Polynomial · 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 |
|---|---|---|---|---|---|---|
| B | membership | {} | ✗ | 1.9500 | ✗ disproven | rigorous_verified |
| N | membership | {} | ✗ | 5.7038 | ✗ disproven | rigorous_verified |
| ||T(f)|| | bound | {} | ✓ | 1.9500 | ✓ proven | rigorous_verified |
| ||S(f)|| | bound | {} | ✓ | 5.7038 | ✓ proven | rigorous_verified |
| S* | membership | {} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| Verifier | Property | Direction | Outcome | Domain r | Witness | Engine |
|---|---|---|---|---|---|---|
| boundary_scan_closed_form_v31 | starlike | disproves | pass | 0.000 | 0.3*exp(i*3.043418) | boundary_v3.1 |
| pointwise_nehari_univalent_iv | nehari_univalent | disproves | pass | 0.168 | [-0.16848739495798318, 2.0633754893197e-17] | gft-0.1.0-reaudit-20260610 |
| pointwise_becker_univalent_iv | becker_univalent | disproves | pass | 0.168 | [-0.16848739495798318, 2.0633754893197e-17] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.326 | [-0.32647058823529407, 3.9981116089810645e-17] | gft-0.1.0-reaudit-20260610 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_closed_form | starlike | disproves | pass | 0.000 | 0.3*exp(i*3.043418) | boundary_v3.0 |