CORE CRR FRAMEWORK
C(x,t) = ∫₀ᵗ L(x,τ) dτ
Coherence Accumulation: Integral of luminous intensity over time. For Betelgeuse, coherence builds over vastly longer timescales than main-sequence stars.
δ(now)
Rupture: Dirac delta marking ontological present. In supergiants: pulsation peaks, cell turnover, mass ejection.
R = ∫ φ(x,τ)·exp(C/Ω)·Θ(τ) dτ
Regeneration: Post-rupture reconstruction weighted by exp(C/Ω). Higher coherence = stronger memory influence on new state.
Ω-SYMMETRY THEOREM
Ω = 1/φ_G
φ_G = phase (radians) of symmetry group's fundamental domain.
Z₂ (binary, φ=π):Ω = 1/π ≈ 0.31831
SO(2) (rotation, φ=2π):Ω = 1/2π ≈ 0.15915
Universal amplification:e^π ≈ 23.14
Connection to FEP: Precision = 1/σ² = 1/Ω = φ_G
GIANT CONVECTION CELLS SO(2)
τ_conv ≈ 1 year
THE defining visual feature! Only ~10-20 cells (vs 10⁶ on Sun), each ~57° and ~3 AU across. Visible in interferometry!
C_cell(t) = ∫ L_thermal(τ) dτ
Coherence: Hot plasma rises over months. Cell brightness tracks coherence.
brightness = 0.5 + 0.5·sin(lifePhase)
Peak at π/2 (max coherence), minimum at 3π/2 (regeneration).
PRIMARY PULSATION SO(2)
τ_pulsation = 400 days
Semi-regular variable (SRc). Entire star undergoes C→δ→R at this timescale.
R(t) = R₀ × (1 + 0.15·sin(ωt))
Radius: ±15% variation (764 R☉ ± 115 R☉)
L ∝ R² × T⁴
Stefan-Boltzmann: ~30% brightness variation. Cooling dominates during expansion.
LIVE PULSATION
Phase: 0° | R: 764 R☉
MASS EJECTION Z₂
τ_ejection ~ 25 years
2019-2020 "Great Dimming": Massive ejection formed dust cloud blocking ~60% of light.
P(ejection) ∝ exp(C/Ω_Z₂)
Z₂ Rupture: Binary event—material ejected or not. Memory weight determines transition probability.
CIRCUMSTELLAR ENVELOPE SO(2)
Ṁ ≈ 10⁻⁶ M☉/year
Intense stellar wind creates nested dust shells to ~100 R*.
v_wind ≈ 15 km/s
Inner shell transit:~10 years
OBSERVER CRR CHAIN
Same timescales for any star—these are OUR perceptual dynamics:
Display (Z₂):τ = 16.67ms
Atmosphere (SO(2)):τ = π ms
Retina (Z₂):τ = 100ms
V1 gamma (SO(2)):τ = 25ms
BETELGEUSE vs SIRIUS
Convection τ:1 yr vs 7 days (52×)
Cell count:~12 vs ~10⁶
Pulsation τ:400d vs 46min (12,500×)
Temperature:3,500K vs 9,940K