1. Catenary Shape (Eq. 1):
z(x) = a · cosh((x − D_h/2) / a) + C
a = T_h / (m·g)

2. Cable Length (Eq. 2):
L² = Δh² + 4a² sinh²(D_h/(2a))

3. Sag (Eq. 3):
S ≈ (m·g·D_h²) / (8·T_h)

4. Tension Profile (Eq. 4):
T(s) = √(T_h² + (m·g·Δz(s))²)

5. Bending Radius (Eq. 5):
R_bend(s) = 1 / ‖d²r/ds²‖

6. Wind Drag (Eq. 6):
f_d = ½·ρ·C_D·d·v²

7. Wind Deflection (Eq. 7):
y_wind(s) ≈ (f_d / (2·T_h))·s·(L−s)

8. Marcuse Bend Loss (Eq. 13):
α_bend(R) = A·R⁻¹/²·exp(−B·R)

9. OH⁻ Absorption (Eq. 15):
α_OH ∝ t^0.57·exp(−Ea/kT)·f(RH)

10. Total Optical Loss (Eq. 16):
Loss_total(s) = α_base·L + ∫α_bend ds + α_strain + α_OH

11. OFDR Anomaly (Eq. 17):
Anomaly = ‖M(s) − B(s)‖²

12. Dew Point (Eq. 19):
T_dew = b·γ/(a−γ), γ = a·T/(b+T) + ln(RH)

13. Natural Frequencies (Eq. 24):
f_n = (n/(2L))·√(T_h/μ)

14. Arrhythmia Index (Eq. 25):
A(s) = ‖S_current − S_baseline‖ / ‖S_baseline‖

15. Resonance Index (Eq. 26):
R_res = max(E_vib) / max(E_baseline)

16. Safety Risk (Eq. 27):
SafetyRisk(s) = Σ w_i·f_i(…) (8 terms)

17. Vitality (Eq. 28-29):
V_spatial = 1 − (1/L)·∫Risk ds
V(t) = α·V_spatial + (1−α)·V(t−Δt)

18. SVI (Structural Vulnerability Index):
SVI(s) = max(f_cut, f_bend, f_impact, f_fric, f_thermal, f_chem, f_fatigue, f_vortex, f_cyber)