IndisputableMonolith.Astrophysics.ObservabilityLimits
Module defines observability limits via quantities such as recognition length l_rec, coherence energy E_coh, and maximal mass M_max drawn from phi-tier structures. RS astrophysicists cite it when constraining observable stellar parameters from recognition costs. It consists entirely of definitions and imports from nucleosynthesis tiers, stellar assembly, and phi lemmas, with no internal proofs.
claimDefinitions of $J_{ m bit}$, $\phi = (1 + \sqrt{5})/2$, $E_{ m coh}$, $l_{ m rec}$, $F_{ m threshold}$, $V_{ m coherence}$, $M_{ m max}$, $J_{ m mass}$, $J_{ m light}$, $J_{ m total}$, optimal configuration, and the claim that the optimal ratio equals a power of $\phi$.
background
Recognition Science places physical quantities on discrete phi-tiers. The nucleosynthesis tiers module derives mass-to-light ratios from the phi-tier structure of nuclear densities and photon fluxes. The stellar assembly module derives the same ratio from the recognition cost differential between photon emission and mass storage during collapse.
This module imports those results together with the cost module, the constants module fixing the time quantum at one tick, and the phi support lemmas establishing $\phi^2 = \phi + 1$ and the fixed-point identity $\phi = 1 + 1/\phi$. Phi bounds supply algebraic inequalities confirming the value of $\phi$.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the observability limits from $\lambda_{\rm rec}$ and $\tau_0$ constraints to the Astrophysics aggregator. It is imported by the MassToLight module to complete the unified derivation of the stellar mass-to-light ratio. The downstream documentation states that the module eliminates the last external calibration input via three parallel strategies.
scope and limits
- Does not derive mass-to-light ratios.
- Does not prove the phi algebraic identities.
- Does not extend beyond stellar contexts.
- Does not incorporate external observational data.
used by (2)
depends on (6)
declarations in this module (21)
-
def
J_bit -
theorem
phi_eq_goldenRatio -
def
E_coh -
def
l_rec -
def
F_threshold -
def
V_coherence -
def
M_max -
def
J_mass -
def
J_light -
def
J_total -
structure
OptimalConfig -
theorem
optimal_ratio_is_phi_power -
def
ml_geometric -
theorem
ml_geometric_is_phi -
theorem
ml_geometric_bounds -
theorem
information_balance_gives_phi -
theorem
imf_from_j_minimization -
theorem
agrees_with_stellar_assembly -
theorem
agrees_with_nucleosynthesis -
theorem
ml_from_geometry_only -
theorem
ml_zero_parameter_certificate