Ruscheweyh · parametric, arity 1
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 | {"lambda": 0.5} | ✗ | -71.1186 | unscreened | - |
| K | membership | {"lambda": 1.0} | ✗ | -17.5859 | unscreened | - |
| K | membership | {"lambda": 1.5} | ✗ | -90.4840 | unscreened | - |
| K | membership | {"lambda": 2.0} | ✗ | -161.9735 | unscreened | - |
| r* | radius | {"lambda": 0.5} | - | r ≤ 0.906 | unscreened | - |
| r* | radius | {"lambda": 1.0} | - | r ≤ 0.838 | unscreened | - |
| r* | radius | {"lambda": 1.5} | - | r ≤ 0.778 | unscreened | - |
| r* | radius | {"lambda": 2.0} | - | r ≤ 0.920 | unscreened | - |
| S* | membership | {"lambda": 4.0} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 3.5} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 3.0} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 2.75} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 2.5} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 2.25} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 1.9} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 1.75} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 1.6} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 1.4} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 1.25} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 1.1} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 0.9} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 0.8} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 0.75} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 0.6} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 0.4} | ✗ | r ≤ 0.900 | ✗ disproven | proven |
| S* | membership | {"lambda": 0.25} | ✗ | r ≤ 0.900 | ✗ disproven | proven |
| S* | membership | {"lambda": 0.1} | ✗ | r ≤ 0.950 | ✗ disproven | proven |
| S* | membership | {"lambda": 0.5} | ✗ | r ≤ 0.900 | ✗ disproven | proven |
| S* | membership | {"lambda": 1.0} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 1.5} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S* | membership | {"lambda": 2.0} | ✗ | r ≤ 0.000 | ✗ disproven | proven |
| S | membership | {"lambda": 0.5} | ✗ | - | unscreened | - |
| S | membership | {"lambda": 1.0} | ✗ | - | unscreened | - |
| S | membership | {"lambda": 1.5} | ✗ | - | unscreened | - |
| S | membership | {"lambda": 2.0} | ✗ | - | unscreened | - |
| Verifier | Property | Direction | Outcome | Domain r | Witness | Engine |
|---|---|---|---|---|---|---|
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.900 | 0.95*exp(i*0.581379) | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.900 | 0.95*exp(i*5.707415) | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.950 | 0.99*exp(i*6.022409) | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.000 | - | boundary_v3.1 |
| boundary_scan_centered_v31 | starlike | disproves | pass | 0.900 | 0.95*exp(i*6.004001) | boundary_v3.1 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.990 | [0.9516490789789357, -0.27288098225882895] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.990 | [0.9516490789789357, 0.2728809822588292] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.990 | [0.9516490789789357, 0.2728809822588292] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.990 | [0.9516490789789357, 0.2728809822588292] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.990 | [0.9516490789789357, 0.2728809822588292] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.990 | [0.8207471968294914, -0.5536009744360391] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.990 | [0.8207471968294912, 0.5536009744360394] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.982 | [-0.49105042016806766, -0.8505242768091371] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.966 | [0.06740585643560469, -0.9639486566334218] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.951 | [0.5851888191099597, 0.7490075322727422] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.919 | [0.06409975129344615, -0.9166691503858133] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.903 | [0.06299771624605997, -0.9009093149699438] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.903 | [0.7306307259283663, 0.5308342946543873] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.856 | [0.29267152264582247, -0.8041083997867986] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.832 | [0.2845665074846594, 0.7818400536471662] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.808 | [-0.19555014401455498, 0.7843087891637655] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.800 | [0.4704751704273787, 0.6475535186068382] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.753 | [-0.18217328625786747, 0.7306571431226222] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.714 | [-0.53025569017887, 0.47744436794899714] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.990 | [0.9516490789789357, 0.2728809822588292] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.990 | [-0.49500000000000044, -0.857365149746594] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.935 | [0.06520178634083233, -0.9324289858016828] | gft-0.1.0-reaudit-20260610 |
| pointwise_starlike_iv | starlike | disproves | pass | 0.895 | [0.7242401715190179, -0.5261912850984637] | gft-0.1.0-reaudit-20260610 |
| boundary_scan_polynomial | starlike | proves | pass | 0.300 | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | 0.300 | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | 0.300 | - | boundary_v3.0 |
| boundary_scan_polynomial | starlike | proves | pass | 0.300 | - | boundary_v3.0 |