φ-Optimized Bio-Synthetic Space Elevator Tether: A Taper-Ratio φ-Proximity Conjecture and Two Pre-Registered Predictions

φ-Optimized Bio-Synthetic Space Elevator Tether — Honest-Framing Revision. This revision restates the taper result at the strength the math supports. The uniform-stress gravitational taper integral, evaluated at theoretical single-shell carbon-nanotube properties (σ_u = 130 GPa, ρ = 1300 kg/m³), gives A_GEO/A_0 = 1.6229, within δ = 0.0030 of φ = 1.6180. This is reported as a numerical-proximity CONJECTURE (PT3), not a confirmation that φ governs tether taper: the taper ratio is a smooth function of material strength that passes through φ only near this specific (not-yet-achievable) limit — at real CNT strengths (~6.5 GPa) the ratio is ~17,400. The exponential taper law has a complete classical derivation (Pearson-Edwards) that makes no reference to φ. PT1 (φ-graded bundle ~2.93× more mass-efficient) and PT2 (φ-spaced nodes suppress resonance ≥ φ²) are pre-registered conjectures awaiting FEA and modal analysis; PT2’s basis in maximal irrationality (KAM) is sound, only the ≥ φ² factor is conjectural. Co-author: E. T. Waldron. All numbers unchanged. DOI corrected to 10.5281/zenodo.20401418.