Polynomial · parametric, arity 1 · polynomial
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 |
|---|---|---|---|---|---|---|
| K | membership | {"variant": 1} | ✗ | -23.0000 | unscreened | - |
| K | membership | {"variant": 2} | ✗ | -166.5196 | unscreened | - |
| r* | radius | {"variant": 1} | - | r ≤ 0.960 | 🔬 screened | numerical_strong |
| r* | radius | {"variant": 2} | - | r ≤ 0.788 | 🔬 screened | numerical_strong |
| S* | membership | {"variant": 1} | ✓ | r ≤ 0.999 | ✓ proven | rigorous_verified |
| S* | membership | {"variant": 2} | ✗ | r ≤ 0.600 | ✗ disproven | proven |
| S | membership | {"variant": 1} | ✗ | - | unscreened | - |
| S | membership | {"variant": 2} | ✗ | - | 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_centered_v31 | starlike | proves | pass | 0.999 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.600 | 0.8*exp(i*0.006136) | boundary_v3.1 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.990 | [0.99, 0.0] | gft-0.1.0-reaudit-20260610 |
| boundary_scan_polynomial | starlike | proves | pass | 0.999 | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | disproves | pass | 0.600 | 0.8*exp(i*6.258642) | boundary_v3.0 |