Rational
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 | {} | ✗ | 2.0015 | ✗ disproven | rigorous_verified |
| K | membership | {} | ✗ | -0.8965 | unscreened | - |
| N | membership | {} | ✓ | 1.3000 | ✓ proven | rigorous_verified |
| ||T(f)|| | bound | {} | ✓ | 2.0015 | ✓ proven | rigorous_verified |
| r* | radius | {} | - | r ≤ 0.960 | 🔬 screened | numerical_strong |
| ||S(f)|| | bound | {} | ✓ | 1.3000 | ✓ 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_becker_univalent_iv | becker_univalent | disproves | pass | 0.153 | [0.15268907563025208, 0.0] | gft-0.1.0-reaudit-20260610 |
| boundary_scan_centered_v31 | starlike | proves | pass | 0.999 | - | boundary_v3.1 |
| boundary_scan_closed_form | starlike | disproves | pass | 0.300 | 0.6*exp(i*1.521709) | boundary_v3.0 |