from Constants, recognition-cost primitives from Cost, and golden-ratio lemmas from PhiSupport.Lemmas. The latter establish $\phi^2 = \phi + 1$ and the fixed-point identity $\phi = 1 + 1/\phi$. StellarAssembly supplies the upstream recognition-cost differential between photon emission and mass storage during collapse. The sole module-level doc-comment states that a $\phi$-tier is an integer index on the $\phi$-ladder.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the $\phi$-tier nucleosynthesis definitions required by the Astrophysics aggregator. It is imported by MassToLight (which unifies three independent M/L derivations) and ObservabilityLimits (which bounds M/L via recognition length and tick constraints). The downstream doc-comment lists "$φ$-tier nucleosynthesis" among the central derivations that remove external calibration inputs.
scope and limits
- Does not derive numerical nuclear reaction cross-sections.
- Does not incorporate observational abundance data.
- Does not extend the ladder beyond integer indices.
- Does not address non-stellar nucleosynthesis channels.
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