Pre-registration: zero-setting Locked Twist with starting angle = silver ratio (1 + √2), from the Tree of Life quantum graph, tested on SPT-3G

Pre-registered prediction, written and SHA-256 hashed before any SPT-3G fit of this model was run. Source of the number: treating the Tree of Life (10 sefirot, 22 paths) as a tight-binding quantum graph, exactly two energy levels are antisymmetric between the left and right pillars, at 1 − √2 and 1 + √2 (the silver ratio, 2.41421). Adding Da'at on the middle pillar leaves both unchanged. Computed by the attached tree_quantum.py. The mapping to physics is a choice, not a derivation. Prediction: the Locked Twist early-dark-energy field with switch-on at matter-radiation equality, width F = 1.2247/9 M_Pl (from record 10.5281/zenodo.23838969) and starting angle θ_i = 1 + √2 = 2.41421 rad. Zero extra free settings over ΛCDM. Test: SPT-3G D1 TT/TE/EE + Planck low-ℓ EE τ prior + DESI DR2 BAO + Pantheon+, no SH0ES. PASS if Δχ² < −2 vs ΛCDM; FAIL if Δχ² ≥ 0; otherwise inconclusive. Angle check (θ_i free): consistent within 2.414 ± 0.15 rad, inconsistent beyond 0.35 rad. Disclosed: the Planck best-fit starting angle (about 0.886π ≈ 2.78 rad) was known when this was written, so the prediction lies below it and may fail. No SPT-3G fit of any Twist model had been run. File SHA-256 (PREREGISTRATION_SPT3G_SILVER.md): 8cd05a4c5314b1f5fd9527ffb21745649ef59c9bec2c7bc080a467cce89db648