Does the signal have sevenfold diffraction symmetry — the rarest rotational order in known quasicrystals?
Tests spectral self-similarity at the septagonal ratio rho = 1 + 2*cos(2*pi/7) ~ 2.247, the largest root of x^3 - 2x^2 - x + 1 = 0. The v2 evolution discovered a triple-conjugate ensemble approach: the three roots of the minimal polynomial (rho, its conjugate, and its reciprocal) provide independent spectral probes. Sevenfold symmetry is crystallographically forbidden and extremely rare even among quasicrystals.
Combined coherence across all three roots of the septagonal minimal polynomial. Tests the algebraic identity x^3 = 2x^2 + x - 1 in spectral space. Evolved via ShinkaEvolve.
Spectral self-coherence at the primary septagonal ratio rho ~ 2.247.
Spectral self-coherence at the conjugate root ~ 1.802. Independent probe of the same algebraic structure.
Spectral self-coherence at the reciprocal root ~ 0.445. Completes the triple-conjugate ensemble.
Generic spectral self-similarity under septagonal-ratio scaling. Shared QC spectral machinery.
| Source | Domain | Value |
|---|---|---|
| Bearing Outer | bearing | 0.2479 |
| LIGO Livingston | astro | 0.2183 |
| Solar Wind IMF | astro | 0.2018 |
| ··· | ||
| Circle Map Quasiperiodic | chaos | -0.2729 |
| Phyllotaxis | bio | -0.2558 |
| Fibonacci Word | exotic | -0.2270 |
| Source | Domain | Value |
|---|---|---|
| Tohoku Aftershock Intervals | geophysics | 0.3376 |
| DNA Centromere | bio | 0.3237 |
| LIGO Hanford | astro | 0.2803 |
| ··· | ||
| Divisor Count | number_theory | 0.0000 |
| Rossler Attractor | chaos | 0.0000 |
| Constant 0xFF | noise | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| Bearing Normal | bearing | 0.3970 |
| LIGO Livingston | astro | 0.3462 |
| Logistic r=3.83 (Period-3 Window) | chaos | 0.2515 |
| ··· | ||
| fBm (Persistent) | noise | -0.6934 |
| Bearing Inner | bearing | -0.5921 |
| Brownian Walk | noise | -0.5870 |
| Source | Domain | Value |
|---|---|---|
| Bearing Outer | bearing | 0.4304 |
| Bearing Inner | bearing | 0.3286 |
| Solar Wind IMF | astro | 0.2987 |
| ··· | ||
| Circle Map Quasiperiodic | chaos | -0.5538 |
| Phyllotaxis | bio | -0.5405 |
| Fibonacci Word | exotic | -0.4819 |
| Source | Domain | Value |
|---|---|---|
| Critical Circle Map | chaos | 0.4014 |
| Deep Earthquake P-wave | geophysics | 0.2290 |
| Phyllotaxis | bio | 0.1858 |
| ··· | ||
| Mackey-Glass | medical | -0.4151 |
| Bearing Normal | bearing | -0.3913 |
| Speech "Five" | speech | -0.2264 |
Septagonal is the most exotic geometry in the quasicrystal lens. The triple-conjugate ensemble (z_primary, z_conjugate, z_reciprocal) provides stronger specificity than single-ratio testing: all three roots must show coherence simultaneously for genuine 7-fold order. Septagonal completes the quasicrystal lens's coverage of crystallographically forbidden symmetries (5, 7, 8, 12-fold).