Trigonometric · decay: O(1/n)
The image of the unit disk under \(f\): concentric circles \(|z|=r\) and radial spokes mapped through \(f(z)=z+a_2z^2+\dots\); the bold curve is the boundary \(f(e^{i\theta})\). Rendered in your browser from the certified Taylor coefficients - nothing is computed server-side.
| Property | Kind | Params | Holds | Value / r | Status | Confidence |
|---|---|---|---|---|---|---|
| B | membership | {} | ✗ | 1.9800 | ✗ disproven | rigorous_verified |
| K | membership | {} | ✗ | -11.8168 | unscreened | - |
| N | membership | {} | ✗ | 2.0000 | ✗ disproven | rigorous_verified |
| ||T(f)|| | bound | {} | ✓ | 1.9800 | ✓ proven | rigorous_verified |
| r* | radius | {} | - | r ≤ 0.960 | 🔬 screened | numerical_strong |
| ||S(f)|| | bound | {} | ✓ | 2.0000 | ✓ proven | rigorous_verified |
| S* | membership | {} | ✓ | r ≤ 0.999 | ✓ proven | rigorous_verified |
| S | membership | {} | ✗ | - | unscreened | - |
Because starlikeness is proven, these properties follow by classical implications (unconditional edges in the lattice):
| Verifier | Property | Direction | Outcome | Domain r | Witness | Engine |
|---|---|---|---|---|---|---|
| boundary_scan_closed_form_v31 | starlike | proves | pass | 0.999 | - | boundary_v3.1 |
| pointwise_nehari_univalent_iv | nehari_univalent | disproves | pass | 0.982 | [0.13668201940506597, 0.9725431024691372] | gft-0.1.0-reaudit-20260610 |
| pointwise_becker_univalent_iv | becker_univalent | disproves | pass | 0.990 | [0.1377813699504648, 0.9803653880541546] | gft-0.1.0-reaudit-20260610 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.950 | 0.99*exp(i*6.039282) | boundary_v3.1 |
| boundary_scan_polynomial | starlike | disproves | pass | 0.950 | 0.99*exp(i*3.38818) | boundary_v3.0 |