IndisputableMonolith.Astrophysics.ObservabilityLimits
This module defines observability limits for Recognition Science astrophysics via quantities such as recognition length l_rec, coherence energy E_coh, and J-cost thresholds built on the golden ratio. Astrophysicists cite it when bounding stellar parameters from RS first principles without external inputs. It is a definitions module that assembles imported lemmas from phi support, nucleosynthesis tiers, and stellar assembly into concrete RS-native objects.
claim$l_{rec}$, $E_{coh}$, $F_{threshold}$, $V_{coherence}$, $M_{max}$, $J_{mass}$, $J_{light}$, $J_{total}$ and the optimal ratio on the phi-ladder, with $J_{bit}$ and $E_{coh}$ expressed via the J-cost function and golden ratio bounds.
background
Recognition Science places physical quantities on discrete phi-tiers, as stated in the NucleosynthesisTiers module: 'physical quantities occupy discrete φ-tiers'. StellarAssembly derives M/L from the recognition cost differential during collapse. Constants fixes the RS time quantum τ₀ = 1 tick. PhiSupport.Lemmas supplies the identities φ² = φ + 1 and the fixed-point property φ = 1 + 1/φ. PhiBounds gives algebraic bounds on φ = (1 + √5)/2. The Cost module supplies the underlying J-cost function.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
This module feeds the Astrophysics aggregator and the MassToLight derivation. It supplies the observability limits from λ_rec and τ0 constraints that complete the unified M/L certificate, eliminating external calibration. The downstream MassToLight doc-comment notes the three parallel strategies that rely on these limits.
scope and limits
- Does not derive numerical values for any observability limit.
- Does not prove theorems about stellar collapse or nucleosynthesis.
- Does not address non-stellar or cosmological scales.
- Does not incorporate general-relativistic or quantum-field corrections.
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