Each n-shell appears as a strand pair: two parallel rows (Strand 1 ↑ matter / Strand 2 ↓ mirror). Noble gases are helix closure nodes (right end of each pair, bold border). The f-block is integrated within the high-n pairs — not exiled to a footnote. Columns represent the same angular position θ(Z) across all shells — the neutron bond axis. Planet labels show the s-orbital sequence P-ENODE-3: Mercury=P1, Earth=P2, Mars=P3, Jupiter=P4, Saturn=P5, Uranus=P6, Neptune=P7. The Atomic Helix Horizon (between P6 and P7) marks where n²=49=7² exits the {2,3,5} prime lattice — every Period 7 element is radioactive.
The n² operator governs three independent domains simultaneously: hydrogen energy levels (E_n = G₁/n²), periodic table capacity (2n² elements per shell), and planetary rotation coordinates (c-exponent structure). Each row below shows one unified index across all three domains. Total Τ = 2G₁ holds for every n.
| n | Planet | n² | Lattice form | G₁/n² (eV) | 2n² capacity | Total Τ | {2,3,5} lattice? |
|---|---|---|---|---|---|---|---|
| 1 | ☿ Mercury | 1 | 1 = 2⁰ | 13.6056 | 2 | 2G₁ | YES ✓ |
| 2 | ♁ Earth | 4 | 2² | 3.4014 | 8 | 2G₁ | YES ✓ |
| 3 | ♂ Mars | 9 | 3² | 1.5117 | 18 | 2G₁ | YES ✓ |
| 4 | ♃ Jupiter | 16 | 2⁴ | 0.8504 | 32 | 2G₁ | YES ✓ |
| 5 | ♄ Saturn | 25 | 5² | 0.5442 | 50 | 2G₁ | YES ✓ |
| 6 | ♅ Uranus | 36 | 2²×3² | 0.3779 | 72 | 2G₁ | YES ✓ — LAST |
| ━━━━ ATOMIC HELIX HORIZON ━━━━ | n²=36 → n²=49 | {2,3,5} lattice → prime-7 domain | P-EQL-6 | |||||||
| 7 | ♆ Neptune | 49 | 7² | 0.2777 | 98 | 2G₁ | NO ✗ — OFF-LATTICE |
P-EQL-7: The n² equalization law is universal — the same operator at three dimensional registers. P-EQL-8: Period 7 universal radioactivity is the Atomic Helix Horizon signature — n²=49=7² is off-lattice. P-EQL-9: Neptune (n=7 planetary position) escapes prime-7 because k=0 (outside planetary Helix Horizon). P-EQL-10: 20,000/π is the universal equalization constant — the n² normalization node. P-EQL-11: 5² bridges hydrogen n=5 and Mars/Venus c=+2 planetary coordinates. P-EQL-12: Reading across any row gives three simultaneous views of the same Τ-field node (P-ENODE-3).